Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-5 &K=Q(sqrt(-7)) &Hdim=7 V=K^7 &HNeighbourhood at <2,-1+w> contains 26 classes: mass of the neighbourhood is 73/39690 Steinitz class <1,w>: &Hlattice (#1 <-- #25) 2 -1 2 0 -1 2 -1 1 0 2 -1 0 1 1 2 0 0 1 1 1 2 1-w -1+w 1-w 0 0 1-w 3 |Aut| = 2^10*3^4*5*7 #short vectors: 0 126 56 2520 9576 &Hlattice (#2 <-- #26) 2 0 2 0 1 2 1 1 1 2 1 1 1 1 2 -1 0 0 0 0 2 -w w w 0 0 0 3 |Aut| = 2^10*3^4*5*7 #short vectors: 0 126 56 2520 9576 &Hlattice (#3 <-- #6) 2 1-w 2 -1+w -1 2 1-w 1 -1 2 -1+w -1 1 -1 2 -1+w -1 1 -1 1 2 w -1 1 -1 1 1 4 |Aut| = 2^11*3^2*5*7 #short vectors: 0 98 168 2492 9464 &Hlattice (#4 <-- #21) 2 -1 2 0 1 2 0 0 1 2 1-w 0 0 0 2 -1 0 0 0 -w 2 w 1-w 1-w 1-w -1+w -1 4 |Aut| = 2^11*3^2*5*7 #short vectors: 0 98 168 2492 9464 &Hlattice (#5 <-- #8) 2 1 2 0 1-w 2 1-w 1-w 1 2 0 0 0 0 2 0 0 0 0 w 2 0 0 0 0 1-w -1 2 |Aut| = 2^11*3^3*7 #short vectors: 0 90 200 2484 9432 &Hlattice (#6 <-- #19) 2 -1 2 0 -1 2 0 1 -1 2 0 -1 1 -1 2 0 -1 1 -1 1 2 0 w 1-w -1+w 1-w 1-w 3 |Aut| = 2^8*3^2*5*7 #short vectors: 0 56 336 2450 9296 &Hlattice (#7 <-- #24) 2 -1 2 0 1 2 0 -1 -1 2 0 1 1 -1 2 -1+w 1-w 1 -1 1 3 -1 1-w -w w -w 0 3 |Aut| = 2^8*3^2*5*7 #short vectors: 0 56 336 2450 9296 &Hlattice (#8 <-- #11) 2 0 2 1-w 0 2 1-w 0 1 2 0 w 0 0 2 -1 w 0 -w 1 3 1-w 1-w 1 1 -1 -1 3 |Aut| = 2^11*3^2 #short vectors: 0 50 360 2444 9272 &Hlattice (#9 <-- #13) 2 0 2 1-w 0 2 0 -1+w 0 2 0 1 0 -w 2 1-w 1-w 1 -1 0 3 -w 1 1 -w 1 1 3 |Aut| = 2^11*3^2 #short vectors: 0 50 360 2444 9272 &Hlattice (#10 <-- #14) 2 0 2 1-w 0 2 0 1 0 2 0 0 0 0 2 1-w -w 1 -w -1 3 -w 0 1 0 -w 1 3 |Aut| = 2^10*3^2 #short vectors: 0 38 408 2432 9224 &Hlattice (#11 <-- #20) 2 0 2 0 0 2 0 0 1-w 2 1 -w 0 0 2 0 -w 1-w 1 1 3 -1+w -1 1 w 0 1 3 |Aut| = 2^10*3^2 #short vectors: 0 38 408 2432 9224 &Hlattice (#12 <-- #18) 2 0 2 0 1 2 0 -1 -1 2 0 -1 -1 1 2 1-w w w -w -w 3 -1 -w -1 1 1 -1 3 |Aut| = 2^6*3^3*5 #short vectors: 0 36 416 2430 9216 &Hlattice (#13 <-- #23) 2 1 2 1 0 2 0 -1 0 2 0 0 0 0 2 -w 1-w 0 -1 -1 3 1-w 0 1-w 0 w 0 3 |Aut| = 2^6*3^3*5 #short vectors: 0 36 416 2430 9216 &Hlattice (#14 <-- #22) 2 0 2 0 -1 2 0 -1 0 2 1-w 1-w 0 -1+w 3 0 -1 1-w 1 1-w 3 1 0 -w w 1 1 3 |Aut| = 2^10*3 #short vectors: 0 34 424 2428 9208 &Hlattice (#15 <-- #16) 2 0 2 0 -1 2 w 0 0 2 0 1 -1 0 2 -w 1-w -1+w -1 1-w 3 -1 w -w -1+w w -1 3 |Aut| = 2^7*3*5 #short vectors: 0 28 448 2422 9184 &Hlattice (#16 <-- #1) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 |Aut| = 2^11*3^2*5*7 #short vectors: 14 112 616 2618 9016 &Hlattice (#17 <-- #2) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 w 2 0 0 0 0 1-w -1 2 |Aut| = 2^11*3^2*7 #short vectors: 8 82 520 2540 9112 &Hlattice (#18 <-- #3) 1 0 1 0 0 1 0 0 0 2 0 0 0 w 2 0 0 0 w 1 2 0 0 0 1 1-w 0 2 |Aut| = 2^11*3^3 #short vectors: 6 72 488 2514 9144 &Hlattice (#19 <-- #4) 1 0 1 0 0 2 0 0 -1 2 0 0 1 -1 2 0 0 -w w -w 2 0 0 1 -1 1 w 3 |Aut| = 2^11*3*5 #short vectors: 4 62 456 2488 9176 &Hlattice (#20 <-- #9) 1 0 1 0 0 2 0 0 -1 2 0 0 1-w 0 2 0 0 1 0 w 2 0 0 -1 1-w 1-w -1 3 |Aut| = 2^11*3*5 #short vectors: 4 62 456 2488 9176 &Hlattice (#21 <-- #5) 1 0 2 0 1-w 2 0 1-w 1 2 0 1-w 1 1 2 0 1-w 1 1 1 2 0 1 0 w 0 w 3 |Aut| = 2^11*3^2*5 #short vectors: 2 76 328 2486 9304 &Hlattice (#22 <-- #7) 1 0 2 0 1-w 2 0 0 0 2 0 0 0 w 2 0 0 0 -1 w 2 0 -1 1-w 0 0 0 2 |Aut| = 2^10*3^2*7^2 #short vectors: 2 88 280 2498 9352 &Hlattice (#23 <-- #10) 1 0 2 0 -1 2 0 0 0 2 0 0 1-w 0 2 0 0 0 1 0 2 0 1-w 0 -w 1 -w 3 |Aut| = 2^9*3^2 #short vectors: 2 40 472 2450 9160 &Hlattice (#24 <-- #12) 1 0 2 0 -1 2 0 0 1-w 2 0 0 1 w 2 0 0 1 w 1 2 0 1-w 0 1 1-w 0 3 |Aut| = 2^11*3^2*5 #short vectors: 2 76 328 2486 9304 &Hlattice (#25 <-- #15) 1 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1 2 0 -1 1 -1 1 2 0 -1 1-w -1+w 1-w 1-w 3 |Aut| = 2^6*3^2*5*7 #short vectors: 2 46 448 2456 9184 &Hlattice (#26 <-- #17) 1 0 2 0 1 2 0 1 1 2 0 1 1 1 2 0 0 0 -1+w -1+w 3 0 w w 0 0 -2+w 3 |Aut| = 2^10*3^2*5 #short vectors: 2 64 376 2474 9256 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 1 63 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 63 28 0 0 0 0 0 36 0 0 0 0 0 0 0 0 0 0 0 0 0 63 0 0 0 0 0 0 0 0 0 35 64 0 0 0 0 0 0 0 0 0 0 0 0 21 0 7 0 0 0 0 0 0 14 0 0 0 0 0 70 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 42 0 0 0 0 0 21 0 0 0 0 84 0 0 0 0 0 0 0 3 7 0 0 0 12 0 0 0 0 1 0 0 0 0 0 0 0 70 0 0 28 0 0 0 0 0 0 0 0 0 0 0 0 28 0 0 0 0 8 0 0 0 0 0 35 0 0 56 0 0 0 0 0 0 0 0 0 0 0 0 28 0 0 0 0 4 0 16 0 0 24 18 0 0 48 0 0 0 1 0 6 6 0 4 0 0 0 0 0 2 0 0 0 0 36 0 0 32 32 0 6 0 0 1 0 0 3 0 0 12 3 0 0 0 0 0 0 0 0 0 16 9 0 9 0 32 0 48 0 0 0 6 0 0 1 6 0 0 0 0 0 0 0 0 4 0 0 12 36 0 0 0 36 24 0 0 2 0 0 0 0 12 1 0 0 0 0 0 0 0 6 0 0 0 0 30 0 10 45 18 0 0 0 0 0 0 0 15 0 0 3 0 0 0 0 0 0 3 15 0 0 0 1 0 45 45 0 0 0 0 0 0 0 0 3 15 0 0 0 0 0 0 0 0 1 8 12 0 16 16 18 40 0 0 0 1 0 1 0 12 0 0 2 0 0 0 0 0 0 0 0 0 5 10 10 4 25 60 0 0 0 0 1 0 0 10 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 28 35 35 21 0 7 0 0 0 0 0 0 0 0 0 1 0 0 7 0 0 0 0 0 0 0 7 10 28 0 42 0 4 28 0 0 0 0 0 0 0 1 0 0 0 3 12 0 0 0 0 0 3 12 6 36 9 0 0 36 9 0 0 0 0 0 0 0 0 0 5 10 0 0 0 0 0 16 0 10 5 3 16 10 0 20 0 32 0 0 0 0 1 0 0 0 0 0 0 20 0 0 10 0 1 0 20 10 3 0 0 40 2 0 20 0 0 6 0 0 0 0 15 0 10 0 32 0 0 0 0 0 15 6 0 1 10 0 0 0 32 0 0 0 0 14 0 0 0 0 0 49 0 0 0 0 0 14 0 0 0 0 1 0 49 0 0 0 0 0 0 0 0 0 3 1 6 3 0 8 18 24 0 1 3 6 3 0 0 43 0 8 0 2 0 0 1 0 0 0 0 30 0 0 0 0 30 0 1 0 0 0 30 30 0 0 1 0 2 0 0 0 0 0 0 7 0 0 0 0 35 0 0 21 0 0 0 0 21 0 0 35 0 1 7 0 1 0 0 0 16 0 0 0 0 0 0 16 30 0 0 0 0 30 0 1 0 0 16 16 1 classes of Z-lattices with respect to the trace form &Dim=14 V=Q^14 &Genus of the trace-forms: det= 823543 = 7^7 2-adic symbol: 1^14_II 7-adic symbol: 1^7 7^7 -1-adic symbol: +^14 -^0 level=7, weight=7 a_0,..,a_8 determine modular form &Gram (#1 <- H1,H2) 4 2 4 2 0 4 2 0 0 4 2 2 0 0 4 2 0 2 0 0 4 2 0 2 0 0 2 4 1 1 1 0 1 0 0 6 1 0 0 1 0 1 1 -2 6 1 1 1 0 0 1 1 2 2 6 0 1 -1 0 1 -1 -1 2 -2 -2 6 0 1 0 -1 0 0 0 2 -2 2 2 6 0 1 0 -1 1 0 0 2 -2 2 2 2 6 0 0 1 -1 0 1 0 2 -2 2 -2 2 2 6 |Aut| = 2^10*3^4*5*7 #short vectors: 0 0 0 126 0 56 0 2520 &Gram (#2 <- H3,H4) 4 1 4 1 2 4 1 2 2 4 1 2 0 2 4 1 2 2 2 2 4 1 2 2 2 2 2 4 1 2 2 2 2 2 2 4 0 1 0 0 0 0 0 0 4 0 0 -1 0 1 0 0 0 0 4 0 0 0 0 0 0 1 0 0 0 4 2 2 0 0 1 1 0 0 -1 2 -2 8 2 2 0 1 1 0 0 0 -1 2 -2 4 8 2 2 0 0 1 0 1 1 -1 2 2 2 2 8 |Aut| = 2^11*3^2*5*7 #short vectors: 0 0 0 98 0 168 0 2492 &Gram (#3 <- H5) 4 2 4 2 0 4 2 0 0 4 0 1 -1 0 4 1 1 0 0 2 4 0 0 -1 0 2 2 4 0 0 1 -1 -2 0 -2 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 -2 4 0 0 0 0 0 0 0 0 2 0 4 0 0 0 0 0 0 0 0 1 1 2 4 0 0 0 0 0 0 0 0 -1 2 -1 1 4 0 0 0 0 0 0 0 0 -2 1 0 -1 1 4 |Aut| = 2^13*3^3*7 #short vectors: 0 0 0 90 0 200 0 2484 &Gram (#4 <- H6,H7) 4 2 4 2 0 4 2 0 2 4 2 0 2 2 4 2 0 2 2 2 4 2 0 2 2 2 2 4 2 1 0 2 0 0 0 6 1 2 -1 1 -1 -1 -1 2 6 1 -1 0 2 0 0 0 2 1 6 2 0 1 0 2 2 2 0 -1 0 6 2 0 0 1 2 2 2 1 0 1 2 6 2 0 0 2 1 2 2 2 1 2 1 2 6 2 0 0 2 2 1 2 2 1 2 1 2 2 6 |Aut| = 2^8*3^2*5*7 #short vectors: 0 0 0 56 0 336 0 2450 &Gram (#5 <- H8,H9) 4 1 4 1 2 4 1 2 0 4 1 2 2 2 4 0 0 0 0 0 4 0 0 0 0 0 1 4 0 0 0 0 0 1 0 4 0 0 0 0 0 0 2 -2 4 0 0 0 0 0 0 0 0 -1 4 1 2 2 2 2 2 -1 2 -1 -2 6 2 0 1 0 0 0 -2 2 -2 0 2 6 2 1 0 1 0 0 -2 2 -2 0 2 2 6 2 2 0 1 1 2 0 1 -1 2 0 0 1 8 |Aut| = 2^11*3^2 #short vectors: 0 0 0 50 0 360 0 2444 &Gram (#6 <- H10,H11) 4 1 4 1 2 4 1 2 0 4 0 0 0 0 4 0 0 0 0 2 4 0 0 0 0 -2 -2 4 0 0 -1 1 0 0 0 4 0 0 0 0 1 1 0 0 4 0 0 0 0 1 0 -1 0 0 4 2 0 0 1 -2 0 2 2 0 -1 6 1 2 2 2 -1 -1 1 0 -2 -2 2 6 2 1 1 0 -2 -2 0 -2 -1 0 0 2 6 1 2 2 2 -2 -2 0 0 -1 0 1 3 3 6 |Aut| = 2^10*3^2 #short vectors: 0 0 0 38 0 408 0 2432 &Gram (#7 <- H12,H13) 4 2 4 0 0 4 0 0 -2 4 0 0 2 -2 4 0 0 2 -2 2 4 0 0 2 -2 2 2 4 1 2 2 0 2 0 0 6 1 -1 -2 2 0 -2 -2 -1 6 2 0 1 1 -1 -1 -1 1 1 6 2 0 1 -2 0 0 0 0 0 1 6 2 0 2 -1 0 0 0 1 0 2 2 6 2 0 2 0 1 0 0 2 1 2 1 2 6 2 0 -2 2 -2 -2 -1 -1 2 1 0 0 0 6 |Aut| = 2^6*3^3*5 #short vectors: 0 0 0 36 0 416 0 2430 &Gram (#8 <- H14) 4 0 4 0 -2 4 0 -2 0 4 0 2 0 0 4 1 0 0 0 0 4 2 2 0 0 2 1 6 1 2 0 -2 0 -2 1 6 1 -2 2 0 -2 -1 0 0 6 2 -2 0 0 -2 0 0 1 0 6 2 -1 1 1 0 0 0 1 0 2 6 0 2 -1 0 1 0 1 0 0 -2 -2 6 0 0 0 1 1 0 2 -1 0 1 2 -1 6 0 0 -1 0 0 0 -2 0 -1 -1 -2 1 -2 6 |Aut| = 2^11*3 #short vectors: 0 0 0 34 0 424 0 2428 &Gram (#9 <- H15) 4 1 4 1 0 4 0 0 0 4 0 0 0 -2 4 0 0 0 -2 0 4 1 2 2 -2 0 0 6 1 2 2 -2 2 0 2 6 2 2 -1 -2 0 2 1 2 6 2 -1 2 -2 0 2 1 2 2 6 1 2 2 -1 1 0 2 3 0 0 6 1 2 2 -1 0 1 3 2 2 2 2 6 1 2 2 0 1 0 2 2 1 1 2 2 6 1 2 2 0 0 -1 3 2 1 1 2 2 2 6 |Aut| = 2^8*3*5 #short vectors: 0 0 0 28 0 448 0 2422 &Gram (#10 <- H16) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 1 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 4 0 0 1 0 0 0 0 0 0 4 0 0 0 1 0 0 0 0 0 0 4 0 0 0 0 1 0 0 0 0 0 0 4 0 0 0 0 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 1 0 0 0 0 0 0 4 |Aut| = 2^18*3^2*5*7 #short vectors: 0 14 0 112 0 616 0 2618 &Gram (#11 <- H17) 2 0 2 0 0 2 0 0 0 2 1 0 0 0 4 0 -1 0 0 0 4 0 0 -1 0 0 0 4 0 0 0 -1 0 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 -2 4 0 0 0 0 0 0 0 0 2 0 4 0 0 0 0 0 0 0 0 1 1 2 4 0 0 0 0 0 0 0 0 -1 2 -1 1 4 0 0 0 0 0 0 0 0 -2 1 0 -1 1 4 |Aut| = 2^16*3^2*7 #short vectors: 0 8 0 82 0 520 0 2540 &Gram (#12 <- H18) 2 0 2 0 0 2 1 0 0 4 0 -1 0 0 4 0 0 -1 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 2 4 0 0 0 0 0 0 2 2 4 0 0 0 0 0 0 2 0 2 4 0 0 0 0 0 0 1 1 0 0 4 0 0 0 0 0 0 1 0 0 0 2 4 0 0 0 0 0 0 1 1 1 1 2 0 4 0 0 0 0 0 0 0 1 0 -1 2 0 0 4 |Aut| = 2^15*3^3 #short vectors: 0 6 0 72 0 488 0 2514 &Gram (#13 <- H19,H20) 2 0 2 1 0 4 0 1 0 4 0 0 0 0 4 0 0 0 0 -2 4 0 0 0 0 -2 2 4 0 0 0 0 -2 0 2 4 0 0 0 0 -2 0 0 0 4 0 0 0 0 1 0 0 0 -1 4 0 0 0 0 -2 1 0 0 2 1 6 0 0 0 0 -2 0 1 1 1 1 0 6 0 0 0 0 -1 2 0 -1 1 -2 2 -1 6 0 0 0 0 -1 -1 -1 0 1 1 0 2 -1 6 |Aut| = 2^13*3*5 #short vectors: 0 4 0 62 0 456 0 2488 &Gram (#14 <- H21,H24) 2 1 4 0 0 4 0 0 1 4 0 0 1 2 4 0 0 1 2 2 4 0 0 -1 -2 0 -2 4 0 0 1 2 2 2 -2 4 0 0 1 2 2 2 -2 2 4 0 0 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 1 0 1 0 0 0 0 4 0 0 0 0 0 1 0 0 0 0 0 0 4 0 0 -2 -1 0 0 1 0 -1 -2 -2 2 2 6 |Aut| = 2^12*3^2*5 #short vectors: 0 2 0 76 0 328 0 2486 &Gram (#15 <- H22) 2 1 4 0 0 4 0 0 -2 4 0 0 -2 0 4 0 0 -1 -1 0 4 0 0 -1 2 -1 -1 4 0 0 -2 1 2 1 1 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 -2 4 0 0 0 0 0 0 0 0 -2 2 4 0 0 0 0 0 0 0 0 -1 -1 1 4 0 0 0 0 0 0 0 0 1 -2 -2 1 4 0 0 0 0 0 0 0 0 2 -2 -1 1 0 4 |Aut| = 2^13*3^2*7^2 #short vectors: 0 2 0 88 0 280 0 2498 &Gram (#16 <- H23) 2 1 4 0 0 4 0 0 2 4 0 0 -2 0 4 0 0 0 1 1 4 0 0 -1 0 0 0 4 0 0 1 1 -1 0 0 4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 -1 4 0 0 0 0 0 0 0 0 1 0 4 0 0 0 -1 0 -2 -2 -2 0 2 2 6 0 0 1 2 1 -1 -2 2 -2 0 -1 0 6 0 0 1 -1 0 -2 1 -2 0 0 0 2 -1 6 |Aut| = 2^11*3^2 #short vectors: 0 2 0 40 0 472 0 2450 &Gram (#17 <- H25) 2 1 4 0 0 4 0 0 2 4 0 0 -2 -2 4 0 0 2 2 -2 4 0 0 2 2 -2 2 4 0 0 -2 -2 2 -2 -2 4 0 0 -1 -2 0 -2 -2 0 6 0 0 1 -1 -1 -1 1 1 0 6 0 0 -2 -1 0 -2 0 2 0 1 6 0 0 2 0 -1 2 0 -2 1 0 -2 6 0 0 -2 -2 0 -1 0 2 0 1 2 -1 6 0 0 2 2 0 2 0 -1 -1 -1 -2 1 -2 6 |Aut| = 2^8*3^2*5*7 #short vectors: 0 2 0 46 0 448 0 2456 &Gram (#18 <- H26) 2 1 4 0 0 4 0 0 -2 4 0 0 -2 2 4 0 0 2 0 -2 4 0 0 -2 0 0 0 4 0 0 2 0 0 0 -2 4 0 0 2 -2 -2 0 0 1 6 0 0 1 -2 0 0 1 -1 1 6 0 0 1 0 -1 1 -1 0 2 -2 6 0 0 1 -1 0 0 0 0 -1 3 0 6 0 0 0 0 0 1 0 0 1 -2 0 -2 6 0 0 0 0 -1 1 1 0 2 -2 0 -2 2 6 |Aut| = 2^12*3^2*5 #short vectors: 0 2 0 64 0 376 0 2474