Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-6 -D6 &K=Q(sqrt(-2)) &Hdim=6 V=K^6 &HNeighbourhood at <3,-1+w> contains 15 classes: mass of the neighbourhood is 19/5120 Steinitz class <1,w>: &Hlattice (#1 <-- #14) 2 -w 2 0 1 2 0 -1 -1 2 0 1 1 -1 2 -1 -w 0 0 0 3 |Aut| = 2^10*3^2*5 #short vectors: 0 72 64 1032 3840 7328 &Hlattice (#2 <-- #7) 2 0 2 w 0 2 -w 0 -1 2 0 1+w 0 0 2 1+w 0 1 -1 0 3 |Aut| = 2^11*3^2 #short vectors: 0 56 128 1032 3584 7520 &Hlattice (#3 <-- #12) 2 -w 2 w -1 2 0 0 0 2 1 0 0 w 3 -w 1 -1 1+w 1-w 3 |Aut| = 2^10*3 #short vectors: 0 40 192 1032 3328 7712 &Hlattice (#4 <-- #5) 2 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1 2 1 -1-w 1+w -1-w 1+w 3 |Aut| = 2^6*3^2*5 #short vectors: 0 32 224 1032 3200 7808 &Hlattice (#5 <-- #13) 2 1 2 1 1 2 -1 -1 -1 2 0 0 0 0 2 1-w 1-w 1-w -1+w -1 3 |Aut| = 2^6*3^2*5 #short vectors: 0 32 224 1032 3200 7808 &Hlattice (#6 <-- #9) 2 0 2 0 -1 2 0 0 0 2 -1 0 0 -1 2 1 -1 1 -w -1+w 3 |Aut| = 2^7*3^2 #short vectors: 0 24 256 1032 3072 7904 &Hlattice (#7 <-- #10) 2 -w 2 0 0 2 -1 -w -1 3 0 1 0 1 3 -w 1 1+w -1 0 3 |Aut| = 2^11 #short vectors: 0 24 256 1032 3072 7904 &Hlattice (#8 <-- #15) 2 -w 2 0 0 2 1 0 1 3 -w 1 -w -1-w 3 1 0 -w 1 1 3 |Aut| = 2^12*3 #short vectors: 0 24 256 1032 3072 7904 &Hlattice (#9 <-- #1) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 |Aut| = 2^10*3^2*5 #short vectors: 12 72 304 1032 2952 7328 &Hlattice (#10 <-- #2) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1-w 2 |Aut| = 2^11*3^2 #short vectors: 8 56 288 1032 2992 7520 &Hlattice (#11 <-- #3) 1 0 1 0 0 2 0 0 -1 2 0 0 -w w 2 0 0 1 -1 1+w 3 |Aut| = 2^10*3 #short vectors: 4 40 272 1032 3032 7712 &Hlattice (#12 <-- #6) 1 0 1 0 0 2 0 0 0 2 0 0 0 1+w 2 0 0 1-w 0 0 2 |Aut| = 2^12*3^2 #short vectors: 4 56 208 1032 3288 7520 &Hlattice (#13 <-- #11) 1 0 1 0 0 2 0 0 -1 2 0 0 w -w 2 0 0 -w 0 -1 2 |Aut| = 2^11*3^2 #short vectors: 4 56 208 1032 3288 7520 &Hlattice (#14 <-- #4) 1 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1 2 0 1+w -1-w 1+w -w 3 |Aut| = 2^6*3^2*5 #short vectors: 2 32 264 1032 3052 7808 &Hlattice (#15 <-- #8) 1 0 2 0 0 2 0 0 -1 2 0 -1 0 1 2 0 1+w 1 -1 -1 3 |Aut| = 2^6*3^2*5 #short vectors: 2 32 264 1032 3052 7808 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 36 80 120 0 96 0 0 0 0 0 0 0 0 0 32 32 20 96 128 0 64 0 0 0 8 0 16 0 0 0 8 16 68 32 64 64 48 0 0 0 16 0 16 32 0 6 0 60 16 60 120 0 30 0 0 30 10 0 12 20 0 20 30 76 16 40 90 0 2 0 0 0 10 20 60 0 4 24 16 48 108 72 0 0 4 24 0 0 48 16 0 0 32 64 0 128 28 16 0 0 32 0 0 0 64 0 0 0 0 128 0 96 12 0 0 0 0 0 128 0 0 0 0 32 0 0 0 0 36 80 120 0 0 96 0 0 8 0 0 0 64 0 0 32 20 96 16 0 0 128 0 0 16 0 32 64 48 0 8 16 68 0 16 64 32 0 32 0 0 128 0 0 0 0 32 0 12 32 128 0 0 0 96 64 0 0 0 0 0 0 96 16 28 0 64 2 0 0 60 20 40 90 0 0 20 30 0 10 16 76 0 0 30 20 12 120 0 30 6 0 60 10 0 60 16 classes of Z-lattices with respect to the trace form (scaled by 1/2) &Dim=12 V=Q^12 &Genus of the trace-forms: det= 64 = 2^6 2-adic symbol: [1^6 2^6]_4 -1-adic symbol: +^12 -^0 level(of 2-scaled form)=8, weight=6 a_0,..,a_6 determine modular form &Gram (#1 <- H1) 2 0 2 0 1 2 0 -1 -1 2 0 1 1 0 2 0 1 0 0 0 2 0 -1 0 0 0 -1 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 -1 1 -1 -1 3 |Aut| = 2^20*3^4*5^2 #short vectors: 0 72 64 1032 3840 7328 &Gram (#2 <- H2) 2 0 2 0 -1 2 0 -1 1 2 0 1 0 -1 2 0 0 0 0 0 2 0 0 0 0 0 1 2 0 0 0 0 0 -1 0 2 0 0 0 0 0 1 0 0 2 1 0 0 0 0 1 0 0 1 3 1 0 0 0 0 -1 0 0 -1 0 3 1 0 0 0 0 1 0 0 1 1 0 3 |Aut| = 2^21*3^4 #short vectors: 0 56 128 1032 3584 7520 &Gram (#3 <- H3) 2 0 2 0 -1 2 0 1 -1 2 0 1 -1 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 1 -1 0 1 -1 0 0 3 1 0 0 0 0 0 1 -1 -1 3 0 -1 0 -1 0 -1 0 0 0 0 3 0 -1 1 0 -1 1 0 0 -1 0 0 3 |Aut| = 2^20*3^2 #short vectors: 0 40 192 1032 3328 7712 &Gram (#4 <- H4,H5) 2 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1 2 0 1 -1 1 -1 2 1 1 0 1 -1 0 3 1 -1 1 -1 1 -1 0 3 1 -1 0 0 0 0 0 1 3 1 -1 0 0 0 0 0 1 1 3 1 -1 0 0 0 0 0 1 1 1 3 1 -1 0 0 0 0 0 1 1 1 1 3 |Aut| = 2^11*3^4*5^2 #short vectors: 0 32 224 1032 3200 7808 &Gram (#5 <- H6) 2 1 2 1 1 2 0 0 0 2 0 0 0 -1 2 0 0 0 1 0 2 1 1 1 -1 0 -1 3 1 0 0 -1 1 0 1 3 1 0 0 1 0 1 0 0 3 1 0 0 -1 0 -1 1 1 0 3 1 1 1 -1 1 0 1 1 0 1 3 1 0 0 -1 0 -1 1 1 0 1 1 3 |Aut| = 2^15*3^4 #short vectors: 0 24 256 1032 3072 7904 &Gram (#6 <- H7,H8) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 1 0 1 0 0 0 3 0 1 1 1 0 1 1 3 1 0 1 0 0 0 0 0 3 0 -1 0 -1 -1 0 1 -1 0 3 1 0 1 0 0 0 1 1 0 0 3 1 0 1 0 0 0 1 0 0 0 1 3 |Aut| = 2^21*3 #short vectors: 0 24 256 1032 3072 7904 &Gram (#7 <- H9) 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 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^20*3^4*5^2 #short vectors: 12 72 304 1032 2952 7328 &Gram (#8 <- H10) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 -1 -1 2 0 0 0 0 1 1 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^21*3^4 #short vectors: 8 56 288 1032 2992 7520 &Gram (#9 <- H11) 1 0 1 0 0 2 0 0 -1 2 0 0 -1 1 2 0 0 -1 0 1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 -1 1 0 0 1 0 0 -1 1 3 |Aut| = 2^20*3^2 #short vectors: 4 40 272 1032 3032 7712 &Gram (#10 <- H12,H13) 1 0 1 0 0 2 0 0 -1 2 0 0 1 -1 2 0 0 -1 0 -1 2 0 0 0 0 0 0 2 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 -1 1 2 0 0 0 0 0 0 1 0 -1 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 |Aut| = 2^21*3^4 #short vectors: 4 56 208 1032 3288 7520 &Gram (#11 <- H14,H15) 1 0 2 0 1 2 0 -1 0 2 0 1 1 0 2 0 1 0 -1 0 2 0 0 0 0 0 0 2 0 1 0 0 1 0 0 3 0 -1 0 0 0 -1 0 -1 3 0 -1 0 0 -1 0 0 -1 1 3 0 1 1 -1 1 0 0 0 0 0 3 0 -1 0 0 -1 0 0 -1 1 1 0 3 |Aut| = 2^11*3^4*5^2 #short vectors: 2 32 264 1032 3052 7808