Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-5 &K=Q(sqrt(-7)) &Hdim=6 V=K^6 &HNeighbourhood at <2,-1+w> contains 11 classes: mass of the neighbourhood is 19/17640 Steinitz class <1,w>: &Hlattice (#1 <- #6) 2 -1 2 w 1-w 2 0 0 0 2 0 0 0 w 2 0 0 0 1-w -1 2 |Aut| = 2^9*3^2*7^2 #short vectors: 0 84 112 1932 5040 &Hlattice (#2 <- #5) 2 1-w 2 1-w 1 2 1-w 1 1 2 1-w 1 1 1 2 1 w 0 w 0 3 |Aut| = 2^10*3^2*5 #short vectors: 0 72 184 1824 4920 &Hlattice (#3 <- #9) 2 -1 2 1-w 0 2 1 0 w 2 0 0 0 1 2 0 1-w 1 1-w 1-w 3 |Aut| = 2^10*3^2*5 #short vectors: 0 72 184 1824 4920 &Hlattice (#4 <- #11) 2 1 2 1 1 2 1 1 1 2 0 -1+w -1+w 0 3 w 0 0 w -2+w 3 |Aut| = 2^9*3^2*5 #short vectors: 0 60 256 1716 4800 &Hlattice (#5 <- #10) 2 1 2 0 -1 2 0 1 -1 2 w w -1 1 3 1-w 1-w -1 1 0 3 |Aut| = 2^5*3^2*5*7 #short vectors: 0 42 364 1554 4620 &Hlattice (#6 <- #8) 2 0 2 1-w 0 2 0 -1+w 0 2 -1 0 0 -1 3 -w 1 1 -w 1+w 3 |Aut| = 2^8*3^2 #short vectors: 0 36 400 1500 4560 &Hlattice (#7 <- #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 84 400 1476 4392 &Hlattice (#8 <- #2) 1 0 1 0 0 1 0 0 0 2 0 0 0 w 2 0 0 0 1-w -1 2 |Aut| = 2^8*3^2*7 #short vectors: 6 66 364 1542 4536 &Hlattice (#9 <- #3) 1 0 1 0 0 2 0 0 1 2 0 0 w w 2 0 0 0 w 1 2 |Aut| = 2^10*3^2 #short vectors: 4 60 352 1564 4584 &Hlattice (#10 <- #4) 1 0 2 0 1 2 0 -1 -1 2 0 -w -w w 2 0 1 1 -1 w 3 |Aut| = 2^9*3*5 #short vectors: 2 54 340 1586 4632 &Hlattice (#11 <- #7) 1 0 2 0 -1 2 0 0 1-w 2 0 0 1 w 2 0 1-w -1 1-w -1 3 |Aut| = 2^9*3*5 #short vectors: 2 54 340 1586 4632 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 0 49 0 0 0 0 14 0 0 0 10 0 0 32 0 0 0 0 15 6 0 0 30 0 2 0 0 1 0 0 0 30 0 1 16 0 16 0 0 0 0 30 0 0 0 0 7 0 35 0 0 0 0 21 0 0 0 0 8 42 0 1 3 6 3 0 1 0 0 0 0 21 20 15 6 0 1 0 0 0 0 7 7 6 21 0 21 0 0 3 0 0 12 3 12 3 24 6 0 5 0 0 16 10 0 10 5 1 16 0 0 1 10 0 20 1 0 20 10 1 classes of Z-lattices with respect to the trace form &Dim=12 V=Q^12 &Genus of the trace-forms: det= 117649 = 7^6 2-adic symbol: 1^12_II 7-adic symbol: 1^6 7^6 -1-adic symbol: +^12 -^0 level=7, weight=6 a_0,..,a_8 determine modular form &Gram (#1 <- H1) 4 2 4 2 0 4 1 -1 2 4 1 2 -1 0 4 2 2 1 1 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 -1 -2 0 4 0 0 0 0 0 0 -1 1 -1 0 4 0 0 0 0 0 0 2 1 2 -1 0 4 |Aut| = 2^11*3^2*7^2 #short vectors: 0 0 0 84 0 112 0 1932 &Gram (#2 <- H2,H3) 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 0 1 0 0 0 0 0 4 0 0 1 0 -1 0 0 0 4 0 0 0 1 0 0 0 0 0 4 2 0 1 0 0 1 1 -2 2 -2 6 1 2 2 2 2 2 1 0 0 0 2 6 |Aut| = 2^10*3^2*5 #short vectors: 0 0 0 72 0 184 0 1824 &Gram (#3 <- H4) 4 2 4 2 2 4 2 2 0 4 2 2 2 0 4 2 0 0 2 0 4 2 0 0 0 0 1 6 1 -1 1 0 -1 2 1 6 0 -1 -1 0 -1 0 -1 2 6 0 0 0 1 0 0 1 -2 0 6 0 0 1 -1 1 -1 -2 -2 -2 0 6 2 0 1 0 0 2 2 2 2 1 -2 6 |Aut| = 2^10*3^2*5 #short vectors: 0 0 0 60 0 256 0 1716 &Gram (#4 <- H5) 4 2 4 2 0 4 2 0 2 4 2 0 2 2 4 2 0 2 2 2 4 1 -1 0 2 0 2 6 1 2 -1 1 -1 1 2 6 2 1 0 2 0 2 3 2 6 2 0 1 0 2 0 -1 -1 0 6 2 0 0 1 0 2 3 1 2 1 6 2 2 2 0 2 1 -2 0 0 1 0 6 |Aut| = 2^6*3^2*5*7 #short vectors: 0 0 0 42 0 364 0 1554 &Gram (#5 <- H6) 4 1 4 1 2 4 1 2 0 4 0 1 0 0 4 0 0 -1 1 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 -1 4 2 -1 1 0 1 -2 0 0 6 2 1 0 1 2 2 0 -2 0 6 2 2 1 0 -1 -2 -2 1 0 -1 6 2 0 0 1 -2 2 0 2 -1 0 1 6 |Aut| = 2^9*3^2 #short vectors: 0 0 0 36 0 400 0 1500 &Gram (#6 <- H7) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 1 0 0 0 0 0 4 0 1 0 0 0 0 0 4 0 0 1 0 0 0 0 0 4 0 0 0 1 0 0 0 0 0 4 0 0 0 0 1 0 0 0 0 0 4 0 0 0 0 0 1 0 0 0 0 0 4 |Aut| = 2^16*3^2*5 #short vectors: 0 12 0 84 0 400 0 1476 &Gram (#7 <- H8) 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 -1 -2 0 4 0 0 0 0 0 0 -1 1 -1 0 4 0 0 0 0 0 0 2 1 2 -1 0 4 |Aut| = 2^12*3^2*7 #short vectors: 0 6 0 66 0 364 0 1542 &Gram (#8 <- H9) 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 2 0 4 0 0 0 0 1 1 0 1 4 0 0 0 0 0 1 0 0 2 4 0 0 0 0 1 1 1 0 2 2 4 0 0 0 0 0 0 1 0 -2 -2 0 4 |Aut| = 2^13*3^2 #short vectors: 0 4 0 60 0 352 0 1564 &Gram (#9 <- H10,H11) 2 1 4 0 0 4 0 0 2 4 0 0 -2 -2 4 0 0 -2 -2 0 4 0 0 -2 0 0 0 4 0 0 0 1 0 0 0 4 0 0 -1 -2 1 2 0 -2 6 0 0 -2 0 0 1 2 2 1 6 0 0 0 -1 -1 0 1 1 1 1 6 0 0 -1 1 0 1 0 -1 -1 0 -2 6 |Aut| = 2^10*3*5 #short vectors: 0 2 0 54 0 340 0 1586