Output of /home/aschiem/bin/hn --invar -t --shells-12 --herm_lll3 0.8 &K=Q(sqrt(-35)) &Hdim=3 V=K^3 &HNeighbourhood at <3,-1+w> contains 10 classes: mass of the neighbourhood is 9/8 Steinitz class <3,-1+w>: &Hlattice (#1 <- #10) <3,-1+w> <3,-1+w> <3,-1+w> 1/3 0 1/3 0 0 1/3 |Aut| = 2^4*3 #short vectors: 0 0 12 0 6 48 6 48 64 60 96 36 &Hlattice (#2 <- #6) <1> <3,-1+w> <1> 3 0 1/3 2-w 0 4 |Aut| = 2^3 #short vectors: 0 0 8 8 10 24 34 48 56 44 72 76 &Hlattice (#3 <- #5) <1> <1> <3,-1+w> 2 1 3 0 -1-1/3w 1 |Aut| = 2^2*3 #short vectors: 0 6 6 0 18 6 36 42 64 42 96 90 &Hlattice (#4 <- #2) <1> <3,-1+w> <1> 2 0 1/3 1-w 0 5 |Aut| = 2^3 #short vectors: 0 4 4 4 26 8 26 44 60 40 84 84 &Hlattice (#5 <- #4) <1> <1> <3,-1+w> 2 -1 3 1/3w 1-1/3w 1 |Aut| = 2^2 #short vectors: 0 2 6 8 14 10 44 46 56 38 72 94 &Hlattice (#6 <- #7) <1> <1> <3,-1+w> 2 1 3 -1 -1/3w 1 |Aut| = 2^2 #short vectors: 0 2 6 8 14 10 44 46 56 38 72 94 &Hlattice (#7 <- #1) <1> <1> <3,-1+w> 1 0 1 0 0 1/3 |Aut| = 2^4 #short vectors: 4 4 4 20 26 8 26 44 28 40 32 84 &Hlattice (#8 <- #3) <1> <1> <3,-1+w> 1 0 3 0 -1+1/3w 2/3 |Aut| = 2^3 #short vectors: 2 2 8 14 8 16 44 46 42 42 52 88 &Hlattice (#9 <- #8) <1> <1> <3,-1+w> 1 0 2 0 -1/3w 2/3 |Aut| = 2^3*3 #short vectors: 2 6 12 2 0 24 36 42 54 54 88 72 &Hlattice (#10 <- #9) <1> <1> <3,-1+w> 1 0 2 0 -1 2/3 |Aut| = 2^3*3 #short vectors: 2 6 12 2 0 24 36 42 54 54 88 72 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 3 6 0 0 0 0 0 0 0 4 1 2 0 2 4 0 0 2 2 0 0 0 0 3 9 0 0 0 1 0 0 2 2 2 0 6 1 0 0 0 0 0 0 3 2 5 0 2 0 1 0 2 3 0 4 2 1 1 0 0 0 0 0 2 4 0 3 4 0 0 0 2 0 0 2 4 2 1 1 1 2 0 0 0 0 6 0 3 1 1 0 6 2 0 0 0 0 3 1 1 classes of Z-lattices with respect to the trace form one representative of each class &Dim=6 V=Q^6 &Genus of the trace-forms: det= 42875 = 5^3 *7^3 2-adic symbol: 1^-6_II 7-adic symbol: 1^-3 7^3 5-adic symbol: 1^3 5^-3 -1-adic symbol: +^6 -^0 level=35, weight=3 a_0,..,a_24 determine modular form 8-classes of trace forms &Gram (#1 <- H1) 6 0 6 0 0 6 -1 0 0 6 0 -1 0 0 6 0 0 -1 0 0 6 |Aut| = 2^7*3 #short vectors: 0 0 0 0 0 12 0 0 0 6 0 48 0 6 0 48 0 64 0 60 0 96 0 36 &Gram (#2 <- H2) 6 0 6 0 0 6 0 -1 0 6 3 0 -2 0 8 2 0 -3 0 2 8 |Aut| = 2^5 #short vectors: 0 0 0 0 0 8 0 8 0 10 0 24 0 34 0 48 0 56 0 44 0 72 0 76 &Gram (#3 <- H3) 4 2 4 2 2 6 2 0 3 10 1 1 3 -1 14 1 0 -2 2 4 14 |Aut| = 2^3*3 #short vectors: 0 0 0 6 0 6 0 0 0 18 0 6 0 36 0 42 0 64 0 42 0 96 0 90 &Gram (#4 <- H4) 4 0 4 0 0 6 0 0 -1 6 1 2 0 0 10 2 1 0 0 1 10 |Aut| = 2^5 #short vectors: 0 0 0 4 0 4 0 4 0 26 0 8 0 26 0 44 0 60 0 40 0 84 0 84 &Gram (#5 <- H5,H6) 4 2 6 0 -2 6 2 0 1 8 2 -1 0 4 10 1 0 -2 -1 -3 12 |Aut| = 2^2 #short vectors: 0 0 0 2 0 6 0 8 0 14 0 10 0 44 0 46 0 56 0 38 0 72 0 94 &Gram (#6 <- H7) 2 0 2 0 0 6 0 0 -1 6 1 0 0 0 18 0 -1 0 0 0 18 |Aut| = 2^7 #short vectors: 0 4 0 4 0 4 0 20 0 26 0 8 0 26 0 44 0 28 0 40 0 32 0 84 &Gram (#7 <- H8) 2 0 4 0 2 6 0 2 1 8 0 -1 -3 3 12 1 0 0 0 0 18 |Aut| = 2^5 #short vectors: 0 2 0 2 0 8 0 14 0 8 0 16 0 44 0 46 0 42 0 42 0 52 0 88 &Gram (#8 <- H9,H10) 2 0 4 0 -2 4 0 -1 0 12 0 -1 1 6 12 1 0 0 0 0 18 |Aut| = 2^4*3 #short vectors: 0 2 0 6 0 12 0 2 0 0 0 24 0 36 0 42 0 54 0 54 0 88 0 72