Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-8 --herm_lll3 0.8 &K=Q(sqrt(-6)) &Hdim=4 V=K^4 &HNeighbourhood at <3,w> contains 9 classes: mass of the neighbourhood is 115/1152 Steinitz class <1,w>: &Hlattice (#1 <- #5) <1> <1> <2,w> <2,w> 4 2+w 4 2+1/2w 2-1/2w 2 -w -1-1/2w -1/2-1/2w 2 |Aut| = 2^5*3 #short vectors: 0 0 0 72 0 192 0 504 &Hlattice (#2 <- #6) 4 w 4 -1 2 4 2-w 1 2+w 6 |Aut| = 2^5*3 #short vectors: 0 0 0 72 0 192 0 504 &Hlattice (#3 <- #8) <1> <1> <2,w> <2,w> 2 1 2 1 0 1 1 1 1/2 1 |Aut| = 2^7*3^2 #short vectors: 0 24 0 24 0 120 0 600 &Hlattice (#4 <- #7) <1> <1> <2,w> <2,w> 2 0 2 -1/2w 0 1 0 -1/2w 0 1 |Aut| = 2^5*3^2 #short vectors: 0 12 0 48 0 156 0 552 &Hlattice (#5 <- #1) 2 0 2 1+w 0 4 0 1+w 0 4 |Aut| = 2^7 #short vectors: 0 8 0 56 0 168 0 536 &Hlattice (#6 <- #9) 2 0 2 -w -1 4 1 0 0 4 |Aut| = 2^7 #short vectors: 0 8 0 56 0 168 0 536 &Hlattice (#7 <- #2) <1> <1> <2,w> <2,w> 2 1 2 1-1/2w 1 2 1-1/2w -1/2w 1 2 |Aut| = 2^3*3^2 #short vectors: 0 6 0 60 0 174 0 528 &Hlattice (#8 <- #4) 2 1 4 1 2-w 4 1-w -2-w 1-2w 8 |Aut| = 2^3*3^2 #short vectors: 0 6 0 60 0 174 0 528 &Hlattice (#9 <- #3) 2 1 4 0 -2+w 4 w 1 -1 4 |Aut| = 2^5 #short vectors: 0 4 0 64 0 180 0 520 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 16 8 0 8 0 0 8 8 0 8 0 0 0 0 0 8 8 24 0 0 0 16 0 0 16 16 0 24 0 4 12 0 0 4 4 0 0 0 0 0 0 0 16 16 16 0 0 0 0 0 16 0 0 32 6 6 1 1 9 0 0 16 9 6 6 1 1 9 0 16 0 9 0 8 0 0 4 8 4 4 20 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=8 V=Q^8 &Genus of the trace-forms: det= 1296 = 2^4 *3^4 2-adic symbol: 1^4_II 2^4_II 3-adic symbol: 1^4 3^4 -1-adic symbol: +^8 -^0 level=6, weight=4 a_0,..,a_8 determine modular form &Gram (#1 <- H1,H2) 4 2 4 2 0 4 2 0 0 4 1 1 1 1 4 1 0 0 0 1 4 1 2 0 0 2 0 4 1 0 2 0 -1 0 0 4 |Aut| = 2^8*3^3 #short vectors: 0 0 0 72 0 192 0 504 &Gram (#2 <- H3) 2 1 2 1 1 2 1 0 1 2 0 0 0 0 6 0 0 0 0 3 6 0 0 0 0 3 0 6 0 0 0 0 3 0 0 6 |Aut| = 2^14*3^4 #short vectors: 0 24 0 24 0 120 0 600 &Gram (#3 <- H4) 2 1 2 0 0 2 0 0 1 2 0 0 0 0 4 0 0 0 0 2 4 0 0 0 0 0 0 4 0 0 0 0 0 0 -2 4 |Aut| = 2^10*3^4 #short vectors: 0 12 0 48 0 156 0 552 &Gram (#4 <- H5,H6) 2 0 2 0 0 2 0 0 0 2 0 -1 -1 0 4 1 0 0 1 0 4 1 0 0 1 0 1 4 0 1 -1 0 0 0 0 4 |Aut| = 2^13 #short vectors: 0 8 0 56 0 168 0 536 &Gram (#5 <- H7,H8) 2 1 2 1 1 4 1 1 -1 4 1 1 2 -1 4 1 1 -1 1 -1 4 1 1 2 0 0 0 6 1 1 2 0 0 0 0 6 |Aut| = 2^5*3^4 #short vectors: 0 6 0 60 0 174 0 528 &Gram (#6 <- H9) 2 0 2 1 1 4 0 -1 1 4 1 0 -1 -2 4 0 1 -1 -2 0 4 0 0 0 -1 1 1 4 0 0 0 1 -1 1 0 4 |Aut| = 2^10 #short vectors: 0 4 0 64 0 180 0 520