Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-12 &K=Q(sqrt(-5)) &Hdim=4 V=K^4 &HNeighbourhood at <3,-1+w> contains 21 classes: mass of the neighbourhood is 15/32 Steinitz class <2,-1+w>: &Hlattice (#1 <-- #14) <1> <1> <2,-1+w> <1> 2 -1 2 1 -1 1 -1+w -w -1/2+1/2w 5 |Aut| = 2^5*3 #short vectors: 0 14 0 54 64 104 256 326 576 646 1024 936 &Hlattice (#2 <-- #18) <1> <1> <2,-1+w> <1> 2 1 2 -1 -1 1 0 w -1/2-1/2w 5 |Aut| = 2^5*3 #short vectors: 0 14 0 54 64 104 256 326 576 646 1024 936 &Hlattice (#3 <-- #3) <2,-1+w> <1> <2,-1+w> <2,-1+w> 1/2 0 2 0 0 1/2 0 -1/2-1/2w 0 1 |Aut| = 2^5*3 #short vectors: 0 10 8 46 64 136 248 310 544 626 976 1000 &Hlattice (#4 <-- #6) <2,-1+w> <1> <2,-1+w> <2,-1+w> 1/2 0 2 0 0 1/2 0 1/2-1/2w 0 1 |Aut| = 2^5*3 #short vectors: 0 10 8 46 64 136 248 310 544 626 976 1000 &Hlattice (#5 <-- #13) <1> <1> <1> <2,-1+w> 2 0 2 0 -w 3 -1/2-1/2w 0 0 1 |Aut| = 2^5*3 #short vectors: 0 10 8 46 64 136 248 310 544 626 976 1000 &Hlattice (#6 <-- #17) <1> <1> <1> <2,-1+w> 2 0 2 -w 0 3 0 -1/2+1/2w 0 1 |Aut| = 2^5*3 #short vectors: 0 10 8 46 64 136 248 310 544 626 976 1000 &Hlattice (#7 <-- #5) <1> <1> <1> <2,-1+w> 2 1 3 0 -1-w 3 0 1/2-1/2w 1/2+1/2w 1 |Aut| = 2^3*3 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Hlattice (#8 <-- #7) <1> <1> <1> <2,-1+w> 2 0 3 1 -1-w 3 0 1/2-1/2w 1/2+1/2w 1 |Aut| = 2^3*3 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Hlattice (#9 <-- #12) <1> <1> <1> <2,-1+w> 2 -1 3 0 1-w 4 0 0 1/2+1/2w 1 |Aut| = 2^5*3 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Hlattice (#10 <-- #16) <1> <1> <2,-1+w> <1> 2 1 3 0 -1/2-1/2w 1 1+w 1 1/2+1/2w 5 |Aut| = 2^5 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Hlattice (#11 <-- #19) <1> <1> <2,-1+w> <1> 2 1 3 0 -1/2+1/2w 1 1+w 1+w 1/2-1/2w 5 |Aut| = 2^5 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Hlattice (#12 <-- #21) <1> <1> <1> <2,-1+w> 2 -1 3 0 1+w 4 0 0 1/2-1/2w 1 |Aut| = 2^5*3 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Hlattice (#13 <-- #9) <2,-1+w> <1> <1> <1> 1/2 0 3 0 1 3 0 w 1+w 3 |Aut| = 2^3*3 #short vectors: 0 2 24 30 64 200 232 278 480 586 880 1128 &Hlattice (#14 <-- #11) <1> <1> <1> <2,-1+w> 2 -1 3 -1 1-w 3 0 -1 -1/2-1/2w 1 |Aut| = 2^3*3 #short vectors: 0 2 24 30 64 200 232 278 480 586 880 1128 &Hlattice (#15 <-- #20) <1> <1> <1> <2,-1+w> 2 -1 3 -1 1 3 0 -1 -1/2+1/2w 1 |Aut| = 2^3*3 #short vectors: 0 2 24 30 64 200 232 278 480 586 880 1128 &Hlattice (#16 <-- #1) <1> <1> <1> <2,-1+w> 1 0 1 0 0 1 0 0 0 1/2 |Aut| = 2^5*3 #short vectors: 6 14 24 54 94 104 160 326 510 646 664 936 &Hlattice (#17 <-- #10) <1> <1> <1> <2,-1+w> 1 0 1 0 0 2 0 0 -1/2-1/2w 1 |Aut| = 2^5*3 #short vectors: 4 10 24 46 84 136 184 310 500 626 736 1000 &Hlattice (#18 <-- #15) <1> <1> <1> <2,-1+w> 1 0 1 0 0 2 0 0 -1/2+1/2w 1 |Aut| = 2^5*3 #short vectors: 4 10 24 46 84 136 184 310 500 626 736 1000 &Hlattice (#19 <-- #2) <1> <1> <2,-1+w> <1> 1 0 2 0 0 1/2 0 -w 0 3 |Aut| = 2^5 #short vectors: 2 6 24 38 74 168 208 294 490 606 808 1064 &Hlattice (#20 <-- #4) <1> <1> <1> <2,-1+w> 1 0 2 0 1 2 0 1/2-1/2w 1 3/2 |Aut| = 2^3*3 #short vectors: 2 6 24 38 74 168 208 294 490 606 808 1064 &Hlattice (#21 <-- #8) <1> <2,-1+w> <2,-1+w> <2,-1+w> 1 0 1/2 0 0 1/2 0 0 0 1/2 |Aut| = 2^5*3 #short vectors: 2 6 24 38 74 168 208 294 490 606 808 1064 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 10 0 0 0 0 12 8 0 6 0 0 0 0 0 0 4 0 0 0 0 10 0 0 0 4 0 0 12 0 0 6 0 0 0 0 0 0 0 0 8 0 0 0 2 4 2 0 12 0 4 0 0 0 4 0 0 0 0 0 12 0 0 0 0 4 2 0 2 0 4 0 0 12 0 12 0 0 4 0 0 0 0 0 0 0 2 0 0 4 0 12 0 12 0 4 0 0 4 0 2 0 0 0 0 4 0 0 2 4 0 4 0 0 12 0 0 0 12 0 0 0 2 0 0 0 3 2 1 0 0 3 6 4 0 0 3 0 0 6 0 0 0 0 6 6 0 0 3 0 3 1 0 4 6 0 3 6 0 0 0 6 2 0 0 0 6 0 0 0 0 0 0 4 0 0 0 0 6 10 8 12 0 0 0 0 0 0 0 2 0 4 0 0 0 8 4 0 0 4 2 0 4 8 0 0 4 0 0 0 0 2 0 0 4 4 4 0 2 4 0 0 8 0 4 0 0 0 0 8 0 0 0 0 4 0 0 0 0 10 6 0 0 0 8 12 0 0 0 0 0 0 0 0 3 1 0 0 0 0 0 6 0 2 4 6 6 0 0 0 3 6 3 0 0 0 0 0 1 6 0 3 3 6 0 6 6 4 0 3 0 0 0 2 0 0 0 0 3 0 0 6 2 0 3 3 6 4 6 0 0 1 6 0 0 0 0 4 0 0 0 8 0 0 0 0 0 0 0 0 10 0 0 6 12 0 0 0 0 0 2 0 0 0 0 0 12 0 0 4 0 0 2 4 0 12 4 0 4 0 0 0 2 0 0 0 0 0 0 0 0 12 0 4 2 12 4 0 0 0 0 4 0 0 0 8 0 0 0 0 4 8 0 2 4 0 4 4 2 2 0 0 0 0 0 6 6 0 6 0 0 6 0 0 3 1 3 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 8 0 0 4 6 0 10 classes of Z-lattices with respect to the trace form (scaled by 1/2) &Dim=8 V=Q^8 &Genus of the trace-forms: det= 625 = 5^4 2-adic symbol: 1^8_4 5-adic symbol: 1^-4 5^-4 -1-adic symbol: +^8 -^0 level(of 2-scaled form)=20, weight=4 a_0,..,a_12 determine modular form &Gram (#1 <- H1,H2) 2 1 2 1 0 2 0 0 0 2 1 0 0 -1 4 1 0 1 1 0 5 1 1 0 1 0 2 5 1 0 1 -1 1 -1 1 5 |Aut| = 2^9*3^2 #short vectors: 0 14 0 54 64 104 256 326 576 646 1024 936 &Gram (#2 <- H3,H4,H5,H6) 2 0 2 0 1 2 0 0 0 2 0 0 0 1 3 1 0 0 0 0 3 0 1 1 0 0 0 4 0 -1 0 0 0 0 -2 4 |Aut| = 2^8*3^2 #short vectors: 0 10 8 46 64 136 248 310 544 626 976 1000 &Gram (#3 <- H7,H8) 2 1 2 1 0 3 1 1 1 3 0 0 -1 -1 3 0 0 -1 -1 0 3 0 0 0 0 1 -1 4 0 0 0 0 1 -1 -1 4 |Aut| = 2^5*3^2 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Gram (#4 <- H9,H10,H11,H12) 2 0 2 1 1 3 1 1 0 3 0 1 1 0 4 0 1 0 1 2 4 1 0 1 0 1 -1 4 0 0 1 0 1 -1 1 4 |Aut| = 2^8*3 #short vectors: 0 6 16 38 64 168 240 294 512 606 928 1064 &Gram (#5 <- H13) 2 1 3 0 0 3 0 0 1 3 0 0 -1 1 3 0 0 0 1 0 3 0 0 0 1 1 -1 3 0 0 0 0 1 1 -1 3 |Aut| = 2^6*3*5 #short vectors: 0 2 24 30 64 200 232 278 480 586 880 1128 &Gram (#6 <- H14,H15) 2 1 3 1 1 3 1 0 1 3 1 0 0 0 3 1 1 1 0 1 3 1 1 0 0 0 0 3 0 1 1 -1 1 0 -1 5 |Aut| = 2^5*3*5 #short vectors: 0 2 24 30 64 200 232 278 480 586 880 1128 &Gram (#7 <- H16) 1 0 1 0 0 1 0 0 0 2 0 0 0 -1 3 0 0 0 0 0 5 0 0 0 0 0 0 5 0 0 0 0 0 0 0 5 |Aut| = 2^10*3^2 #short vectors: 6 14 24 54 94 104 160 326 510 646 664 936 &Gram (#8 <- H17,H18) 1 0 1 0 0 2 0 0 -1 2 0 0 1 0 4 0 0 -1 0 1 4 0 0 0 0 0 0 5 0 0 0 0 0 0 0 5 |Aut| = 2^9*3^2 #short vectors: 4 10 24 46 84 136 184 310 500 626 736 1000 &Gram (#9 <- H19,H21) 1 0 2 0 0 2 0 0 0 2 0 0 0 1 3 0 0 -1 0 0 3 0 1 0 0 0 0 3 0 0 0 0 0 0 0 5 |Aut| = 2^9*3 #short vectors: 2 6 24 38 74 168 208 294 490 606 808 1064 &Gram (#10 <- H20) 1 0 2 0 1 2 0 1 0 3 0 -1 -1 -1 3 0 0 0 1 -1 4 0 0 0 1 -1 -1 4 0 0 0 0 0 0 0 5 |Aut| = 2^6*3^2 #short vectors: 2 6 24 38 74 168 208 294 490 606 808 1064