Output of /home/aschiem/Pgm/Hn/hn --invar -t --herm_lll2 0.0001 --shells-16 --herm_lll3 0.8 &K=Q(sqrt(-6)) &Hdim=4 V=K^4 &HNeighbourhood at <3,w> contains 25 classes: mass of the neighbourhood is 23/24 Steinitz class <2,w>: &Hlattice (#1 <- #25) <1> <1> <1> <2,w> 3 -1 3 -1+w 1-w 4 1+1/2w -1 -1/2w 3/2 |Aut| = 2^4 #short vectors: 0 0 8 38 72 76 168 234 248 528 648 634 1104 1392 1224 1922 &Hlattice (#2 <- #26) <1> <1> <1> <2,w> 3 -1-w 4 -w 2+w 4 1+1/2w -2+1/2w 1/2w 2 |Aut| = 2^4 #short vectors: 0 0 8 38 72 76 168 234 248 528 648 634 1104 1392 1224 1922 &Hlattice (#3 <- #31) <2,w> <1> <1> <1> 1 1-1/2w 4 -1/2w 2 4 -1/2w 2-w 1-w 5 |Aut| = 2^3*3 #short vectors: 0 0 4 50 60 88 164 210 276 480 708 598 1144 1440 1172 1970 &Hlattice (#4 <- #32) <1> <1> <1> <2,w> 3 -1-w 4 w -2-w 4 -1+1/2w -1/2w 1+1/2w 3/2 |Aut| = 2^3*3 #short vectors: 0 0 4 50 60 88 164 210 276 480 708 598 1144 1440 1172 1970 &Hlattice (#5 <- #6) <1> <1> <1> <2,w> 2 0 2 0 -1 2 -1/2w -1 0 3/2 |Aut| = 2^5*3 #short vectors: 0 14 0 42 16 82 192 226 304 420 832 622 1248 1360 1024 1938 &Hlattice (#6 <- #8) <1> <2,w> <2,w> <2,w> 2 0 1/2 0 0 1/2 -1/2w 0 0 1 |Aut| = 2^5*3 #short vectors: 0 10 4 34 40 94 136 242 360 396 808 646 1040 1424 1136 1906 &Hlattice (#7 <- #23) <2,w> <1> <1> <1> 1/2 0 2 0 0 3 0 1 -1+w 3 |Aut| = 2^3*3 #short vectors: 0 8 10 18 68 64 156 274 276 528 668 694 1032 1312 1232 1842 &Hlattice (#8 <- #24) <2,w> <1> <1> <1> 1/2 0 2 0 0 3 0 -1 -1-w 3 |Aut| = 2^3*3 #short vectors: 0 8 10 18 68 64 156 274 276 528 668 694 1032 1312 1232 1842 &Hlattice (#9 <- #29) <1> <1> <1> <2,w> 2 1 3 1 -1 3 -1/2w -1-1/2w 1 3/2 |Aut| = 2^3*3 #short vectors: 0 8 12 18 52 64 204 274 220 528 652 694 1128 1312 1180 1842 &Hlattice (#10 <- #30) <1> <1> <1> <2,w> 2 1 2 -w -w 5 1-1/2w -1/2w 2+1/2w 2 |Aut| = 2^3*3 #short vectors: 0 8 12 18 52 64 204 274 220 528 652 694 1128 1312 1180 1842 &Hlattice (#11 <- #9) <1> <2,w> <1> <1> 3 -1+1/2w 1 0 0 5 0 0 -2w 5 |Aut| = 2^5 #short vectors: 0 6 12 18 64 82 144 274 304 468 688 694 960 1392 1240 1842 &Hlattice (#12 <- #10) <1> <1> <1> <2,w> 2 1 3 -w 0 4 1 1 1/2w 1 |Aut| = 2^5*3 #short vectors: 0 6 16 26 0 106 272 258 192 372 720 670 1216 1488 1040 1874 &Hlattice (#13 <- #13) <1> <1> <1> <2,w> 2 0 2 0 1-w 4 1-1/2w 0 0 3/2 |Aut| = 2^5 #short vectors: 0 6 8 34 40 82 200 242 248 468 712 646 1168 1392 1128 1906 &Hlattice (#14 <- #14) <2,w> <1> <1> <1> 1 0 4 -1 -1-w 5 1-1/2w -w -2+w 7 |Aut| = 2^5 #short vectors: 0 6 16 18 32 82 240 274 192 468 656 694 1152 1392 1136 1842 &Hlattice (#15 <- #15) <1> <1> <1> <2,w> 2 0 2 1 -1 4 -1/2w -1 0 3/2 |Aut| = 2^5 #short vectors: 0 6 0 50 48 82 160 210 304 468 768 598 1184 1392 1120 1970 &Hlattice (#16 <- #21) <1> <1> <1> <2,w> 3 -1-w 4 -1+w -2 5 1+1/2w -2+1/2w 2-1/2w 2 |Aut| = 2^4 #short vectors: 0 4 8 30 72 64 168 250 248 552 648 658 1104 1328 1224 1890 &Hlattice (#17 <- #22) <1> <1> <1> <2,w> 2 1 3 0 1 3 -1/2w -1 -1 3/2 |Aut| = 2^4 #short vectors: 0 4 8 30 72 64 168 250 248 552 648 658 1104 1328 1224 1890 &Hlattice (#18 <- #16) <1> <1> <2,w> <1> 3 1+w 4 -1 0 1 -1+w 1+w -1/2w 4 |Aut| = 2^3 #short vectors: 0 2 8 34 72 70 168 242 248 540 648 646 1104 1360 1224 1906 &Hlattice (#19 <- #1) <1> <1> <1> <2,w> 1 0 1 0 0 1 0 0 0 1/2 |Aut| = 2^5*3 #short vectors: 6 14 22 42 68 82 144 226 246 420 632 622 996 1360 1172 1938 &Hlattice (#20 <- #4) <1> <1> <1> <2,w> 1 0 1 0 0 2 0 0 1/2w 1 |Aut| = 2^5*3 #short vectors: 4 10 24 34 32 94 232 242 172 396 632 646 1128 1424 1096 1906 &Hlattice (#21 <- #5) <1> <1> <1> <2,w> 1 0 1 0 0 3 0 0 -1+1/2w 1 |Aut| = 2^5 #short vectors: 4 6 16 50 72 82 160 210 228 468 624 598 1080 1392 1184 1970 &Hlattice (#22 <- #2) <1> <2,w> <2,w> <2,w> 1 0 1/2 0 0 1/2 0 0 0 1/2 |Aut| = 2^5*3 #short vectors: 2 6 18 26 60 106 128 258 322 372 696 670 876 1488 1228 1874 &Hlattice (#23 <- #3) <1> <1> <2,w> <1> 1 0 2 0 0 1/2 0 1-w 0 4 |Aut| = 2^5 #short vectors: 2 6 14 34 68 82 152 242 266 468 656 646 1020 1392 1212 1906 &Hlattice (#24 <- #17) <1> <1> <1> <2,w> 1 0 3 0 1 3 0 -1/2w -1 1 |Aut| = 2^3*3 #short vectors: 2 0 12 50 72 88 164 210 238 480 636 598 1092 1440 1204 1970 &Hlattice (#25 <- #18) <1> <1> <1> <2,w> 1 0 3 0 1+w 3 0 -1/2w -1 1 |Aut| = 2^3*3 #short vectors: 2 0 12 50 72 88 164 210 238 480 636 598 1092 1440 1204 1970 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 2^4]_4 3-adic symbol: 1^-4 3^-4 -1-adic symbol: +^8 -^0 level(of 2-scaled form)=24, weight=4 a_0,..,a_16 determine modular form &Gram (#1 <- H1,H2) 3 1 3 0 -1 3 1 0 -1 3 1 0 -1 0 4 1 0 -1 0 0 4 1 0 -1 0 2 0 4 1 0 -1 0 0 2 0 4 |Aut| = 2^7 #short vectors: 0 0 8 38 72 76 168 234 248 528 648 634 1104 1392 1224 1922 &Gram (#2 <- H3,H4) 3 0 3 1 1 4 1 1 -1 4 1 1 2 1 4 1 1 2 -1 2 4 1 1 2 0 0 0 4 1 1 0 2 2 0 0 4 |Aut| = 2^5*3^2 #short vectors: 0 0 4 50 60 88 164 210 276 480 708 598 1144 1440 1172 1970 &Gram (#3 <- H5) 2 0 2 0 -1 2 0 1 -1 2 0 1 0 1 4 1 0 0 0 0 5 1 0 0 0 0 2 5 1 0 0 0 0 -1 2 5 |Aut| = 2^10*3^2 #short vectors: 0 14 0 42 16 82 192 226 304 420 832 622 1248 1360 1024 1938 &Gram (#4 <- H6) 2 1 2 0 0 2 0 0 0 2 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 2 4 |Aut| = 2^10*3^2 #short vectors: 0 10 4 34 40 94 136 242 360 396 808 646 1040 1424 1136 1906 &Gram (#5 <- H7,H8) 2 0 2 0 1 2 0 -1 0 3 0 0 0 -1 3 0 0 0 0 0 3 0 1 0 -1 1 0 5 0 -1 0 1 -1 0 1 5 |Aut| = 2^5*3^2 #short vectors: 0 8 10 18 68 64 156 274 276 528 668 694 1032 1312 1232 1842 &Gram (#6 <- H9,H10) 2 0 2 0 -1 2 1 1 -1 3 0 -1 1 -1 4 1 -1 0 0 2 5 1 0 0 1 1 1 5 1 0 0 1 1 1 -1 5 |Aut| = 2^5*3^2 #short vectors: 0 8 12 18 52 64 204 274 220 528 652 694 1128 1312 1180 1842 &Gram (#7 <- H11) 2 0 2 0 0 2 1 0 0 3 1 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 -1 -1 0 0 4 |Aut| = 2^10 #short vectors: 0 6 12 18 64 82 144 274 304 468 688 694 960 1392 1240 1842 &Gram (#8 <- H12) 2 0 2 1 1 3 1 1 0 3 0 0 0 0 4 0 0 0 0 2 4 0 0 0 0 1 2 4 0 0 0 0 -1 -2 -1 4 |Aut| = 2^10*3^2 #short vectors: 0 6 16 26 0 106 272 258 192 372 720 670 1216 1488 1040 1874 &Gram (#9 <- H13) 2 0 2 0 0 2 1 0 0 3 1 0 0 1 3 0 -1 -1 0 0 4 0 0 0 1 -1 0 4 0 -1 -1 0 0 1 0 4 |Aut| = 2^10 #short vectors: 0 6 8 34 40 82 200 242 248 468 712 646 1168 1392 1128 1906 &Gram (#10 <- H14) 2 0 2 0 0 2 1 1 -1 3 0 0 0 0 4 0 0 0 0 -2 4 1 0 1 0 -2 1 5 1 0 -1 1 -2 1 1 5 |Aut| = 2^10 #short vectors: 0 6 16 18 32 82 240 274 192 468 656 694 1152 1392 1136 1842 &Gram (#11 <- H15) 2 0 2 0 0 2 1 -1 1 4 1 -1 1 2 4 0 0 0 1 -1 4 0 -1 1 2 0 1 5 0 1 -1 -2 0 -1 -2 5 |Aut| = 2^10 #short vectors: 0 6 0 50 48 82 160 210 304 468 768 598 1184 1392 1120 1970 &Gram (#12 <- H16,H17) 2 0 2 0 -1 3 1 0 -1 3 1 -1 0 1 4 1 -1 0 1 0 4 1 0 -1 0 2 0 5 1 0 -1 0 0 2 1 5 |Aut| = 2^7 #short vectors: 0 4 8 30 72 64 168 250 248 552 648 658 1104 1328 1224 1890 &Gram (#13 <- H18) 2 0 3 0 1 3 0 -1 1 3 0 1 1 -1 4 1 -1 -1 0 1 4 1 1 1 0 -1 0 4 0 -1 1 1 0 0 0 4 |Aut| = 2^7 #short vectors: 0 2 8 34 72 70 168 242 248 540 648 646 1104 1360 1224 1906 &Gram (#14 <- H19) 1 0 1 0 0 1 0 0 0 2 0 0 0 0 3 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 |Aut| = 2^10*3^2 #short vectors: 6 14 22 42 68 82 144 226 246 420 632 622 996 1360 1172 1938 &Gram (#15 <- H20) 1 0 1 0 0 2 0 0 -1 2 0 0 0 0 4 0 0 0 0 -2 4 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 |Aut| = 2^10*3^2 #short vectors: 4 10 24 34 32 94 232 242 172 396 632 646 1128 1424 1096 1906 &Gram (#16 <- H21) 1 0 1 0 0 2 0 0 -1 3 0 0 1 0 3 0 0 0 1 -1 4 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 |Aut| = 2^10 #short vectors: 4 6 16 50 72 82 160 210 228 468 624 598 1080 1392 1184 1970 &Gram (#17 <- H22) 1 0 2 0 0 2 0 0 0 2 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 3 0 0 0 0 0 0 0 6 |Aut| = 2^10*3^2 #short vectors: 2 6 18 26 60 106 128 258 322 372 696 670 876 1488 1228 1874 &Gram (#18 <- H23) 1 0 2 0 0 2 0 0 0 2 0 0 0 0 3 0 -1 0 -1 0 4 0 1 0 -1 0 0 4 0 0 0 0 0 0 0 6 |Aut| = 2^10 #short vectors: 2 6 14 34 68 82 152 242 266 468 656 646 1020 1392 1212 1906 &Gram (#19 <- H24,H25) 1 0 3 0 1 3 0 1 1 3 0 0 -1 -1 3 0 0 1 1 0 3 0 -1 -1 -1 1 -1 3 0 0 0 0 0 0 0 6 |Aut| = 2^5*3^2 #short vectors: 2 0 12 50 72 88 164 210 238 480 636 598 1092 1440 1204 1970