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 28 classes: mass of the neighbourhood is 115/96 Steinitz class <1,w>: &Hlattice (#1 <- #9) 3 1+w 3 0 1 3 -1 0 1 3 |Aut| = 2^3 #short vectors: 0 0 16 24 48 128 144 216 400 384 528 888 864 1152 1872 1752 &Hlattice (#2 <- #10) 3 1+w 3 0 1 3 -1 0 0 3 |Aut| = 2^4 #short vectors: 0 0 16 24 48 128 144 216 400 384 528 888 864 1152 1872 1752 &Hlattice (#3 <- #23) 3 -w 3 -1 1 3 1 1 -w 3 |Aut| = 2^4 #short vectors: 0 0 16 24 48 128 144 216 400 384 528 888 864 1152 1872 1752 &Hlattice (#4 <- #21) 2 -1 2 -1 0 2 -w -1+w w 7 |Aut| = 2^7*3 #short vectors: 0 24 0 24 0 104 128 216 512 336 768 888 1024 960 1664 1752 &Hlattice (#5 <- #5) <2,w> <2,w> <2,w> <2,w> 1/2 0 1/2 0 0 1/2 0 0 0 1/2 |Aut| = 2^7*3 #short vectors: 0 8 8 24 64 56 192 216 288 624 448 888 1152 832 1840 1752 &Hlattice (#6 <- #8) <1> <1> <2,w> <2,w> 2 0 2 0 -1/2w 1 1-1/2w 0 0 3/2 |Aut| = 2^4*3 #short vectors: 0 8 8 24 56 104 104 216 456 432 584 888 880 1024 1864 1752 &Hlattice (#7 <- #18) <1> <2,w> <2,w> <1> 2 0 1/2 0 0 1/2 1-w 0 0 4 |Aut| = 2^6 #short vectors: 0 8 4 40 32 104 160 184 400 432 608 840 1088 1024 1752 1816 &Hlattice (#8 <- #22) <1> <2,w> <2,w> <1> 2 1 1 1 1/2 1 1-w 1-1/2w -1/2w 5 |Aut| = 2^7*3 #short vectors: 0 8 0 24 128 56 0 216 512 624 512 888 768 832 2048 1752 &Hlattice (#9 <- #28) 2 1 4 0 -1 4 1-w 1 -2 5 |Aut| = 2^6 #short vectors: 0 8 0 40 64 104 64 184 512 432 640 840 896 1024 1856 1816 &Hlattice (#10 <- #13) 2 -1 3 0 1-w 4 -1-w 1+w 0 6 |Aut| = 2^3*3 #short vectors: 0 6 12 24 36 122 140 216 428 372 588 888 904 1104 1820 1752 &Hlattice (#11 <- #17) 2 -1 3 -1 1 4 0 -1-w -w 4 |Aut| = 2^3*3 #short vectors: 0 6 12 24 36 122 140 216 428 372 588 888 904 1104 1820 1752 &Hlattice (#12 <- #15) <1> <1> <2,w> <2,w> 2 -1 3 -1 1 1 -1 1-1/2w 1/2 3/2 |Aut| = 2^4 #short vectors: 0 4 16 16 48 116 144 232 400 408 528 912 864 1088 1872 1720 &Hlattice (#13 <- #24) 2 1 3 -w 0 4 0 -1-w -1 4 |Aut| = 2^4 #short vectors: 0 4 8 32 56 116 104 200 456 408 584 864 880 1088 1864 1784 &Hlattice (#14 <- #26) <1> <1> <2,w> <2,w> 2 0 2 1-1/2w 0 3/2 0 1-1/2w 0 3/2 |Aut| = 2^5 #short vectors: 0 4 16 16 48 116 144 232 400 408 528 912 864 1088 1872 1720 &Hlattice (#15 <- #27) 2 1 3 0 -w 3 -w 0 -1 4 |Aut| = 2^5 #short vectors: 0 4 16 16 48 116 144 232 400 408 528 912 864 1088 1872 1720 &Hlattice (#16 <- #6) <2,w> <1> <1> <2,w> 1/2 0 3 0 -1-w 3 0 -1/2w 1 1 |Aut| = 2^3*3 #short vectors: 0 2 14 24 52 110 156 216 372 444 508 888 936 1072 1864 1752 &Hlattice (#17 <- #7) <2,w> <1> <1> <2,w> 1/2 0 3 0 1-w 3 0 -1 -1-1/2w 3/2 |Aut| = 2^3*3 #short vectors: 0 2 14 24 52 110 156 216 372 444 508 888 936 1072 1864 1752 &Hlattice (#18 <- #14) 2 1 3 1 1 3 0 -w -1 3 |Aut| = 2^3 #short vectors: 0 2 16 20 48 122 144 224 400 396 528 900 864 1120 1872 1736 &Hlattice (#19 <- #16) 2 1 3 1-w 1-w 5 0 -1 -2 5 |Aut| = 2^3 #short vectors: 0 2 16 20 48 122 144 224 400 396 528 900 864 1120 1872 1736 &Hlattice (#20 <- #19) <1> <1> <2,w> <2,w> 2 1 3 -1/2w -1 3/2 -1/2w -1/2w 1/2 3/2 |Aut| = 2^3*3 #short vectors: 0 2 12 24 68 110 108 216 428 444 524 888 840 1072 1916 1752 &Hlattice (#21 <- #20) 2 -1 3 0 1-w 4 1 -1-w 2 5 |Aut| = 2^3*3 #short vectors: 0 2 12 24 68 110 108 216 428 444 524 888 840 1072 1916 1752 &Hlattice (#22 <- #1) 1 0 1 0 0 1 0 0 0 1 |Aut| = 2^7*3 #short vectors: 8 24 32 24 48 104 128 216 360 336 480 888 816 960 1792 1752 &Hlattice (#23 <- #11) 1 0 1 0 0 2 0 0 -1-w 4 |Aut| = 2^6 #short vectors: 4 8 16 40 88 104 64 184 436 432 496 840 792 1024 1920 1816 &Hlattice (#24 <- #25) <1> <1> <2,w> <2,w> 1 0 1 0 0 1/2 0 0 0 1/2 |Aut| = 2^6 #short vectors: 4 8 20 40 56 104 160 184 324 432 464 840 984 1024 1816 1816 &Hlattice (#25 <- #2) <1> <1> <2,w> <2,w> 1 0 2 0 0 1/2 0 -1/2w 0 1 |Aut| = 2^4*3 #short vectors: 2 8 18 24 52 104 152 216 362 432 496 888 924 1024 1844 1752 &Hlattice (#26 <- #3) 1 0 2 0 0 3 0 -1 -1-w 3 |Aut| = 2^3*3 #short vectors: 2 6 20 24 48 122 140 216 390 372 516 888 852 1104 1852 1752 &Hlattice (#27 <- #4) 1 0 2 0 1 2 0 1-w 1 5 |Aut| = 2^3*3 #short vectors: 2 6 20 24 48 122 140 216 390 372 516 888 852 1104 1852 1752 &Hlattice (#28 <- #12) <1> <1> <2,w> <2,w> 1 0 2 0 0 1/2 0 1-1/2w 0 3/2 |Aut| = 2^4 #short vectors: 2 4 18 32 52 116 152 200 362 408 496 864 924 1088 1844 1784 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 16 4 4 0 0 4 0 0 0 2 2 0 0 0 0 2 2 0 0 2 2 0 0 0 4 2 2 0 8 0 0 0 0 0 0 0 0 0 0 0 8 0 0 4 4 8 8 0 0 0 0 0 0 4 4 0 8 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 8 8 4 4 0 0 0 0 0 0 8 0 0 0 0 0 16 0 0 0 16 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 16 0 0 0 0 0 0 0 16 0 0 0 24 0 0 2 0 8 0 2 0 2 2 0 0 0 0 0 0 0 0 2 2 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 8 8 0 8 0 0 8 8 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 16 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 16 8 0 0 0 8 8 0 0 0 0 0 0 0 0 0 6 0 6 1 0 1 3 0 0 0 4 6 3 0 0 0 0 6 0 6 0 0 0 0 0 6 0 0 6 0 6 1 0 1 3 0 0 4 0 6 3 0 0 0 0 0 6 0 6 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 4 4 8 8 4 4 0 0 0 0 4 4 0 0 8 0 0 0 0 2 0 4 2 2 0 4 0 4 0 0 8 8 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 4 8 0 0 12 12 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 8 8 4 0 0 12 12 0 0 0 0 4 0 0 0 0 6 6 0 0 1 0 3 0 0 0 0 6 0 0 0 0 4 0 6 6 0 0 0 0 1 6 0 3 6 6 0 0 1 0 3 0 0 0 0 6 0 0 0 4 0 6 0 0 6 0 0 0 1 0 6 3 0 4 4 0 0 0 0 0 1 2 0 4 4 3 3 0 2 0 12 0 2 0 0 1 0 2 0 4 0 4 4 0 0 0 0 0 1 0 2 4 4 3 3 2 0 12 0 2 0 0 0 1 0 0 2 4 6 0 6 0 0 1 0 1 0 6 0 6 3 0 0 6 0 0 6 0 4 0 3 0 0 0 0 0 6 0 6 0 0 1 0 1 0 0 6 6 3 0 0 0 6 6 0 4 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 16 16 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 8 8 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 8 8 0 0 0 0 8 0 0 0 16 24 0 0 0 2 4 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 2 0 0 8 2 2 0 6 6 0 0 0 0 0 0 0 6 0 6 0 0 0 6 0 6 0 0 0 1 3 0 1 0 4 3 6 6 0 0 0 0 0 0 0 0 6 6 0 0 0 0 6 0 6 0 0 1 3 0 1 4 0 3 0 0 8 0 0 0 2 0 0 0 0 0 0 4 0 2 2 8 8 0 0 0 2 4 0 2 2 4 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]_0 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,H3) 3 1 3 0 -1 3 1 0 1 3 0 0 1 0 3 0 0 0 1 -1 3 1 0 0 0 0 -1 3 0 1 0 0 1 0 -1 3 |Aut| = 2^5*3 #short vectors: 0 0 16 24 48 128 144 216 400 384 528 888 864 1152 1872 1752 &Gram (#2 <- H4) 2 1 2 1 0 2 1 0 0 2 0 0 0 0 6 0 0 0 0 0 6 0 0 0 0 0 0 6 1 0 1 0 3 -3 -3 7 |Aut| = 2^14*3^2 #short vectors: 0 24 0 24 0 104 128 216 512 336 768 888 1024 960 1664 1752 &Gram (#3 <- H5) 2 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 3 |Aut| = 2^14*3^2 #short vectors: 0 8 8 24 64 56 192 216 288 624 448 888 1152 832 1840 1752 &Gram (#4 <- H6) 2 0 2 0 1 2 1 0 0 3 1 0 0 1 3 0 0 0 1 -1 4 0 0 0 0 0 0 4 0 0 0 0 0 0 -2 4 |Aut| = 2^8*3^2 #short vectors: 0 8 8 24 56 104 104 216 456 432 584 888 880 1024 1864 1752 &Gram (#5 <- H7) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 3 0 0 0 0 0 3 1 0 0 1 0 0 4 1 0 0 -1 0 0 0 4 |Aut| = 2^12 #short vectors: 0 8 4 40 32 104 160 184 400 432 608 840 1088 1024 1752 1816 &Gram (#6 <- H8) 2 0 2 0 0 2 0 0 0 2 1 1 -1 1 5 1 1 -1 -1 1 5 1 1 -1 -1 1 2 5 1 1 -1 -1 1 2 2 5 |Aut| = 2^14*3^2 #short vectors: 0 8 0 24 128 56 0 216 512 624 512 888 768 832 2048 1752 &Gram (#7 <- H9) 2 0 2 0 0 2 0 0 0 2 1 0 1 0 4 1 0 1 0 1 4 1 1 1 -1 1 1 5 1 -1 1 -1 1 1 1 5 |Aut| = 2^12 #short vectors: 0 8 0 40 64 104 64 184 512 432 640 840 896 1024 1856 1816 &Gram (#8 <- H10,H11) 2 1 2 1 0 3 1 0 0 3 1 0 0 0 4 1 0 0 0 2 4 1 0 0 0 0 0 6 1 0 0 0 0 0 0 6 |Aut| = 2^5*3^2 #short vectors: 0 6 12 24 36 122 140 216 428 372 588 888 904 1104 1820 1752 &Gram (#9 <- H12) 2 0 2 1 -1 3 1 1 0 3 0 0 -1 1 4 0 0 1 1 0 4 0 0 1 0 1 2 5 0 0 1 0 1 2 2 5 |Aut| = 2^9 #short vectors: 0 4 16 16 48 116 144 232 400 408 528 912 864 1088 1872 1720 &Gram (#10 <- H13) 2 0 2 1 0 3 1 0 0 3 0 1 -1 -1 4 0 1 -1 -1 2 4 0 0 0 0 1 -1 4 0 0 -1 -1 1 1 0 4 |Aut| = 2^8 #short vectors: 0 4 8 32 56 116 104 200 456 408 584 864 880 1088 1864 1784 &Gram (#11 <- H14,H15) 2 0 2 1 0 3 0 -1 0 3 0 -1 0 1 3 1 0 0 0 0 3 0 0 0 1 -1 0 4 0 0 1 0 0 1 0 4 |Aut| = 2^9 #short vectors: 0 4 16 16 48 116 144 232 400 408 528 912 864 1088 1872 1720 &Gram (#12 <- H16,H17) 2 0 3 0 1 3 0 1 1 3 0 -1 -1 -1 3 0 0 1 1 -1 3 0 0 -1 -1 1 0 3 0 0 0 0 0 0 0 3 |Aut| = 2^5*3^2 #short vectors: 0 2 14 24 52 110 156 216 372 444 508 888 936 1072 1864 1752 &Gram (#13 <- H18,H19) 2 1 3 1 1 3 1 0 0 3 0 0 1 0 3 0 0 1 0 0 3 0 -1 1 1 1 1 4 1 1 1 0 1 1 -1 5 |Aut| = 2^5 #short vectors: 0 2 16 20 48 122 144 224 400 396 528 900 864 1120 1872 1736 &Gram (#14 <- H20,H21) 2 1 3 1 0 3 1 1 0 3 0 -1 -1 -1 4 0 -1 -1 -1 1 4 0 -1 -1 -1 1 1 4 1 1 0 1 -1 -1 -1 5 |Aut| = 2^5*3^2 #short vectors: 0 2 12 24 68 110 108 216 428 444 524 888 840 1072 1916 1752 &Gram (#15 <- H22) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 6 0 0 0 0 0 6 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 |Aut| = 2^14*3^2 #short vectors: 8 24 32 24 48 104 128 216 360 336 480 888 816 960 1792 1752 &Gram (#16 <- H23) 1 0 1 0 0 2 0 0 0 2 0 0 1 -1 4 0 0 1 1 0 4 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 |Aut| = 2^12 #short vectors: 4 8 16 40 88 104 64 184 436 432 496 840 792 1024 1920 1816 &Gram (#17 <- H24) 1 0 1 0 0 2 0 0 0 2 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 6 0 0 0 0 0 0 0 6 |Aut| = 2^12 #short vectors: 4 8 20 40 56 104 160 184 324 432 464 840 984 1024 1816 1816 &Gram (#18 <- H25) 1 0 2 0 -1 2 0 0 0 2 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 0 -2 4 0 0 0 0 0 0 0 6 |Aut| = 2^8*3^2 #short vectors: 2 8 18 24 52 104 152 216 362 432 496 888 924 1024 1844 1752 &Gram (#19 <- H26,H27) 1 0 2 0 1 2 0 -1 0 3 0 0 0 -1 3 0 1 0 -1 1 5 0 -1 0 1 -1 1 5 0 0 0 0 0 0 0 6 |Aut| = 2^5*3^2 #short vectors: 2 6 20 24 48 122 140 216 390 372 516 888 852 1104 1852 1752 &Gram (#20 <- H28) 1 0 2 0 0 2 0 -1 0 3 0 1 0 -1 3 0 0 0 0 0 3 0 0 0 -1 -1 0 4 0 0 0 0 0 0 0 6 |Aut| = 2^8 #short vectors: 2 4 18 32 52 116 152 200 362 408 496 864 924 1088 1844 1784