Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-8 -D5 &K=Q(sqrt(-11)) &Hdim=5 V=K^5 &HNeighbourhood at <3,-1+w> contains 10 classes: mass of the neighbourhood is 85/2816 Steinitz class <1,w>: &Hlattice (#1 <- #10) 3 2-w 3 w -1 3 1 w -w 3 1-w 1 -1-w 2-w 3 |Aut| = 2^3*3*5*11 #short vectors: 0 0 110 330 462 1320 2640 3960 &Hlattice (#2 <- #4) 2 -1 2 1 -1 2 1 -1 1 3 -1+w 1-w -1+w -2+w 3 |Aut| = 2^4*3*5 #short vectors: 0 20 70 210 782 1260 2440 4000 &Hlattice (#3 <- #7) 2 0 2 -1 0 2 0 0 -w 3 0 1 1 -1 3 |Aut| = 2^4*3^2 #short vectors: 0 12 86 258 654 1284 2520 3984 &Hlattice (#4 <- #9) 2 -1 2 0 0 2 0 -1 1 3 -w w 1 1 3 |Aut| = 2^4*3^2 #short vectors: 0 12 86 258 654 1284 2520 3984 &Hlattice (#5 <- #1) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 |Aut| = 2^8*3*5 #short vectors: 10 40 100 250 612 1200 2240 4040 &Hlattice (#6 <- #2) 1 0 1 0 0 1 0 0 0 2 0 0 0 -w 2 |Aut| = 2^6*3^2 #short vectors: 6 24 104 282 552 1248 2400 4008 &Hlattice (#7 <- #3) 1 0 2 0 -1 2 0 1 -1 2 0 -w w 1-w 3 |Aut| = 2^5*3*5 #short vectors: 2 20 84 242 684 1260 2440 4000 &Hlattice (#8 <- #5) 1 0 2 0 0 2 0 0 -w 2 0 -1+w 0 0 2 |Aut| = 2^6*3^2 #short vectors: 2 24 76 218 748 1248 2400 4008 &Hlattice (#9 <- #6) 1 0 2 0 0 2 0 1 1 2 0 1-w 1 1-w 3 |Aut| = 2^5*3*5 #short vectors: 2 20 84 242 684 1260 2440 4000 &Hlattice (#10 <- #8) 1 0 2 0 0 2 0 1 0 2 0 -w 1 1-w 3 |Aut| = 2^5*3^2 #short vectors: 2 12 100 290 556 1284 2520 3984 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 11 0 0 55 0 0 0 0 0 55 0 35 20 35 1 0 15 10 5 0 6 21 27 36 0 6 0 1 15 9 0 12 43 27 0 2 9 9 0 19 0 16 0 0 5 60 40 0 0 0 0 0 8 24 9 22 0 10 12 36 0 10 0 50 0 10 1 15 25 10 0 24 36 4 0 10 12 15 18 2 0 30 30 0 5 0 10 10 1 35 12 0 38 18 0 18 21 1 6 7 classes of Z-lattices with respect to the trace form &Dim=10 V=Q^10 &Genus of the trace-forms: det= 161051 = 11^5 2-adic symbol: 1^-10_II 11-adic symbol: 1^-5 11^-5 -1-adic symbol: +^10 -^0 level=11, weight=5 a_0,..,a_10 determine modular form &Gram (#1 <- H1) 6 3 6 2 -1 6 2 0 -1 6 2 3 1 -2 6 2 2 -2 2 2 6 2 2 -2 3 1 2 6 2 -1 2 2 1 0 0 6 0 -2 3 1 -1 0 -2 0 6 3 1 0 1 2 1 3 0 0 6 |Aut| = 2^4*3*5*11 #short vectors: 0 0 0 0 0 110 0 330 0 462 &Gram (#2 <- H2) 4 2 4 2 2 4 2 2 2 4 2 2 0 2 6 2 2 0 2 1 6 1 1 1 1 -1 0 6 1 0 0 0 2 1 0 6 0 -1 0 0 -2 -1 0 0 6 0 0 0 -1 -2 -1 0 0 0 6 |Aut| = 2^5*3*5 #short vectors: 0 0 0 20 0 70 0 210 0 782 &Gram (#3 <- H3,H4) 4 2 4 0 0 4 0 0 -2 4 2 0 -2 0 6 2 0 2 -2 1 6 0 1 -2 0 0 0 6 1 0 -2 0 1 1 0 6 2 2 1 0 1 0 -1 -1 6 2 0 1 -1 0 3 0 1 2 6 |Aut| = 2^4*3^2 #short vectors: 0 0 0 12 0 86 0 258 0 654 &Gram (#4 <- H5) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 1 0 0 0 0 6 0 1 0 0 0 0 6 0 0 1 0 0 0 0 6 0 0 0 1 0 0 0 0 6 0 0 0 0 1 0 0 0 0 6 |Aut| = 2^13*3*5 #short vectors: 0 10 0 40 0 100 0 250 0 612 &Gram (#5 <- H6) 2 0 2 0 0 2 0 0 0 4 0 0 0 -2 4 0 0 0 -1 0 4 0 0 0 0 -1 2 4 1 0 0 0 0 0 0 6 0 1 0 0 0 0 0 0 6 0 0 1 0 0 0 0 0 0 6 |Aut| = 2^10*3^2 #short vectors: 0 6 0 24 0 104 0 282 0 552 &Gram (#6 <- H7,H9) 2 0 4 0 -2 4 0 -2 0 4 0 2 0 -2 4 0 1 -2 -1 1 6 0 -1 -1 0 0 0 6 0 2 0 -1 2 -1 -2 6 0 2 -1 -2 2 0 -1 0 6 1 0 0 0 0 0 0 0 0 6 |Aut| = 2^6*3*5 #short vectors: 0 2 0 20 0 84 0 242 0 684 &Gram (#7 <- H8) 2 0 4 0 2 4 0 -1 0 4 0 0 -1 -2 4 0 0 0 0 0 4 0 0 0 0 0 2 4 0 0 0 0 0 -1 -1 4 0 0 0 0 0 1 0 -2 4 1 0 0 0 0 0 0 0 0 6 |Aut| = 2^9*3^2 #short vectors: 0 2 0 24 0 76 0 218 0 748 &Gram (#8 <- H10) 2 0 4 0 -2 4 0 0 0 4 0 0 0 2 4 0 1 -2 -2 0 6 0 2 -1 2 0 1 6 0 2 -2 1 2 1 1 6 0 -2 0 -1 1 1 -2 -2 6 1 0 0 0 0 0 0 0 0 6 |Aut| = 2^7*3^2 #short vectors: 0 2 0 12 0 100 0 290 0 556