Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-8 -D5 &K=Q(sqrt(-11)) &Hdim=4 V=K^4 &HNeighbourhood at <3,-1+w> contains 6 classes: mass of the neighbourhood is 61/1920 Steinitz class <1,w>: &Hlattice (#1 <- #4) 2 -w 2 0 0 2 0 0 -w 2 |Aut| = 2^5*3^2 #short vectors: 0 24 24 168 312 480 624 1080 &Hlattice (#2 <- #3) 2 1 2 -1 -1 2 1-w -w w 3 |Aut| = 2^4*3*5 #short vectors: 0 20 40 160 280 500 640 1120 &Hlattice (#3 <- #5) 2 -1 2 1 -1 2 -w -1+w 1-w 3 |Aut| = 2^4*3*5 #short vectors: 0 20 40 160 280 500 640 1120 &Hlattice (#4 <- #6) 2 1 2 0 0 2 1-w -w 1 3 |Aut| = 2^4*3^2 #short vectors: 0 12 72 144 216 540 672 1200 &Hlattice (#5 <- #1) 1 0 1 0 0 1 0 0 0 1 |Aut| = 2^7*3 #short vectors: 8 24 48 120 256 416 736 1112 &Hlattice (#6 <- #2) 1 0 1 0 0 2 0 0 -w 2 |Aut| = 2^5*3 #short vectors: 4 16 68 128 220 488 712 1176 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 2 12 18 2 0 6 15 0 5 10 0 10 10 10 0 15 5 0 1 9 6 6 0 18 0 8 0 0 4 28 2 0 4 12 7 15 classes of Z-lattices with respect to the trace form &Dim=8 V=Q^8 &Genus of the trace-forms: det= 14641 = 11^4 2-adic symbol: 1^8_II 11-adic symbol: 1^4 11^4 -1-adic symbol: +^8 -^0 level=11, weight=4 a_0,..,a_8 determine modular form &Gram (#1 <- H1) 4 2 4 1 0 4 0 1 -2 4 0 0 0 0 4 0 0 0 0 -2 4 0 0 0 0 -1 0 4 0 0 0 0 0 -1 2 4 |Aut| = 2^7*3^2 #short vectors: 0 0 0 24 0 24 0 168 &Gram (#2 <- H2,H3) 4 2 4 2 2 4 2 2 2 4 1 -1 1 1 6 1 2 2 2 -1 6 2 1 0 0 1 1 6 2 0 1 0 2 1 0 6 |Aut| = 2^4*3*5 #short vectors: 0 0 0 20 0 40 0 160 &Gram (#3 <- H4) 4 2 4 0 0 4 0 0 2 4 1 -1 2 0 6 2 1 2 0 0 6 2 0 -1 -2 1 1 6 2 0 2 1 2 2 -1 6 |Aut| = 2^5*3^2 #short vectors: 0 0 0 12 0 72 0 144 &Gram (#4 <- H5) 2 0 2 0 0 2 0 0 0 2 1 0 0 0 6 0 1 0 0 0 6 0 0 1 0 0 0 6 0 0 0 1 0 0 0 6 |Aut| = 2^11*3 #short vectors: 0 8 0 24 0 48 0 120 &Gram (#5 <- H6) 2 0 2 0 0 4 0 0 -2 4 0 0 -1 0 4 0 0 0 -1 2 4 1 0 0 0 0 0 6 0 1 0 0 0 0 0 6 |Aut| = 2^8*3 #short vectors: 0 4 0 16 0 68 0 128