Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-5 &K=Q(sqrt(-7)) &Hdim=4 V=K^4 &HNeighbourhood at <2,-1+w> contains 3 classes: mass of the neighbourhood is 5/1008 Steinitz class <1,w>: &Hlattice (#1 <- #3) 2 1 2 0 1-w 2 1-w 1-w 1 2 |Aut| = 2^7*3^2 #short vectors: 0 48 144 384 528 &Hlattice (#2 <- #1) 1 0 1 0 0 1 0 0 0 1 |Aut| = 2^7*3 #short vectors: 8 40 128 328 656 &Hlattice (#3 <- #2) 1 0 2 0 1-w 2 0 -1 1-w 2 |Aut| = 2^5*3*7 #short vectors: 2 46 140 370 560 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 3 12 1 10 4 7 7 1 classes of Z-lattices with respect to the trace form &Dim=8 V=Q^8 &Genus of the trace-forms: det= 2401 = 7^4 2-adic symbol: 1^8_II 7-adic symbol: 1^4 7^4 -1-adic symbol: +^8 -^0 level=7, weight=4 a_0,..,a_4 determine modular form &Gram (#1 <- H1) 4 2 4 2 0 4 2 0 0 4 0 1 -1 0 4 1 1 0 0 2 4 0 0 -1 1 2 0 4 0 -1 0 0 -2 0 0 4 |Aut| = 2^8*3^2 #short vectors: 0 0 0 48 &Gram (#2 <- H2) 2 0 2 0 0 2 0 0 0 2 1 0 0 0 4 0 1 0 0 0 4 0 0 1 0 0 0 4 0 0 0 1 0 0 0 4 |Aut| = 2^11*3 #short vectors: 0 8 0 40 &Gram (#3 <- H3) 2 1 4 0 0 4 0 0 -2 4 0 0 -2 0 4 0 0 -1 -1 0 4 0 0 1 -2 -1 0 4 0 0 2 -1 0 0 1 4 |Aut| = 2^7*3*7 #short vectors: 0 2 0 46