Output of /home/aschiem/Pgm/Hn/hn.debug --invar -t -D5 &K=Q(sqrt(-3)) &Hdim=9 V=K^9 &HNeighbourhood at <3,1+w> contains 4 classes: mass of the neighbourhood is 809/2612138803200 Steinitz class <1,w>: &Hlattice (#1 <-- #3) 2 -w 2 1 w 2 1 w 1 2 1 w 1 1 2 1 w 1 1 1 2 1 w 1 1 1 1 2 1 w 1 1 1 1 1 2 0 1 0 0 0 0 0 0 3 |Aut| = 2^8*3^12*5*7 #short vectors: 0 648 17712 &Hlattice (#2 <-- #1) 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 |Aut| = 2^16*3^13*5*7 #short vectors: 54 &Hlattice (#3 <-- #2) 1 0 1 0 0 1 0 0 0 2 0 0 0 1 2 0 0 0 1 1 2 0 0 0 1 1 1 2 0 0 0 0 0 0 0 2 0 0 0 1-w 1-w 1-w -w 1 2 |Aut| = 2^13*3^11*5*7 #short vectors: 18 864 &Hlattice (#4 <-- #4) 1 0 2 0 -w 2 0 1 0 2 0 -w 1 -w 2 0 1-w w 1-w w 2 0 -w 0 -w 1 1-w 2 0 -w 0 -w 1 1-w 1 2 0 1-w w 0 0 1 0 0 2 |Aut| = 2^15*3^7*5^2*7 #short vectors: 6 720 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 7400 1 252 2187 768 1008 8064 0 2688 112 2504 4536 5760 0 1120 2960 classes of Z-lattices with respect to the trace form &Dim=18 V=Q^18 &Genus of the trace-forms: det= 19683 = 3^9 2-adic symbol: 1^-18_II 3-adic symbol: 1^-9 3^-9 -1-adic symbol: +^18 -^0 level=3, weight=9 a_0,..,a_6 determine modular form &Gram (#1 <- H1) 4 2 4 2 2 4 1 2 2 4 1 -1 -1 -2 4 1 -1 1 1 1 4 2 1 2 2 -1 2 4 2 2 1 2 -1 1 2 4 2 0 0 -1 2 0 0 0 4 2 0 0 -1 2 0 0 0 1 4 2 2 2 2 -1 1 2 2 0 0 4 2 0 0 -1 2 0 0 0 2 2 1 4 2 0 0 -1 2 0 0 0 2 2 0 2 4 2 0 0 -1 2 0 0 0 2 2 0 2 1 4 1 1 1 1 -2 -1 1 1 0 0 1 0 0 0 4 1 -1 1 -1 0 0 0 -1 0 1 1 1 0 1 2 6 1 -1 1 -1 0 0 0 -1 2 0 1 1 2 0 2 3 6 2 0 0 1 0 1 2 2 0 2 2 2 0 2 1 2 -1 6 |Aut| = 2^9*3^12*5*7 #short vectors: 0 0 0 648 0 17712 &Gram (#2 <- H2) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 |Aut| = 2^25*3^13*5*7 #short vectors: 0 54 0 1296 0 18198 &Gram (#3 <- H3) 2 1 2 0 0 2 0 0 -1 2 0 0 0 0 2 0 0 0 0 1 2 0 0 0 0 0 0 4 0 0 0 0 0 0 -2 4 0 0 0 0 0 0 -2 2 4 0 0 0 0 0 0 -2 2 2 4 0 0 0 0 0 0 1 1 -1 1 4 0 0 0 0 0 0 -1 -1 1 1 0 4 0 0 0 0 0 0 1 -2 -2 0 1 0 4 0 0 0 0 0 0 -1 -1 1 1 0 2 0 4 0 0 0 0 0 0 -2 1 2 0 -1 0 -1 0 4 0 0 0 0 0 0 -2 2 1 0 0 -1 -1 -1 2 4 0 0 0 0 0 0 2 0 0 -1 0 -2 -1 0 -1 -1 4 0 0 0 0 0 0 2 0 0 0 0 -1 -1 0 -2 -2 2 4 |Aut| = 2^17*3^11*5*7 #short vectors: 0 18 0 864 0 17874 &Gram (#4 <- H4) 2 1 2 0 0 4 0 0 2 4 0 0 -2 -2 4 0 0 -2 -2 0 4 0 0 2 0 -2 0 4 0 0 2 2 -2 -2 0 4 0 0 2 2 -2 0 2 0 4 0 0 2 1 -1 -1 1 1 1 4 0 0 1 0 1 -1 0 0 0 -1 4 0 0 -1 1 0 0 -1 0 0 -2 1 4 0 0 -1 0 1 -1 -1 0 -1 -2 0 2 4 0 0 1 0 -1 0 2 0 1 2 0 -2 -2 4 0 0 1 1 -1 -1 0 1 1 -1 0 0 0 0 4 0 0 -1 0 0 1 0 0 0 1 -2 -1 0 0 -2 4 0 0 1 1 -1 -1 0 1 0 -1 0 0 0 0 2 -2 4 0 0 1 1 -1 -1 0 1 0 2 0 0 0 0 -1 1 -2 4 |Aut| = 2^17*3^7*5^2*7 #short vectors: 0 6 0 720 0 17766