Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-4 &K=Q(sqrt(-5)) &Hdim=4 V=K^4 &HNeighbourhood at <3,-1+w> contains 13 classes: mass of the neighbourhood is 13/192 Steinitz class <1,w>: &Hlattice (#1 <-- #6) 4 1-w 4 2+w 1+w 4 -1+w -2-w 0 4 |Aut| = 2^4*3^2 #short vectors: 0 0 0 120 &Hlattice (#2 <-- #11) 4 -1 4 1-w 2+w 4 -1 -2+w -1+w 4 |Aut| = 2^5*3*5 #short vectors: 0 0 0 120 &Hlattice (#3 <-- #12) 4 -w 4 -w w 4 2-w 0 1+w 4 |Aut| = 2^4*3*5 #short vectors: 0 0 0 120 &Hlattice (#4 <-- #1) 2 -1 2 -1 0 2 0 1-w w 6 |Aut| = 2^7*3 #short vectors: 0 24 0 24 &Hlattice (#5 <-- #5) <1> <1> <2,-1+w> <2,-1+w> 2 1 2 1 1 1 1 0 1/2 1 |Aut| = 2^7*3^2 #short vectors: 0 24 0 24 &Hlattice (#6 <-- #4) 2 0 2 1 0 2 -w -w 0 6 |Aut| = 2^4*3*5 #short vectors: 0 20 0 40 &Hlattice (#7 <-- #3) <1> <2,-1+w> <2,-1+w> <1> 2 1/2+1/2w 1 0 0 1 -1 -1/2+1/2w -1/2+1/2w 4 |Aut| = 2^5*3^2 #short vectors: 0 12 0 72 &Hlattice (#8 <-- #7) 4 -w 6 -1+w 2 6 -w -2w -2-w 6 |Aut| = 2^4*3^2 #short vectors: 0 12 0 72 &Hlattice (#9 <-- #8) 2 1 2 -w 0 4 -w -w 2 4 |Aut| = 2^4*3^2 #short vectors: 0 12 0 72 &Hlattice (#10 <-- #13) <1> <1> <2,-1+w> <2,-1+w> 2 0 2 1/2-1/2w 0 1 0 1/2-1/2w 0 1 |Aut| = 2^5*3^2 #short vectors: 0 12 0 72 &Hlattice (#11 <-- #2) 2 0 2 1 1-w 4 -w -1 -1-w 4 |Aut| = 2^6 #short vectors: 0 8 0 88 &Hlattice (#12 <-- #9) 2 0 2 1-w -1 4 1 0 1 4 |Aut| = 2^7 #short vectors: 0 8 0 88 &Hlattice (#13 <-- #10) <1> <1> <2,-1+w> <2,-1+w> 2 -w 4 1 1/2+1/2w 1 1 -1/2+1/2w 1/2 1 |Aut| = 2^7*3 #short vectors: 0 8 0 88 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 6 6 0 0 0 9 0 0 1 18 0 0 20 0 0 0 0 0 0 0 20 0 0 0 0 10 0 0 0 0 0 0 10 0 0 0 15 5 0 0 0 0 4 8 16 0 0 0 12 0 0 0 0 0 12 0 0 0 16 0 0 0 0 12 0 0 0 5 0 0 0 10 10 0 0 15 0 2 0 0 0 0 0 0 8 18 0 0 0 12 0 0 6 0 2 6 4 0 0 4 18 0 0 0 6 0 0 0 6 1 0 0 9 18 0 0 18 0 0 12 0 0 0 8 2 0 0 0 0 8 0 0 2 0 0 0 8 8 0 0 12 2 0 0 8 0 0 8 0 0 0 0 24 0 0 0 0 8 0 4 0 0 0 0 16 12 0 0 classes of Z-lattices with respect to the trace form (scaled by 1/2) &Dim=8 V=Q^8 &Genus of the trace-forms: det= 625 = 5^4 2-adic symbol: 1^8_II 5-adic symbol: 1^4 5^4 -1-adic symbol: +^8 -^0 level=5, weight=4 a_0,..,a_4 determine modular form &Gram (#1 <- H1,H2,H3) 4 2 4 2 0 4 2 0 0 4 1 -1 0 1 4 0 1 1 0 0 4 1 0 2 1 1 1 4 1 -1 1 0 0 -1 0 4 |Aut| = 2^7*3^2*5^2 #short vectors: 0 0 0 120 &Gram (#2 <- H4,H5) 2 1 2 1 0 2 1 0 0 2 1 0 0 1 6 1 0 1 0 -2 6 1 0 1 0 -2 1 6 1 0 1 0 -2 1 1 6 |Aut| = 2^13*3^3 #short vectors: 0 24 0 24 &Gram (#3 <- H6) 2 1 2 1 0 2 1 0 1 2 0 0 0 0 4 0 0 0 0 -1 4 0 0 0 0 1 1 4 0 0 0 0 1 1 -1 4 |Aut| = 2^8*3^2*5^2 #short vectors: 0 20 0 40 &Gram (#4 <- H7,H8,H9,H10) 2 1 2 0 0 2 0 0 1 2 0 0 1 0 4 0 0 -1 0 1 4 1 1 0 0 0 0 4 1 0 0 0 0 0 2 4 |Aut| = 2^7*3^4 #short vectors: 0 12 0 72 &Gram (#5 <- H11,H12,H13) 2 0 2 0 0 2 0 0 0 2 0 1 1 1 4 1 0 1 -1 0 4 1 1 1 0 1 1 4 1 1 0 1 1 0 1 4 |Aut| = 2^11*3 #short vectors: 0 8 0 88