Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-5

&K=Q(sqrt(-7))
&Hdim=3      V=K^3
&HNeighbourhood at <2,-1+w> contains 2 classes:
mass of the neighbourhood is 1/42
  Steinitz class <1,w>:
&Hlattice (#1 <- #2)
       2 
      -1        2 
       w      1-w        2 
  |Aut| = 2^4*3*7
  #short vectors:
    0   42   56   84  168


&Hlattice (#2 <- #1)
       1 
       0        1 
       0        0        1 
  |Aut| = 2^4*3
  #short vectors:
    6   24   56  114  168



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0   7 
  1   6 


classes of Z-lattices with respect to the trace form
&Dim=6      V=Q^6

&Genus of the trace-forms:
det= 343 = 7^3
   2-adic symbol:  1^6_II 
   7-adic symbol:  1^3 7^3 
  -1-adic symbol:  +^6 -^0 
level=7, weight=3
a_0,..,a_4 determine modular form

&Gram (#1 <- H1)
  4 
  2   4 
  2   0   4 
  1  -1   2   4 
  1   2   1  -1   4 
  2   0   1   0  -1   4 
  |Aut| = 2^5*3*7
  #short vectors:
    0    0    0   42

&Gram (#2 <- H2)
  2 
  0   2 
  0   0   2 
  1   0   0   4 
  0   1   0   0   4 
  0   0   1   0   0   4 
  |Aut| = 2^7*3
  #short vectors:
    0    6    0   24

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