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

&K=Q(sqrt(-7))
&Hdim=5      V=K^5
&HNeighbourhood at <2,-1+w> contains 5 classes:
mass of the neighbourhood is 1/630
  Steinitz class <1,w>:
&Hlattice (#1 <- #4)
       2 
     1-w        2 
    -1+w       -1        2 
    -1+w       -1        1        2 
       w       -1        1        1        3 
  |Aut| = 2^8*3*5
  #short vectors:
    0   50  240  900 1872


&Hlattice (#2 <- #5)
       2 
      -1        2 
     1-w        0        2 
       1        0        w        2 
      -1      1-w      1-w       -1        3 
  |Aut| = 2^8*3*5
  #short vectors:
    0   50  240  900 1872


&Hlattice (#3 <- #1)
       1 
       0        1 
       0        0        1 
       0        0        0        1 
       0        0        0        0        1 
  |Aut| = 2^8*3*5
  #short vectors:
   10   60  240  750 1872


&Hlattice (#4 <- #2)
       1 
       0        1 
       0        0        2 
       0        0        w        2 
       0        0      1-w       -1        2 
  |Aut| = 2^7*3*7
  #short vectors:
    4   54  240  840 1872


&Hlattice (#5 <- #3)
       1 
       0        2 
       0      1-w        2 
       0      1-w        1        2 
       0        1        0        w        2 
  |Aut| = 2^8*3^2
  #short vectors:
    2   52  240  870 1872



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0  16   0  10   5 
 10   0   1   0  20 
  1   0  15  10   5 
  0   7   7   3  14 
 12   3   3  12   1 


classes of Z-lattices with respect to the trace form
&Dim=10      V=Q^10

&Genus of the trace-forms:
det= 16807 = 7^5
   2-adic symbol:  1^10_II 
   7-adic symbol:  1^5 7^5 
  -1-adic symbol:  +^10 -^0 
level=7, weight=5
a_0,..,a_6 determine modular form

&Gram (#1 <- H1,H2)
  4 
  1   4 
  1   2   4 
  1   2   2   4 
  1   2   0   2   4 
  1   2   2   2   2   4 
  0   1   0   0   0   0   4 
  0   0  -1   0   1   0   0   4 
  0   0   0  -1   0   0   0   0   4 
  2   2   0   0   1   1  -1   2   2   6 
  |Aut| = 2^8*3*5
  #short vectors:
    0    0    0   50    0  240

&Gram (#2 <- H3)
  2 
  0   2 
  0   0   2 
  0   0   0   2 
  0   0   0   0   2 
  1   0   0   0   0   4 
  0   1   0   0   0   0   4 
  0   0   1   0   0   0   0   4 
  0   0   0   1   0   0   0   0   4 
  0   0   0   0   1   0   0   0   0   4 
  |Aut| = 2^13*3*5
  #short vectors:
    0   10    0   60    0  240

&Gram (#3 <- H4)
  2 
  0   2 
  1   0   4 
  0  -1   0   4 
  0   0   0   0   4 
  0   0   0   0  -2   4 
  0   0   0   0   2   0   4 
  0   0   0   0   1   1   2   4 
  0   0   0   0  -1   2  -1   1   4 
  0   0   0   0  -2   1   0  -1   1   4 
  |Aut| = 2^10*3*7
  #short vectors:
    0    4    0   54    0  240

&Gram (#4 <- H5)
  2 
  1   4 
  0   0   4 
  0   0   2   4 
  0   0  -2   0   4 
  0   0   2   0   0   4 
  0   0   1   0   0   1   4 
  0   0   1   1   0   1   2   4 
  0   0  -1   0   1   0  -2   0   4 
  0   0   0   0  -1   0  -2   0   0   4 
  |Aut| = 2^10*3^2
  #short vectors:
    0    2    0   52    0  240

<end>