(An explanation of this table appears at the bottom of this page.)
Total relations: 8.
ell m11m22m33m44m55m12m13m23m14m24m34m15m25m35m45 cusp:term terms dimM140(ell) #rels
6 2 2 2 2 2 0 0 0 1 1 0 0 1 1 0 1/0: q7/1 56 41 8
NUMBER OF RESTRICTION MAPS: 1 TOTAL RELS: 8
Because the net set of coefficients has size 8,
and these 8 relations are independent,
this implies S58 has dimension at most 8-8=0.
That is, dim S58 = 0.
- ell: This is the level.
- The next 15 numbers give the entries of the matrix.
- The cusps (of G0(ell))
are listed vertically in form a/c.
To the right of each of these is the maximum term kept in the corresponding
For example, q15/3 would indicate that
the expansion is in powers of q1/3,
and that we keep the first 16 terms (q0/3 through q15/3).
- The number under "terms" is the total number of terms kept
over the various cusps.
- The next entry is dim M140(G0(ell)).
The number under "rels" is the number of relations (on the net set) obtained from
this particular restriction map.
The number is usually the difference between the "terms" and "dim"
unless the matrix has some "self-similarity" in the sense that the matrix
box-operation with a cusp yields something that is a multiple of the original matrix.