S_{4}^{12}
There are 8 relations from doing WittErohkin method on 8 reducible forms
(those marked by * in the table of coefficient forms).
(An explanation of this table appears at the bottom of this page.)
ell m11m22m33m44m12m13m23m14m24m34 cusp:term terms dimM_{1}^{48}(ell) #rels
2 2 2 2 2 0 0 0 1 1 1 1/0: q^{8/1} 18 13 2
1/1: q^{8/2}
5 2 2 2 2 1 0 0 1 0 1 1/0: q^{8/1} 27 25 2
1/1: q^{17/5}
6 2 2 2 4 1 1 0 1 0 0 1/0: q^{10/1} 54 49 5
1/1: q^{14/6}
1/2: q^{17/3}
1/3: q^{9/2}
8 3 3 3 3 1 1 1 1 1 1 1/0: q^{13/1} 53 49 4
1/1: q^{18/8}
1/2: q^{11/2}
1/4: q^{7/1}
9 4 4 4 4 1 2 1 2 2 1 1/0: q^{17/1} 54 49 2
1/1: q^{17/9}
1/3: q^{8/1}
2/3: q^{8/1}
NUMBER OF RESTRICTION MAPS: 7 TOTAL RELS: 15
Including 8 WittErohkin relations, total relations: 23.
Total independent relations: 22.
Because the net set of coefficients has size 23,
this implies the kernel of S_{4}^{12} under the WittErohkin map has dimension at most 2322=1.
Because the image of the WittErohkin map is 1dimensional,
this proves that
dim S_{4}^{12} is at most 2.
Because we can produce two linearly independent cusp forms in S_{4}^{12}
(for example, E_{4} J_{8} and ?),
we conclude
dim S_{4}^{12} = 2.
 ell: This is the level.
 The next 10 numbers give the entries of the matrix.
 The cusps (of G_{0}(ell))
are listed vertically in form a/c.
To the right of each of these is the maximum term kept in the corresponding
cusp expansion.
For example, q^{15/3} would indicate that
the expansion is in powers of q^{1/3},
and that we keep the first 16 terms (q^{0/3} through q^{15/3}).
 The number under "terms" is the total number of terms kept
over the various cusps.
 The next entry is dim M_{1}^{48}(G_{0}(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 "selfsimilarity" in the sense that the matrix
boxoperation with a cusp yields something that is a multiple of the original matrix.