## Coefficients in Computations of S68

The following table gives the list of coefficients used in the computations (Restriction to Modular Curves Method) of spaces of modular cusp forms in degree 6 of weight 8.
• The first column is just an index to enumerate these forms.
• The second column DT gives the dyadic trace.
• The third column gives 64 times the determinant.
• The next 15 columns give twice the entries of the half-integral integer-valued forms, in the order m11 m22 m33 m44 m55 m66 m12 m13 m23 m14 m24 m34 m15 m25 m35 m45 m16 m26 m36 m46 m56.
• The next 5 columns denote whether the coefficient is used in the calculation of the space S68.
• "C" denotes that the form is in the determining set.
• "B" denotes that the form is in the net set.
• "*" indicates that this form was used in the Witt-Erohkin calculation.
• The last column denotes if the form is Reducible. An "R" denotes that the form is reducible.
For example, form 0 is 1/2 E5 and form 1 is 1/2 D5. And form 3 is 1/2 A5.
Note that the forms are ordered by dyadic trace. (All the forms of dyadic trace 4.25 or less are in this table.)
```index  DT  32det m11m22m33m44m55m66m12m13m23m14m24m34m15m25m35m45m16m26m36m46m56  S68  Reducible
0   2.25   3    2  2  2  2  2  2  0  0  1  1  0  1  1  1  1  1  1  1  1  1  1   C
1   3      4    2  2  2  2  2  2  0  0  0  1  1  0  0  1  1  1  1  0  1  1  1   C
2   3.25  11    2  2  2  2  2  4  0  0  1  1  0  1  1  1  1  1  1  1  1  1  1   C
3   3.5    7    2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1   C
4   3.5    8    2  2  2  2  2  2  0  0  0  0  0  1  0  1  1  1  0 -1  1  1  0   C    R
5   3.5   12    2  2  2  2  2  2  0  0  0  0  0  1  0  0  0  0  1  1  0  0  1   C    R
6   3.5   15    2  2  2  2  2  4  0  0  1  0  1  1  1  1  1  1  1  0  1  1  1   C
7   3.75  27    2  2  2  2  4  4  0  1  1  1  1  1  0  1  1  1  1  1  1  1 -1   C
8   4     12    2  2  2  2  2  2  0  0  0  0  0  0  0  1  0  1  0  0  1  1  1   C    R
9   4     12    2  2  2  2  2  4  0  0  1  1  1  1  1 -1 -1  0  1  0  0  1  1   C
10   4     15    2  2  2  2  2  2  0  0  1  0  0  0  0  0  0  1  1  0  0  1  1   C    R
11   4     16    2  2  2  2  2  2  0  0  1  1  0  0  1  0  0  1  0  1  1  0  0   C    R
12   4     16    2  2  2  2  2  2  0  0  0  0  0  0  0  0  1  1  0  0  1  1  1   C    R
13   4     16    2  2  2  2  2  4  0  0  1  0  1  1  1  1  1  1  1  1  1  1  1   C
14   4     20    2  2  2  2  2  4  0  0  0  0  1  1  0  1  1  1  1  0  1  0  1   C
15   4     23    2  2  2  2  2  4  0  0  0  0  0  1  0  1  1  1  1  1  1  1  1   C
16   4     28    2  2  2  2  2  4  0  0  1  0  0  0  1  0  0  1  1  1  1  1  1   C
17   4     32    2  2  2  2  2  4  0  0  0  0  0  1  0  0  1  1  1  1  0  1  1   C
18   4     32    2  2  2  2  4  4  0  0  1  1  1  1  1  0  1  1  1  1  0  1 -1   C
19   4     48    2  2  2  2  2  4  0  0  0  0  0  0  0  0  0  0  1  1  1  1  1   C
20   4     48    2  2  2  2  4  4  0  1  0  0  1  0  0  0 -1  1  1  1  0  1  2   C
21   4     64    2  2  2  2  4  4  0  0  0  0  0  0  1  1  1  1  1  1 -1  1  1   C
22   4.25  19    2  2  2  2  2  6  1  0 -1  0 -1  1  1  0  1  1  1  0  1  1  1   C
23   4.25  35    2  2  2  2  4  4  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1   C
24   4.25  39    2  2  2  2  4  4  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1   C
25   4.25  63    2  2  2  4  4  4  1  1  1  0  1  1  0  1  1  1  1  1  1  2 -1   C
```