## Coefficients in Computations of S58 through S510

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 5 of weights 8 through 10.
• The first column is just an index to enumerate these forms.
• The second column DT gives the dyadic trace.
• The third column gives 32 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 m12 m13 m23 m14 m24 m34 m15 m25 m35 m45.
• The next 5 columns denote whether the coefficient is used in the calculation of the space S58, S510.
• "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 D5 and form 1 is 1/2 A5. And form 56 is the identity matrix.
Note that the forms are ordered by dyadic trace. (All the forms of dyadic trace 5.25 or less are in this table.)
```index  DT  16det m11m22m33m44m55m12m13m23m14m24m34m15m25m35m45  S58 S510 Reducible
0   2.5    4    2  2  2  2  2  0  0  0  1  0  0  1  1  1  0   C    C
1   3      6    2  2  2  2  2  0  0  0  1  1  0  0  1  1  0   C    C
2   3      8    2  2  2  2  2  0  0  0  0  0  0  0  1  1  1   C   *C    R
3   3.5   10    2  2  2  2  2  0  0  0  1  0  0  0  0  1  1   C   *C    R
4   3.5   12    2  2  2  2  2  0  0  0  1  0  0  0  1  1  0   C   *C    R
5   3.5   12    2  2  2  2  4  0  0  0  1  1  1  0  0  1  0   C    C
6   3.5   14    2  2  2  2  4  1  0  0  1  0  1  0  0  0  1   C    C
7   3.5   20    2  2  2  2  4  0  0  0  1  1  0  0  0  1  1   C    C
8   4     16    2  2  2  2  2  0  0  0  0  0  0  1  1  0  0   -   *C    R
9   4     16    2  2  2  2  4  0  0  0  1  1  1  0  0  0  0   -   *C    R
10   4     16    2  2  2  2  4  1  0  0  1  0  1  0  0  1  0   -    C
11   4     18    2  2  2  2  2  0  0  0  1  0  0  0  1  0  0   -   *C    R
12   4     22    2  2  2  2  4  0  0  0  1  1  0  0  1  1  0   -    C
13   4     24    2  2  2  2  4  0  0  0  1  1  0  0  0  0  1   -   *C    R
14   4     24    2  2  2  2  4  1  0  0  0  0  1  0  1  0  1   -    C
15   4     28    2  2  2  2  4  0  0  0  1  0  0  0  1  1  1   -    C
16   4     30    2  2  2  4  4  1  1  0  0  1  0  0  0  1  2   -    C
17   4     32    2  2  2  2  4  0  0  0  0  0  0  1  1  1  1   -    C
18   4     32    2  2  2  4  4  1  1  0  0  0  0  1  0  0  2   -    C
19   4     40    2  2  2  4  4  1  0  0  1  0  1  1  0  1  0   -    C
20   4     48    2  2  2  4  4  0  0  0  0  0  0  1  1  1  2   -    C
21   4     64    2  2  4  4  4  0  0  0  0  0  0  1  1  2  2   -    C
22   4.5   20    2  2  2  2  4  1  0  0  1  0  1  0  0  0  0   -   *C    R
23   4.5   20    2  2  2  2  6  0  0  0  1  1  1  0  1  0  0   -    C
24   4.5   24    2  2  2  2  2  0  0  0  0  0  0  0  1  0  0   -   *C    R
25   4.5   24    2  2  2  2  6  1  0  0  1  0  1  0  0  0  1   -    C
26   4.5   26    2  2  2  2  4  0  0  0  1  1  0  1  0  0  0   -   *C    R
27   4.5   28    2  2  2  2  4  0  0  0  1  1  0  0  0  1  0   -   *C    R
28   4.5   30    2  2  2  2  4  1  0  0  0  0  1  0  0  0  1   -   *C    R
29   4.5   34    2  2  2  2  4  0  0  0  1  0  0  1  0  1  0   -   *C    R
30   4.5   36    2  2  2  2  4  0  0  0  1  0  0  0  1  1  0   -   *C    R
31   4.5   36    2  2  2  2  6  0  0  0  1  1  0  0  0  1  1   -    C
32   4.5   36    2  2  2  4  4  1  1  0  0  0  0  0  1  0  2   -    C
33   4.5   36    2  2  2  4  4  1  1  0  1  0  0  1  0  0  1   -    C
34   4.5   38    2  2  2  4  4  1  1  0  0  1  0  1  0  0  0   -    C
35   4.5   40    2  2  2  2  4  0  0  0  0  0  0  1  1  0  1   -   *C    R
36   4.5   40    2  2  2  4  4  1  1  0  0  1  0  0  1  0  0   -    C
37   4.5   44    2  2  2  4  4  1  0  0  0  0  0  1  0  1  2   -    C
38   4.5   44    2  2  2  4  4  1  1  0  0  0  0  1  0  0  1   -    C
39   4.5   46    2  2  2  4  4  1  0  0  0  0  1  1  0  0  2   -    C
40   4.5   48    2  2  2  4  4  1  0  0  1  0  1  0  1  1  0   -    C
41   4.5   50    2  2  2  4  4  1  0  0  1  0  0  0  1  0 -2   -   *C    R
42   4.5   52    2  2  2  4  4  0  0  0  1  0  0  0  1  1  2   -    C
43   4.5   54    2  2  2  4  4  0  0  0  1  1  0  0  1  1  2   -    C
44   4.5   54    2  2  2  4  4  1  0  0  1  0  1  1  0  0  0   -    C
45   4.5   60    2  2  2  4  4  0  0  0  1  1  1  1  0 -1  0   -    C
46   4.5   60    2  2  4  4  4  1  1  0  0  1  0  0  0  2  2   -    C
47   4.5   64    2  2  4  4  4  1  0  0  0  0  0  1  0  2  2   -    C
48   4.5   70    2  2  4  4  4  1  0  0  1  0  1  1  0  2  0   -    C
49   4.5   72    2  2  4  4  4  0  1  0  1  0  0  0  1  2 -2   -    C
50   4.5   76    2  2  4  4  4  0  0  0  0  1  0  1  0  2  2   -    C
51   4.5   84    2  2  4  4  4  0  0  0  0  0  1  1  1  2  2   -    C
52   4.5   96    2  4  4  4  4  0  0  0  1  0  0  0  2  2  2   -    C
53   4.5  108    2  4  4  4  4  0  0  0  0  1  0  1  2  2  2   -    C
54   5     24    2  2  2  2  6  0  0  0  1  1  1  0  0  0  0   -   *B    R
55   5     26    2  2  2  2  6  1  0  0  1  0  1  0  0  1  0   -    B
56   5     32    2  2  2  2  2  0  0  0  0  0  0  0  0  0  0   -   *B    R
57   5     32    2  2  2  2  4  0  0  0  1  1  0  0  0  0  0   -   *B    R
58   5     36    2  2  2  2  4  1  0  0  0  0  1  0  0  0  0   -   *B    R
59   5     38    2  2  2  2  6  0  0  0  1  1  0  1  0  1  0   -    B
60   5     40    2  2  2  2  4  0  0  0  1  0  0  0  0  0  1   -   *B    R
61   5     40    2  2  2  2  6  0  0  0  1  1  0  0  0  0  1   -   *B    R
62   5     42    2  2  2  2  4  0  0  0  1  0  0  0  0  1  0   -   *B    R
63   5     42    2  2  2  2  6  1  0  0  0  0  1  1  0  1  0   -    B
64   5     42    2  2  2  4  4  1  1  0  0  1  0  0  0  1  0   -    B
65   5     48    2  2  2  2  4  0  0  0  0  0  0  1  1  0  0   -   *B    R
66   5     48    2  2  2  4  4  1  1  0  0  0  0  0  0  0  2   -   *B    R
67   5     48    2  2  2  4  4  1  1  0  0  0  0  0  1  0  1   -    B
68   5     48    2  2  2  4  4  1  1  0  0  0  0  1  0  0  0   -   *B    R
69   5     52    2  2  2  2  6  0  0  0  1  0  0  1  1  1  0   -    B
70   5     54    2  2  2  4  6  1  1  0  1  0  0  0  1  0  1   -    B
71   5     56    2  2  2  4  4  1  0  0  0  0  0  0  1  0  2   -   *B    R
72   5     56    2  2  2  4  4  1  0  0  1  0  1  0  1  0  0   -    B
73   5     56    2  2  2  4  6  1  1  0  0  1  0  1  0  0  1   -    B
74   5     56    2  2  2  4  6  1  1  0  1  0  0  1  0  0  0   -    B
75   5     58    2  2  2  4  4  1  0  0  0  0  1  1  0  1  0   -    B
76   5     60    2  2  2  4  4  1  0  0  0  0  1  0  0  0  2   -   *B    R
77   5     62    2  2  2  4  4  1  0  0  0  0  0  0  1  1  1   -    B
78   5     64    2  2  2  2  6  0  0  0  0  0  0  1  1  1  1   -    B
79   5     64    2  2  2  4  4  0  0  0  0  0  0  1  1  0  2   -   *B    R
80   5     64    2  2  2  4  4  1  0  0  0  0  1  0  1  0  1   -    B
81   5     64    2  2  2  4  4  1  0  0  1  0  0  1  0  0  0   -   *B    R
82   5     64    2  2  2  4  6  1  1  0  0  0  0  1  0  0  2   -    B
83   5     66    2  2  2  4  4  0  0  0  1  0  0  0  1  0  2   -   *B    R
84   5     68    2  2  2  4  4  0  0  0  1  0  0  1  1  1  0   -    B
85   5     70    2  2  2  4  4  0  0  0  1  1  0  1  0  1  0   -    B
86   5     72    2  2  2  4  4  0  0  0  0  0  0  1  1  1  1   -    B
87   5     72    2  2  2  4  4  0  0  0  1  1  0  1 -1  0  0   -   *B    R
88   5     72    2  2  4  4  4  1  0  0  0  0  2  0  1  0  2   -    B
89   5     74    2  2  2  4  6  1  0  0  1  0  1  1  0  1  0   -    B
90   5     76    2  2  2  4  4  0  0  0  1  0  0  0  1  1  1   -    B
91   5     78    2  2  4  4  4  1  0  0  0  0  1  1  0  2  2   -    B
92   5     80    2  2  2  4  6  1  0  0  1  0  0  0  1  1 -2   -    B
93   5     80    2  2  4  4  4  0  0  0  0  0  2  1  1  0  2   -    B
94   5     80    2  2  4  4  4  1  1  0  0  1  0  1  1  0  2   -    B
95   5     84    2  2  4  4  4  0  0  0  0  1  2  1  0  2  0   -    B
96   5     84    2  2  4  4  4  1  0  0  0  0  2  0  1  2  1   -    B
97   5     86    2  2  4  4  4  1  0  0  1  0  1  0  1  2  0   -    B
98   5     88    2  2  2  4  6  0  0  0  1  1  1  0  0  0  2   -    B
99   5     88    2  2  4  4  4  0  0  0  1  1  2  1  0  1  0   -    B
100   5     88    2  2  4  4  4  1  0  0  1  0  0  1  0  2  0   -    B
101   5     90    2  2  4  4  4  0  1  0  0  1  1  0  1  2  0   -    B
102   5     90    2  2  4  4  4  1  0  0  1  0  1  1  1  0  2   -    B
103   5     94    2  2  4  4  4  0  0  0  0  1  2  1  1  1  0   -    B
104   5     96    2  2  4  4  4  0  0  0  0  0  0  0  1  2  2   -   *B    R
105   5     96    2  2  4  4  4  0  0  0  0  0  2  1  1  2  1   -    B
106   5     96    2  2  4  4  4  0  0  0  1  1  2  1  1  0  1   -    B
107   5     96    2  2  4  4  4  0  1  1  1  0  0  0  1  0  2   -    B
108   5     96    2  2  4  4  4  1  1  0  1  0  0  1  0  0  0   -    B
109   5    100    2  2  4  4  4  0  0  0  0  1  2  1  0  2  1   -    B
110   5    104    2  2  4  4  4  0  1  1  1  0  0  1  1  0  0   -    B
111   5    104    2  2  4  4  4  1  0  0  1  0  1  1  0  1  0   -    B
112   5    106    2  2  4  4  4  0  1  0  0  1  1  0  1 -2  0   -    B
113   5    110    2  2  4  4  4  0  0  0  0  1  2  1  1  1  1   -    B
114   5    112    2  2  4  4  4  0  0  0  0  0  0  1  1  2  1   -    B
115   5    112    2  4  4  4  4  0  0  0  0  2  0  1  0  2  2   -    B
116   5    120    2  2  4  4  4  0  1  1  0  0  1  1  1  1  1   -    B
117   5    124    2  4  4  4  4  0  0  0  1  0  1  1  2  2  0   -    B
118   5    126    2  4  4  4  4  0  0  1  1  2  2  0  2  2  1   -    B
119   5    128    2  2  4  4  6  0  0  0  1  1  2  0  0  0  2   -    B
120   5    128    2  4  4  4  4  0  0  0  0  0  0  0  2  2  2   -   *B    R
121   5    128    4  4  4  4  4  0  0  0  2  0  0  2  2  2  0   -    B
122   5    132    2  4  4  4  4  0  0  2  0  1  2  1  0  2  0   -    B
123   5    136    2  4  4  4  4  0  0  0  1  0  1  0  2  2  2   -    B
124   5    136    2  4  4  4  4  0  0  0  1  2  2  0  1  1  0   -    B
125   5    144    2  4  4  4  4  0  0  0  0  2  0  1  1  2  2   -    B
126   5    150    2  4  4  4  4  1  0  1  1  0  1  1 -1  1  0   -    B
127   5    154    2  4  4  4  4  0  0  1  0  1  0  1  2  2 -1   -    B
128   5    160    2  4  4  4  4  0  0  0  0  0  0  1  2  1  2   -    B
129   5    160    4  4  4  4  4  1  1  0  0  0  0  0  2  2  2   -    B
130   5    162    4  4  4  4  4  1  1  1  1  1  1  2  2  2 -1   -    B
131   5    180    4  4  4  4  4  1  0  0  0  0  1  2  2  2  2   -    B
132   5    192    4  4  4  4  4  2  1  0  2  0  0  2  0  0  0   -    B
133   5    196    4  4  4  4  4  1  0  0  2  2  2  2  0  1  2   -    B
134   5.25 216    4  4  4  4  4  1  0  0  2  2  2  1  1  0  2   -    B
```