Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(979))\).
|
Total |
New |
Old |
| Modular forms
| 925 |
827 |
98 |
| Cusp forms
| 45 |
45 |
0 |
| Eisenstein series
| 880 |
782 |
98 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(979))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
| 979.1.b |
\(\chi_{979}(978, \cdot)\) |
979.1.b.a |
1 |
1 |
| 979.1.b.b |
2 |
| 979.1.c |
\(\chi_{979}(802, \cdot)\) |
None |
0 |
1 |
| 979.1.e |
\(\chi_{979}(835, \cdot)\) |
979.1.e.a |
2 |
2 |
| 979.1.i |
\(\chi_{979}(12, \cdot)\) |
None |
0 |
4 |
| 979.1.k |
\(\chi_{979}(90, \cdot)\) |
None |
0 |
4 |
| 979.1.l |
\(\chi_{979}(266, \cdot)\) |
None |
0 |
4 |
| 979.1.o |
\(\chi_{979}(123, \cdot)\) |
None |
0 |
8 |
| 979.1.q |
\(\chi_{979}(32, \cdot)\) |
979.1.q.a |
10 |
10 |
| 979.1.r |
\(\chi_{979}(87, \cdot)\) |
979.1.r.a |
10 |
10 |
| 979.1.s |
\(\chi_{979}(37, \cdot)\) |
None |
0 |
16 |
| 979.1.v |
\(\chi_{979}(10, \cdot)\) |
979.1.v.a |
20 |
20 |
| 979.1.x |
\(\chi_{979}(23, \cdot)\) |
None |
0 |
40 |
| 979.1.z |
\(\chi_{979}(50, \cdot)\) |
None |
0 |
40 |
| 979.1.ba |
\(\chi_{979}(2, \cdot)\) |
None |
0 |
40 |
| 979.1.bc |
\(\chi_{979}(17, \cdot)\) |
None |
0 |
80 |
| 979.1.bf |
\(\chi_{979}(3, \cdot)\) |
None |
0 |
160 |
