Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(579))\).
|
Total |
New |
Old |
| Modular forms
| 421 |
227 |
194 |
| Cusp forms
| 37 |
37 |
0 |
| Eisenstein series
| 384 |
190 |
194 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(579))\)
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 |
| 579.1.b |
\(\chi_{579}(194, \cdot)\) |
None |
0 |
1 |
| 579.1.c |
\(\chi_{579}(578, \cdot)\) |
579.1.c.a |
1 |
1 |
| 579.1.c.b |
2 |
| 579.1.g |
\(\chi_{579}(305, \cdot)\) |
579.1.g.a |
2 |
2 |
| 579.1.i |
\(\chi_{579}(278, \cdot)\) |
None |
0 |
2 |
| 579.1.j |
\(\chi_{579}(470, \cdot)\) |
579.1.j.a |
4 |
2 |
| 579.1.l |
\(\chi_{579}(236, \cdot)\) |
579.1.l.a |
4 |
4 |
| 579.1.m |
\(\chi_{579}(242, \cdot)\) |
None |
0 |
4 |
| 579.1.o |
\(\chi_{579}(50, \cdot)\) |
579.1.o.a |
8 |
8 |
| 579.1.r |
\(\chi_{579}(200, \cdot)\) |
None |
0 |
8 |
| 579.1.s |
\(\chi_{579}(8, \cdot)\) |
579.1.s.a |
16 |
16 |
| 579.1.u |
\(\chi_{579}(59, \cdot)\) |
None |
0 |
16 |
| 579.1.x |
\(\chi_{579}(13, \cdot)\) |
None |
0 |
32 |
| 579.1.y |
\(\chi_{579}(2, \cdot)\) |
None |
0 |
32 |
| 579.1.bb |
\(\chi_{579}(10, \cdot)\) |
None |
0 |
64 |
