Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(301))\).
|
Total |
New |
Old |
| Modular forms
| 276 |
228 |
48 |
| Cusp forms
| 24 |
24 |
0 |
| Eisenstein series
| 252 |
204 |
48 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(301))\)
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 |
| 301.1.b |
\(\chi_{301}(85, \cdot)\) |
None |
0 |
1 |
| 301.1.d |
\(\chi_{301}(216, \cdot)\) |
None |
0 |
1 |
| 301.1.j |
\(\chi_{301}(50, \cdot)\) |
None |
0 |
2 |
| 301.1.k |
\(\chi_{301}(122, \cdot)\) |
None |
0 |
2 |
| 301.1.l |
\(\chi_{301}(178, \cdot)\) |
None |
0 |
2 |
| 301.1.m |
\(\chi_{301}(87, \cdot)\) |
None |
0 |
2 |
| 301.1.n |
\(\chi_{301}(37, \cdot)\) |
None |
0 |
2 |
| 301.1.q |
\(\chi_{301}(93, \cdot)\) |
None |
0 |
2 |
| 301.1.r |
\(\chi_{301}(128, \cdot)\) |
301.1.r.a |
4 |
2 |
| 301.1.t |
\(\chi_{301}(6, \cdot)\) |
301.1.t.a |
2 |
2 |
| 301.1.v |
\(\chi_{301}(41, \cdot)\) |
301.1.v.a |
6 |
6 |
| 301.1.x |
\(\chi_{301}(8, \cdot)\) |
None |
0 |
6 |
| 301.1.bc |
\(\chi_{301}(13, \cdot)\) |
301.1.bc.a |
12 |
12 |
| 301.1.be |
\(\chi_{301}(2, \cdot)\) |
None |
0 |
12 |
| 301.1.bf |
\(\chi_{301}(30, \cdot)\) |
None |
0 |
12 |
| 301.1.bi |
\(\chi_{301}(18, \cdot)\) |
None |
0 |
12 |
| 301.1.bj |
\(\chi_{301}(47, \cdot)\) |
None |
0 |
12 |
| 301.1.bk |
\(\chi_{301}(10, \cdot)\) |
None |
0 |
12 |
| 301.1.bl |
\(\chi_{301}(17, \cdot)\) |
None |
0 |
12 |
| 301.1.bm |
\(\chi_{301}(29, \cdot)\) |
None |
0 |
12 |
