Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(247))\).
|
Total |
New |
Old |
| Modular forms
| 218 |
188 |
30 |
| Cusp forms
| 2 |
2 |
0 |
| Eisenstein series
| 216 |
186 |
30 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(247))\)
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 |
| 247.1.b |
\(\chi_{247}(170, \cdot)\) |
None |
0 |
1 |
| 247.1.d |
\(\chi_{247}(246, \cdot)\) |
247.1.d.a |
1 |
1 |
| 247.1.d.b |
1 |
| 247.1.j |
\(\chi_{247}(96, \cdot)\) |
None |
0 |
2 |
| 247.1.k |
\(\chi_{247}(126, \cdot)\) |
None |
0 |
2 |
| 247.1.m |
\(\chi_{247}(56, \cdot)\) |
None |
0 |
2 |
| 247.1.n |
\(\chi_{247}(12, \cdot)\) |
None |
0 |
2 |
| 247.1.o |
\(\chi_{247}(88, \cdot)\) |
None |
0 |
2 |
| 247.1.s |
\(\chi_{247}(107, \cdot)\) |
None |
0 |
2 |
| 247.1.t |
\(\chi_{247}(27, \cdot)\) |
None |
0 |
2 |
| 247.1.u |
\(\chi_{247}(94, \cdot)\) |
None |
0 |
2 |
| 247.1.v |
\(\chi_{247}(69, \cdot)\) |
None |
0 |
2 |
| 247.1.ba |
\(\chi_{247}(102, \cdot)\) |
None |
0 |
4 |
| 247.1.bb |
\(\chi_{247}(83, \cdot)\) |
None |
0 |
4 |
| 247.1.bc |
\(\chi_{247}(20, \cdot)\) |
None |
0 |
4 |
| 247.1.bg |
\(\chi_{247}(7, \cdot)\) |
None |
0 |
4 |
| 247.1.bh |
\(\chi_{247}(108, \cdot)\) |
None |
0 |
6 |
| 247.1.bj |
\(\chi_{247}(22, \cdot)\) |
None |
0 |
6 |
| 247.1.bk |
\(\chi_{247}(14, \cdot)\) |
None |
0 |
6 |
| 247.1.bl |
\(\chi_{247}(51, \cdot)\) |
None |
0 |
6 |
| 247.1.bm |
\(\chi_{247}(10, \cdot)\) |
None |
0 |
6 |
| 247.1.bp |
\(\chi_{247}(3, \cdot)\) |
None |
0 |
6 |
| 247.1.bt |
\(\chi_{247}(28, \cdot)\) |
None |
0 |
12 |
| 247.1.bu |
\(\chi_{247}(6, \cdot)\) |
None |
0 |
12 |
| 247.1.bv |
\(\chi_{247}(5, \cdot)\) |
None |
0 |
12 |
