Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(407))\).
|
Total |
New |
Old |
| Modular forms
| 383 |
337 |
46 |
| Cusp forms
| 23 |
23 |
0 |
| Eisenstein series
| 360 |
314 |
46 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(407))\)
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 |
| 407.1.c |
\(\chi_{407}(186, \cdot)\) |
None |
0 |
1 |
| 407.1.d |
\(\chi_{407}(406, \cdot)\) |
407.1.d.a |
1 |
1 |
| 407.1.d.b |
2 |
| 407.1.d.c |
4 |
| 407.1.g |
\(\chi_{407}(265, \cdot)\) |
None |
0 |
2 |
| 407.1.i |
\(\chi_{407}(175, \cdot)\) |
407.1.i.a |
2 |
2 |
| 407.1.j |
\(\chi_{407}(10, \cdot)\) |
407.1.j.a |
2 |
2 |
| 407.1.m |
\(\chi_{407}(73, \cdot)\) |
None |
0 |
4 |
| 407.1.n |
\(\chi_{407}(112, \cdot)\) |
None |
0 |
4 |
| 407.1.p |
\(\chi_{407}(23, \cdot)\) |
None |
0 |
4 |
| 407.1.t |
\(\chi_{407}(120, \cdot)\) |
407.1.t.a |
6 |
6 |
| 407.1.u |
\(\chi_{407}(21, \cdot)\) |
407.1.u.a |
6 |
6 |
| 407.1.v |
\(\chi_{407}(31, \cdot)\) |
None |
0 |
8 |
| 407.1.y |
\(\chi_{407}(63, \cdot)\) |
None |
0 |
8 |
| 407.1.z |
\(\chi_{407}(85, \cdot)\) |
None |
0 |
8 |
| 407.1.ba |
\(\chi_{407}(56, \cdot)\) |
None |
0 |
12 |
| 407.1.be |
\(\chi_{407}(14, \cdot)\) |
None |
0 |
16 |
| 407.1.bf |
\(\chi_{407}(28, \cdot)\) |
None |
0 |
24 |
| 407.1.bh |
\(\chi_{407}(7, \cdot)\) |
None |
0 |
24 |
| 407.1.bi |
\(\chi_{407}(5, \cdot)\) |
None |
0 |
48 |
