Defining parameters
| Level: | \( N \) | = | \( 475 = 5^{2} \cdot 19 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(18000\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(475))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 521 | 360 | 161 |
| Cusp forms | 17 | 11 | 6 |
| Eisenstein series | 504 | 349 | 155 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 11 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(475))\)
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 |
|---|---|---|---|---|
| 475.1.c | \(\chi_{475}(151, \cdot)\) | 475.1.c.a | 1 | 1 |
| 475.1.c.b | 2 | |||
| 475.1.d | \(\chi_{475}(474, \cdot)\) | None | 0 | 1 |
| 475.1.f | \(\chi_{475}(343, \cdot)\) | None | 0 | 2 |
| 475.1.i | \(\chi_{475}(274, \cdot)\) | None | 0 | 2 |
| 475.1.k | \(\chi_{475}(126, \cdot)\) | None | 0 | 2 |
| 475.1.m | \(\chi_{475}(94, \cdot)\) | 475.1.m.a | 4 | 4 |
| 475.1.o | \(\chi_{475}(56, \cdot)\) | 475.1.o.a | 4 | 4 |
| 475.1.q | \(\chi_{475}(7, \cdot)\) | None | 0 | 4 |
| 475.1.s | \(\chi_{475}(51, \cdot)\) | None | 0 | 6 |
| 475.1.t | \(\chi_{475}(124, \cdot)\) | None | 0 | 6 |
| 475.1.w | \(\chi_{475}(58, \cdot)\) | None | 0 | 8 |
| 475.1.y | \(\chi_{475}(31, \cdot)\) | None | 0 | 8 |
| 475.1.z | \(\chi_{475}(69, \cdot)\) | None | 0 | 8 |
| 475.1.ba | \(\chi_{475}(43, \cdot)\) | None | 0 | 12 |
| 475.1.bd | \(\chi_{475}(83, \cdot)\) | None | 0 | 16 |
| 475.1.bf | \(\chi_{475}(21, \cdot)\) | None | 0 | 24 |
| 475.1.bh | \(\chi_{475}(14, \cdot)\) | None | 0 | 24 |
| 475.1.bj | \(\chi_{475}(17, \cdot)\) | None | 0 | 48 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(475))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(475)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)