Defining parameters
| Level: | \( N \) | = | \( 575 = 5^{2} \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(26400\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(575))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 634 | 446 | 188 |
| Cusp forms | 18 | 15 | 3 |
| Eisenstein series | 616 | 431 | 185 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 15 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(575))\)
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 |
|---|---|---|---|---|
| 575.1.c | \(\chi_{575}(574, \cdot)\) | 575.1.c.a | 2 | 1 |
| 575.1.c.b | 6 | |||
| 575.1.d | \(\chi_{575}(551, \cdot)\) | 575.1.d.a | 1 | 1 |
| 575.1.d.b | 3 | |||
| 575.1.d.c | 3 | |||
| 575.1.f | \(\chi_{575}(93, \cdot)\) | None | 0 | 2 |
| 575.1.h | \(\chi_{575}(91, \cdot)\) | None | 0 | 4 |
| 575.1.j | \(\chi_{575}(114, \cdot)\) | None | 0 | 4 |
| 575.1.l | \(\chi_{575}(47, \cdot)\) | None | 0 | 8 |
| 575.1.n | \(\chi_{575}(51, \cdot)\) | None | 0 | 10 |
| 575.1.o | \(\chi_{575}(74, \cdot)\) | None | 0 | 10 |
| 575.1.q | \(\chi_{575}(18, \cdot)\) | None | 0 | 20 |
| 575.1.t | \(\chi_{575}(14, \cdot)\) | None | 0 | 40 |
| 575.1.v | \(\chi_{575}(11, \cdot)\) | None | 0 | 40 |
| 575.1.x | \(\chi_{575}(2, \cdot)\) | None | 0 | 80 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(575))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(575)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)