Defining parameters
| Level: | \( N \) | = | \( 507 = 3 \cdot 13^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 5 \) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(18928\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(507))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 487 | 234 | 253 |
| Cusp forms | 31 | 29 | 2 |
| Eisenstein series | 456 | 205 | 251 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 29 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(507))\)
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 |
|---|---|---|---|---|
| 507.1.c | \(\chi_{507}(170, \cdot)\) | 507.1.c.a | 1 | 1 |
| 507.1.d | \(\chi_{507}(506, \cdot)\) | None | 0 | 1 |
| 507.1.g | \(\chi_{507}(70, \cdot)\) | None | 0 | 2 |
| 507.1.h | \(\chi_{507}(23, \cdot)\) | 507.1.h.a | 2 | 2 |
| 507.1.i | \(\chi_{507}(146, \cdot)\) | 507.1.i.a | 2 | 2 |
| 507.1.l | \(\chi_{507}(19, \cdot)\) | None | 0 | 4 |
| 507.1.n | \(\chi_{507}(38, \cdot)\) | 507.1.n.a | 12 | 12 |
| 507.1.o | \(\chi_{507}(14, \cdot)\) | 507.1.o.a | 12 | 12 |
| 507.1.r | \(\chi_{507}(31, \cdot)\) | None | 0 | 24 |
| 507.1.u | \(\chi_{507}(29, \cdot)\) | None | 0 | 24 |
| 507.1.v | \(\chi_{507}(17, \cdot)\) | None | 0 | 24 |
| 507.1.w | \(\chi_{507}(7, \cdot)\) | None | 0 | 48 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(507))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(507)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)