Defining parameters
| Level: | \( N \) | = | \( 531 = 3^{2} \cdot 59 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(20880\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(531))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 474 | 264 | 210 |
| Cusp forms | 10 | 7 | 3 |
| Eisenstein series | 464 | 257 | 207 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(531))\)
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 |
|---|---|---|---|---|
| 531.1.b | \(\chi_{531}(296, \cdot)\) | None | 0 | 1 |
| 531.1.c | \(\chi_{531}(235, \cdot)\) | 531.1.c.a | 1 | 1 |
| 531.1.g | \(\chi_{531}(58, \cdot)\) | 531.1.g.a | 6 | 2 |
| 531.1.h | \(\chi_{531}(119, \cdot)\) | None | 0 | 2 |
| 531.1.k | \(\chi_{531}(10, \cdot)\) | None | 0 | 28 |
| 531.1.l | \(\chi_{531}(17, \cdot)\) | None | 0 | 28 |
| 531.1.n | \(\chi_{531}(5, \cdot)\) | None | 0 | 56 |
| 531.1.o | \(\chi_{531}(13, \cdot)\) | None | 0 | 56 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(531))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(531)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)