Defining parameters
| Level: | \( N \) | = | \( 961 = 31^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(76880\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(961))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 706 | 674 | 32 |
| Cusp forms | 16 | 14 | 2 |
| Eisenstein series | 690 | 660 | 30 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 14 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(961))\)
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 |
|---|---|---|---|---|
| 961.1.b | \(\chi_{961}(960, \cdot)\) | None | 0 | 1 |
| 961.1.e | \(\chi_{961}(440, \cdot)\) | 961.1.e.a | 2 | 2 |
| 961.1.f | \(\chi_{961}(333, \cdot)\) | 961.1.f.a | 4 | 4 |
| 961.1.h | \(\chi_{961}(115, \cdot)\) | 961.1.h.a | 8 | 8 |
| 961.1.j | \(\chi_{961}(30, \cdot)\) | None | 0 | 30 |
| 961.1.m | \(\chi_{961}(6, \cdot)\) | None | 0 | 60 |
| 961.1.n | \(\chi_{961}(15, \cdot)\) | None | 0 | 120 |
| 961.1.p | \(\chi_{961}(3, \cdot)\) | None | 0 | 240 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(961))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(961)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 1}\)