Defining parameters
| Level: | \( N \) | = | \( 261 = 3^{2} \cdot 29 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(5040\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(261))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 232 | 126 | 106 |
| Cusp forms | 8 | 4 | 4 |
| Eisenstein series | 224 | 122 | 102 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 0 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(261))\)
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 |
|---|---|---|---|---|
| 261.1.b | \(\chi_{261}(233, \cdot)\) | None | 0 | 1 |
| 261.1.d | \(\chi_{261}(260, \cdot)\) | None | 0 | 1 |
| 261.1.f | \(\chi_{261}(46, \cdot)\) | 261.1.f.a | 4 | 2 |
| 261.1.h | \(\chi_{261}(86, \cdot)\) | None | 0 | 2 |
| 261.1.j | \(\chi_{261}(59, \cdot)\) | None | 0 | 2 |
| 261.1.m | \(\chi_{261}(70, \cdot)\) | None | 0 | 4 |
| 261.1.n | \(\chi_{261}(35, \cdot)\) | None | 0 | 6 |
| 261.1.p | \(\chi_{261}(53, \cdot)\) | None | 0 | 6 |
| 261.1.s | \(\chi_{261}(10, \cdot)\) | None | 0 | 12 |
| 261.1.t | \(\chi_{261}(20, \cdot)\) | None | 0 | 12 |
| 261.1.v | \(\chi_{261}(5, \cdot)\) | None | 0 | 12 |
| 261.1.w | \(\chi_{261}(31, \cdot)\) | None | 0 | 24 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(261)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)