Defining parameters
| Level: | \( N \) | = | \( 136 = 2^{3} \cdot 17 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(1152\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(136))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 109 | 37 | 72 |
| Cusp forms | 13 | 7 | 6 |
| Eisenstein series | 96 | 30 | 66 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(136))\)
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 |
|---|---|---|---|---|
| 136.1.d | \(\chi_{136}(103, \cdot)\) | None | 0 | 1 |
| 136.1.e | \(\chi_{136}(67, \cdot)\) | 136.1.e.a | 1 | 1 |
| 136.1.f | \(\chi_{136}(35, \cdot)\) | None | 0 | 1 |
| 136.1.g | \(\chi_{136}(135, \cdot)\) | None | 0 | 1 |
| 136.1.j | \(\chi_{136}(115, \cdot)\) | 136.1.j.a | 2 | 2 |
| 136.1.l | \(\chi_{136}(47, \cdot)\) | None | 0 | 2 |
| 136.1.m | \(\chi_{136}(15, \cdot)\) | None | 0 | 4 |
| 136.1.p | \(\chi_{136}(19, \cdot)\) | 136.1.p.a | 4 | 4 |
| 136.1.q | \(\chi_{136}(5, \cdot)\) | None | 0 | 8 |
| 136.1.t | \(\chi_{136}(41, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(136))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(136)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)