Defining parameters
| Level: | \( N \) | = | \( 117 = 3^{2} \cdot 13 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(1008\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(117))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 100 | 52 | 48 |
| Cusp forms | 4 | 2 | 2 |
| Eisenstein series | 96 | 50 | 46 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(117))\)
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 |
|---|---|---|---|---|
| 117.1.c | \(\chi_{117}(53, \cdot)\) | None | 0 | 1 |
| 117.1.d | \(\chi_{117}(116, \cdot)\) | None | 0 | 1 |
| 117.1.j | \(\chi_{117}(73, \cdot)\) | 117.1.j.a | 2 | 2 |
| 117.1.k | \(\chi_{117}(29, \cdot)\) | None | 0 | 2 |
| 117.1.m | \(\chi_{117}(23, \cdot)\) | None | 0 | 2 |
| 117.1.n | \(\chi_{117}(38, \cdot)\) | None | 0 | 2 |
| 117.1.o | \(\chi_{117}(17, \cdot)\) | None | 0 | 2 |
| 117.1.p | \(\chi_{117}(35, \cdot)\) | None | 0 | 2 |
| 117.1.s | \(\chi_{117}(14, \cdot)\) | None | 0 | 2 |
| 117.1.u | \(\chi_{117}(68, \cdot)\) | None | 0 | 2 |
| 117.1.v | \(\chi_{117}(95, \cdot)\) | None | 0 | 2 |
| 117.1.w | \(\chi_{117}(58, \cdot)\) | None | 0 | 4 |
| 117.1.y | \(\chi_{117}(31, \cdot)\) | None | 0 | 4 |
| 117.1.bb | \(\chi_{117}(7, \cdot)\) | None | 0 | 4 |
| 117.1.bd | \(\chi_{117}(19, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(117))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(117)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)