Defining parameters
| Level: | \( N \) | = | \( 297 = 3^{3} \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(6480\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(297))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 312 | 152 | 160 |
| Cusp forms | 12 | 8 | 4 |
| Eisenstein series | 300 | 144 | 156 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(297))\)
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 |
|---|---|---|---|---|
| 297.1.b | \(\chi_{297}(188, \cdot)\) | None | 0 | 1 |
| 297.1.c | \(\chi_{297}(109, \cdot)\) | None | 0 | 1 |
| 297.1.h | \(\chi_{297}(10, \cdot)\) | 297.1.h.a | 2 | 2 |
| 297.1.i | \(\chi_{297}(89, \cdot)\) | None | 0 | 2 |
| 297.1.l | \(\chi_{297}(28, \cdot)\) | None | 0 | 4 |
| 297.1.m | \(\chi_{297}(26, \cdot)\) | None | 0 | 4 |
| 297.1.p | \(\chi_{297}(23, \cdot)\) | None | 0 | 6 |
| 297.1.q | \(\chi_{297}(43, \cdot)\) | 297.1.q.a | 6 | 6 |
| 297.1.r | \(\chi_{297}(71, \cdot)\) | None | 0 | 8 |
| 297.1.s | \(\chi_{297}(19, \cdot)\) | None | 0 | 8 |
| 297.1.v | \(\chi_{297}(5, \cdot)\) | None | 0 | 24 |
| 297.1.w | \(\chi_{297}(7, \cdot)\) | None | 0 | 24 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(297))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(297)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)