Defining parameters
| Level: | \( N \) | = | \( 711 = 3^{2} \cdot 79 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(37440\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(711))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 673 | 366 | 307 |
| Cusp forms | 49 | 19 | 30 |
| Eisenstein series | 624 | 347 | 277 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 19 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(711))\)
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 |
|---|---|---|---|---|
| 711.1.c | \(\chi_{711}(80, \cdot)\) | None | 0 | 1 |
| 711.1.d | \(\chi_{711}(631, \cdot)\) | 711.1.d.a | 1 | 1 |
| 711.1.d.b | 2 | |||
| 711.1.d.c | 4 | |||
| 711.1.i | \(\chi_{711}(497, \cdot)\) | None | 0 | 2 |
| 711.1.k | \(\chi_{711}(340, \cdot)\) | None | 0 | 2 |
| 711.1.l | \(\chi_{711}(451, \cdot)\) | None | 0 | 2 |
| 711.1.m | \(\chi_{711}(157, \cdot)\) | None | 0 | 2 |
| 711.1.o | \(\chi_{711}(134, \cdot)\) | None | 0 | 2 |
| 711.1.p | \(\chi_{711}(317, \cdot)\) | None | 0 | 2 |
| 711.1.s | \(\chi_{711}(23, \cdot)\) | None | 0 | 2 |
| 711.1.t | \(\chi_{711}(103, \cdot)\) | None | 0 | 2 |
| 711.1.v | \(\chi_{711}(91, \cdot)\) | 711.1.v.a | 12 | 12 |
| 711.1.w | \(\chi_{711}(8, \cdot)\) | None | 0 | 12 |
| 711.1.bc | \(\chi_{711}(7, \cdot)\) | None | 0 | 24 |
| 711.1.bd | \(\chi_{711}(2, \cdot)\) | None | 0 | 24 |
| 711.1.bg | \(\chi_{711}(38, \cdot)\) | None | 0 | 24 |
| 711.1.bh | \(\chi_{711}(26, \cdot)\) | None | 0 | 24 |
| 711.1.bj | \(\chi_{711}(58, \cdot)\) | None | 0 | 24 |
| 711.1.bk | \(\chi_{711}(28, \cdot)\) | None | 0 | 24 |
| 711.1.bl | \(\chi_{711}(34, \cdot)\) | None | 0 | 24 |
| 711.1.bn | \(\chi_{711}(11, \cdot)\) | None | 0 | 24 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(711))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(711)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(237))\)\(^{\oplus 2}\)