Defining parameters
| Level: | \( N \) | = | \( 712 = 2^{3} \cdot 89 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 5 \) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(31680\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(712))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 623 | 219 | 404 |
| Cusp forms | 95 | 45 | 50 |
| Eisenstein series | 528 | 174 | 354 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 45 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(712))\)
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 |
|---|---|---|---|---|
| 712.1.c | \(\chi_{712}(355, \cdot)\) | 712.1.c.a | 1 | 1 |
| 712.1.c.b | 2 | |||
| 712.1.d | \(\chi_{712}(535, \cdot)\) | None | 0 | 1 |
| 712.1.g | \(\chi_{712}(179, \cdot)\) | None | 0 | 1 |
| 712.1.h | \(\chi_{712}(711, \cdot)\) | None | 0 | 1 |
| 712.1.i | \(\chi_{712}(55, \cdot)\) | None | 0 | 2 |
| 712.1.l | \(\chi_{712}(123, \cdot)\) | 712.1.l.a | 2 | 2 |
| 712.1.n | \(\chi_{712}(393, \cdot)\) | None | 0 | 4 |
| 712.1.p | \(\chi_{712}(37, \cdot)\) | None | 0 | 4 |
| 712.1.r | \(\chi_{712}(87, \cdot)\) | None | 0 | 10 |
| 712.1.s | \(\chi_{712}(67, \cdot)\) | 712.1.s.a | 10 | 10 |
| 712.1.v | \(\chi_{712}(39, \cdot)\) | None | 0 | 10 |
| 712.1.w | \(\chi_{712}(11, \cdot)\) | 712.1.w.a | 10 | 10 |
| 712.1.y | \(\chi_{712}(99, \cdot)\) | 712.1.y.a | 20 | 20 |
| 712.1.bb | \(\chi_{712}(47, \cdot)\) | None | 0 | 20 |
| 712.1.bc | \(\chi_{712}(13, \cdot)\) | None | 0 | 40 |
| 712.1.be | \(\chi_{712}(33, \cdot)\) | None | 0 | 40 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(712))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(712)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(356))\)\(^{\oplus 2}\)