Defining parameters
| Level: | \( N \) | = | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(18816\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(588))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 644 | 112 | 532 |
| Cusp forms | 44 | 16 | 28 |
| Eisenstein series | 600 | 96 | 504 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(588))\)
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 the newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 588.1.c | \(\chi_{588}(197, \cdot)\) | 588.1.c.a | 1 | 1 |
| 588.1.c.b | 1 | |||
| 588.1.d | \(\chi_{588}(97, \cdot)\) | None | 0 | 1 |
| 588.1.g | \(\chi_{588}(295, \cdot)\) | None | 0 | 1 |
| 588.1.h | \(\chi_{588}(587, \cdot)\) | None | 0 | 1 |
| 588.1.j | \(\chi_{588}(215, \cdot)\) | None | 0 | 2 |
| 588.1.l | \(\chi_{588}(67, \cdot)\) | None | 0 | 2 |
| 588.1.m | \(\chi_{588}(313, \cdot)\) | None | 0 | 2 |
| 588.1.p | \(\chi_{588}(557, \cdot)\) | 588.1.p.a | 2 | 2 |
| 588.1.r | \(\chi_{588}(83, \cdot)\) | None | 0 | 6 |
| 588.1.s | \(\chi_{588}(43, \cdot)\) | None | 0 | 6 |
| 588.1.v | \(\chi_{588}(13, \cdot)\) | None | 0 | 6 |
| 588.1.w | \(\chi_{588}(29, \cdot)\) | None | 0 | 6 |
| 588.1.z | \(\chi_{588}(53, \cdot)\) | 588.1.z.a | 12 | 12 |
| 588.1.bc | \(\chi_{588}(61, \cdot)\) | None | 0 | 12 |
| 588.1.bd | \(\chi_{588}(151, \cdot)\) | None | 0 | 12 |
| 588.1.bf | \(\chi_{588}(47, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(588))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(588)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)