Defining parameters
| Level: | \( N \) | = | \( 597 = 3 \cdot 199 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(26400\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(597))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 436 | 228 | 208 |
| Cusp forms | 40 | 32 | 8 |
| Eisenstein series | 396 | 196 | 200 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 32 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(597))\)
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 |
|---|---|---|---|---|
| 597.1.b | \(\chi_{597}(200, \cdot)\) | None | 0 | 1 |
| 597.1.d | \(\chi_{597}(397, \cdot)\) | None | 0 | 1 |
| 597.1.f | \(\chi_{597}(292, \cdot)\) | None | 0 | 2 |
| 597.1.g | \(\chi_{597}(92, \cdot)\) | 597.1.g.a | 2 | 2 |
| 597.1.k | \(\chi_{597}(19, \cdot)\) | None | 0 | 6 |
| 597.1.l | \(\chi_{597}(242, \cdot)\) | None | 0 | 6 |
| 597.1.n | \(\chi_{597}(85, \cdot)\) | None | 0 | 10 |
| 597.1.p | \(\chi_{597}(62, \cdot)\) | 597.1.p.a | 10 | 10 |
| 597.1.s | \(\chi_{597}(5, \cdot)\) | 597.1.s.a | 20 | 20 |
| 597.1.t | \(\chi_{597}(55, \cdot)\) | None | 0 | 20 |
| 597.1.w | \(\chi_{597}(2, \cdot)\) | None | 0 | 60 |
| 597.1.x | \(\chi_{597}(22, \cdot)\) | None | 0 | 60 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(597))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(597)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(199))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(597))\)\(^{\oplus 1}\)