Defining parameters
| Level: | \( N \) | = | \( 621 = 3^{3} \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(28512\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(621))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 702 | 360 | 342 |
| Cusp forms | 42 | 24 | 18 |
| Eisenstein series | 660 | 336 | 324 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 24 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(621))\)
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 |
|---|---|---|---|---|
| 621.1.b | \(\chi_{621}(323, \cdot)\) | None | 0 | 1 |
| 621.1.d | \(\chi_{621}(298, \cdot)\) | None | 0 | 1 |
| 621.1.f | \(\chi_{621}(91, \cdot)\) | 621.1.f.a | 6 | 2 |
| 621.1.h | \(\chi_{621}(116, \cdot)\) | None | 0 | 2 |
| 621.1.k | \(\chi_{621}(22, \cdot)\) | 621.1.k.a | 18 | 6 |
| 621.1.l | \(\chi_{621}(47, \cdot)\) | None | 0 | 6 |
| 621.1.n | \(\chi_{621}(28, \cdot)\) | None | 0 | 10 |
| 621.1.p | \(\chi_{621}(26, \cdot)\) | None | 0 | 10 |
| 621.1.r | \(\chi_{621}(8, \cdot)\) | None | 0 | 20 |
| 621.1.t | \(\chi_{621}(10, \cdot)\) | None | 0 | 20 |
| 621.1.w | \(\chi_{621}(2, \cdot)\) | None | 0 | 60 |
| 621.1.x | \(\chi_{621}(7, \cdot)\) | None | 0 | 60 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(621))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(621)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)