Defining parameters
| Level: | \( N \) | = | \( 200 = 2^{3} \cdot 5^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(2400\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(200))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 180 | 45 | 135 |
| Cusp forms | 12 | 4 | 8 |
| Eisenstein series | 168 | 41 | 127 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(200))\)
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 |
|---|---|---|---|---|
| 200.1.b | \(\chi_{200}(151, \cdot)\) | None | 0 | 1 |
| 200.1.e | \(\chi_{200}(99, \cdot)\) | 200.1.e.a | 2 | 1 |
| 200.1.g | \(\chi_{200}(51, \cdot)\) | 200.1.g.a | 1 | 1 |
| 200.1.g.b | 1 | |||
| 200.1.h | \(\chi_{200}(199, \cdot)\) | None | 0 | 1 |
| 200.1.i | \(\chi_{200}(93, \cdot)\) | None | 0 | 2 |
| 200.1.l | \(\chi_{200}(57, \cdot)\) | None | 0 | 2 |
| 200.1.n | \(\chi_{200}(11, \cdot)\) | None | 0 | 4 |
| 200.1.p | \(\chi_{200}(39, \cdot)\) | None | 0 | 4 |
| 200.1.r | \(\chi_{200}(31, \cdot)\) | None | 0 | 4 |
| 200.1.s | \(\chi_{200}(19, \cdot)\) | None | 0 | 4 |
| 200.1.u | \(\chi_{200}(17, \cdot)\) | None | 0 | 8 |
| 200.1.x | \(\chi_{200}(13, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(200))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(200)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)