Defining parameters
| Level: | \( N \) | = | \( 1816 = 2^{3} \cdot 227 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(206112\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1816))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1494 | 570 | 924 |
| Cusp forms | 138 | 120 | 18 |
| Eisenstein series | 1356 | 450 | 906 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 118 | 0 | 2 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1816))\)
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 |
|---|---|---|---|---|
| 1816.1.d | \(\chi_{1816}(455, \cdot)\) | None | 0 | 1 |
| 1816.1.e | \(\chi_{1816}(453, \cdot)\) | 1816.1.e.a | 3 | 1 |
| 1816.1.e.b | 3 | |||
| 1816.1.f | \(\chi_{1816}(1363, \cdot)\) | None | 0 | 1 |
| 1816.1.g | \(\chi_{1816}(1361, \cdot)\) | 1816.1.g.a | 2 | 1 |
| 1816.1.k | \(\chi_{1816}(17, \cdot)\) | None | 0 | 112 |
| 1816.1.l | \(\chi_{1816}(3, \cdot)\) | 1816.1.l.a | 112 | 112 |
| 1816.1.m | \(\chi_{1816}(5, \cdot)\) | None | 0 | 112 |
| 1816.1.n | \(\chi_{1816}(7, \cdot)\) | None | 0 | 112 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1816))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1816)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(227))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(908))\)\(^{\oplus 2}\)