Defining parameters
| Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1764.cd (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 147 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(336\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1764, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 168 | 0 | 168 |
| Cusp forms | 24 | 0 | 24 |
| Eisenstein series | 144 | 0 | 144 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 0 | 0 | 0 | 0 |
Decomposition of \(S_{1}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)