Defining parameters
| Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 315.p (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(192\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 304 | 124 | 180 |
| Cusp forms | 272 | 116 | 156 |
| Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)