Defining parameters
| Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 8 \) |
| Character orbit: | \([\chi]\) | \(=\) | 315.cc (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(384\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(315, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1360 | 1008 | 352 |
| Cusp forms | 1328 | 1008 | 320 |
| Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(315, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{8}^{\mathrm{old}}(315, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)