Defining parameters
| Level: | \( N \) | \(=\) | \( 656 = 2^{4} \cdot 41 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 656.bi (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 328 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(336\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(656, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1024 | 0 | 1024 |
| Cusp forms | 992 | 0 | 992 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{4}^{\mathrm{old}}(656, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(656, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(328, [\chi])\)\(^{\oplus 2}\)