Defining parameters
| Level: | \( N \) | \(=\) | \( 616 = 2^{3} \cdot 7 \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 616.ch (of order \(30\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 308 \) |
| Character field: | \(\Q(\zeta_{30})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(616, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2368 | 0 | 2368 |
| Cusp forms | 2240 | 0 | 2240 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{4}^{\mathrm{old}}(616, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(616, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 2}\)