Defining parameters
| Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 704.q (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 352 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(704, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1168 | 0 | 1168 |
| Cusp forms | 1136 | 0 | 1136 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{4}^{\mathrm{old}}(704, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(352, [\chi])\)\(^{\oplus 2}\)