Defining parameters
| Level: | \( N \) | \(=\) | \( 704 = 2^{6} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 704.z (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 64 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Sturm bound: | \(384\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(704, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2320 | 1920 | 400 |
| Cusp forms | 2288 | 1920 | 368 |
| Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(704, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(704, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(704, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)