Defining parameters
| Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 693.bg (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 77 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(384\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(693, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 592 | 244 | 348 |
| Cusp forms | 560 | 236 | 324 |
| Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(693, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(693, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)