Defining parameters
| Level: | \( N \) | \(=\) | \( 816 = 2^{4} \cdot 3 \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 816.bx (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 272 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(816, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1744 | 864 | 880 |
| Cusp forms | 1712 | 864 | 848 |
| Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(816, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(816, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(816, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 2}\)