Defining parameters
| Level: | \( N \) | \(=\) | \( 408 = 2^{3} \cdot 3 \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 408.bh (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 51 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Sturm bound: | \(288\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(408, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1792 | 432 | 1360 |
| Cusp forms | 1664 | 432 | 1232 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(408, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(408, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(408, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)