Defining parameters
| Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2304.be (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 192 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Sturm bound: | \(1536\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(2304, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 9344 | 768 | 8576 |
| Cusp forms | 9088 | 768 | 8320 |
| Eisenstein series | 256 | 0 | 256 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)