Defining parameters
| Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 576.r (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 72 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(384\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(576, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 600 | 144 | 456 |
| Cusp forms | 552 | 144 | 408 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(576, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(576, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)