Defining parameters
| Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 648.w (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 108 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(432\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(648, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2016 | 0 | 2016 |
| Cusp forms | 1872 | 0 | 1872 |
| Eisenstein series | 144 | 0 | 144 |
Decomposition of \(S_{4}^{\mathrm{old}}(648, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(648, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)