Defining parameters
| Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 324.h (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Sturm bound: | \(216\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(324, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 348 | 148 | 200 |
| Cusp forms | 300 | 140 | 160 |
| Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(324, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(324, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(324, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)