Defining parameters
| Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1296.bq (of order \(54\) and degree \(18\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 324 \) |
| Character field: | \(\Q(\zeta_{54})\) | ||
| Sturm bound: | \(864\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1296, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 11772 | 2916 | 8856 |
| Cusp forms | 11556 | 2916 | 8640 |
| Eisenstein series | 216 | 0 | 216 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1296, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)