Defining parameters
| Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
| Weight: | \( k \) | \(=\) | \( 6 \) |
| Character orbit: | \([\chi]\) | \(=\) | 729.g (of order \(27\) and degree \(18\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 81 \) |
| Character field: | \(\Q(\zeta_{27})\) | ||
| Sturm bound: | \(486\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(729, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 7452 | 3312 | 4140 |
| Cusp forms | 7128 | 3168 | 3960 |
| Eisenstein series | 324 | 144 | 180 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(729, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{6}^{\mathrm{old}}(729, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(729, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(243, [\chi])\)\(^{\oplus 2}\)