Defining parameters
| Level: | \( N \) | \(=\) | \( 459 = 3^{3} \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 459.k (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 51 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(162\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(459, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 456 | 192 | 264 |
| Cusp forms | 408 | 192 | 216 |
| Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(459, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(459, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(459, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)