Defining parameters
| Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 684.cd (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 228 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Sturm bound: | \(360\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1488 | 480 | 1008 |
| Cusp forms | 1392 | 480 | 912 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)