Defining parameters
| Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2160.dg (of order \(18\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1080 \) |
| Character field: | \(\Q(\zeta_{18})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1296\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(2160, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5232 | 0 | 5232 |
| Cusp forms | 5136 | 0 | 5136 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{3}^{\mathrm{old}}(2160, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(2160, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)