Defining parameters
| Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 360.o (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 60 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(288\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 232 | 0 | 232 |
| Cusp forms | 200 | 0 | 200 |
| Eisenstein series | 32 | 0 | 32 |
Decomposition of \(S_{4}^{\mathrm{old}}(360, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(360, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)