Defining parameters
| Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1560.do (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 156 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1344\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1560, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2048 | 0 | 2048 |
| Cusp forms | 1984 | 0 | 1984 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{4}^{\mathrm{old}}(1560, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1560, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)