Defining parameters
| Level: | \( N \) | \(=\) | \( 9360 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9360.rp (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 520 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(4032\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9360, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8192 | 0 | 8192 |
| Cusp forms | 7936 | 0 | 7936 |
| Eisenstein series | 256 | 0 | 256 |
Decomposition of \(S_{2}^{\mathrm{old}}(9360, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1040, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3120, [\chi])\)\(^{\oplus 2}\)