Defining parameters
| Level: | \( N \) | \(=\) | \( 9240 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9240.kj (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 220 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(4608\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9240, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 18688 | 0 | 18688 |
| Cusp forms | 18176 | 0 | 18176 |
| Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{old}}(9240, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(660, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3080, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4620, [\chi])\)\(^{\oplus 2}\)