Defining parameters
| Level: | \( N \) | \(=\) | \( 9840 = 2^{4} \cdot 3 \cdot 5 \cdot 41 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 9840.pr (of order \(40\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 820 \) |
| Character field: | \(\Q(\zeta_{40})\) | ||
| Sturm bound: | \(4032\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(9840, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 32640 | 4032 | 28608 |
| Cusp forms | 31872 | 4032 | 27840 |
| Eisenstein series | 768 | 0 | 768 |
Decomposition of \(S_{2}^{\mathrm{new}}(9840, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(9840, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(9840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(820, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3280, [\chi])\)\(^{\oplus 2}\)