Defining parameters
| Level: | \( N \) | \(=\) | \( 17640 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 17640.jc (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 315 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(8064\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(17640, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 16384 | 2880 | 13504 |
| Cusp forms | 15872 | 2880 | 12992 |
| Eisenstein series | 512 | 0 | 512 |
Decomposition of \(S_{2}^{\mathrm{new}}(17640, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(17640, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(17640, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1260, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2205, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2520, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4410, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(8820, [\chi])\)\(^{\oplus 2}\)