Defining parameters
| Level: | \( N \) | \(=\) | \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8624.fk (of order \(70\) and degree \(24\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 539 \) |
| Character field: | \(\Q(\zeta_{70})\) | ||
| Sturm bound: | \(2688\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8624, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 32544 | 8112 | 24432 |
| Cusp forms | 31968 | 8016 | 23952 |
| Eisenstein series | 576 | 96 | 480 |
Decomposition of \(S_{2}^{\mathrm{new}}(8624, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8624, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8624, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4312, [\chi])\)\(^{\oplus 2}\)