Defining parameters
| Level: | \( N \) | \(=\) | \( 8568 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 17 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8568.hc (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 136 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(3456\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8568, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 6976 | 2160 | 4816 |
| Cusp forms | 6848 | 2160 | 4688 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{2}^{\mathrm{new}}(8568, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8568, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8568, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(952, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2856, [\chi])\)\(^{\oplus 2}\)