Defining parameters
| Level: | \( N \) | \(=\) | \( 8512 = 2^{6} \cdot 7 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8512.dk (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 608 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2560\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8512, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5152 | 0 | 5152 |
| Cusp forms | 5088 | 0 | 5088 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{2}^{\mathrm{old}}(8512, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8512, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4256, [\chi])\)\(^{\oplus 2}\)