Defining parameters
| Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8008.ju (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 364 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2688\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8008, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5440 | 0 | 5440 |
| Cusp forms | 5312 | 0 | 5312 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{2}^{\mathrm{old}}(8008, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(728, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4004, [\chi])\)\(^{\oplus 2}\)