Defining parameters
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.mp (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4004 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
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 | 10880 | 0 | 10880 |
Cusp forms | 10624 | 0 | 10624 |
Eisenstein series | 256 | 0 | 256 |
Decomposition of \(S_{2}^{\mathrm{old}}(8008, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(4004, [\chi])\)\(^{\oplus 2}\)