Defining parameters
| Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4008.bc (of order \(166\) and degree \(82\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 2004 \) |
| Character field: | \(\Q(\zeta_{166})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1344\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4008, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 55760 | 0 | 55760 |
| Cusp forms | 54448 | 0 | 54448 |
| Eisenstein series | 1312 | 0 | 1312 |
Decomposition of \(S_{2}^{\mathrm{old}}(4008, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(2004, [\chi])\)\(^{\oplus 2}\)