Defining parameters
| Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4008.u (of order \(166\) and degree \(82\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 1336 \) |
| Character field: | \(\Q(\zeta_{166})\) | ||
| Sturm bound: | \(1344\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4008, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 55432 | 27552 | 27880 |
| Cusp forms | 54776 | 27552 | 27224 |
| Eisenstein series | 656 | 0 | 656 |
Decomposition of \(S_{2}^{\mathrm{new}}(4008, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4008, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1336, [\chi])\)\(^{\oplus 2}\)