Defining parameters
| Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4004.ec (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 364 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(1344\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4004, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2720 | 2240 | 480 |
| Cusp forms | 2656 | 2240 | 416 |
| Eisenstein series | 64 | 0 | 64 |
Decomposition of \(S_{2}^{\mathrm{new}}(4004, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4004, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 2}\)