Defining parameters
| Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8002.v (of order \(1000\) and degree \(400\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4001 \) |
| Character field: | \(\Q(\zeta_{1000})\) | ||
| Sturm bound: | \(2001\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8002, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 400800 | 133600 | 267200 |
| Cusp forms | 399200 | 133600 | 265600 |
| Eisenstein series | 1600 | 0 | 1600 |
Decomposition of \(S_{2}^{\mathrm{new}}(8002, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8002, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(4001, [\chi])\)\(^{\oplus 2}\)