Defining parameters
| Level: | \( N \) | \(=\) | \( 2000 = 2^{4} \cdot 5^{3} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2000.cc (of order \(100\) and degree \(40\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 500 \) |
| Character field: | \(\Q(\zeta_{100})\) | ||
| Sturm bound: | \(600\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12240 | 3000 | 9240 |
| Cusp forms | 11760 | 3000 | 8760 |
| Eisenstein series | 480 | 0 | 480 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2000, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(2000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2000, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 2}\)