Defining parameters
| Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 10000.be (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 400 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Sturm bound: | \(3000\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(10000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12240 | 7776 | 4464 |
| Cusp forms | 11760 | 7584 | 4176 |
| Eisenstein series | 480 | 192 | 288 |
Decomposition of \(S_{2}^{\mathrm{new}}(10000, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(10000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(10000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)