Defining parameters
| Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 10000.bh (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(3000\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(10000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12480 | 0 | 12480 |
| Cusp forms | 11520 | 0 | 11520 |
| Eisenstein series | 960 | 0 | 960 |
Decomposition of \(S_{2}^{\mathrm{old}}(10000, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(10000, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(5000, [\chi])\)\(^{\oplus 2}\)