Defining parameters
| Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 10000.bo (of order \(25\) and degree \(20\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 125 \) |
| Character field: | \(\Q(\zeta_{25})\) | ||
| Sturm bound: | \(3000\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(10000, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 30600 | 4560 | 26040 |
| Cusp forms | 29400 | 4440 | 24960 |
| Eisenstein series | 1200 | 120 | 1080 |
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
\( S_{2}^{\mathrm{old}}(10000, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1000, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1250, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2000, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2500, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(5000, [\chi])\)\(^{\oplus 2}\)