Defining parameters
| Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5625.t (of order \(25\) and degree \(20\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 125 \) |
| Character field: | \(\Q(\zeta_{25})\) | ||
| Sturm bound: | \(1500\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5625, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 15400 | 3820 | 11580 |
| Cusp forms | 14600 | 3700 | 10900 |
| Eisenstein series | 800 | 120 | 680 |
Decomposition of \(S_{2}^{\mathrm{new}}(5625, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(5625, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5625, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1125, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1875, [\chi])\)\(^{\oplus 2}\)