Defining parameters
| Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5625.ba (of order \(60\) and degree \(16\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 225 \) |
| Character field: | \(\Q(\zeta_{60})\) | ||
| Sturm bound: | \(1500\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5625, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 12480 | 7872 | 4608 |
| Cusp forms | 11520 | 7488 | 4032 |
| Eisenstein series | 960 | 384 | 576 |
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
\( S_{2}^{\mathrm{old}}(5625, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1125, [\chi])\)\(^{\oplus 2}\)