Defining parameters
| Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1800.cs (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1440\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8768 | 0 | 8768 |
| Cusp forms | 8512 | 0 | 8512 |
| Eisenstein series | 256 | 0 | 256 |
Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1800, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)