Defining parameters
| Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3600.ch (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(2160\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5824 | 0 | 5824 |
| Cusp forms | 5696 | 0 | 5696 |
| Eisenstein series | 128 | 0 | 128 |
Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1200, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)