Defining parameters
| Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1800.r (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 120 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(1080\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1488 | 288 | 1200 |
| Cusp forms | 1392 | 288 | 1104 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)