Defining parameters
| Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1800.cm (of order \(15\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 225 \) |
| Character field: | \(\Q(\zeta_{15})\) | ||
| Sturm bound: | \(1440\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1800, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8704 | 2160 | 6544 |
| Cusp forms | 8576 | 2160 | 6416 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1800, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1800, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1800, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)