Defining parameters
| Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2400.ck (of order \(10\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 200 \) |
| Character field: | \(\Q(\zeta_{10})\) | ||
| Sturm bound: | \(1920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(2400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5824 | 720 | 5104 |
| Cusp forms | 5696 | 720 | 4976 |
| Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(2400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(2400, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(2400, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)