Defining parameters
| Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 600.w (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 120 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(480\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 744 | 440 | 304 |
| Cusp forms | 696 | 424 | 272 |
| Eisenstein series | 48 | 16 | 32 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(600, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(600, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)