Defining parameters
| Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1500.x (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 75 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Sturm bound: | \(1200\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1500, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 7440 | 720 | 6720 |
| Cusp forms | 6960 | 720 | 6240 |
| Eisenstein series | 480 | 0 | 480 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1500, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1500, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1500, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(750, [\chi])\)\(^{\oplus 2}\)