Defining parameters
| Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 810.f (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(648\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(810, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1020 | 144 | 876 |
| Cusp forms | 924 | 144 | 780 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(810, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(810, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(810, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 2}\)