Defining parameters
| Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1620.x (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 45 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(1296\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1620, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4032 | 288 | 3744 |
| Cusp forms | 3744 | 288 | 3456 |
| Eisenstein series | 288 | 0 | 288 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1620, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)