Defining parameters
| Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3600.da (of order \(12\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 180 \) |
| Character field: | \(\Q(\zeta_{12})\) | ||
| Sturm bound: | \(2160\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(3600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5904 | 864 | 5040 |
| Cusp forms | 5616 | 864 | 4752 |
| Eisenstein series | 288 | 0 | 288 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(3600, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(3600, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(3600, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(720, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1800, [\chi])\)\(^{\oplus 2}\)