Defining parameters
| Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3240.cq (of order \(36\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 540 \) |
| Character field: | \(\Q(\zeta_{36})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1296\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3240, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8064 | 0 | 8064 |
| Cusp forms | 7488 | 0 | 7488 |
| Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{old}}(3240, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3240, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1080, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1620, [\chi])\)\(^{\oplus 2}\)