Defining parameters
| Level: | \( N \) | \(=\) | \( 4320 = 2^{5} \cdot 3^{3} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4320.fb (of order \(36\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 432 \) |
| Character field: | \(\Q(\zeta_{36})\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1728\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4320, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 10464 | 0 | 10464 |
| Cusp forms | 10272 | 0 | 10272 |
| Eisenstein series | 192 | 0 | 192 |
Decomposition of \(S_{2}^{\mathrm{old}}(4320, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4320, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2160, [\chi])\)\(^{\oplus 2}\)