Defining parameters
| Level: | \( N \) | \(=\) | \( 8880 = 2^{4} \cdot 3 \cdot 5 \cdot 37 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8880.mu (of order \(36\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 111 \) |
| Character field: | \(\Q(\zeta_{36})\) | ||
| Sturm bound: | \(3648\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8880, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 22176 | 3648 | 18528 |
| Cusp forms | 21600 | 3648 | 17952 |
| Eisenstein series | 576 | 0 | 576 |
Decomposition of \(S_{2}^{\mathrm{new}}(8880, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8880, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8880, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1776, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2220, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4440, [\chi])\)\(^{\oplus 2}\)