Defining parameters
| Level: | \( N \) | \(=\) | \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 8820.gi (of order \(42\) and degree \(12\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 441 \) |
| Character field: | \(\Q(\zeta_{42})\) | ||
| Sturm bound: | \(4032\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(8820, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 24336 | 2688 | 21648 |
| Cusp forms | 24048 | 2688 | 21360 |
| Eisenstein series | 288 | 0 | 288 |
Decomposition of \(S_{2}^{\mathrm{new}}(8820, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(8820, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(8820, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2205, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4410, [\chi])\)\(^{\oplus 2}\)