Defining parameters
| Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 4400.kd (of order \(20\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 880 \) |
| Character field: | \(\Q(\zeta_{20})\) | ||
| Sturm bound: | \(1440\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(4400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5856 | 3488 | 2368 |
| Cusp forms | 5664 | 3424 | 2240 |
| Eisenstein series | 192 | 64 | 128 |
Decomposition of \(S_{2}^{\mathrm{new}}(4400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(4400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(4400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(880, [\chi])\)\(^{\oplus 2}\)