Defining parameters
| Level: | \( N \) | \(=\) | \( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5600.cu (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 160 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(1920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3888 | 1728 | 2160 |
| Cusp forms | 3792 | 1728 | 2064 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{2}^{\mathrm{new}}(5600, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(5600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)