Defining parameters
| Level: | \( N \) | \(=\) | \( 5200 = 2^{4} \cdot 5^{2} \cdot 13 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 5200.cm (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 104 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(1680\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5200, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1728 | 0 | 1728 |
| Cusp forms | 1632 | 0 | 1632 |
| Eisenstein series | 96 | 0 | 96 |
Decomposition of \(S_{2}^{\mathrm{old}}(5200, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5200, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2600, [\chi])\)\(^{\oplus 2}\)