Defining parameters
| Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 400.o (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(120\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 144 | 0 | 144 |
| Cusp forms | 96 | 0 | 96 |
| Eisenstein series | 48 | 0 | 48 |
Decomposition of \(S_{2}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(400, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)