Defining parameters
| Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1600.h (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 0 \) | ||
| Sturm bound: | \(240\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 44 | 2 | 42 |
| Cusp forms | 8 | 0 | 8 |
| Eisenstein series | 36 | 2 | 34 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 0 | 0 | 0 | 0 |
Decomposition of \(S_{1}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1600, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)