Defining parameters
| Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1600.d (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
| Character field: | \(\Q\) | ||
| Sturm bound: | \(960\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1600, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 756 | 114 | 642 |
| Cusp forms | 684 | 114 | 570 |
| Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{4}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)