Defining parameters
| Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
| Weight: | \( k \) | \(=\) | \( 3 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1280.p (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
| Character field: | \(\Q(i)\) | ||
| Sturm bound: | \(576\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1280, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 816 | 200 | 616 |
| Cusp forms | 720 | 184 | 536 |
| Eisenstein series | 96 | 16 | 80 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{3}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)