Defining parameters
| Level: | \( N \) | \(=\) | \( 6400 = 2^{8} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 6400.y (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 32 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Sturm bound: | \(1920\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4032 | 632 | 3400 |
| Cusp forms | 3648 | 584 | 3064 |
| Eisenstein series | 384 | 48 | 336 |
Decomposition of \(S_{2}^{\mathrm{new}}(6400, [\chi])\) into newform subspaces
The newforms in this space have not yet been added to the LMFDB.
Decomposition of \(S_{2}^{\mathrm{old}}(6400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1600, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3200, [\chi])\)\(^{\oplus 2}\)