Defining parameters
Level: | \( N \) | \(=\) | \( 6400 = 2^{8} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6400.cl (of order \(32\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 640 \) |
Character field: | \(\Q(\zeta_{32})\) | ||
Newform subspaces: | \( 0 \) | ||
Sturm bound: | \(1920\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(6400, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15552 | 0 | 15552 |
Cusp forms | 15168 | 0 | 15168 |
Eisenstein series | 384 | 0 | 384 |
Decomposition of \(S_{2}^{\mathrm{old}}(6400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(6400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3200, [\chi])\)\(^{\oplus 2}\)