Defining parameters
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 528 | 76 | 452 |
Cusp forms | 432 | 68 | 364 |
Eisenstein series | 96 | 8 | 88 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1600, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 3}\)