Defining parameters
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.o (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(39\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(79\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 552 | 72 | 480 |
Cusp forms | 408 | 72 | 336 |
Eisenstein series | 144 | 0 | 144 |
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
\( S_{2}^{\mathrm{old}}(1600, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(800, [\chi])\)\(^{\oplus 2}\)