Defining parameters
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.n (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 19 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1280, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 432 | 104 | 328 |
Cusp forms | 336 | 88 | 248 |
Eisenstein series | 96 | 16 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1280, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)