Defining parameters
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.bg (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(11\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1040, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 360 | 88 | 272 |
Cusp forms | 312 | 80 | 232 |
Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1040, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1040, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1040, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(520, [\chi])\)\(^{\oplus 2}\)