Defining parameters
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.df (of order \(60\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 155 \) |
Character field: | \(\Q(\zeta_{60})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1376 | 800 | 576 |
Cusp forms | 1184 | 736 | 448 |
Eisenstein series | 192 | 64 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
775.2.df.a | $160$ | $6.188$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
775.2.df.b | $224$ | $6.188$ | None | \(12\) | \(14\) | \(0\) | \(-6\) | ||
775.2.df.c | $352$ | $6.188$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(775, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(775, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)