Defining parameters
Level: | \( N \) | \(=\) | \( 666 = 2 \cdot 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 666.w (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 333 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(228\) | ||
Trace bound: | \(8\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 708 | 228 | 480 |
Cusp forms | 660 | 228 | 432 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
666.2.w.a | $114$ | $5.318$ | None | \(0\) | \(6\) | \(0\) | \(-3\) | ||
666.2.w.b | $114$ | $5.318$ | None | \(0\) | \(6\) | \(0\) | \(-3\) |
Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)