Defining parameters
Level: | \( N \) | \(=\) | \( 666 = 2 \cdot 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 666.bj (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(228\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 732 | 96 | 636 |
Cusp forms | 636 | 96 | 540 |
Eisenstein series | 96 | 0 | 96 |
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.bj.a | $12$ | $5.318$ | \(\Q(\zeta_{36})\) | None | \(0\) | \(0\) | \(0\) | \(-12\) | \(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(-\zeta_{36}^{2}-\zeta_{36}^{3}+\cdots)q^{5}+\cdots\) |
666.2.bj.b | $12$ | $5.318$ | \(\Q(\zeta_{36})\) | None | \(0\) | \(0\) | \(0\) | \(-12\) | \(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(\zeta_{36}^{2}-\zeta_{36}^{3}+\cdots)q^{5}+\cdots\) |
666.2.bj.c | $12$ | $5.318$ | \(\Q(\zeta_{36})\) | None | \(0\) | \(0\) | \(0\) | \(-12\) | \(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(-\zeta_{36}+\zeta_{36}^{2}+\cdots)q^{5}+\cdots\) |
666.2.bj.d | $12$ | $5.318$ | \(\Q(\zeta_{36})\) | None | \(0\) | \(0\) | \(0\) | \(24\) | \(q+\zeta_{36}q^{2}+\zeta_{36}^{2}q^{4}+(\zeta_{36}+\zeta_{36}^{3}+\cdots)q^{5}+\cdots\) |
666.2.bj.e | $24$ | $5.318$ | None | \(0\) | \(0\) | \(0\) | \(-6\) | ||
666.2.bj.f | $24$ | $5.318$ | None | \(0\) | \(0\) | \(0\) | \(6\) |
Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)