Defining parameters
Level: | \( N \) | \(=\) | \( 666 = 2 \cdot 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 666.s (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 37 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(228\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 244 | 28 | 216 |
Cusp forms | 212 | 28 | 184 |
Eisenstein series | 32 | 0 | 32 |
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.s.a | $4$ | $5.318$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-6\) | \(4\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\) |
666.2.s.b | $4$ | $5.318$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{7}+\zeta_{12}^{3}q^{8}+\cdots\) |
666.2.s.c | $4$ | $5.318$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{5}+\cdots\) |
666.2.s.d | $4$ | $5.318$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(6\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}-\zeta_{12}^{3})q^{5}+\cdots\) |
666.2.s.e | $4$ | $5.318$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(6\) | \(-8\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(2-\zeta_{12}^{2})q^{5}+\cdots\) |
666.2.s.f | $8$ | $5.318$ | 8.0.303595776.1 | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{5}q^{2}+(1+\beta _{4})q^{4}+(-2\beta _{1}+\beta _{5}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)