Defining parameters
Level: | \( N \) | \(=\) | \( 666 = 2 \cdot 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 666.be (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 111 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(228\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 488 | 40 | 448 |
Cusp forms | 424 | 40 | 384 |
Eisenstein series | 64 | 0 | 64 |
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.be.a | $8$ | $5.318$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots\) |
666.2.be.b | $8$ | $5.318$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(2\zeta_{24}^{3}+2\zeta_{24}^{7})q^{5}+\cdots\) |
666.2.be.c | $8$ | $5.318$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(12\) | \(q+\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{7})q^{5}+\cdots\) |
666.2.be.d | $16$ | $5.318$ | 16.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\beta _{10}q^{2}-\beta _{9}q^{4}+(\beta _{1}+\beta _{7})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(666, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)