Defining parameters
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.f (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(126, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 12 | 44 |
Cusp forms | 40 | 12 | 28 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(126, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
126.2.f.a | $2$ | $1.006$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(0\) | \(3\) | \(-1\) | \(q+\zeta_{6}q^{2}+(1-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\) |
126.2.f.b | $2$ | $1.006$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(3\) | \(-2\) | \(1\) | \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\) |
126.2.f.c | $4$ | $1.006$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(-2\) | \(4\) | \(-2\) | \(2\) | \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\) |
126.2.f.d | $4$ | $1.006$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(2\) | \(-1\) | \(-3\) | \(-2\) | \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(126, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)