Defining parameters
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(2\) | ||
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 | 16 | 40 |
Cusp forms | 40 | 16 | 24 |
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.e.a | $2$ | $1.006$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(-3\) | \(-4\) | \(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}-3\zeta_{6}q^{5}+\cdots\) |
126.2.e.b | $2$ | $1.006$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(3\) | \(-4\) | \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+3\zeta_{6}q^{5}+\cdots\) |
126.2.e.c | $6$ | $1.006$ | 6.0.309123.1 | None | \(-6\) | \(2\) | \(1\) | \(2\) | \(q-q^{2}+(-\beta _{2}-\beta _{4})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\) |
126.2.e.d | $6$ | $1.006$ | 6.0.309123.1 | None | \(6\) | \(-2\) | \(-5\) | \(4\) | \(q+q^{2}+(\beta _{3}-\beta _{4}-\beta _{5})q^{3}+q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(126, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)