Defining parameters
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.t (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 117 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(117, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 32 | 0 |
Cusp forms | 24 | 24 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(117, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
117.2.t.a | $2$ | $0.934$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-3\) | \(-6\) | \(-6\) | \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots\) |
117.2.t.b | $2$ | $0.934$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-3\) | \(6\) | \(6\) | \(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\) |
117.2.t.c | $20$ | $0.934$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q-\beta _{17}q^{2}+\beta _{10}q^{3}+(1-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\) |