Defining parameters
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 171 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 44 | 0 |
Cusp forms | 36 | 36 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
171.2.g.a | $2$ | $1.365$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(-3\) | \(6\) | \(-1\) | \(q+\zeta_{6}q^{2}+(-2+\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\) |
171.2.g.b | $2$ | $1.365$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(3\) | \(-2\) | \(-3\) | \(q+\zeta_{6}q^{2}+(2-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\) |
171.2.g.c | $32$ | $1.365$ | None | \(1\) | \(-2\) | \(-6\) | \(1\) |