Defining parameters
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.h (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: | \(5\) | ||
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.h.a | $2$ | $1.365$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(-3\) | \(-1\) | \(q-q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}-3\zeta_{6}q^{5}+\cdots\) |
171.2.h.b | $2$ | $1.365$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(1\) | \(-3\) | \(q-q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\zeta_{6}q^{5}+\cdots\) |
171.2.h.c | $32$ | $1.365$ | None | \(-2\) | \(1\) | \(3\) | \(1\) |