Defining parameters
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.f (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 48 | 20 | 28 |
Cusp forms | 32 | 16 | 16 |
Eisenstein series | 16 | 4 | 12 |
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.f.a | $2$ | $1.365$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(0\) | \(0\) | \(2\) | \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{7}+3q^{8}+\cdots\) |
171.2.f.b | $6$ | $1.365$ | 6.0.954288.1 | None | \(-1\) | \(0\) | \(2\) | \(-2\) | \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\) |
171.2.f.c | $8$ | $1.365$ | 8.0.764411904.5 | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\beta _{5}q^{2}+(-1-\beta _{3}+\beta _{4}-\beta _{6})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(171, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(171, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 2}\)