Properties

 Label 171.3.r Level $171$ Weight $3$ Character orbit 171.r Rep. character $\chi_{171}(26,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $3$ Sturm bound $60$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$171 = 3^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 171.r (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$57$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$60$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(171, [\chi])$$.

Total New Old
Modular forms 88 24 64
Cusp forms 72 24 48
Eisenstein series 16 0 16

Trace form

 $$24 q + 12 q^{4} + 16 q^{7} + O(q^{10})$$ $$24 q + 12 q^{4} + 16 q^{7} + 20 q^{10} + 20 q^{13} - 12 q^{16} + 36 q^{19} + 16 q^{22} - 40 q^{25} + 32 q^{28} - 56 q^{31} - 76 q^{34} - 128 q^{37} - 120 q^{40} + 84 q^{43} - 128 q^{46} - 176 q^{49} - 32 q^{52} + 60 q^{55} + 320 q^{58} + 40 q^{61} + 144 q^{64} + 252 q^{67} + 120 q^{70} - 120 q^{73} + 348 q^{76} + 148 q^{79} - 460 q^{82} + 480 q^{85} - 888 q^{88} - 244 q^{91} - 720 q^{94} - 704 q^{97} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(171, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.3.r.a $4$ $4.659$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$-6$$ $$0$$ $$12$$ $$20$$ $$q+(-1-\beta _{2})q^{2}-\beta _{2}q^{4}+(2-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots$$
171.3.r.b $4$ $4.659$ $$\Q(\sqrt{-2}, \sqrt{-3})$$ None $$6$$ $$0$$ $$-12$$ $$20$$ $$q+(2-\beta _{2})q^{2}+(-1+\beta _{2})q^{4}+(-4+\cdots)q^{5}+\cdots$$
171.3.r.c $16$ $4.659$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-24$$ $$q+\beta _{1}q^{2}+(-2\beta _{2}+\beta _{6}+\beta _{8}-\beta _{9}+\cdots)q^{4}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(171, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(171, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(57, [\chi])$$$$^{\oplus 2}$$