# Properties

 Label 171.2.f Level $171$ Weight $2$ Character orbit 171.f Rep. character $\chi_{171}(64,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $3$ Sturm bound $40$ Trace bound $1$

# Related objects

## 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

 $$16 q - 8 q^{4} + 2 q^{5} - 8 q^{7} + 12 q^{8} + O(q^{10})$$ $$16 q - 8 q^{4} + 2 q^{5} - 8 q^{7} + 12 q^{8} + 4 q^{10} + 4 q^{11} - 2 q^{14} - 8 q^{16} - 4 q^{17} + 4 q^{19} - 44 q^{20} + 8 q^{22} + 10 q^{23} - 4 q^{25} + 32 q^{26} + 12 q^{28} - 4 q^{29} - 32 q^{31} - 12 q^{32} + 4 q^{34} + 18 q^{35} - 8 q^{37} - 42 q^{38} - 16 q^{41} + 8 q^{43} + 14 q^{44} - 16 q^{46} - 24 q^{47} - 16 q^{49} + 56 q^{50} + 4 q^{52} - 2 q^{53} + 12 q^{55} + 48 q^{56} + 64 q^{58} + 10 q^{59} - 20 q^{61} - 26 q^{62} - 56 q^{64} - 12 q^{65} + 8 q^{67} - 8 q^{68} + 48 q^{70} - 12 q^{71} - 28 q^{73} + 4 q^{74} + 88 q^{76} - 20 q^{77} + 16 q^{79} + 10 q^{80} - 44 q^{82} + 8 q^{83} + 48 q^{85} - 18 q^{86} - 72 q^{88} - 22 q^{89} - 16 q^{91} + 2 q^{92} - 96 q^{94} - 2 q^{95} - 32 q^{97} - 20 q^{98} + O(q^{100})$$

## 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

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