# Properties

 Label 189.2.f Level $189$ Weight $2$ Character orbit 189.f Rep. character $\chi_{189}(64,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $12$ Newform subspaces $2$ Sturm bound $48$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.f (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$9$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(189, [\chi])$$.

Total New Old
Modular forms 60 12 48
Cusp forms 36 12 24
Eisenstein series 24 0 24

## Trace form

 $$12 q + 2 q^{2} - 6 q^{4} - 2 q^{5} + O(q^{10})$$ $$12 q + 2 q^{2} - 6 q^{4} - 2 q^{5} + 4 q^{11} + 4 q^{14} - 6 q^{16} + 12 q^{17} - 12 q^{19} - 22 q^{20} + 6 q^{22} + 12 q^{23} + 8 q^{26} + 10 q^{29} + 6 q^{31} - 8 q^{32} - 6 q^{34} - 16 q^{35} - 12 q^{37} + 14 q^{38} - 12 q^{40} - 22 q^{41} + 6 q^{43} - 76 q^{44} + 24 q^{46} - 6 q^{47} - 6 q^{49} + 4 q^{50} + 18 q^{52} + 24 q^{53} - 12 q^{55} + 12 q^{56} + 18 q^{58} - 12 q^{59} + 96 q^{62} + 10 q^{65} + 12 q^{67} + 12 q^{68} - 36 q^{71} - 36 q^{73} - 24 q^{74} + 6 q^{76} + 8 q^{77} + 6 q^{79} + 8 q^{80} - 30 q^{83} - 18 q^{85} + 40 q^{86} - 6 q^{88} - 20 q^{89} - 12 q^{91} + 18 q^{92} - 6 q^{94} + 4 q^{95} - 4 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(189, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
189.2.f.a $6$ $1.509$ 6.0.309123.1 None $$-1$$ $$0$$ $$-5$$ $$3$$ $$q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots$$
189.2.f.b $6$ $1.509$ $$\Q(\zeta_{18})$$ None $$3$$ $$0$$ $$3$$ $$-3$$ $$q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(189, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(189, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 2}$$