# Properties

 Label 189.2.v Level $189$ Weight $2$ Character orbit 189.v Rep. character $\chi_{189}(22,\cdot)$ Character field $\Q(\zeta_{9})$ Dimension $108$ Newform subspaces $2$ Sturm bound $48$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 189.v (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$27$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 156 108 48
Cusp forms 132 108 24
Eisenstein series 24 0 24

## Trace form

 $$108 q - 6 q^{5} - 18 q^{8} - 6 q^{9} + O(q^{10})$$ $$108 q - 6 q^{5} - 18 q^{8} - 6 q^{9} - 12 q^{11} - 36 q^{12} - 18 q^{15} - 30 q^{18} + 6 q^{20} - 18 q^{22} - 12 q^{23} + 72 q^{24} - 18 q^{25} - 36 q^{26} + 6 q^{27} + 36 q^{29} - 48 q^{30} - 18 q^{31} + 42 q^{32} - 48 q^{33} - 18 q^{34} - 24 q^{35} + 48 q^{36} - 24 q^{38} - 24 q^{39} - 66 q^{41} - 30 q^{42} - 18 q^{43} - 12 q^{44} + 42 q^{45} - 54 q^{47} - 78 q^{48} + 144 q^{50} + 60 q^{51} - 54 q^{52} + 72 q^{53} - 36 q^{54} + 42 q^{57} - 54 q^{58} + 42 q^{59} + 126 q^{60} - 54 q^{64} + 48 q^{65} + 6 q^{66} + 18 q^{67} + 6 q^{68} + 48 q^{69} - 72 q^{71} + 30 q^{72} + 12 q^{74} - 24 q^{75} + 108 q^{76} - 120 q^{78} + 36 q^{79} - 180 q^{80} - 42 q^{81} - 30 q^{83} - 24 q^{84} + 36 q^{85} - 24 q^{86} - 96 q^{87} + 108 q^{88} + 48 q^{89} + 6 q^{90} - 42 q^{92} + 114 q^{93} - 54 q^{94} - 36 q^{95} + 144 q^{96} - 18 q^{97} - 6 q^{98} - 66 q^{99} + O(q^{100})$$

## 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.v.a $54$ $1.509$ None $$0$$ $$-3$$ $$-3$$ $$0$$
189.2.v.b $54$ $1.509$ None $$0$$ $$3$$ $$-3$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(189, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(27, [\chi])$$$$^{\oplus 2}$$