# Properties

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

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## 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

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

## 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

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

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database