# Properties

 Label 189.2.w Level 189 Weight 2 Character orbit w Rep. character $$\chi_{189}(25,\cdot)$$ Character field $$\Q(\zeta_{9})$$ Dimension 132 Newform subspaces 1 Sturm bound 48 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$189 = 3^{3} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 189.w (of order $$9$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$189$$ Character field: $$\Q(\zeta_{9})$$ Newform subspaces: $$1$$ Sturm bound: $$48$$ Trace bound: $$0$$

## Dimensions

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

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

## Trace form

 $$132q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 18q^{6} - 6q^{7} - 6q^{8} + 3q^{9} + O(q^{10})$$ $$132q - 3q^{2} - 3q^{3} - 3q^{4} - 3q^{5} - 18q^{6} - 6q^{7} - 6q^{8} + 3q^{9} - 6q^{10} + 3q^{11} - 3q^{12} - 12q^{13} + 15q^{14} - 9q^{16} - 54q^{17} - 3q^{18} - 6q^{19} - 18q^{20} - 21q^{21} - 12q^{22} + 45q^{24} - 3q^{25} + 30q^{26} - 12q^{27} - 12q^{28} - 30q^{29} - 57q^{30} - 3q^{31} + 51q^{32} + 15q^{33} - 18q^{34} - 12q^{35} - 60q^{36} + 3q^{37} - 57q^{38} - 66q^{39} - 66q^{40} + 33q^{42} - 12q^{43} + 3q^{44} + 33q^{45} + 3q^{46} - 21q^{47} + 90q^{48} + 12q^{49} - 39q^{50} - 48q^{51} + 9q^{52} + 9q^{53} - 63q^{54} - 24q^{55} + 57q^{56} - 18q^{57} - 3q^{58} - 18q^{59} + 81q^{60} + 33q^{61} + 75q^{62} + 63q^{63} - 30q^{64} + 81q^{65} + 69q^{66} - 3q^{67} + 6q^{68} - 6q^{69} - 42q^{70} - 18q^{71} - 105q^{72} + 21q^{73} - 93q^{74} + 18q^{75} - 24q^{76} + 87q^{77} - 30q^{78} + 15q^{79} + 102q^{80} + 39q^{81} - 6q^{82} - 42q^{83} - 36q^{84} - 63q^{85} + 159q^{86} + 30q^{87} + 57q^{88} - 150q^{89} - 39q^{90} + 6q^{91} - 66q^{92} - 27q^{93} + 33q^{94} - 147q^{95} + 81q^{96} - 12q^{97} + 99q^{98} + 24q^{99} + O(q^{100})$$

## 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.w.a $$132$$ $$1.509$$ None $$-3$$ $$-3$$ $$-3$$ $$-6$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database