# Properties

 Label 189.2.ba Level 189 Weight 2 Character orbit ba Rep. character $$\chi_{189}(5,\cdot)$$ Character field $$\Q(\zeta_{18})$$ 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.ba (of order $$18$$ and degree $$6$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$189$$ Character field: $$\Q(\zeta_{18})$$ 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

 $$132q - 3q^{2} - 9q^{3} - 3q^{4} - 9q^{5} - 18q^{6} - 6q^{7} - 18q^{8} + 3q^{9} + O(q^{10})$$ $$132q - 3q^{2} - 9q^{3} - 3q^{4} - 9q^{5} - 18q^{6} - 6q^{7} - 18q^{8} + 3q^{9} - 9q^{11} - 9q^{12} + 3q^{14} - 24q^{15} + 3q^{16} - 18q^{17} - 3q^{18} + 18q^{20} - 21q^{21} - 12q^{22} - 6q^{23} - 9q^{24} - 3q^{25} - 12q^{28} + 6q^{29} + 51q^{30} - 9q^{31} + 3q^{32} - 9q^{33} - 18q^{34} + 18q^{35} + 3q^{37} - 99q^{38} - 36q^{39} - 54q^{40} - 45q^{42} - 12q^{43} - 9q^{44} - 9q^{45} + 3q^{46} + 45q^{47} - 24q^{49} - 9q^{50} - 48q^{51} - 9q^{52} - 45q^{53} + 171q^{54} + 3q^{56} - 3q^{58} + 36q^{59} + 57q^{60} - 9q^{61} - 99q^{62} - 33q^{63} + 18q^{64} + 69q^{65} - 9q^{66} - 3q^{67} + 36q^{68} + 108q^{69} + 66q^{70} + 18q^{71} - 129q^{72} - 9q^{73} + 75q^{74} + 36q^{75} + 36q^{76} + 15q^{77} + 66q^{78} - 21q^{79} + 72q^{80} - 33q^{81} - 18q^{82} - 90q^{83} - 120q^{84} + 9q^{85} - 105q^{86} - 54q^{87} - 63q^{88} - 18q^{89} + 81q^{90} + 6q^{91} + 150q^{92} + 21q^{93} - 9q^{94} + 45q^{95} - 81q^{96} + 27q^{98} + 96q^{99} + O(q^{100})$$

## 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.ba.a $$132$$ $$1.509$$ None $$-3$$ $$-9$$ $$-9$$ $$-6$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database