# Properties

 Label 432.2.bg Level 432 Weight 2 Character orbit bg Rep. character $$\chi_{432}(13,\cdot)$$ Character field $$\Q(\zeta_{36})$$ Dimension 840 Newform subspaces 1 Sturm bound 144 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$432 = 2^{4} \cdot 3^{3}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 432.bg (of order $$36$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$432$$ Character field: $$\Q(\zeta_{36})$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(432, [\chi])$$.

Total New Old
Modular forms 888 888 0
Cusp forms 840 840 0
Eisenstein series 48 48 0

## Trace form

 $$840q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 6q^{8} + O(q^{10})$$ $$840q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 6q^{8} - 6q^{10} - 12q^{11} - 30q^{12} - 12q^{13} - 12q^{14} - 24q^{15} - 12q^{16} - 12q^{17} - 12q^{18} - 6q^{19} - 54q^{20} - 12q^{21} - 12q^{22} + 18q^{24} - 24q^{26} - 12q^{27} - 24q^{28} - 12q^{29} - 12q^{30} - 24q^{31} - 12q^{32} - 24q^{33} - 6q^{35} - 12q^{36} - 6q^{37} - 12q^{38} - 12q^{40} - 72q^{42} - 12q^{43} - 6q^{44} - 12q^{45} - 6q^{46} - 24q^{47} - 12q^{48} - 24q^{49} - 168q^{50} + 6q^{51} - 12q^{52} - 24q^{53} + 156q^{54} - 54q^{56} + 42q^{58} - 48q^{59} - 72q^{60} - 12q^{61} + 60q^{62} - 24q^{63} - 6q^{64} - 24q^{65} - 198q^{66} - 12q^{67} - 66q^{68} - 12q^{69} - 54q^{70} - 144q^{72} - 96q^{74} - 96q^{75} - 12q^{76} - 12q^{77} - 90q^{78} - 24q^{79} - 204q^{80} - 24q^{81} - 24q^{82} + 48q^{83} + 36q^{84} + 18q^{85} - 72q^{86} - 12q^{88} - 66q^{90} - 6q^{91} + 102q^{92} - 12q^{93} - 12q^{94} - 24q^{95} - 120q^{96} - 24q^{97} - 6q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(432, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
432.2.bg.a $$840$$ $$3.450$$ None $$-12$$ $$-12$$ $$-12$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database