# Properties

 Label 9.12.c Level 9 Weight 12 Character orbit c Rep. character $$\chi_{9}(4,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 20 Newforms 1 Sturm bound 12 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$9 = 3^{2}$$ Weight: $$k$$ = $$12$$ Character orbit: $$[\chi]$$ = 9.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$9$$ Character field: $$\Q(\zeta_{3})$$ Newforms: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{12}(9, [\chi])$$.

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

## Trace form

 $$20q - 33q^{2} - 12q^{3} - 9217q^{4} - 7230q^{5} + 20583q^{6} + 8512q^{7} - 29118q^{8} + 135504q^{9} + O(q^{10})$$ $$20q - 33q^{2} - 12q^{3} - 9217q^{4} - 7230q^{5} + 20583q^{6} + 8512q^{7} - 29118q^{8} + 135504q^{9} + 4092q^{10} - 112776q^{11} + 1027860q^{12} + 279706q^{13} - 3901584q^{14} - 6358608q^{15} - 7342081q^{16} + 27765792q^{17} + 8682876q^{18} + 7029400q^{19} - 34163508q^{20} + 55012206q^{21} + 2274591q^{22} - 69371616q^{23} - 211100355q^{24} - 45286204q^{25} + 481929144q^{26} - 83699352q^{27} - 61345796q^{28} - 25437246q^{29} - 23582592q^{30} + 114575368q^{31} + 80396559q^{32} + 31338342q^{33} - 243855063q^{34} - 178147464q^{35} - 19984653q^{36} - 134218328q^{37} + 489799995q^{38} - 1999064976q^{39} + 107425416q^{40} + 331873026q^{41} + 4171968882q^{42} - 1118847584q^{43} + 278477274q^{44} + 1749349170q^{45} + 2882537592q^{46} - 1469650704q^{47} - 9335236125q^{48} - 3553434720q^{49} - 6643771701q^{50} + 1736777052q^{51} + 3632448874q^{52} + 14914261944q^{53} + 18127857753q^{54} + 4981449984q^{55} - 27669139026q^{56} - 7855424196q^{57} - 1387480560q^{58} - 26505032592q^{59} - 10283356116q^{60} + 990409066q^{61} + 91044996180q^{62} + 51565206888q^{63} - 7516709566q^{64} - 39045315390q^{65} - 93201828246q^{66} + 6557215720q^{67} - 77299152993q^{68} + 6907292550q^{69} - 785437278q^{70} + 122053719744q^{71} + 161899013547q^{72} - 12612893936q^{73} - 109519086216q^{74} - 218383044348q^{75} + 14574055597q^{76} - 88616208018q^{77} + 150319870614q^{78} - 7621233248q^{79} + 399166683072q^{80} + 222307104312q^{81} - 59168477334q^{82} - 99007044180q^{83} - 711968015814q^{84} + 12911595156q^{85} - 214357830519q^{86} + 99715491216q^{87} - 54423523605q^{88} + 476597704824q^{89} + 620021743884q^{90} + 138211652216q^{91} - 461776423998q^{92} - 572981484354q^{93} + 13393667064q^{94} - 418952909328q^{95} + 118587589272q^{96} + 123483551938q^{97} + 1310123604078q^{98} + 621154334268q^{99} + O(q^{100})$$

## Decomposition of $$S_{12}^{\mathrm{new}}(9, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
9.12.c.a $$20$$ $$6.915$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$-33$$ $$-12$$ $$-7230$$ $$8512$$ $$q+(\beta _{1}-3\beta _{3})q^{2}+(24-51\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots$$