# Properties

 Label 43.8.g Level 43 Weight 8 Character orbit g Rep. character $$\chi_{43}(9,\cdot)$$ Character field $$\Q(\zeta_{21})$$ Dimension 300 Newform subspaces 1 Sturm bound 29 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$8$$ Character orbit: $$[\chi]$$ $$=$$ 43.g (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$43$$ Character field: $$\Q(\zeta_{21})$$ Newform subspaces: $$1$$ Sturm bound: $$29$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{8}(43, [\chi])$$.

Total New Old
Modular forms 324 324 0
Cusp forms 300 300 0
Eisenstein series 24 24 0

## Trace form

 $$300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} + O(q^{10})$$ $$300q - 40q^{2} - 12q^{3} - 3028q^{4} + 235q^{5} + 1274q^{6} - 4122q^{7} + 762q^{8} + 8097q^{9} - 1681q^{10} + 4580q^{11} + 9330q^{12} - 20444q^{13} - 45798q^{14} + 50477q^{15} - 74504q^{16} - 25312q^{17} + 2046q^{18} + 4046q^{19} + 140781q^{20} + 100555q^{21} + 95810q^{22} + 1648q^{23} - 292592q^{24} + 419068q^{25} + 393435q^{26} + 274140q^{27} + 233644q^{28} + 605697q^{29} - 1216016q^{30} + 358580q^{31} - 19194q^{32} + 1280291q^{33} + 1137255q^{34} + 652739q^{35} - 8980975q^{36} - 2360047q^{37} - 308490q^{38} + 536339q^{39} + 3057993q^{40} - 1376320q^{41} + 8417790q^{42} + 7173000q^{43} - 3856780q^{44} + 2761486q^{45} - 7073993q^{46} + 1437090q^{47} - 9543469q^{48} - 16053170q^{49} - 3046893q^{50} + 2972901q^{51} + 17415142q^{52} + 3320604q^{53} + 6000486q^{54} + 13427750q^{55} - 5450793q^{56} + 3333100q^{57} - 7876190q^{58} - 7084765q^{59} + 7356443q^{60} + 3354606q^{61} - 719427q^{62} + 14716815q^{63} - 16086234q^{64} - 19914646q^{65} - 8293345q^{66} + 13025470q^{67} - 22191927q^{68} - 33964295q^{69} + 8094727q^{70} + 30843495q^{71} + 93841607q^{72} - 3067637q^{73} + 18179570q^{74} - 41508571q^{75} - 19751872q^{76} - 15169179q^{77} - 69509396q^{78} - 12090149q^{79} - 69662530q^{80} + 3387954q^{81} + 39226888q^{82} + 16408777q^{83} + 98603231q^{84} - 13423424q^{85} + 111906660q^{86} + 49022010q^{87} + 76213954q^{88} - 12540205q^{89} - 92608607q^{90} - 59091937q^{91} - 50489370q^{92} - 52218334q^{93} - 3441600q^{94} - 79947551q^{95} - 23449784q^{96} - 116467587q^{97} + 73909552q^{98} - 20061115q^{99} + O(q^{100})$$

## Decomposition of $$S_{8}^{\mathrm{new}}(43, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
43.8.g.a $$300$$ $$13.433$$ None $$-40$$ $$-12$$ $$235$$ $$-4122$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database