# Properties

 Label 547.2.j Level 547 Weight 2 Character orbit j Rep. character $$\chi_{547}(11,\cdot)$$ Character field $$\Q(\zeta_{39})$$ Dimension 1080 Newform subspaces 1 Sturm bound 91 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$547$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 547.j (of order $$39$$ and degree $$24$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$547$$ Character field: $$\Q(\zeta_{39})$$ Newform subspaces: $$1$$ Sturm bound: $$91$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(547, [\chi])$$.

Total New Old
Modular forms 1128 1128 0
Cusp forms 1080 1080 0
Eisenstein series 48 48 0

## Trace form

 $$1080q - 25q^{2} - 74q^{3} + 21q^{4} - 27q^{5} - 75q^{6} - 28q^{7} + 4q^{8} + 1010q^{9} + O(q^{10})$$ $$1080q - 25q^{2} - 74q^{3} + 21q^{4} - 27q^{5} - 75q^{6} - 28q^{7} + 4q^{8} + 1010q^{9} - 16q^{10} - 14q^{11} - 69q^{12} - 10q^{13} - 15q^{14} - 97q^{15} + 39q^{16} - 22q^{17} - 145q^{18} - 24q^{19} - 51q^{20} - 77q^{21} - 19q^{22} - 53q^{23} - 45q^{24} + 40q^{25} - 68q^{26} - 278q^{27} - 50q^{28} + 39q^{29} + 14q^{30} - 2q^{31} - 45q^{32} - 105q^{33} - 98q^{34} - 18q^{35} - 172q^{36} - 16q^{37} - 37q^{38} + 30q^{39} - 33q^{40} + 62q^{41} + 170q^{42} + 12q^{43} - 22q^{44} - 128q^{45} + 79q^{46} - 58q^{47} - 27q^{48} + 17q^{49} - 40q^{50} - 39q^{51} + 97q^{52} + 17q^{53} - 278q^{54} + 9q^{55} + 47q^{56} - 174q^{57} - 134q^{58} - 126q^{59} - 414q^{60} - 79q^{61} + 15q^{62} - 398q^{63} - 308q^{64} + 47q^{65} - 142q^{66} + 22q^{67} + 7q^{68} - 77q^{69} + 396q^{70} - 22q^{71} - 172q^{72} + 9q^{73} - 43q^{74} - 143q^{75} + 46q^{76} + 56q^{77} - 33q^{78} + 72q^{79} + 131q^{80} + 944q^{81} + 74q^{82} + 41q^{83} - 582q^{84} - 66q^{85} + 20q^{86} - 182q^{87} - 459q^{88} - 92q^{89} - 265q^{90} + 65q^{91} + 86q^{92} - 28q^{93} - 17q^{94} + 37q^{95} - 70q^{96} + 91q^{97} + 139q^{98} - 237q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(547, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
547.2.j.a $$1080$$ $$4.368$$ None $$-25$$ $$-74$$ $$-27$$ $$-28$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database