# Properties

 Label 547.2.f Level 547 Weight 2 Character orbit f Rep. character $$\chi_{547}(46,\cdot)$$ Character field $$\Q(\zeta_{13})$$ Dimension 528 Newform subspaces 1 Sturm bound 91 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$547$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 547.f (of order $$13$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$547$$ Character field: $$\Q(\zeta_{13})$$ 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 552 552 0
Cusp forms 528 528 0
Eisenstein series 24 24 0

## Trace form

 $$528q - 8q^{2} - 46q^{3} - 50q^{4} - 9q^{5} - 21q^{6} - 3q^{7} + 14q^{8} + 466q^{9} + O(q^{10})$$ $$528q - 8q^{2} - 46q^{3} - 50q^{4} - 9q^{5} - 21q^{6} - 3q^{7} + 14q^{8} + 466q^{9} + 7q^{10} - 16q^{11} - 53q^{12} - 12q^{13} - 38q^{15} - 38q^{16} + 7q^{17} - 23q^{18} + 5q^{19} + 45q^{20} + 4q^{21} + 43q^{22} + 2q^{23} - 51q^{24} - 69q^{25} - 4q^{26} - 142q^{27} - 2q^{28} - 72q^{29} - 50q^{30} + 25q^{31} + 66q^{32} - 4q^{34} + 33q^{35} - 55q^{36} + 21q^{37} + 40q^{38} - 142q^{39} + 78q^{40} - 140q^{41} - 248q^{42} + 23q^{43} + 64q^{44} - 163q^{45} + 14q^{46} + 37q^{47} - 35q^{48} + q^{49} + 70q^{50} - 72q^{51} - 74q^{52} - 17q^{53} - 76q^{54} + 6q^{55} - 38q^{56} + 5q^{57} + 29q^{58} + 30q^{59} - 108q^{60} - 94q^{61} - 75q^{62} - 77q^{63} - 252q^{64} - 122q^{65} + 79q^{66} + 43q^{67} - 193q^{68} + 14q^{69} - 267q^{70} + 61q^{71} + 49q^{72} + 11q^{73} + 85q^{74} + 120q^{75} - 23q^{76} + 31q^{77} - 90q^{78} + 65q^{79} + 58q^{80} + 280q^{81} + 10q^{82} - 8q^{83} - 136q^{84} + 33q^{85} + 91q^{86} - 70q^{87} - 198q^{88} + 41q^{89} - 68q^{90} + 38q^{91} + 43q^{92} + 132q^{93} + 8q^{94} - 49q^{95} + 262q^{96} - 14q^{97} + 41q^{98} - 36q^{99} + O(q^{100})$$

## 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.f.a $$528$$ $$4.368$$ None $$-8$$ $$-46$$ $$-9$$ $$-3$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database