# Properties

 Label 547.2.h Level 547 Weight 2 Character orbit h Rep. character $$\chi_{547}(13,\cdot)$$ Character field $$\Q(\zeta_{21})$$ Dimension 540 Newform subspaces 1 Sturm bound 91 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$547$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 547.h (of order $$21$$ and degree $$12$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$547$$ Character field: $$\Q(\zeta_{21})$$ 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 564 564 0
Cusp forms 540 540 0
Eisenstein series 24 24 0

## Trace form

 $$540q - 13q^{2} - 10q^{3} + 33q^{4} - 15q^{5} + 10q^{6} - 2q^{7} - 26q^{8} - 96q^{9} + O(q^{10})$$ $$540q - 13q^{2} - 10q^{3} + 33q^{4} - 15q^{5} + 10q^{6} - 2q^{7} - 26q^{8} - 96q^{9} - 4q^{10} - 8q^{11} - 18q^{12} - 11q^{13} + 5q^{14} - 7q^{15} + 53q^{16} - 10q^{17} - 59q^{18} - 12q^{19} - 18q^{20} + 20q^{21} + 70q^{22} - 15q^{23} - 46q^{24} + 26q^{25} - 39q^{26} - q^{27} - 56q^{28} - 40q^{29} - 100q^{30} + 59q^{31} - 5q^{32} - 15q^{33} - 8q^{34} + 36q^{35} + 43q^{36} - 32q^{37} - 108q^{38} + 34q^{39} - 27q^{40} + 39q^{41} + 46q^{42} - 16q^{43} - 110q^{44} - 103q^{45} + 12q^{46} - 60q^{47} + 42q^{48} + 57q^{49} - 168q^{50} + 57q^{51} - 46q^{52} - 30q^{53} + 113q^{54} + 38q^{55} + 64q^{56} + 22q^{57} - 88q^{58} + 55q^{59} + 9q^{60} + 26q^{61} - 32q^{62} + 6q^{63} - 50q^{64} + 73q^{65} + 72q^{66} - 104q^{67} - 181q^{68} - 125q^{69} - 50q^{70} + 39q^{71} - 434q^{72} + 46q^{73} - 178q^{74} + 248q^{75} - 126q^{76} - 52q^{77} - 82q^{78} + 86q^{79} + 208q^{80} - 4q^{81} + 177q^{82} + 39q^{83} + 124q^{84} - 12q^{85} + 2q^{86} + 162q^{87} - 34q^{88} + 63q^{89} + 121q^{90} + 21q^{91} + q^{92} - 57q^{93} + 67q^{94} - 143q^{95} + 489q^{96} + 119q^{97} - 10q^{98} - 120q^{99} + O(q^{100})$$

## 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.h.a $$540$$ $$4.368$$ None $$-13$$ $$-10$$ $$-15$$ $$-2$$

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database