# Properties

 Label 403.2.ch Level 403 Weight 2 Character orbit ch Rep. character $$\chi_{403}(11,\cdot)$$ Character field $$\Q(\zeta_{60})$$ Dimension 560 Newforms 1 Sturm bound 74 Trace bound 0

# Learn more about

## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.ch (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{60})$$ Newforms: $$1$$ Sturm bound: $$74$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(403, [\chi])$$.

Total New Old
Modular forms 624 624 0
Cusp forms 560 560 0
Eisenstein series 64 64 0

## Trace form

 $$560q - 12q^{2} - 10q^{3} - 18q^{4} - 8q^{5} - 36q^{6} - 32q^{7} + 50q^{8} + 114q^{9} + O(q^{10})$$ $$560q - 12q^{2} - 10q^{3} - 18q^{4} - 8q^{5} - 36q^{6} - 32q^{7} + 50q^{8} + 114q^{9} - 24q^{10} - 18q^{11} - 26q^{12} + 6q^{13} + 4q^{14} - 8q^{15} - 58q^{16} - 30q^{17} + 44q^{18} - 30q^{19} + 10q^{20} - 42q^{21} - 60q^{22} - 30q^{23} + 32q^{24} + 24q^{26} - 100q^{27} - 66q^{28} - 10q^{29} - 12q^{31} + 20q^{32} + 70q^{33} + 28q^{34} - 2q^{35} - 78q^{36} - 38q^{37} + 108q^{38} - 22q^{39} - 28q^{40} - 10q^{41} - 40q^{42} - 126q^{43} + 60q^{44} - 120q^{45} - 4q^{46} - 32q^{47} - 64q^{48} + 78q^{49} - 150q^{50} - 36q^{51} - 26q^{52} - 84q^{53} - 62q^{54} - 10q^{55} + 216q^{56} + 22q^{57} - 158q^{58} - 50q^{59} - 152q^{60} - 36q^{61} - 42q^{62} + 78q^{63} - 270q^{64} + 54q^{65} - 56q^{66} - 46q^{67} + 162q^{69} + 90q^{70} + 34q^{71} - 42q^{72} - 40q^{73} + 80q^{74} - 38q^{75} + 10q^{76} - 72q^{77} + 6q^{78} - 32q^{79} + 78q^{80} - 62q^{81} - 30q^{82} + 16q^{83} + 126q^{84} - 42q^{85} + 154q^{86} - 56q^{87} - 54q^{88} - 46q^{89} + 90q^{90} + 134q^{91} - 12q^{93} - 24q^{94} - 78q^{95} - 136q^{96} + 204q^{97} - 130q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(403, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
403.2.ch.a $$560$$ $$3.218$$ None $$-12$$ $$-10$$ $$-8$$ $$-32$$