# Properties

 Label 403.2.g Level 403 Weight 2 Character orbit g Rep. character $$\chi_{403}(87,\cdot)$$ Character field $$\Q(\zeta_{3})$$ Dimension 70 Newform subspaces 1 Sturm bound 74 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.g (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ 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 78 78 0
Cusp forms 70 70 0
Eisenstein series 8 8 0

## Trace form

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

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
403.2.g.a $$70$$ $$3.218$$ None $$-2$$ $$-8$$ $$-2$$ $$-4$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database