# Properties

 Label 403.2.bj Level 403 Weight 2 Character orbit bj Rep. character $$\chi_{403}(100,\cdot)$$ Character field $$\Q(\zeta_{15})$$ Dimension 280 Newforms 1 Sturm bound 74 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$403 = 13 \cdot 31$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 403.bj (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{15})$$ 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 312 312 0
Cusp forms 280 280 0
Eisenstein series 32 32 0

## Trace form

 $$280q - 3q^{2} + 3q^{3} + 29q^{4} - 8q^{5} + 5q^{6} - q^{7} - 29q^{8} - 63q^{9} + O(q^{10})$$ $$280q - 3q^{2} + 3q^{3} + 29q^{4} - 8q^{5} + 5q^{6} - q^{7} - 29q^{8} - 63q^{9} + 12q^{10} + 3q^{11} - 50q^{12} - 24q^{13} + 24q^{15} + 23q^{16} - 9q^{17} - 15q^{18} - 3q^{19} - 75q^{20} - 34q^{21} - 22q^{22} - 12q^{23} + 43q^{24} - 112q^{25} - 21q^{26} + 48q^{27} + 33q^{28} - 11q^{29} + 24q^{30} - 22q^{31} + q^{32} + 53q^{33} - 49q^{34} - 34q^{35} - 67q^{36} - 34q^{37} - 23q^{38} - 25q^{39} + 31q^{40} + 7q^{41} + 28q^{42} + 41q^{43} - 42q^{44} - q^{45} - 39q^{46} - 20q^{47} + 84q^{48} + 42q^{49} + 24q^{50} - 71q^{51} + 109q^{52} - 8q^{53} + 31q^{54} + 35q^{55} + 63q^{56} + 21q^{57} - 191q^{58} - 46q^{59} + 2q^{60} + 53q^{61} + 18q^{62} + 17q^{63} - 91q^{64} + 47q^{65} - 62q^{66} + 7q^{67} - 166q^{68} + 53q^{69} + 134q^{70} - 79q^{71} + 65q^{72} - 31q^{73} + 12q^{74} + 73q^{75} - 46q^{76} - 80q^{77} + 114q^{78} - 142q^{79} + 87q^{80} - 27q^{81} - 9q^{82} + 94q^{83} + 85q^{84} - 45q^{85} - 34q^{86} - 11q^{87} + 61q^{88} + 75q^{89} + 43q^{90} - 104q^{91} - 294q^{92} + 26q^{93} - 57q^{94} - 101q^{95} + 24q^{96} + 46q^{97} - 146q^{98} + 12q^{99} + O(q^{100})$$

## 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.bj.a $$280$$ $$3.218$$ None $$-3$$ $$3$$ $$-8$$ $$-1$$