# Properties

 Label 403.2.bp Level 403 Weight 2 Character orbit bp Rep. character $$\chi_{403}(10,\cdot)$$ Character field $$\Q(\zeta_{30})$$ 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.bp (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$403$$ Character field: $$\Q(\zeta_{30})$$ 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

 $$280q - 9q^{2} - 9q^{3} - 35q^{4} - 21q^{6} - 3q^{7} - 45q^{8} - 63q^{9} + O(q^{10})$$ $$280q - 9q^{2} - 9q^{3} - 35q^{4} - 21q^{6} - 3q^{7} - 45q^{8} - 63q^{9} - 24q^{10} - 9q^{11} - 8q^{12} - 6q^{13} + 4q^{14} + 23q^{16} - 21q^{17} - 45q^{18} - 27q^{19} - 75q^{20} + 76q^{21} - 22q^{22} - 10q^{23} - 15q^{24} + 96q^{25} - 15q^{26} - 24q^{27} + 5q^{28} + 13q^{29} + 36q^{30} - 2q^{31} - 141q^{32} - 3q^{33} + 9q^{34} + 32q^{35} + 97q^{36} - 49q^{38} + 15q^{39} - 75q^{40} - 33q^{41} - 16q^{42} + 21q^{43} - 18q^{44} - 27q^{45} + 51q^{46} - 68q^{48} - 24q^{49} + 90q^{50} + 47q^{51} + 73q^{52} + 12q^{53} - 33q^{54} - 65q^{55} + 25q^{56} + 105q^{57} - 3q^{58} + 12q^{59} - 90q^{60} - 57q^{61} + 12q^{62} + 201q^{63} + 13q^{64} + 11q^{65} + 22q^{66} - 45q^{67} + 142q^{68} - 139q^{69} - 15q^{71} - 15q^{72} - 9q^{73} + 4q^{74} - 75q^{75} - 80q^{76} - 24q^{77} - 104q^{78} + 54q^{79} - 21q^{80} - 107q^{81} + 43q^{82} - 54q^{83} - 15q^{84} - 117q^{85} - 84q^{86} - 21q^{87} + 49q^{88} - 9q^{89} + 11q^{90} - 10q^{91} + 266q^{92} - 22q^{93} + 33q^{94} + 75q^{95} - 204q^{96} - 10q^{97} + 168q^{99} + O(q^{100})$$

## 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.bp.a $$280$$ $$3.218$$ None $$-9$$ $$-9$$ $$0$$ $$-3$$