# Properties

 Label 403.2.bt Level 403 Weight 2 Character orbit bt Rep. character $$\chi_{403}(82,\cdot)$$ 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.bt (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

 $$280q - 9q^{2} - 3q^{3} - 35q^{4} - 15q^{7} + 45q^{8} + 24q^{9} + O(q^{10})$$ $$280q - 9q^{2} - 3q^{3} - 35q^{4} - 15q^{7} + 45q^{8} + 24q^{9} + 3q^{10} - 8q^{12} - 6q^{13} + 4q^{14} - 45q^{15} + 23q^{16} + 27q^{17} + 45q^{18} - 15q^{19} - 12q^{20} - 76q^{21} + 41q^{22} - 10q^{23} - 33q^{24} + 96q^{25} + 9q^{26} - 24q^{27} - 32q^{28} + 13q^{29} + 36q^{30} + 2q^{31} - 141q^{32} - 93q^{33} - 9q^{34} - 43q^{35} - 194q^{36} + 3q^{37} - 49q^{38} + 50q^{39} - 75q^{40} - 15q^{41} + 17q^{42} + 33q^{43} + 18q^{44} - 15q^{45} - 9q^{46} - 59q^{48} + 3q^{49} + 36q^{50} + 47q^{51} - 56q^{52} + 12q^{53} - 33q^{54} - 5q^{55} - 50q^{56} - 105q^{57} - 3q^{58} - 15q^{59} + 90q^{60} - 57q^{61} - 72q^{62} + 201q^{63} + 13q^{64} - 43q^{65} + 22q^{66} - 71q^{68} - 7q^{69} - 42q^{71} + 90q^{72} + 9q^{73} - 113q^{74} + 45q^{75} + 14q^{76} - 24q^{77} + 61q^{78} + 54q^{79} + 30q^{80} + 106q^{81} + 16q^{82} + 54q^{83} + 60q^{84} + 18q^{85} + 84q^{86} + 42q^{87} - 98q^{88} - 99q^{89} + 11q^{90} + 60q^{91} + 266q^{92} - 104q^{93} + 33q^{94} - 120q^{95} + 204q^{96} - 50q^{97} - 15q^{98} - 168q^{99} + O(q^{100})$$

## 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.bt.a $$280$$ $$3.218$$ None $$-9$$ $$-3$$ $$0$$ $$-15$$