# Properties

 Label 287.2.s Level 287 Weight 2 Character orbit s Rep. character $$\chi_{287}(16,\cdot)$$ Character field $$\Q(\zeta_{15})$$ Dimension 208 Newforms 1 Sturm bound 56 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$287 = 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 287.s (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$287$$ Character field: $$\Q(\zeta_{15})$$ Newforms: $$1$$ Sturm bound: $$56$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(287, [\chi])$$.

Total New Old
Modular forms 240 240 0
Cusp forms 208 208 0
Eisenstein series 32 32 0

## Trace form

 $$208q - 3q^{2} - 8q^{3} + 21q^{4} - 7q^{5} - 8q^{6} - 6q^{7} - 32q^{8} - 92q^{9} + O(q^{10})$$ $$208q - 3q^{2} - 8q^{3} + 21q^{4} - 7q^{5} - 8q^{6} - 6q^{7} - 32q^{8} - 92q^{9} - 24q^{10} + q^{11} + 19q^{12} - 12q^{13} - 62q^{14} - 6q^{15} + 21q^{16} + 3q^{17} + q^{19} - 48q^{20} + 20q^{21} - 68q^{22} - 6q^{23} - 18q^{24} + 3q^{25} + 15q^{26} + 28q^{27} - 11q^{28} + 44q^{29} - 5q^{30} - 11q^{31} - 6q^{32} + 10q^{33} - 108q^{34} - 30q^{35} + 66q^{36} - 32q^{37} - 10q^{38} - 2q^{39} + 70q^{40} - 6q^{41} + 24q^{42} - 8q^{43} - 68q^{44} + 12q^{45} - 66q^{46} + 31q^{47} + 110q^{48} + 10q^{49} + 64q^{50} - 2q^{51} + 69q^{52} - 42q^{53} + 43q^{54} - 80q^{55} + 10q^{56} - 30q^{57} - q^{58} - 29q^{59} + 22q^{60} - 9q^{61} + 30q^{62} + 54q^{63} - 4q^{64} - 14q^{65} + 78q^{66} + q^{67} - 42q^{68} + 46q^{69} - 179q^{70} - 10q^{71} - 13q^{72} + 30q^{73} + 61q^{74} + 52q^{75} + 118q^{76} - 56q^{77} - 94q^{78} + 2q^{79} - 17q^{80} - 16q^{81} - 21q^{82} - 208q^{83} - 33q^{84} + 36q^{85} + 39q^{86} + 10q^{87} + 24q^{88} - 89q^{89} + 242q^{90} + 18q^{91} - 10q^{92} + 71q^{93} + 81q^{94} - 83q^{95} - 64q^{96} - 24q^{97} + 26q^{98} - 12q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(287, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
287.2.s.a $$208$$ $$2.292$$ None $$-3$$ $$-8$$ $$-7$$ $$-6$$