Properties

 Label 287.2.z Level 287 Weight 2 Character orbit z Rep. character $$\chi_{287}(4,\cdot)$$ Character field $$\Q(\zeta_{30})$$ 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.z (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$287$$ Character field: $$\Q(\zeta_{30})$$ 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

 $$208q - 3q^{2} + 21q^{4} + q^{5} - 40q^{6} - 10q^{7} - 8q^{8} + 84q^{9} + O(q^{10})$$ $$208q - 3q^{2} + 21q^{4} + q^{5} - 40q^{6} - 10q^{7} - 8q^{8} + 84q^{9} - 6q^{10} - 5q^{11} - 35q^{12} - 20q^{13} - 50q^{15} + 21q^{16} - 5q^{17} + 18q^{18} - 5q^{19} - 96q^{20} + 8q^{21} + 20q^{22} + 40q^{24} + 27q^{25} - 5q^{26} + 5q^{28} + 20q^{29} - 45q^{30} - 11q^{31} - 30q^{32} - 10q^{33} + 100q^{34} - 106q^{36} - 16q^{37} - 4q^{39} + 6q^{40} - 14q^{41} - 8q^{42} - 8q^{43} + 34q^{45} - 32q^{46} + 25q^{47} - 50q^{48} + 14q^{49} - 120q^{50} + 2q^{51} - 105q^{52} + 20q^{53} - 35q^{54} + 100q^{56} - 98q^{57} - 5q^{58} - 37q^{59} - 100q^{60} + 51q^{61} - 70q^{62} - 30q^{63} - 100q^{64} + 40q^{65} - 176q^{66} + 15q^{67} - 30q^{69} + 105q^{70} - 10q^{71} - 33q^{72} - 34q^{73} - 23q^{74} - 120q^{75} + 110q^{76} + 72q^{77} - 18q^{78} + 127q^{80} - 24q^{81} - 63q^{82} - 128q^{83} + 33q^{84} - 61q^{86} + 28q^{87} + 150q^{88} + 35q^{89} - 34q^{90} + 14q^{91} + 102q^{92} - 55q^{93} - 155q^{94} + 55q^{95} + 20q^{97} + 88q^{98} + 120q^{99} + O(q^{100})$$

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.z.a $$208$$ $$2.292$$ None $$-3$$ $$0$$ $$1$$ $$-10$$