# Properties

 Label 287.2.w Level 287 Weight 2 Character orbit w Rep. character $$\chi_{287}(3,\cdot)$$ Character field $$\Q(\zeta_{24})$$ 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.w (of order $$24$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$287$$ Character field: $$\Q(\zeta_{24})$$ 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

 $$208q - 4q^{2} - 12q^{3} - 12q^{5} - 8q^{7} - 32q^{8} + 4q^{9} + O(q^{10})$$ $$208q - 4q^{2} - 12q^{3} - 12q^{5} - 8q^{7} - 32q^{8} + 4q^{9} - 24q^{10} - 4q^{11} - 12q^{12} - 4q^{14} + 8q^{15} + 72q^{16} + 24q^{17} - 8q^{18} + 12q^{19} - 48q^{21} - 96q^{22} - 60q^{24} - 36q^{26} - 24q^{28} + 16q^{29} - 36q^{30} + 48q^{32} + 48q^{33} + 32q^{35} - 80q^{36} + 16q^{37} + 72q^{38} - 4q^{39} + 80q^{42} - 64q^{43} - 12q^{44} - 44q^{46} + 12q^{47} - 72q^{49} - 8q^{50} + 16q^{51} + 12q^{52} - 28q^{53} - 180q^{54} - 32q^{56} - 16q^{57} - 24q^{59} - 4q^{60} - 12q^{61} + 36q^{63} - 8q^{65} + 4q^{67} - 84q^{68} + 20q^{70} + 32q^{71} - 48q^{73} + 40q^{74} + 168q^{75} - 104q^{77} - 48q^{78} - 120q^{80} + 132q^{82} + 112q^{84} + 64q^{85} - 144q^{87} - 32q^{88} + 36q^{89} - 56q^{91} + 16q^{92} + 4q^{93} + 96q^{94} - 4q^{95} + 12q^{96} - 136q^{98} - 224q^{99} + O(q^{100})$$

## 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.w.a $$208$$ $$2.292$$ None $$-4$$ $$-12$$ $$-12$$ $$-8$$