# Properties

 Label 287.2.r Level 287 Weight 2 Character orbit r Rep. character $$\chi_{287}(9,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 104 Newforms 3 Sturm bound 56 Trace bound 3

# Related objects

## Defining parameters

 Level: $$N$$ = $$287 = 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 287.r (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$287$$ Character field: $$\Q(\zeta_{12})$$ Newforms: $$3$$ Sturm bound: $$56$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$3$$

## Dimensions

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

Total New Old
Modular forms 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

## Trace form

 $$104q - 2q^{3} + 44q^{4} - 24q^{6} - 4q^{7} + O(q^{10})$$ $$104q - 2q^{3} + 44q^{4} - 24q^{6} - 4q^{7} - 28q^{10} + 2q^{11} + 14q^{12} - 8q^{13} + 10q^{14} - 8q^{15} - 36q^{16} - 8q^{17} - 20q^{18} - 6q^{19} - 8q^{22} - 4q^{23} - 36q^{24} + 32q^{25} + 8q^{26} - 8q^{27} - 28q^{28} - 32q^{29} + 8q^{30} + 28q^{31} + 16q^{34} + 2q^{35} - 16q^{38} + 80q^{40} - 56q^{41} - 72q^{42} + 6q^{44} - 4q^{45} + 18q^{47} - 20q^{48} - 32q^{51} + 10q^{52} - 8q^{53} + 18q^{54} - 24q^{55} + 6q^{56} + 72q^{57} + 4q^{58} - 44q^{59} + 48q^{60} + 10q^{63} - 72q^{64} - 12q^{65} + 68q^{66} + 14q^{67} - 18q^{68} + 16q^{69} - 22q^{70} - 8q^{71} + 100q^{72} - 58q^{75} - 88q^{76} - 120q^{78} - 20q^{79} - 40q^{81} - 6q^{82} + 48q^{83} - 116q^{85} + 44q^{86} + 20q^{89} - 128q^{92} - 74q^{93} + 100q^{94} + 42q^{95} + 14q^{96} + 44q^{97} - 116q^{98} - 96q^{99} + O(q^{100})$$

## 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.r.a $$4$$ $$2.292$$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$-6$$ $$10$$ $$q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots$$
287.2.r.b $$4$$ $$2.292$$ $$\Q(\zeta_{12})$$ None $$0$$ $$4$$ $$6$$ $$0$$ $$q+\zeta_{12}q^{2}+(1+\zeta_{12})q^{3}-\zeta_{12}^{2}q^{4}+\cdots$$
287.2.r.c $$96$$ $$2.292$$ None $$0$$ $$-4$$ $$0$$ $$-14$$