# Properties

 Label 65.2.o Level 65 Weight 2 Character orbit o Rep. character $$\chi_{65}(2,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 20 Newforms 1 Sturm bound 14 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$65 = 5 \cdot 13$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 65.o (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$65$$ Character field: $$\Q(\zeta_{12})$$ Newforms: $$1$$ Sturm bound: $$14$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(65, [\chi])$$.

Total New Old
Modular forms 36 36 0
Cusp forms 20 20 0
Eisenstein series 16 16 0

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(65, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
65.2.o.a $$20$$ $$0.519$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$-4$$ $$-2$$ $$-6$$ $$-6$$ $$q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}+\cdots)q^{3}+\cdots$$