# Properties

 Label 65.2.t Level 65 Weight 2 Character orbit t Rep. character $$\chi_{65}(7,\cdot)$$ 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.t (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

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

## 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.t.a $$20$$ $$0.519$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$-6$$ $$-2$$ $$0$$ $$-2$$ $$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$$