# Properties

 Label 65.2.n Level 65 Weight 2 Character orbit n Rep. character $$\chi_{65}(9,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 12 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.n (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$65$$ Character field: $$\Q(\zeta_{6})$$ 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 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

## Trace form

 $$12q + 4q^{4} - 6q^{5} - 10q^{6} + 6q^{9} + O(q^{10})$$ $$12q + 4q^{4} - 6q^{5} - 10q^{6} + 6q^{9} + 7q^{10} - 44q^{14} - 4q^{15} - 16q^{16} + 12q^{19} - q^{20} - 8q^{21} + 32q^{24} - 2q^{25} + 24q^{26} + 18q^{29} + 4q^{30} - 16q^{31} + 16q^{34} + 10q^{35} - 2q^{36} - 32q^{39} + 70q^{40} + 14q^{41} - 4q^{44} - 29q^{45} + 10q^{46} + 6q^{49} - 31q^{50} + 24q^{51} - 22q^{54} - 26q^{55} - 16q^{56} - 4q^{59} - 96q^{60} + 6q^{61} - 12q^{64} + 23q^{65} + 4q^{66} - 24q^{69} + 20q^{70} - 12q^{71} + 8q^{74} + 2q^{75} - 10q^{76} - 104q^{79} + 33q^{80} + 14q^{81} + 90q^{84} + 21q^{85} - 4q^{86} + 20q^{89} + 62q^{90} - 44q^{91} + 56q^{94} + 20q^{95} + 12q^{96} + 104q^{99} + O(q^{100})$$

## 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.n.a $$12$$ $$0.519$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-6$$ $$0$$ $$q-\beta _{4}q^{2}+(\beta _{4}-\beta _{11})q^{3}+(-\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots$$