# Properties

 Label 65.2.k Level $65$ Weight $2$ Character orbit 65.k Rep. character $\chi_{65}(8,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $10$ Newform subspaces $2$ Sturm bound $14$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$65 = 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 65.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$65$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$14$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 18 18 0
Cusp forms 10 10 0
Eisenstein series 8 8 0

## Trace form

 $$10q - 2q^{2} - 4q^{3} + 6q^{4} - 4q^{6} - 6q^{8} + O(q^{10})$$ $$10q - 2q^{2} - 4q^{3} + 6q^{4} - 4q^{6} - 6q^{8} - 8q^{10} + 4q^{11} + 4q^{13} - 10q^{16} - 14q^{17} + 4q^{19} - 20q^{20} - 16q^{21} + 8q^{22} + 20q^{23} - 4q^{24} + 6q^{25} + 12q^{26} + 20q^{27} + 16q^{30} + 12q^{31} + 6q^{32} - 12q^{33} + 2q^{34} - 16q^{35} - 8q^{38} + 4q^{39} + 28q^{40} + 2q^{41} + 20q^{42} + 4q^{43} + 12q^{44} + 2q^{45} + 8q^{46} - 16q^{48} - 18q^{49} - 26q^{50} - 28q^{52} - 14q^{53} - 12q^{54} + 16q^{55} - 60q^{57} + 8q^{59} + 44q^{60} - 8q^{61} + 40q^{62} + 20q^{63} - 34q^{64} - 14q^{65} - 40q^{66} - 20q^{67} + 2q^{68} + 8q^{69} + 28q^{70} - 8q^{71} - 24q^{73} - 44q^{75} + 16q^{76} + 20q^{77} + 40q^{78} + 4q^{80} - 10q^{81} - 34q^{82} + 20q^{84} - 18q^{85} - 48q^{86} + 16q^{87} + 16q^{88} - 18q^{89} + 10q^{90} + 28q^{91} + 44q^{92} + 28q^{95} + 40q^{96} + 16q^{97} + 98q^{98} + O(q^{100})$$

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
65.2.k.a $$2$$ $$0.519$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$2$$ $$-2$$ $$0$$ $$q+q^{2}+(1+i)q^{3}-q^{4}+(-1-2i)q^{5}+\cdots$$
65.2.k.b $$8$$ $$0.519$$ 8.0.619810816.2 None $$-4$$ $$-6$$ $$2$$ $$0$$ $$q+\beta _{5}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots$$