# Properties

 Label 65.2.f Level $65$ Weight $2$ Character orbit 65.f Rep. character $\chi_{65}(18,\cdot)$ 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.f (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

 $$10 q - 4 q^{3} - 6 q^{4} - 6 q^{5} - 4 q^{6} - 4 q^{7} + O(q^{10})$$ $$10 q - 4 q^{3} - 6 q^{4} - 6 q^{5} - 4 q^{6} - 4 q^{7} + 8 q^{10} + 4 q^{11} + 10 q^{13} - 4 q^{15} - 10 q^{16} + 14 q^{17} + 18 q^{18} - 4 q^{19} - 6 q^{20} - 16 q^{21} + 8 q^{22} - 20 q^{23} + 4 q^{24} - 6 q^{25} + 12 q^{26} + 20 q^{27} - 12 q^{28} - 16 q^{30} + 12 q^{31} - 2 q^{34} - 16 q^{35} - 44 q^{37} + 8 q^{38} - 4 q^{39} + 28 q^{40} + 2 q^{41} + 20 q^{42} - 4 q^{43} - 12 q^{44} + 24 q^{45} + 8 q^{46} + 28 q^{47} - 16 q^{48} + 18 q^{49} + 36 q^{50} - 42 q^{52} - 14 q^{53} + 12 q^{54} + 16 q^{55} + 24 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 40 q^{62} + 34 q^{64} + 2 q^{65} - 40 q^{66} + 2 q^{68} - 8 q^{69} - 72 q^{70} - 8 q^{71} - 22 q^{72} + 44 q^{75} + 16 q^{76} - 20 q^{77} + 4 q^{78} - 22 q^{80} - 10 q^{81} + 34 q^{82} + 60 q^{83} - 20 q^{84} + 38 q^{85} - 48 q^{86} + 16 q^{87} - 16 q^{88} + 18 q^{89} - 10 q^{90} + 28 q^{91} + 44 q^{92} - 20 q^{93} - 28 q^{95} + 40 q^{96} + O(q^{100})$$

## 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.f.a $2$ $0.519$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$-4$$ $$-4$$ $$q+iq^{2}+(1-i)q^{3}+q^{4}+(-2-i)q^{5}+\cdots$$
65.2.f.b $8$ $0.519$ 8.0.619810816.2 None $$0$$ $$-6$$ $$-2$$ $$0$$ $$q-\beta _{6}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots$$