# Properties

 Label 65.2.c Level $65$ Weight $2$ Character orbit 65.c Rep. character $\chi_{65}(51,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $1$ Sturm bound $14$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$65 = 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 65.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$1$$ 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 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

## Trace form

 $$6 q - 4 q^{3} - 10 q^{4} + 6 q^{9} + O(q^{10})$$ $$6 q - 4 q^{3} - 10 q^{4} + 6 q^{9} + 2 q^{10} - 8 q^{13} + 8 q^{14} + 10 q^{16} + 8 q^{17} - 24 q^{22} + 16 q^{23} - 6 q^{25} + 14 q^{26} - 28 q^{27} - 4 q^{29} + 20 q^{30} - 4 q^{35} - 34 q^{36} - 20 q^{38} - 16 q^{39} - 6 q^{40} + 44 q^{42} + 24 q^{43} + 36 q^{48} + 2 q^{49} + 8 q^{51} + 20 q^{52} + 12 q^{53} - 12 q^{55} - 48 q^{56} - 12 q^{61} + 8 q^{62} + 30 q^{64} + 2 q^{65} + 24 q^{66} - 88 q^{68} - 32 q^{69} + 20 q^{74} + 4 q^{75} + 36 q^{77} - 52 q^{78} + 24 q^{79} + 30 q^{81} - 28 q^{82} - 4 q^{87} + 60 q^{88} - 34 q^{90} + 32 q^{91} - 20 q^{92} - 8 q^{94} + 16 q^{95} + O(q^{100})$$

## 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.c.a $6$ $0.519$ 6.0.5089536.1 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+(-1-\beta _{1})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots$$