# Properties

 Label 65.2.d Level $65$ Weight $2$ Character orbit 65.d Rep. character $\chi_{65}(64,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $14$ Trace bound $2$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

## Trace form

 $$4 q - 4 q^{4} - 4 q^{9} + O(q^{10})$$ $$4 q - 4 q^{4} - 4 q^{9} + 4 q^{10} - 4 q^{16} - 12 q^{25} - 12 q^{26} + 24 q^{29} + 16 q^{30} + 4 q^{36} + 16 q^{39} - 12 q^{40} - 28 q^{49} - 16 q^{55} + 24 q^{61} + 28 q^{64} - 12 q^{65} + 16 q^{66} - 48 q^{69} - 24 q^{74} + 32 q^{75} - 44 q^{81} - 4 q^{90} + 32 q^{94} + 48 q^{95} + O(q^{100})$$

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