# Properties

 Label 165.2.d Level $165$ Weight $2$ Character orbit 165.d Rep. character $\chi_{165}(164,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $3$ Sturm bound $48$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 165.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$165$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$48$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(165, [\chi])$$.

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

## Trace form

 $$20q - 24q^{4} - 10q^{9} + O(q^{10})$$ $$20q - 24q^{4} - 10q^{9} - 3q^{15} + 14q^{25} - 20q^{31} + 16q^{34} + 28q^{36} + 37q^{45} - 12q^{49} + 6q^{55} - 54q^{60} + 64q^{64} - 48q^{66} - 30q^{69} + 16q^{70} + 33q^{75} - 34q^{81} - 128q^{91} + 70q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(165, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
165.2.d.a $$2$$ $$1.318$$ $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$-1$$ $$3$$ $$0$$ $$q-\beta q^{3}+2q^{4}+(1+\beta )q^{5}+(-3+\beta )q^{9}+\cdots$$
165.2.d.b $$2$$ $$1.318$$ $$\Q(\sqrt{-11})$$ $$\Q(\sqrt{-11})$$ $$0$$ $$1$$ $$-3$$ $$0$$ $$q+\beta q^{3}+2q^{4}+(-2+\beta )q^{5}+(-3+\cdots)q^{9}+\cdots$$
165.2.d.c $$16$$ $$1.318$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2-\beta _{7})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$