# Properties

 Label 165.2.k Level $165$ Weight $2$ Character orbit 165.k Rep. character $\chi_{165}(23,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $40$ Newform subspaces $4$ Sturm bound $48$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 165.k (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$48$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 56 40 16
Cusp forms 40 40 0
Eisenstein series 16 0 16

## Trace form

 $$40q - 2q^{3} - 8q^{6} + O(q^{10})$$ $$40q - 2q^{3} - 8q^{6} + 8q^{12} - 16q^{13} + 4q^{15} - 32q^{16} - 12q^{18} - 16q^{21} - 12q^{25} + 4q^{27} + 32q^{28} + 16q^{30} - 32q^{31} + 2q^{33} + 24q^{36} - 36q^{37} + 8q^{40} - 64q^{42} + 8q^{45} - 4q^{48} + 16q^{51} + 88q^{52} + 12q^{55} + 40q^{57} + 8q^{58} - 80q^{60} + 4q^{63} - 28q^{67} - 40q^{70} + 48q^{72} - 44q^{75} + 96q^{76} - 40q^{78} - 52q^{81} + 8q^{82} - 8q^{85} + 16q^{87} - 24q^{88} - 16q^{90} - 48q^{91} + 58q^{93} + 128q^{96} + 76q^{97} + O(q^{100})$$

## 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.k.a $$4$$ $$1.318$$ $$\Q(\zeta_{8})$$ None $$-4$$ $$-4$$ $$-8$$ $$-8$$ $$q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots$$
165.2.k.b $$4$$ $$1.318$$ $$\Q(\zeta_{8})$$ None $$4$$ $$0$$ $$8$$ $$-8$$ $$q+(1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{3}+\cdots$$
165.2.k.c $$16$$ $$1.318$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-4$$ $$-2$$ $$-8$$ $$8$$ $$q+\beta _{3}q^{2}-\beta _{15}q^{3}+(-\beta _{1}-\beta _{3}-\beta _{13}+\cdots)q^{4}+\cdots$$
165.2.k.d $$16$$ $$1.318$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$4$$ $$4$$ $$8$$ $$8$$ $$q+\beta _{1}q^{2}+\beta _{11}q^{3}+(\beta _{1}+\beta _{3}+\beta _{13}+\cdots)q^{4}+\cdots$$