# Properties

 Label 165.1.l Level $165$ Weight $1$ Character orbit 165.l Rep. character $\chi_{165}(32,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $2$ Sturm bound $24$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 165.l (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$165$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$24$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(165, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 4 0 0 0

## Trace form

 $$4 q - 2 q^{3} + O(q^{10})$$ $$4 q - 2 q^{3} + 2 q^{12} - 2 q^{15} - 4 q^{16} - 4 q^{25} - 2 q^{27} + 2 q^{33} + 4 q^{37} + 2 q^{48} + 4 q^{55} + 2 q^{60} - 4 q^{67} + 2 q^{75} + 4 q^{81} - 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(165, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.1.l.a $2$ $0.082$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-11})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+iq^{4}+iq^{5}+q^{9}-iq^{11}+\cdots$$
165.1.l.b $2$ $0.082$ $$\Q(\sqrt{-1})$$ $D_{4}$ $$\Q(\sqrt{-11})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+iq^{4}-iq^{5}-q^{9}+iq^{11}+\cdots$$