# Properties

 Label 180.1.f Level $180$ Weight $1$ Character orbit 180.f Rep. character $\chi_{180}(19,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $36$ Trace bound $0$

# Learn more

## Defining parameters

 Level: $$N$$ $$=$$ $$180 = 2^{2} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 180.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$36$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(180, [\chi])$$.

Total New Old
Modular forms 10 4 6
Cusp forms 2 2 0
Eisenstein series 8 2 6

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

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2 q - 2 q^{4} + O(q^{10})$$ $$2 q - 2 q^{4} - 2 q^{10} + 2 q^{16} - 2 q^{25} + 4 q^{34} + 2 q^{40} - 2 q^{49} - 4 q^{61} - 2 q^{64} + 4 q^{85} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(180, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
180.1.f.a $$2$$ $$0.090$$ $$\Q(\sqrt{-1})$$ $$D_{2}$$ $$\Q(\sqrt{-1})$$, $$\Q(\sqrt{-15})$$ $$\Q(\sqrt{15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots$$