# Properties

 Label 180.1.p Level $180$ Weight $1$ Character orbit 180.p Rep. character $\chi_{180}(79,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $4$ Newform subspaces $2$ Sturm bound $36$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$180 = 2^{2} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 180.p (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$180$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$36$$ Trace bound: $$2$$

## Dimensions

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

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

 $$4 q - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{9} + O(q^{10})$$ $$4 q - 2 q^{4} - 2 q^{5} + 4 q^{6} - 2 q^{9} + 2 q^{14} - 2 q^{16} - 2 q^{20} - 4 q^{21} - 2 q^{24} - 2 q^{25} + 2 q^{29} - 2 q^{30} + 4 q^{36} + 2 q^{41} + 4 q^{45} - 4 q^{46} - 2 q^{54} + 2 q^{56} + 2 q^{61} + 4 q^{64} + 2 q^{69} + 2 q^{70} + 4 q^{80} - 2 q^{81} + 2 q^{84} - 4 q^{86} - 4 q^{89} + 2 q^{94} - 2 q^{96} + O(q^{100})$$

## 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.p.a $$2$$ $$0.090$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-1$$ $$-1$$ $$1$$ $$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$
180.1.p.b $$2$$ $$0.090$$ $$\Q(\sqrt{-3})$$ $$D_{3}$$ $$\Q(\sqrt{-5})$$ None $$1$$ $$1$$ $$-1$$ $$-1$$ $$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$$