# Properties

 Label 273.1.x Level $273$ Weight $1$ Character orbit 273.x Rep. character $\chi_{273}(179,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $2$ Newform subspaces $1$ Sturm bound $37$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 273.x (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$37$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(273, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 2 2 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 2 0 0 0

## Trace form

 $$2 q - 2 q^{3} + q^{4} - q^{7} + 2 q^{9} + O(q^{10})$$ $$2 q - 2 q^{3} + q^{4} - q^{7} + 2 q^{9} - q^{12} + q^{13} - q^{16} + q^{21} + q^{25} - 2 q^{27} - 2 q^{28} + q^{36} - 3 q^{37} - q^{39} + q^{43} + q^{48} - q^{49} - q^{52} + 2 q^{61} - q^{63} - 2 q^{64} + 3 q^{73} - q^{75} + 3 q^{76} + 2 q^{79} + 2 q^{81} + 2 q^{84} - 2 q^{91} - 3 q^{97} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(273, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
273.1.x.a $2$ $0.136$ $$\Q(\sqrt{-3})$$ $D_{6}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$-1$$ $$q-q^{3}-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots$$