# Properties

 Label 273.1.bs Level $273$ Weight $1$ Character orbit 273.bs Rep. character $\chi_{273}(59,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $4$ 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.bs (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{12})$$ 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 20 20 0
Cusp forms 4 4 0
Eisenstein series 16 16 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

 $$4 q + 2 q^{9} + O(q^{10})$$ $$4 q + 2 q^{9} + 2 q^{12} - 4 q^{16} - 2 q^{19} - 2 q^{21} - 2 q^{28} - 2 q^{31} + 2 q^{37} - 4 q^{39} - 6 q^{43} + 2 q^{49} + 2 q^{52} - 2 q^{57} + 2 q^{67} + 2 q^{73} + 4 q^{75} + 4 q^{76} - 2 q^{81} + 4 q^{91} + 4 q^{93} + 2 q^{97} + O(q^{100})$$

## 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.bs.a $4$ $0.136$ $$\Q(\zeta_{12})$$ $D_{12}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$$