Properties

 Label 273.1.s Level $273$ Weight $1$ Character orbit 273.s Rep. character $\chi_{273}(74,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $6$ Newform subspaces $2$ Sturm bound $37$ Trace bound $1$

Related objects

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 14 14 0
Cusp forms 6 6 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 4 0 0

Trace form

 $$6 q - q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} + q^{9} + O(q^{10})$$ $$6 q - q^{3} + 2 q^{4} - 2 q^{6} - 3 q^{7} + q^{9} + 2 q^{10} - q^{12} - 5 q^{13} - 2 q^{15} - 2 q^{16} + q^{19} - q^{21} - 2 q^{24} - q^{25} + 2 q^{27} - q^{28} + 4 q^{34} - q^{36} + 2 q^{37} + 2 q^{39} + 2 q^{40} + 4 q^{42} - q^{43} + 4 q^{46} - q^{48} - 3 q^{49} + 2 q^{51} - q^{52} - 4 q^{54} - 2 q^{57} - 2 q^{58} + q^{61} + 4 q^{63} - 2 q^{64} - 2 q^{67} + 2 q^{69} - 4 q^{70} - q^{73} + 2 q^{75} + q^{76} + 2 q^{78} - 4 q^{79} - 3 q^{81} + 2 q^{82} - q^{84} - 2 q^{85} - 4 q^{87} + 4 q^{90} + 4 q^{91} + 4 q^{93} + 2 q^{94} + 3 q^{97} + O(q^{100})$$

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.s.a $2$ $0.136$ $$\Q(\sqrt{-3})$$ $D_{3}$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-1$$ $$q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$$
273.1.s.b $4$ $0.136$ $$\Q(\zeta_{12})$$ $A_{4}$ None None $$0$$ $$0$$ $$0$$ $$-2$$ $$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots$$