# Properties

 Label 273.2.br Level $273$ Weight $2$ Character orbit 273.br Rep. character $\chi_{273}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $66$ Newform subspaces $2$ Sturm bound $74$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.br (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$74$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(273, [\chi])$$.

Total New Old
Modular forms 82 82 0
Cusp forms 66 66 0
Eisenstein series 16 16 0

## Trace form

 $$66q - 3q^{3} + 52q^{4} - 2q^{7} + 3q^{9} + O(q^{10})$$ $$66q - 3q^{3} + 52q^{4} - 2q^{7} + 3q^{9} - 6q^{10} - 12q^{12} - 10q^{13} - 9q^{15} + 24q^{16} - 36q^{18} + q^{19} - 9q^{21} - 18q^{22} - 12q^{24} + 11q^{25} + 10q^{28} - 22q^{30} + 29q^{31} - 15q^{33} - 24q^{34} - 10q^{36} - 12q^{39} - 54q^{40} + 39q^{42} - 4q^{43} - 6q^{45} - 42q^{48} + 4q^{49} - 14q^{51} - 52q^{52} + 18q^{54} + 42q^{55} + 30q^{58} - 9q^{60} + 33q^{61} - 44q^{64} - 9q^{66} + 27q^{67} - 39q^{69} - 84q^{70} - 123q^{72} - 22q^{73} + 16q^{76} - 11q^{78} - 9q^{79} - 9q^{81} - 66q^{82} + 21q^{84} - 30q^{85} - 30q^{88} + 122q^{91} + 84q^{94} - 24q^{96} + 7q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(273, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
273.2.br.a $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$4$$ $$q+(2-\zeta_{6})q^{3}-2q^{4}+(3-2\zeta_{6})q^{7}+\cdots$$
273.2.br.b $$64$$ $$2.180$$ None $$0$$ $$-6$$ $$0$$ $$-6$$