Properties

 Label 273.2.u Level $273$ Weight $2$ Character orbit 273.u Rep. character $\chi_{273}(62,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $68$ Newform subspaces $3$ Sturm bound $74$ Trace bound $3$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.u (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ Sturm bound: $$74$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$, $$19$$

Dimensions

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

Total New Old
Modular forms 84 84 0
Cusp forms 68 68 0
Eisenstein series 16 16 0

Trace form

 $$68q - 36q^{4} - 9q^{7} + O(q^{10})$$ $$68q - 36q^{4} - 9q^{7} + 18q^{15} - 40q^{16} + 24q^{22} - 60q^{25} - 6q^{28} + 20q^{30} + 38q^{36} - 12q^{37} - 36q^{39} + 22q^{43} - 84q^{46} - 3q^{49} + 52q^{51} - 48q^{58} - 63q^{63} + 144q^{64} + 18q^{67} - 66q^{72} + 166q^{78} - 52q^{79} - 48q^{81} + 66q^{84} + 132q^{85} - 15q^{91} - 120q^{93} + O(q^{100})$$

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.u.a $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$-3$$ $$0$$ $$-4$$ $$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+\cdots$$
273.2.u.b $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$-5$$ $$q+(1+\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+\zeta_{6})q^{7}+\cdots$$
273.2.u.c $$64$$ $$2.180$$ None $$0$$ $$0$$ $$0$$ $$0$$