# Properties

 Label 273.2.ba Level $273$ Weight $2$ Character orbit 273.ba Rep. character $\chi_{273}(38,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $68$ Newform subspaces $3$ Sturm bound $74$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.ba (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: $$7$$ 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

 $$68 q - 6 q^{3} - 36 q^{4} - 6 q^{9} + O(q^{10})$$ $$68 q - 6 q^{3} - 36 q^{4} - 6 q^{9} - 12 q^{10} + 6 q^{12} - 40 q^{16} - 24 q^{22} + 18 q^{25} - 22 q^{30} + 68 q^{36} + 9 q^{39} - 108 q^{40} + 24 q^{42} - 20 q^{43} - 6 q^{49} + 28 q^{51} + 30 q^{52} + 24 q^{61} + 90 q^{66} - 90 q^{75} - 68 q^{78} - 10 q^{79} + 42 q^{81} + 120 q^{82} + 60 q^{87} + 12 q^{88} - 39 q^{91} + 168 q^{94} + O(q^{100})$$

## 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.ba.a $2$ $2.180$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$-1$$ $$q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots$$
273.2.ba.b $2$ $2.180$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$1$$ $$q+(1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots$$
273.2.ba.c $64$ $2.180$ None $$0$$ $$-12$$ $$0$$ $$0$$