# Properties

 Label 273.2.bn Level $273$ Weight $2$ Character orbit 273.bn Rep. character $\chi_{273}(146,\cdot)$ 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.bn (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

 $$68 q + 28 q^{4} - 5 q^{7} - 4 q^{9} + O(q^{10})$$ $$68 q + 28 q^{4} - 5 q^{7} - 4 q^{9} - 18 q^{15} - 24 q^{16} + 8 q^{18} - 26 q^{21} - 32 q^{22} + 28 q^{25} + 38 q^{28} - 40 q^{30} + 6 q^{36} - 8 q^{37} + 24 q^{39} - 12 q^{42} + 14 q^{43} - 36 q^{46} - 11 q^{49} - 28 q^{51} - 44 q^{57} - 116 q^{60} + 7 q^{63} - 16 q^{64} - 50 q^{67} - 64 q^{70} + 62 q^{72} - 2 q^{78} + 4 q^{79} - 8 q^{81} - 18 q^{84} + 28 q^{85} + 80 q^{88} - 7 q^{91} + 16 q^{93} - 32 q^{99} + O(q^{100})$$

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