# Properties

 Label 273.2.bj Level $273$ Weight $2$ Character orbit 273.bj Rep. character $\chi_{273}(25,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $36$ Newform subspaces $4$ 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.bj (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$74$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

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

Total New Old
Modular forms 84 36 48
Cusp forms 68 36 32
Eisenstein series 16 0 16

## Trace form

 $$36q + 2q^{3} + 16q^{4} - 18q^{9} + O(q^{10})$$ $$36q + 2q^{3} + 16q^{4} - 18q^{9} - 8q^{10} - 4q^{12} + 6q^{13} + 36q^{14} - 28q^{16} - 4q^{17} + 16q^{22} + 4q^{23} + 18q^{25} + 22q^{26} - 4q^{27} - 32q^{35} - 32q^{36} - 44q^{38} - q^{39} + 44q^{40} + 8q^{42} - 12q^{43} - 16q^{48} - 70q^{49} - 12q^{51} + 38q^{52} + 40q^{53} - 96q^{55} + 108q^{56} + 36q^{61} - 208q^{62} - 144q^{64} + 26q^{65} + 16q^{66} - 8q^{68} + 40q^{69} - 24q^{74} - 30q^{75} + 4q^{77} + 60q^{78} - 10q^{79} - 18q^{81} + 36q^{87} - 12q^{88} + 16q^{90} - 77q^{91} + 32q^{92} + 4q^{94} + 20q^{95} + O(q^{100})$$

## 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.bj.a $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ None $$-3$$ $$1$$ $$-6$$ $$1$$ $$q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{3}+\zeta_{6}q^{4}+(-2+\cdots)q^{5}+\cdots$$
273.2.bj.b $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ None $$3$$ $$1$$ $$6$$ $$-1$$ $$q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{3}+\zeta_{6}q^{4}+(2+2\zeta_{6})q^{5}+\cdots$$
273.2.bj.c $$16$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+(\beta _{1}+\beta _{9})q^{2}-\beta _{10}q^{3}+(\beta _{10}-\beta _{11}+\cdots)q^{4}+\cdots$$
273.2.bj.d $$16$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$8$$ $$0$$ $$0$$ $$q-\beta _{8}q^{2}+\beta _{3}q^{3}+(\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(273, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(273, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 2}$$