# Properties

 Label 273.2.t Level $273$ Weight $2$ Character orbit 273.t Rep. character $\chi_{273}(4,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $38$ Newform subspaces $4$ Sturm bound $74$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.t (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: $$1$$ 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 38 44
Cusp forms 66 38 28
Eisenstein series 16 0 16

## Trace form

 $$38q + 3q^{3} - 40q^{4} + 4q^{7} - 19q^{9} + O(q^{10})$$ $$38q + 3q^{3} - 40q^{4} + 4q^{7} - 19q^{9} - 8q^{10} - 12q^{11} - 8q^{12} - 2q^{13} - 24q^{14} + 28q^{16} + 8q^{17} + 3q^{19} - 24q^{20} - 7q^{21} + 10q^{22} - 8q^{23} + 25q^{25} - 26q^{26} - 6q^{27} + 8q^{28} - 3q^{31} - 2q^{35} + 20q^{36} + 16q^{38} + 13q^{39} + 14q^{40} + 18q^{41} + 26q^{42} + 4q^{43} + 12q^{44} + 36q^{47} + 18q^{48} - 2q^{49} - 102q^{50} - 2q^{52} - 8q^{53} + 30q^{55} - 6q^{56} - 12q^{58} + 36q^{60} + 17q^{61} - 40q^{62} - 5q^{63} - 20q^{64} - 10q^{65} + 16q^{66} - 33q^{67} + 16q^{68} - 20q^{69} + 36q^{70} + 18q^{71} - 42q^{73} - 24q^{74} + 26q^{75} + 58q^{77} - 18q^{78} + 19q^{79} + 48q^{80} - 19q^{81} + 6q^{82} + 28q^{84} - 48q^{85} + 36q^{86} - 36q^{87} - 12q^{88} + 16q^{90} + 140q^{92} + 52q^{94} - 40q^{95} - 30q^{96} + 27q^{97} + 102q^{98} + O(q^{100})$$

## 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.t.a $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-6$$ $$5$$ $$q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-4+\cdots)q^{5}+\cdots$$
273.2.t.b $$4$$ $$2.180$$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ None $$0$$ $$-2$$ $$6$$ $$0$$ $$q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$$
273.2.t.c $$12$$ $$2.180$$ 12.0.$$\cdots$$.1 None $$0$$ $$-6$$ $$-6$$ $$-3$$ $$q+(\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-1-\beta _{4})q^{3}+\cdots$$
273.2.t.d $$20$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$10$$ $$6$$ $$2$$ $$q+(\beta _{2}+\beta _{3})q^{2}+\beta _{11}q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots$$

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

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