# Properties

 Label 273.2.l Level $273$ Weight $2$ Character orbit 273.l Rep. character $\chi_{273}(16,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $38$ Newform subspaces $3$ Sturm bound $74$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$273 = 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 273.l (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ 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

 $$38q - 3q^{3} + 40q^{4} - 19q^{9} + O(q^{10})$$ $$38q - 3q^{3} + 40q^{4} - 19q^{9} - 8q^{10} - 4q^{11} - 8q^{12} + 2q^{13} - 16q^{14} + 60q^{16} - 8q^{17} - 3q^{19} - 8q^{20} - 5q^{21} - 2q^{22} + 8q^{23} + 12q^{24} - 25q^{25} + 46q^{26} + 6q^{27} - 16q^{28} - 11q^{31} - 40q^{32} - 56q^{34} + 10q^{35} - 20q^{36} - 46q^{37} + 24q^{38} + 13q^{39} - 34q^{40} + 18q^{41} - 14q^{42} + 4q^{43} - 20q^{44} + 16q^{46} + 12q^{47} - 18q^{48} + 6q^{49} - 2q^{50} + 8q^{51} - 66q^{52} + 24q^{53} - 34q^{55} - 74q^{56} - 38q^{57} + 20q^{58} + 64q^{59} + 32q^{60} - 9q^{61} + 16q^{62} + 3q^{63} + 36q^{64} - 30q^{65} - 16q^{66} + 17q^{67} - 64q^{68} - 12q^{69} + 76q^{70} + 10q^{71} + 4q^{73} - 24q^{74} + 58q^{75} - 12q^{76} - 10q^{77} + 10q^{78} - 19q^{79} + 20q^{80} - 19q^{81} - 14q^{82} + 64q^{83} - 8q^{84} - 20q^{85} + 20q^{86} + 60q^{87} + 12q^{88} - 32q^{89} + 16q^{90} + 4q^{91} - 4q^{92} + 34q^{93} - 64q^{94} + 72q^{95} + 14q^{96} + 23q^{97} - 58q^{98} + 8q^{99} + O(q^{100})$$

## 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.l.a $$2$$ $$2.180$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$0$$ $$-4$$ $$q-\zeta_{6}q^{3}-2q^{4}+(-3+2\zeta_{6})q^{7}+(-1+\cdots)q^{9}+\cdots$$
273.2.l.b $$16$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$8$$ $$0$$ $$1$$ $$q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{9}q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots$$
273.2.l.c $$20$$ $$2.180$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$-10$$ $$0$$ $$3$$ $$q-\beta _{4}q^{2}+(-1+\beta _{7})q^{3}+(2+\beta _{2})q^{4}+\cdots$$

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

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