# Properties

 Label 546.2.j Level $546$ Weight $2$ Character orbit 546.j Rep. character $\chi_{546}(289,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $36$ Newform subspaces $5$ Sturm bound $224$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.j (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$5$$ Sturm bound: $$224$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(546, [\chi])$$.

Total New Old
Modular forms 240 36 204
Cusp forms 208 36 172
Eisenstein series 32 0 32

## Trace form

 $$36q + 2q^{3} + 36q^{4} + 2q^{7} - 18q^{9} + O(q^{10})$$ $$36q + 2q^{3} + 36q^{4} + 2q^{7} - 18q^{9} + 8q^{10} + 4q^{11} + 2q^{12} + 2q^{13} + 36q^{16} + 8q^{17} + 6q^{19} - 2q^{21} - 4q^{22} - 16q^{23} - 6q^{25} - 4q^{26} - 4q^{27} + 2q^{28} + 4q^{29} + 20q^{31} - 16q^{35} - 18q^{36} + 68q^{37} - 4q^{38} - 24q^{39} + 8q^{40} + 4q^{41} - 6q^{43} + 4q^{44} + 24q^{46} - 24q^{47} + 2q^{48} + 18q^{49} - 16q^{50} - 12q^{51} + 2q^{52} - 12q^{53} + 4q^{55} + 20q^{57} - 8q^{58} - 32q^{59} + 26q^{61} + 20q^{62} - 4q^{63} + 36q^{64} + 40q^{65} + 16q^{66} - 16q^{67} + 8q^{68} + 8q^{69} - 64q^{70} + 44q^{71} - 6q^{73} + 24q^{74} - 44q^{75} + 6q^{76} - 28q^{77} - 16q^{78} + 24q^{79} - 18q^{81} + 24q^{82} - 112q^{83} - 2q^{84} - 4q^{86} - 24q^{87} - 4q^{88} - 16q^{89} - 16q^{90} + 28q^{91} - 16q^{92} - 56q^{93} + 40q^{94} - 64q^{95} - 30q^{97} - 24q^{98} - 8q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(546, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
546.2.j.a $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$2$$ $$1$$ $$0$$ $$1$$ $$q+q^{2}+\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}+(2-3\zeta_{6})q^{7}+\cdots$$
546.2.j.b $$8$$ $$4.360$$ 8.0.6498455769.2 None $$-8$$ $$-4$$ $$-2$$ $$3$$ $$q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots$$
546.2.j.c $$8$$ $$4.360$$ 8.0.447703281.1 None $$8$$ $$-4$$ $$2$$ $$3$$ $$q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots$$
546.2.j.d $$8$$ $$4.360$$ 8.0.447703281.1 None $$8$$ $$4$$ $$2$$ $$-3$$ $$q+q^{2}-\beta _{3}q^{3}+q^{4}+(2\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$$
546.2.j.e $$10$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-10$$ $$5$$ $$-2$$ $$-2$$ $$q-q^{2}+(1+\beta _{5})q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\cdots)q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(546, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(546, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$