# Properties

 Label 546.2.bm Level $546$ Weight $2$ Character orbit 546.bm Rep. character $\chi_{546}(205,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $36$ Newform subspaces $2$ Sturm bound $224$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.bm (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$224$$ Trace bound: $$1$$ 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

 $$36q - 2q^{3} - 36q^{4} - 2q^{7} - 18q^{9} + O(q^{10})$$ $$36q - 2q^{3} - 36q^{4} - 2q^{7} - 18q^{9} + 8q^{10} + 12q^{11} + 2q^{12} - 2q^{13} + 8q^{14} + 36q^{16} - 8q^{17} + 6q^{19} + 14q^{21} - 4q^{22} + 16q^{23} + 6q^{25} + 4q^{26} + 4q^{27} + 2q^{28} + 4q^{29} + 8q^{35} + 18q^{36} + 4q^{38} - 24q^{39} - 8q^{40} - 36q^{41} - 14q^{43} - 12q^{44} - 72q^{47} - 2q^{48} + 2q^{49} + 48q^{50} + 4q^{51} + 2q^{52} + 20q^{53} + 4q^{55} - 8q^{56} + 48q^{58} - 2q^{61} + 4q^{62} + 4q^{63} - 36q^{64} + 32q^{65} - 16q^{66} + 60q^{67} + 8q^{68} + 24q^{69} + 48q^{70} - 36q^{71} + 42q^{73} + 24q^{74} - 12q^{75} - 6q^{76} - 68q^{77} - 24q^{79} - 18q^{81} + 24q^{82} - 14q^{84} + 72q^{85} - 36q^{86} - 24q^{87} + 4q^{88} - 16q^{90} - 12q^{91} - 16q^{92} - 40q^{94} - 102q^{97} - 72q^{98} + O(q^{100})$$

## 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.bm.a $$16$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$8$$ $$0$$ $$-2$$ $$q+(\beta _{12}+\beta _{13})q^{2}+\beta _{3}q^{3}-q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$$
546.2.bm.b $$20$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$-10$$ $$0$$ $$0$$ $$q+(-\beta _{10}+\beta _{11})q^{2}+\beta _{12}q^{3}-q^{4}+\cdots$$

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

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