# Properties

 Label 546.2.bd Level $546$ Weight $2$ Character orbit 546.bd Rep. character $\chi_{546}(121,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $36$ Newform subspaces $2$ Sturm bound $224$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.bd (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

 $$36q + 4q^{3} + 18q^{4} + 2q^{7} + 36q^{9} + O(q^{10})$$ $$36q + 4q^{3} + 18q^{4} + 2q^{7} + 36q^{9} - 16q^{10} + 2q^{12} - 2q^{13} + 8q^{14} - 18q^{16} + 4q^{17} - 14q^{21} - 4q^{22} - 8q^{23} + 6q^{25} + 4q^{26} + 4q^{27} + 4q^{28} + 4q^{29} + 20q^{35} + 18q^{36} + 30q^{37} + 4q^{38} + 18q^{39} - 8q^{40} - 36q^{41} - 14q^{43} + 12q^{44} - 12q^{46} + 72q^{47} - 2q^{48} + 2q^{49} + 48q^{50} + 4q^{51} + 2q^{52} + 20q^{53} + 4q^{55} + 4q^{56} + 4q^{61} + 4q^{62} + 2q^{63} - 36q^{64} - 28q^{65} - 16q^{66} - 4q^{68} + 24q^{69} - 48q^{70} - 36q^{71} - 42q^{73} - 12q^{74} + 6q^{75} - 6q^{76} - 68q^{77} - 24q^{79} + 36q^{81} - 48q^{82} - 16q^{84} + 72q^{85} + 36q^{86} + 12q^{87} - 8q^{88} - 24q^{89} - 16q^{90} - 112q^{91} - 16q^{92} - 24q^{93} + 80q^{94} - 102q^{97} - 24q^{98} + O(q^{100})$$

## 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.bd.a $$16$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$-16$$ $$0$$ $$8$$ $$q+\beta _{13}q^{2}-q^{3}+\beta _{3}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$$
546.2.bd.b $$20$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$20$$ $$0$$ $$-6$$ $$q-\beta _{10}q^{2}+q^{3}-\beta _{12}q^{4}+\beta _{4}q^{5}+\cdots$$

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

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