# Properties

 Label 546.2.bk Level $546$ Weight $2$ Character orbit 546.bk Rep. character $\chi_{546}(25,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $40$ Newform subspaces $3$ 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.bk (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$3$$ 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 40 200
Cusp forms 208 40 168
Eisenstein series 32 0 32

## Trace form

 $$40q + 20q^{4} - 20q^{9} + O(q^{10})$$ $$40q + 20q^{4} - 20q^{9} + 8q^{10} - 4q^{14} - 20q^{16} + 4q^{17} + 8q^{22} - 8q^{23} + 20q^{25} + 4q^{26} - 8q^{29} + 56q^{35} - 40q^{36} + 4q^{38} + 4q^{39} - 8q^{40} + 36q^{49} + 16q^{51} - 28q^{53} + 64q^{55} - 20q^{56} - 4q^{61} + 64q^{62} - 40q^{64} - 4q^{65} - 16q^{66} - 4q^{68} - 48q^{69} + 24q^{74} + 16q^{75} - 32q^{77} - 24q^{78} - 8q^{79} - 20q^{81} - 24q^{87} + 4q^{88} - 16q^{90} + 52q^{91} - 16q^{92} - 28q^{94} - 48q^{95} + O(q^{100})$$

## 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.bk.a $$8$$ $$4.360$$ 8.0.3317760000.2 None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}-\beta _{4}q^{3}+\beta _{4}q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$$
546.2.bk.b $$12$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$0$$ $$q-\beta _{6}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{8}q^{5}+\cdots$$
546.2.bk.c $$20$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$0$$ $$10$$ $$0$$ $$0$$ $$q+\beta _{8}q^{2}+\beta _{3}q^{3}+\beta _{3}q^{4}-\beta _{9}q^{5}+\cdots$$

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

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