# Properties

 Label 546.2.g Level $546$ Weight $2$ Character orbit 546.g Rep. character $\chi_{546}(209,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $4$ 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.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$4$$ 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 120 32 88
Cusp forms 104 32 72
Eisenstein series 16 0 16

## Trace form

 $$32q - 32q^{4} - 4q^{7} + 8q^{9} + O(q^{10})$$ $$32q - 32q^{4} - 4q^{7} + 8q^{9} + 24q^{15} + 32q^{16} - 16q^{21} + 48q^{25} + 4q^{28} + 4q^{30} - 8q^{36} - 24q^{37} + 22q^{42} - 64q^{43} + 40q^{46} + 52q^{49} - 52q^{51} - 32q^{57} - 40q^{58} - 24q^{60} - 20q^{63} - 32q^{64} - 48q^{70} + 72q^{79} + 40q^{81} + 16q^{84} + 64q^{85} - 8q^{91} + 56q^{93} + O(q^{100})$$

## 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.g.a $$4$$ $$4.360$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$-2$$ $$4$$ $$6$$ $$q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$
546.2.g.b $$4$$ $$4.360$$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$2$$ $$-4$$ $$6$$ $$q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots$$
546.2.g.c $$12$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$-2$$ $$4$$ $$-8$$ $$q-\beta _{5}q^{2}+\beta _{3}q^{3}-q^{4}-\beta _{4}q^{5}+\beta _{6}q^{6}+\cdots$$
546.2.g.d $$12$$ $$4.360$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$2$$ $$-4$$ $$-8$$ $$q-\beta _{5}q^{2}-\beta _{3}q^{3}-q^{4}+\beta _{4}q^{5}-\beta _{6}q^{6}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(546, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$