# Properties

 Label 546.2.q Level $546$ Weight $2$ Character orbit 546.q Rep. character $\chi_{546}(251,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $10$ 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.q (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$10$$ Sturm bound: $$224$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$, $$11$$, $$17$$

## Dimensions

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

Total New Old
Modular forms 240 72 168
Cusp forms 208 72 136
Eisenstein series 32 0 32

## Trace form

 $$72q - 36q^{4} - 4q^{9} + O(q^{10})$$ $$72q - 36q^{4} - 4q^{9} - 12q^{15} - 36q^{16} - 56q^{25} - 16q^{30} - 4q^{36} + 48q^{39} + 16q^{42} - 20q^{43} + 12q^{46} - 12q^{49} - 48q^{51} + 96q^{63} + 72q^{64} - 84q^{67} + 12q^{72} - 44q^{78} + 16q^{79} + 56q^{81} - 120q^{85} + 32q^{91} + 48q^{93} + O(q^{100})$$

## 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.q.a $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-3$$ $$0$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.q.b $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$3$$ $$0$$ $$5$$ $$q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.q.c $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-3$$ $$0$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.q.d $$2$$ $$4.360$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$3$$ $$0$$ $$5$$ $$q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.q.e $$4$$ $$4.360$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-2$$ $$-1$$ $$0$$ $$2$$ $$q-\beta _{2}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots$$
546.2.q.f $$4$$ $$4.360$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$-2$$ $$1$$ $$0$$ $$10$$ $$q+(-1+\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$$
546.2.q.g $$4$$ $$4.360$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$-2$$ $$0$$ $$2$$ $$q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
546.2.q.h $$4$$ $$4.360$$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$2$$ $$2$$ $$0$$ $$10$$ $$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
546.2.q.i $$24$$ $$4.360$$ None $$-12$$ $$0$$ $$0$$ $$-18$$
546.2.q.j $$24$$ $$4.360$$ None $$12$$ $$0$$ $$0$$ $$-18$$

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

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