# Properties

 Label 546.2.bg Level $546$ Weight $2$ Character orbit 546.bg Rep. character $\chi_{546}(311,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $72$ Newform subspaces $2$ Sturm bound $224$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.bg (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$224$$ Trace bound: $$2$$ 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 72 168
Cusp forms 208 72 136
Eisenstein series 32 0 32

## Trace form

 $$72q - 36q^{4} + 8q^{9} + O(q^{10})$$ $$72q - 36q^{4} + 8q^{9} - 36q^{16} + 28q^{25} + 14q^{30} - 16q^{36} - 32q^{42} - 32q^{43} + 24q^{49} - 6q^{51} + 12q^{52} - 72q^{61} + 72q^{64} - 48q^{66} + 108q^{75} + 40q^{78} + 40q^{79} - 40q^{81} - 48q^{82} - 48q^{87} - 4q^{91} - 144q^{94} + O(q^{100})$$

## 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.bg.a $$36$$ $$4.360$$ None $$-18$$ $$0$$ $$0$$ $$0$$
546.2.bg.b $$36$$ $$4.360$$ None $$18$$ $$0$$ $$0$$ $$0$$

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

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