# Properties

 Label 546.2.ch Level $546$ Weight $2$ Character orbit 546.ch Rep. character $\chi_{546}(137,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $152$ Newform subspaces $1$ Sturm bound $224$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.ch (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$273$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$1$$ Sturm bound: $$224$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 480 152 328
Cusp forms 416 152 264
Eisenstein series 64 0 64

## Trace form

 $$152q + 8q^{7} + O(q^{10})$$ $$152q + 8q^{7} - 152q^{16} - 8q^{18} + 36q^{19} + 8q^{21} + 24q^{27} - 12q^{28} - 24q^{30} - 36q^{31} + 12q^{33} + 24q^{36} - 12q^{37} - 8q^{39} - 36q^{42} + 84q^{43} - 40q^{45} + 8q^{46} + 4q^{49} - 20q^{52} - 12q^{54} + 16q^{55} - 8q^{57} + 8q^{58} + 24q^{60} - 32q^{61} - 28q^{63} + 16q^{66} + 92q^{67} + 84q^{69} - 8q^{72} + 84q^{73} - 48q^{76} - 8q^{78} + 32q^{79} - 24q^{81} - 48q^{82} - 8q^{84} - 152q^{85} - 96q^{87} - 88q^{91} - 48q^{93} + 32q^{94} - 100q^{97} + 16q^{99} + O(q^{100})$$

## 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.ch.a $$152$$ $$4.360$$ None $$0$$ $$0$$ $$0$$ $$8$$

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

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