# Properties

 Label 546.2.bv Level $546$ Weight $2$ Character orbit 546.bv Rep. character $\chi_{546}(317,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $144$ 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.bv (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 480 144 336
Cusp forms 416 144 272
Eisenstein series 64 0 64

## Trace form

 $$144q - 16q^{7} + O(q^{10})$$ $$144q - 16q^{7} + 72q^{16} + 16q^{18} + 8q^{19} + 8q^{21} + 24q^{27} - 8q^{28} - 8q^{31} + 12q^{33} - 8q^{37} + 16q^{39} - 40q^{45} + 8q^{46} + 8q^{52} - 12q^{54} - 32q^{55} + 16q^{57} + 8q^{58} - 32q^{61} - 40q^{63} - 32q^{66} - 8q^{67} + 16q^{72} + 80q^{73} - 16q^{76} + 16q^{78} - 112q^{79} - 48q^{81} + 16q^{84} - 80q^{85} + 96q^{87} - 32q^{91} + 36q^{93} - 64q^{94} - 144q^{97} - 32q^{99} + O(q^{100})$$

## 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.bv.a $$144$$ $$4.360$$ None $$0$$ $$0$$ $$0$$ $$-16$$

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

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