# Properties

 Label 546.2.bz Level $546$ Weight $2$ Character orbit 546.bz Rep. character $\chi_{546}(31,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $80$ Newform subspaces $2$ Sturm bound $224$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.bz (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$224$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 480 80 400
Cusp forms 416 80 336
Eisenstein series 64 0 64

## Trace form

 $$80q + 40q^{9} + O(q^{10})$$ $$80q + 40q^{9} - 8q^{11} + 8q^{14} + 40q^{16} + 48q^{19} + 8q^{21} + 16q^{22} + 48q^{29} - 16q^{35} - 40q^{37} - 8q^{39} - 8q^{44} + 16q^{46} + 64q^{50} - 8q^{53} - 32q^{57} + 24q^{58} - 24q^{61} + 16q^{65} - 24q^{67} - 24q^{68} + 16q^{70} + 16q^{71} - 24q^{73} - 80q^{74} - 16q^{78} - 40q^{81} - 16q^{84} - 80q^{85} - 40q^{86} - 144q^{87} - 96q^{89} - 16q^{91} - 32q^{92} - 72q^{94} - 16q^{99} + O(q^{100})$$

## 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.bz.a $$40$$ $$4.360$$ None $$0$$ $$0$$ $$0$$ $$-4$$
546.2.bz.b $$40$$ $$4.360$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

$$S_{2}^{\mathrm{old}}(546, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$