# Properties

 Label 546.2.cg Level $546$ Weight $2$ Character orbit 546.cg Rep. character $\chi_{546}(145,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $72$ Newform subspaces $2$ Sturm bound $224$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.cg (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: $$1$$ 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 72 408
Cusp forms 416 72 344
Eisenstein series 64 0 64

## Trace form

 $$72q + 36q^{9} + O(q^{10})$$ $$72q + 36q^{9} + 16q^{11} - 4q^{12} + 8q^{14} - 72q^{16} + 28q^{19} + 12q^{21} - 8q^{22} + 4q^{28} - 24q^{29} + 4q^{31} + 8q^{35} + 28q^{37} + 48q^{39} + 48q^{41} + 60q^{43} - 8q^{44} - 8q^{46} - 4q^{49} - 32q^{50} + 24q^{51} - 4q^{52} - 8q^{53} - 24q^{55} + 24q^{56} + 20q^{57} + 24q^{58} + 24q^{61} + 72q^{62} + 88q^{65} - 28q^{67} + 16q^{70} - 8q^{71} + 44q^{73} - 80q^{74} - 56q^{75} - 32q^{76} - 16q^{78} - 36q^{81} - 48q^{82} + 48q^{83} - 16q^{84} - 8q^{85} - 40q^{86} - 96q^{89} - 48q^{91} - 32q^{92} - 56q^{93} - 124q^{97} - 96q^{98} + 8q^{99} + O(q^{100})$$

## 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.cg.a $$32$$ $$4.360$$ None $$0$$ $$0$$ $$0$$ $$-4$$
546.2.cg.b $$40$$ $$4.360$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

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