# Properties

 Label 546.2.o Level $546$ Weight $2$ Character orbit 546.o Rep. character $\chi_{546}(265,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $32$ Newform subspaces $4$ Sturm bound $224$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.o (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$91$$ Character field: $$\Q(i)$$ Newform subspaces: $$4$$ Sturm bound: $$224$$ Trace bound: $$11$$ 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 32 208
Cusp forms 208 32 176
Eisenstein series 32 0 32

## Trace form

 $$32q - 4q^{7} - 32q^{9} + O(q^{10})$$ $$32q - 4q^{7} - 32q^{9} - 16q^{11} - 8q^{14} - 32q^{16} - 12q^{21} - 16q^{22} - 4q^{28} + 16q^{35} - 24q^{37} + 40q^{39} - 16q^{44} + 8q^{46} + 32q^{50} + 32q^{53} - 24q^{57} - 24q^{58} + 4q^{63} - 64q^{65} + 80q^{67} + 56q^{70} + 80q^{71} + 32q^{74} - 8q^{78} - 48q^{79} + 32q^{81} - 12q^{84} + 80q^{85} - 80q^{86} - 36q^{91} - 16q^{92} - 56q^{93} - 48q^{98} + 16q^{99} + O(q^{100})$$

## 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.o.a $$8$$ $$4.360$$ 8.0.7442857984.4 None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{6}q^{3}+\beta _{6}q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots$$
546.2.o.b $$8$$ $$4.360$$ 8.0.836829184.2 None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{2}q^{2}+\beta _{7}q^{3}+\beta _{7}q^{4}+(\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots$$
546.2.o.c $$8$$ $$4.360$$ 8.0.836829184.2 None $$0$$ $$0$$ $$4$$ $$-8$$ $$q+\beta _{3}q^{2}+\beta _{7}q^{3}-\beta _{7}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$$
546.2.o.d $$8$$ $$4.360$$ 8.0.7442857984.4 None $$0$$ $$0$$ $$4$$ $$4$$ $$q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{6}q^{4}+(-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots$$

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

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