# Properties

 Label 546.2.i Level $546$ Weight $2$ Character orbit 546.i Rep. character $\chi_{546}(79,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $32$ Newform subspaces $11$ Sturm bound $224$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$11$$ Sturm bound: $$224$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$17$$

## 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

 $$32 q - 16 q^{4} + 8 q^{5} + 8 q^{6} - 12 q^{7} - 16 q^{9} + O(q^{10})$$ $$32 q - 16 q^{4} + 8 q^{5} + 8 q^{6} - 12 q^{7} - 16 q^{9} + 4 q^{10} + 8 q^{11} + 8 q^{13} - 4 q^{14} - 8 q^{15} - 16 q^{16} - 12 q^{17} - 8 q^{19} - 16 q^{20} - 4 q^{24} - 20 q^{25} + 12 q^{28} - 24 q^{29} - 8 q^{30} + 20 q^{31} - 4 q^{33} + 16 q^{34} - 24 q^{35} + 32 q^{36} + 20 q^{38} + 4 q^{40} + 64 q^{41} + 12 q^{42} - 32 q^{43} + 8 q^{44} + 8 q^{45} - 8 q^{46} + 24 q^{47} - 16 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{52} + 12 q^{53} - 4 q^{54} + 8 q^{55} - 4 q^{56} + 16 q^{57} + 12 q^{58} + 4 q^{60} - 4 q^{61} + 16 q^{62} + 32 q^{64} - 8 q^{65} + 16 q^{67} - 12 q^{68} - 32 q^{69} - 12 q^{70} - 16 q^{73} + 16 q^{76} - 8 q^{77} + 12 q^{79} + 8 q^{80} - 16 q^{81} - 32 q^{85} - 16 q^{86} + 4 q^{87} - 16 q^{89} - 8 q^{90} + 16 q^{91} - 8 q^{93} + 4 q^{94} - 24 q^{95} - 4 q^{96} - 40 q^{97} - 48 q^{98} - 16 q^{99} + O(q^{100})$$

## 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.i.a $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$-3$$ $$-1$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.i.b $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$1$$ $$-1$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.i.c $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$4$$ $$-1$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.i.d $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$0$$ $$-5$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.i.e $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$2$$ $$-5$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.i.f $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$-1$$ $$-1$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.i.g $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$2$$ $$-1$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
546.2.i.h $4$ $4.360$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$-2$$ $$0$$ $$2$$ $$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots$$
546.2.i.i $4$ $4.360$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$2$$ $$4$$ $$-2$$ $$q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots$$
546.2.i.j $4$ $4.360$ $$\Q(\sqrt{-3}, \sqrt{7})$$ None $$2$$ $$-2$$ $$2$$ $$0$$ $$q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$$
546.2.i.k $6$ $4.360$ 6.0.21870000.1 None $$3$$ $$3$$ $$-3$$ $$3$$ $$q+(1+\beta _{2})q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(546, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$