# Properties

 Label 546.2.l Level $546$ Weight $2$ Character orbit 546.l Rep. character $\chi_{546}(211,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $32$ Newform subspaces $12$ 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.l (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$224$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## 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

 $$32 q - 4 q^{2} - 16 q^{4} - 8 q^{5} + 8 q^{8} - 16 q^{9} + O(q^{10})$$ $$32 q - 4 q^{2} - 16 q^{4} - 8 q^{5} + 8 q^{8} - 16 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{13} + 8 q^{15} - 16 q^{16} + 12 q^{17} + 8 q^{18} - 16 q^{19} + 4 q^{20} - 8 q^{22} + 8 q^{23} + 40 q^{25} - 20 q^{26} + 4 q^{29} - 8 q^{30} - 4 q^{32} + 8 q^{33} + 8 q^{34} - 8 q^{35} - 16 q^{36} + 4 q^{37} - 16 q^{38} - 8 q^{39} - 8 q^{40} - 4 q^{41} - 4 q^{42} - 4 q^{43} - 16 q^{44} + 4 q^{45} + 12 q^{46} + 16 q^{47} - 16 q^{49} - 16 q^{50} + 8 q^{51} - 8 q^{52} - 8 q^{53} + 24 q^{55} + 4 q^{58} - 16 q^{60} + 28 q^{61} + 32 q^{64} + 44 q^{65} - 16 q^{66} + 12 q^{67} + 12 q^{68} + 8 q^{69} - 8 q^{71} - 4 q^{72} + 88 q^{73} + 12 q^{74} - 16 q^{76} - 32 q^{77} + 8 q^{78} - 32 q^{79} + 4 q^{80} - 16 q^{81} - 4 q^{82} - 64 q^{83} + 20 q^{85} - 16 q^{86} - 8 q^{88} - 8 q^{90} + 8 q^{91} - 16 q^{92} - 48 q^{95} + 8 q^{97} - 4 q^{98} - 16 q^{99} + O(q^{100})$$

## 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.l.a $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$-1$$ $$q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.b $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$6$$ $$1$$ $$q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.c $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-4$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.d $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-4$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.e $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.f $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$-4$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.g $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$4$$ $$1$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.h $2$ $4.360$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$8$$ $$-1$$ $$q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots$$
546.2.l.i $4$ $4.360$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$-2$$ $$-2$$ $$-6$$ $$2$$ $$q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$
546.2.l.j $4$ $4.360$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$-2$$ $$-2$$ $$2$$ $$-2$$ $$q+\beta _{1}q^{2}+\beta _{1}q^{3}+(-1-\beta _{1})q^{4}+\beta _{2}q^{5}+\cdots$$
546.2.l.k $4$ $4.360$ $$\Q(\sqrt{-3}, \sqrt{-43})$$ None $$-2$$ $$2$$ $$-8$$ $$2$$ $$q-\beta _{2}q^{2}+\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-2q^{5}+\cdots$$
546.2.l.l $4$ $4.360$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$-2$$ $$2$$ $$-2$$ $$-2$$ $$q+(-1+\beta _{2})q^{2}+(1-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(546, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$