# Properties

 Label 546.2.c Level $546$ Weight $2$ Character orbit 546.c Rep. character $\chi_{546}(337,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $5$ Sturm bound $224$ Trace bound $10$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$546 = 2 \cdot 3 \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 546.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$224$$ Trace bound: $$10$$ 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 120 12 108
Cusp forms 104 12 92
Eisenstein series 16 0 16

## Trace form

 $$12 q - 12 q^{4} + 12 q^{9} + O(q^{10})$$ $$12 q - 12 q^{4} + 12 q^{9} + 16 q^{13} + 12 q^{16} + 16 q^{17} - 8 q^{22} - 8 q^{23} + 4 q^{25} + 24 q^{29} + 8 q^{30} + 8 q^{35} - 12 q^{36} - 16 q^{38} - 8 q^{39} - 4 q^{42} - 24 q^{43} - 12 q^{49} + 16 q^{51} - 16 q^{52} + 40 q^{53} - 64 q^{55} + 16 q^{61} - 12 q^{64} - 24 q^{65} + 16 q^{66} - 16 q^{68} - 16 q^{69} - 16 q^{74} + 32 q^{77} + 4 q^{78} + 16 q^{79} + 12 q^{81} - 8 q^{82} - 8 q^{87} + 8 q^{88} + 4 q^{91} + 8 q^{92} - 8 q^{94} + O(q^{100})$$

## 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.c.a $2$ $4.360$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+iq^{2}-q^{3}-q^{4}-iq^{5}-iq^{6}+iq^{7}+\cdots$$
546.2.c.b $2$ $4.360$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots$$
546.2.c.c $2$ $4.360$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}-iq^{7}+\cdots$$
546.2.c.d $2$ $4.360$ $$\Q(\sqrt{-1})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots$$
546.2.c.e $4$ $4.360$ $$\Q(i, \sqrt{17})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots$$

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

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