Properties

 Label 546.2.s Level $546$ Weight $2$ Character orbit 546.s Rep. character $\chi_{546}(43,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $24$ Newform subspaces $5$ 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.s (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ 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 24 216
Cusp forms 208 24 184
Eisenstein series 32 0 32

Trace form

 $$24 q + 12 q^{4} - 12 q^{9} + O(q^{10})$$ $$24 q + 12 q^{4} - 12 q^{9} + 24 q^{11} + 8 q^{13} + 24 q^{15} - 12 q^{16} + 8 q^{17} + 8 q^{22} + 8 q^{23} - 40 q^{25} - 8 q^{30} - 24 q^{33} - 8 q^{35} + 12 q^{36} + 16 q^{38} + 8 q^{39} - 24 q^{41} + 4 q^{42} - 12 q^{43} + 12 q^{46} + 12 q^{49} + 8 q^{51} + 16 q^{52} - 64 q^{53} - 8 q^{55} - 24 q^{58} + 96 q^{59} + 8 q^{61} - 24 q^{64} + 24 q^{65} - 16 q^{66} + 36 q^{67} - 8 q^{68} - 8 q^{69} + 24 q^{71} - 8 q^{74} - 32 q^{77} + 8 q^{78} + 32 q^{79} - 12 q^{81} + 8 q^{82} - 72 q^{85} - 16 q^{87} - 8 q^{88} - 72 q^{89} + 8 q^{91} + 16 q^{92} - 16 q^{94} - 48 q^{95} + O(q^{100})$$

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.s.a $4$ $4.360$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
546.2.s.b $4$ $4.360$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
546.2.s.c $4$ $4.360$ $$\Q(\zeta_{12})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
546.2.s.d $4$ $4.360$ $$\Q(\zeta_{12})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+\zeta_{12}q^{2}+(1-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots$$
546.2.s.e $8$ $4.360$ 8.0.195105024.2 None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(1+\beta _{4})q^{3}-\beta _{4}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(546, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(26, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(39, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(78, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(91, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(182, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(273, [\chi])$$$$^{\oplus 2}$$