# Properties

 Label 168.2.q Level $168$ Weight $2$ Character orbit 168.q Rep. character $\chi_{168}(25,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $8$ Newform subspaces $3$ Sturm bound $64$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 168.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$3$$ Sturm bound: $$64$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(168, [\chi])$$.

Total New Old
Modular forms 80 8 72
Cusp forms 48 8 40
Eisenstein series 32 0 32

## Trace form

 $$8 q + 2 q^{3} - 4 q^{9} + O(q^{10})$$ $$8 q + 2 q^{3} - 4 q^{9} + 4 q^{11} + 12 q^{13} - 4 q^{15} + 4 q^{17} + 14 q^{19} - 4 q^{21} - 12 q^{23} - 14 q^{25} - 4 q^{27} - 8 q^{29} - 10 q^{33} - 36 q^{35} - 2 q^{37} - 2 q^{39} + 24 q^{41} - 4 q^{43} - 12 q^{49} - 4 q^{51} - 28 q^{53} + 28 q^{55} + 12 q^{57} - 20 q^{61} + 6 q^{63} - 16 q^{65} + 2 q^{67} + 8 q^{69} + 16 q^{71} + 10 q^{73} + 22 q^{75} + 36 q^{77} - 20 q^{79} - 4 q^{81} + 40 q^{83} + 24 q^{85} + 2 q^{87} + 32 q^{89} - 26 q^{91} + 10 q^{93} + 32 q^{95} - 12 q^{97} - 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(168, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
168.2.q.a $2$ $1.341$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$1$$ $$q-\zeta_{6}q^{3}+(1-\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots$$
168.2.q.b $2$ $1.341$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-2$$ $$5$$ $$q+\zeta_{6}q^{3}+(-2+2\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots$$
168.2.q.c $4$ $1.341$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$2$$ $$1$$ $$-6$$ $$q+(1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(168, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(168, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 2}$$