# Properties

 Label 168.2.ba Level $168$ Weight $2$ Character orbit 168.ba Rep. character $\chi_{168}(5,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $56$ 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.ba (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$168$$ Character field: $$\Q(\zeta_{6})$$ 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 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

## Trace form

 $$56 q - 2 q^{4} - 8 q^{7} - 2 q^{9} + O(q^{10})$$ $$56 q - 2 q^{4} - 8 q^{7} - 2 q^{9} - 6 q^{10} - 18 q^{12} - 20 q^{15} - 10 q^{16} - 4 q^{22} - 12 q^{24} + 8 q^{25} - 18 q^{28} + 22 q^{30} - 12 q^{31} - 6 q^{33} + 4 q^{36} - 8 q^{39} - 66 q^{40} + 36 q^{42} - 8 q^{46} - 16 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 22 q^{58} - 8 q^{60} - 30 q^{63} + 4 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 36 q^{79} + 6 q^{81} + 48 q^{82} + 48 q^{84} - 24 q^{87} - 26 q^{88} + 48 q^{94} + 90 q^{96} + O(q^{100})$$

## 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.ba.a $4$ $1.341$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$-6$$ $$6$$ $$-2$$ $$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$$
168.2.ba.b $4$ $1.341$ $$\Q(\sqrt{2}, \sqrt{-3})$$ $$\Q(\sqrt{-6})$$ $$0$$ $$6$$ $$-6$$ $$-2$$ $$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-1+\cdots)q^{5}+\cdots$$
168.2.ba.c $48$ $1.341$ None $$0$$ $$0$$ $$0$$ $$-4$$