# Properties

 Label 168.2.v Level 168 Weight 2 Character orbit v Rep. character $$\chi_{168}(11,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 56 Newform subspaces 1 Sturm bound 64 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$168 = 2^{3} \cdot 3 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 168.v (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$168$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$64$$ Trace bound: $$0$$

## 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

 $$56q - 2q^{3} - 2q^{4} - 8q^{6} - 2q^{9} + O(q^{10})$$ $$56q - 2q^{3} - 2q^{4} - 8q^{6} - 2q^{9} + 6q^{10} + 10q^{12} - 10q^{16} - 10q^{18} - 4q^{19} - 20q^{22} - 8q^{24} - 16q^{25} - 8q^{27} - 22q^{28} - 12q^{30} - 14q^{33} - 56q^{34} + 4q^{36} + 14q^{40} - 8q^{42} - 16q^{43} - 12q^{46} + 64q^{48} - 16q^{49} - 34q^{51} - 8q^{52} + 32q^{54} + 4q^{57} - 18q^{58} + 40q^{60} + 4q^{64} - 20q^{66} - 36q^{67} - 42q^{70} + 22q^{72} + 4q^{73} + 104q^{76} + 28q^{78} - 10q^{81} + 52q^{82} + 4q^{84} + 46q^{88} + 140q^{90} + 72q^{91} - 46q^{96} - 32q^{97} - 44q^{99} + O(q^{100})$$

## 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.v.a $$56$$ $$1.341$$ None $$0$$ $$-2$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database