# Properties

 Label 68.1.f Level 68 Weight 1 Character orbit f Rep. character $$\chi_{68}(47,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 2 Newforms 1 Sturm bound 9 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$68 = 2^{2} \cdot 17$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 68.f (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$68$$ Character field: $$\Q(i)$$ Newforms: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(68, [\chi])$$.

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 2 0 0 0

## Trace form

 $$2q$$ $$\mathstrut -\mathstrut 2q^{4}$$ $$\mathstrut -\mathstrut 2q^{5}$$ $$\mathstrut +\mathstrut O(q^{10})$$ $$2q$$ $$\mathstrut -\mathstrut 2q^{4}$$ $$\mathstrut -\mathstrut 2q^{5}$$ $$\mathstrut +\mathstrut 2q^{10}$$ $$\mathstrut +\mathstrut 2q^{16}$$ $$\mathstrut -\mathstrut 2q^{17}$$ $$\mathstrut -\mathstrut 2q^{18}$$ $$\mathstrut +\mathstrut 2q^{20}$$ $$\mathstrut +\mathstrut 2q^{29}$$ $$\mathstrut -\mathstrut 2q^{37}$$ $$\mathstrut -\mathstrut 2q^{40}$$ $$\mathstrut +\mathstrut 2q^{41}$$ $$\mathstrut +\mathstrut 2q^{45}$$ $$\mathstrut -\mathstrut 2q^{50}$$ $$\mathstrut -\mathstrut 2q^{58}$$ $$\mathstrut -\mathstrut 2q^{61}$$ $$\mathstrut -\mathstrut 2q^{64}$$ $$\mathstrut +\mathstrut 2q^{68}$$ $$\mathstrut +\mathstrut 2q^{72}$$ $$\mathstrut +\mathstrut 2q^{73}$$ $$\mathstrut +\mathstrut 2q^{74}$$ $$\mathstrut -\mathstrut 2q^{80}$$ $$\mathstrut -\mathstrut 2q^{81}$$ $$\mathstrut +\mathstrut 2q^{82}$$ $$\mathstrut +\mathstrut 2q^{85}$$ $$\mathstrut +\mathstrut 2q^{90}$$ $$\mathstrut -\mathstrut 2q^{97}$$ $$\mathstrut +\mathstrut 2q^{98}$$ $$\mathstrut +\mathstrut O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(68, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field Image CM RM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
68.1.f.a $$2$$ $$0.034$$ $$\Q(\sqrt{-1})$$ $$D_{4}$$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$$