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Let K be a knot in an integral homology 3-sphere and let B denote the 2-foldbranched cover of the integral homology sphere branched along K. We construct amap from the slice of characters with trace free along meridians in the SL(2,C)-character variety of the knot exterior to the SL(2, C)-character variety of2-fold branched cover B. When this map is surjective, it describes the slice asthe 2-fold branched cover over the SL(2, C)-character variety of B withbranched locus given by the abelian characters, whose preimage is precisely theset of metabelian characters. We show that each of metabelian character can berepresented as the character of a binary dihedral representation of the knotgroup. This map is shown to be surjective for all 2-bridge knots and allpretzel knots of type (p, q, r). An extension of this framework to n-foldbranched covers is also described.

On the geometry of the slice of trace--free SL(2,C)-characters of a knot group