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It is known that for any knot $K$ every (meridionally) trace-free$SL_2(C)$-representation of the knot group $G(K)$ gives an$SL_2(C)$-representation of the fundamental group $\pi_1(\Sigma_2K)$ of the2-fold branched covering $\Sigma_2K$ of the 3-sphere branched along $K$. Inthis paper, we show by using a notion called a ghost character of a knot thatfor the (4,5)-torus knot $T_{4,5}$ the fundamental group$\pi_1(\Sigma_2T_{4,5})$ has an $SL(2,C)$-representation which cannot be givenby any trace-free $SL_2(C)$-representation of $G(T_{4,5})$.

Ghost characters and character varieties of 2-fold branched covers