  We show that Mildenhall's theorem implies that the indecomposable higher Chow
group of a self-product of an elliptic curve over the complex number field is
infinite dimensional, if the elliptic curve is modular and defined over
rational numbers. For the moment we cannot prove even the nontriviality of the
indecomposable higher Chow group by a complex analytic method in this case.
