  By dimensionally reducing the higher derivative corrections of
ten-dimensional IIB theory on a torus we deduce constraints on the E_{n+1}
automorphic forms that occur in d=10-n dimensions. In particular we argue that
these automorphic forms involve the representation of E_{n+1} with fundamental
weight \lambda^{n+1}, which is also the representation to which the string
charges in d dimensions belong. We also consider a similar calculation for the
reduction of higher derivative terms in eleven-dimensional M-theory.
