  We propose a manifestly U-duality invariant modular form for the D^4 R^4
interaction in type IIB string theory compactified on T^2. It receives
perturbative contributions upto two loops, and non-perturbative contributions
from D-instantons and (p,q) string instantons wrapping T^2. We provide evidence
for this modular form by showing that the coefficients at tree level and at one
loop precisely match those obtained using string perturbation theory. Using
duality, parts of the perturbative amplitude are also shown to match exactly
the results obtained from eleven dimensional supergravity compactified on T^3
at one loop. Decompactifying the theory to nine dimensions, we obtain a
U-duality invariant modular form, whose coefficients at tree level and at one
loop agree with string perturbation theory.
