  Using the circle method, we show that for a fixed positive definite integral
quadratic form $A$, the expected asymptotic formula for the number of
representations of a positive definite integral quadratic form $B$ by $A$ holds
true, providing that the dimension of $A$ is large enough in terms of the
dimension of $B$ and the maximum ratio of the successive minima of $B$, and
providing that $B$ is sufficiently large in terms of $A$.
