Siegel's formula for genus 2

Let $S$ be a semi-integral, symmetric, positive-definite $m\times m$ matrix; $m\geqslant n\geqslant1$. By the Siegel fundamental formula we mean the identity between the Siegel theta series of genus $n$, associated with the genus of the matrix $S$, and the correspond ing Eisenstein-Siegel series (C. L. Siegel, Lectures on the Analytical Theory of Quadratic Forms, 3rd rev. edition, Peppmüller, Göttingen, 1963). The validity of the mentioned formula for $m/2\leqslant n+1$ is an open problem in the general case. In this paper we prove Siegel's formula for $n=2$, $m=6$.