  Using the theory of Stienstra and Beukers, we prove various elementary
congruences for the numbers \sum
\binom{2i_1}{i_1}^2\binom{2i_2}{i_2}^2...\binom{2i_k}{i_k}^2, where k,n \in N,
and the summation is over the integers i_1, i_2, ...i_k >= 0 such that
i_1+i_2+...+i_k=n. To obtain that, we study the arithmetic properties of
Fourier coefficients of certain (weakly holomorphic) modular forms.
