  Generalizing the method of Faltings-Serre, we rigorously verify that certain
abelian surfaces without extra endomorphisms are paramodular. To compute the
required Hecke eigenvalues, we develop a method of specialization of Siegel
paramodular forms to modular curves. In the appendix, Serre proves a result
extending his work on the reduction of G-invariant bilinear forms modulo primes
to the case of G-covariant forms.
