  Let f be a newform, as specified by its Hecke eigenvalues, on a Shimura curve
X. We describe a method for evaluating f. The most interesting case is when X
arises as a compact quotient of the hyperbolic plane, so that classical
q-expansions are not available. The method takes the form of an explicit,
rapidly-convergent formula that is well-suited for numerical computation. We
apply it to the problem of computing modular parametrizations of elliptic
curves, and illustrate with some numerical examples.
