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arXiv · 1210.1243

Evaluating modular forms on Shimura curves

Paul D. Nelson
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Abstract

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.

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Paul D. Nelson. 2012-10-03. Evaluating modular forms on Shimura curves. https://arxiv.org/abs/1210.1243

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