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If I have a modular curve, how does one in general find a Hauptmodul for this curve?

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In general one does not, since (here I assume we are talking about congruence subgroups of $\operatorname{SL}_2(\mathbb{Z})$) there are only finitely many modular curves of genus zero. This finite list is known and Hauptmoduls have been written down, probably more than a century ago in most cases. Would you be satisfied by references to the literature, or is there more to your question than that? –  Pete L. Clark Jun 30 '11 at 17:39
Yes I would definitely be satisfied by references. Thanks! –  ADF Jun 30 '11 at 19:08

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