If I have a modular curve, how does one in general find a Hauptmodul for this curve?
Hauptmoduls for modular curves
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number-theory
algebraic-geometry
modular-forms
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3In 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? – 2011-06-30
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0Yes I would definitely be satisfied by references. Thanks! – 2011-06-30