• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1445-1457
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• 2016

For a positive integer N divisible by 4, let ${\mathcal{O}}^1_N({\mathbb{Q}})$ be the ring of weakly holomorphic modular functions for the congruence subgroup ${\Gamma}^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring ${\mathcal{O}}^1_N({\mathbb{Q}})$ over ${\mathbb{Q}}$ in terms of both Fricke functions and Siegel functions, from which we are able to classify all Fricke families of such level N.