• Title, Summary, Keyword: congruence of Fourier coefficients

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DETERMINATION OF THE FRICKE FAMILIES

  • Eum, Ick Sun;Shin, Dong Hwa
    • 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.