Abstract
Kaneko and Zagier proved the relation between the Atkin orthogonal polynomials and supersingular j-polynomials for PSL 2(ℤ). Tsutsumi also proved its relation for the Hecke subgroups of level less than or equal to 4. In this paper, we define the Atkin inner product for the Fricke groups of level less than or equal to 3 and construct the Atkin orthogonal polynomials. Then, we give the relation between supersingular [Formula: see text]-polynomials defined by Koike and its polynomials. We also give extremal quasimodular forms of depth 1 by using its orthogonal polynomials.
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