A class of modular functions (Q1032762)

In this paper, the author relaxes the condition in Theorem 2 of [\textit{W. Kohnen}, Proc. Am. Math. Soc. 133, No. 1, 65--70 (2004; Zbl 1105.11009)] that if a modular form \(f\) of integral weight on \(\Gamma_ 0(N)\), \(N\) squarefree, has no zeros or poles in \(\mathcal H\), then the uniquely determined complex numbers \(c(n)\) depend only on the \(\gcd(n,N)\), in order to include a larger class of \(N\). Then similar results on congruence subgroups other than \(\Gamma_0(N)\) are proved.