Weierstrass points and modular forms (Q762573)

Let \(X=X_ 0(p)\) be the compact Riemann surface which is the modular curve \(X=\Gamma_ 0(p)\setminus H\cup \{cusps\}.\) The Weierstrass points on X are given as the zeros of the Wronskian W of X, which in this case is a modular form of weight \(g(g+1)\) for \(\Gamma_ 0(p)\) which can be given rather explicitly. Atkin proved that the cusps of \(X_ 0(p)\) are not Weierstrass points [cf. \textit{A. P. Ogg}, Ill. J. Math. 22, 31-35 (1978; Zbl 0374.14005)]. In this paper it is shown that the Fourier coefficients of W are integral, and that W satisfies a particular congruence modulo p (with \(p\geq 23\), cf. theorem on page 137). From this the result of Atkin follows.