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What is knowns about Weierstrass points on modular curves? Are there any explicit formulas of them, or any information about Weierstrass gaps? I am interested in (compactifications of) the quotients of the upper half plane by $\Gamma(n)$, $\Gamma_1(n)$ or $\Gamma_0(n)$. The level $n$ may be assumed to be prime, if that helps.

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You might try google or MathSciNet yourself before asking on MathOverflow. It took 1 minute to find the following three articles:

MR2059755 (2006b:11056) Ahlgren, Scott . The arithmetic of Weierstrass points on modular curves X0(p). Galois theory and modular forms, 3--12, Dev. Math., 11, Kluwer Acad. Publ., Boston, MA, 2004.

MR1962053 (2004b:11086) Ahlgren, Scott ; Ono, Ken . Weierstrass points on X0(p) and supersingular j-invariants. Math. Ann. 325 (2003), no. 2, 355--368.

MR1946403 (2003j:11065) Ahlgren, Scott ; Papanikolas, Matthew . Higher Weierstrass points on X0(p). Trans. Amer. Math. Soc. 355 (2003), no. 4, 1521--1535 (electronic).

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