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.



Weierstrass points on modular curves
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).


