TITLE: Picard-Fuchs equations for modular functions
QUESTION [14 upvotes]: Hello, MathOverflow community!
Suppose we have a modular curve of genus $0$, whose rational function field is generated by the modular function $f$. We can view $f$ as the parameter for some pencil of elliptic curves over $\mathbb{C}$. Under certain conditions, it is possible to express $f$ as the inverse function of the ratio of two linearly independent solutions of a second-order linear differential equation. The prototypical example is the case of the period integrals of the Legendre elliptic curve $y^2=x(x-1)(x-\lambda)$, which satisfy the Fuchsian equation $$\lambda(1-\lambda)D^2y + (1-2\lambda)Dy - y/4=0,$$ where $D=d/d\lambda$. We can interpret this differential equation as measuring the variation of the periods of an elliptic curve, as the parameter $\lambda$ changes. 
Now my question is : have other Picard-Fuchs equations been calculated for modular functions? In principle, there should be many such equations; the Picard-Fuchs equation for Klein's $j$ function, without the calculation, is given in (Harnad, McKay). I have seen the calculation for the $\lambda$ case carried out in a few books. But I have not seen such equations for the Hauptmodul associated to the other genus $0$ modular curves.
Any thoughts, comments, questions or references are much appreciated.
Please be kind, as I am only an undergraduate. (There seems to be much "tough love" here!)

REPLY [2 votes]: See the following papers as well...

Linear Ordinary Differential
Equations Satisfied by Modular
Forms by Xiaolong Ji and Yujie
Ma
Modular Functions and Their
Differential Equations by Joshua
L. Wiczer See also
http://arxiv.org/PS_cache/math/pdf/0611/0611291v1.pdf
MR2031441 (2005b:11049)  Yang, Yifan
. On differential equations
satisfied by modular forms. Math. Z.
246  (2004),  no. 1-2, 1--19.