  This paper gives a quick way to construct all modular functions for the group
$\Gamma_0(N)$ having only a pole at $\tau = i \infty$. We assume that we are
given two modular functions $f,g$ for $\Gamma_0(N)$ with poles only at $i
\infty$ and coprime pole orders. As an application we obtain two new identities
from which one can derive that $p(11n+6)\equiv 0\pmod{11}$, here $p(n)$ is the
usual partition function.
