Recently, Bruinier, Kohnen and Ono obtained an explicit description of the action of the theta-operator on meromorphic modular forms
f
f
on
S
L
2
(
Z
)
SL_2(\mathbb {Z})
in terms of the values of modular functions at points in the divisor of
f
f
. Using this result, they studied the exponents in the infinite product expansion of a modular form and recurrence relations for Fourier coefficients of a modular form. In this paper, we extend these results to meromorphic modular forms on
Γ
0
(
N
)
\Gamma _0(N)
for an arbitrary positive integer
N
>
1
N>1
.