A modular form is a function $f(\tau)$ that obeys
$$f\left(\frac{a \tau+b}{c \tau+d}\right) = \frac1{(c \tau+d)^n} f(\tau).$$
for some integer $n$, and some subgroup of matrices $\pmatrix{a&b\cr c&d\cr}\in SL(2,\Bbb{Z}).$ Usually, $f$ is expanded into a $q$-series
$$f = ... + a_0 + a_1 q + a_2 q^2 + ...$$
(I am not sure wether it is ok for this series to have a tail) where $q = \exp(2\pi i \tau)$.
Can you write down a formula for how $\pmatrix{a&b\cr c&d\cr}$ acts, directly on $q$-series?
In author words, is $\Bbb{C}[[q]]$ or $\Bbb{C}((q))$ a $SL(2,\Bbb{Z})$-module?