  Given a modular form which is not a cusp form
$M_k(z)=\sum_{n=0}^{\infty}r_ne^{2\pi inz}$ of weight $k \geq 4$, we define the
series $M_{k,s}(x)=\sum_{n=1}^{\infty}\frac{r_n}{n^s}\sin(2\pi nx),$ which
converges for all $x\in\mathbb{R}$ when $s>k$. In this paper, we compute the
H\"{o}lder regularity exponent of $M_{k,s}$ at irrational points. In our
analysis we apply wavelets methods proposed by Jaffard in 1996 in the study of
the Riemann series. We find that the H\"{o}lder regularity exponent at a point
$x$ is related to the fine diophantine properties of $x$, in a very precise
way.
