Series involving bessel functions

Question

I'm dealing with the following type of series:

$$S = \sum_{m = 1}^{\infty} a_{m} \frac{J_{\nu+\lambda}(m \pi)}{m^{\lambda}},$$

where $\sum_{m = 1}^{\infty} a_{m} < \infty.$ There is anyway to know the sign of $S$?

Thanks in advanced