  We study the multiplicity of the jumping numbers of an $\mathfrak m$-primary
ideal $\mathfrak a$ in a two-dimensional local ring with a rational
singularity. The formula we provide for the multiplicities leads to a very
simple and efficient method to detect whether a given rational number is a
jumping number. We also give an explicit description of the Poincar\'e series
of multiplier ideals associated to $\mathfrak a$ proving, in particular, that
it is a rational function.
