  In this paper we discuss the problem of numerically computing Petersson inner
products of modular forms, given their $q$-expansion at $\infty$. A formula of
Nelson reduces this to obtaining $q$-expansions at all cusps, and we describe
two algorithms based on linear interpolation for numerically obtaining such
expansions. We apply our methods to numerically verify constants arising in an
explicit version of Ichino's triple-product formula relating $\langle
fg,h\rangle$ to the central value of $L(f\times g\times \bar{h},s)$, for three
modular forms $f,g,h$ of compatible weights and characters.
