  This article offers sharp spatial and temporal mean-square regularity results
for a class of semi-linear parabolic stochastic partial differential equations
(SPDEs) driven by infinite dimensional fractional Brownian motion with the
Hurst parameter greater than one-half. In addition, mean-square numerical
approximation of such problem are investigated, performed by the spectral
Galerkin method in space and the linear implicit Euler method in time. The
obtained sharp regularity properties of the problems enable us to identify
optimal mean-square convergence rates of the full discrete scheme. These
theoretical findings are accompanied by several numerical examples.
