The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultra-high dimensional setting, that is, when the dimension to sample size ratio p/n→∞. Based on this CLT result, we extend the covariance matrix test problem to the new ultrahigh dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the general asymptotic normality of eigenvalue statistics, as well as the two developed tests.