  In this paper we discuss Waldspurger's local period integral for newforms in
new cases. The main ingredient is the work \cite{HN18} on Waldspurger's period
integral using the minimal vectors, and the explicit relation between the
newforms and the minimal vectors. We use a representation theoretical trick to
simplify computations for newforms. As an example, we compute the local
integral coming from a special arithmetic setting which was used to study
3-part full BSD conjecture in \cite{HSY}.
