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In this paper we give quantitative local test vectors for Waldspurger'speriod integral (i.e., a toric period on $\text{GL}_2$) in new cases with jointramifications. The construction involves minimal vectors, rather than newformsand their variants. This paper gives a uniform treatment for the matrix algebraand division algebra cases under mild assumptions, and establishes an explicitrelation between the size of the local integral and the finite conductor$C(\pi\times\pi_{\chi^{-1}})$. As an application, we combine the test vectorresults with the relative trace formula, and prove a hybrid type subconvexitybound which can be as strong as the Weyl bound in proper range.

New test vector for Waldspurger's period integral, relative trace formula, and hybrid subconvexity bounds