Distribution of mass of holomorphic cusp forms

We prove an upper bound for the L 4 -norm and for the L 2 -norm restricted to the vertical geodesic of a holomorphic Hecke cusp form f of large weight k . The method is based on Watson’s formula and estimating a mean value of certain L -functions of degree 6. Further applications to restriction problems of Siegel modular forms and subconvexity bounds of degree 8 L -functions are given.