In a 1984 paper, Kohnen and Zagier study certain generators for the space of modular cusp forms of even weight and full level, which have rational Eichler-Shimura periods. After recalling the Eichler-Shimura theory, I will present a formula decomposing an arbitrary cusp form in terms of these generators. As an application, I discuss an explicit version of the Shimura correspondence between forms of integral and half-integral weight.