Cusp forms as p-adic limits

Ahlgren and Samart relate three cusp forms with complex multiplication to certain weakly holomorphic modular using p-adic bounds related their Fourier coefficients. In these examples, result strengthens a theorem of Guerzhoy, Kent, Ono which pairs CM via limits. use only the theory Hecke operators, whereas harmonic Maass forms. Here we extend Samart's work all cases where form space is one-dimensional has trivial Nebentypus. Along way, obtain duality relating two families that arise naturally in each case.