Weakly holomorphic Hecke eigenforms and Hecke eigenpolynomials

In the work of Bringmann, Guerzhoy, Kent and Ono [2] weakly holomorphic Hecke eigenforms are defined and constructed in the level one case by making use of harmonic weak Maass forms. In this paper we extend their results to higher level cases and give an explicit construction in terms of weakly holomorphic modular forms without relying on the theory of harmonic weak Maass forms. Moreover we find a basis for the space of period polynomials consisting of Hecke eigenpolynomials.