Let M#k(52) be the space of weight k level 52 weakly holomorphic modular forms with poles only at infinity, and S#k(52) the subspace of forms which vanish at all cusps other than infinity. For these spaces we construct canonical bases, indexed by the order of vanishing at infinity. We prove that the coefficients of the canonical basis elements satisfy a duality property. Further, we give closed forms for the generating functions of these basis elements.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Adams, Daniel Meade, "Spaces of Weakly Holomorphic Modular Forms in Level 52" (2017). All Theses and Dissertations. 6482.
modular forms, Zagier duality, weakly holomorphic