Abstract
Let Mk!(p) be the space of weakly holomorphic modular forms of weight k on Γ0(p), and let Mk!−(p) be the minus space which is the subspace of Mk!(p) consisting of all eigenforms of the Fricke involution Wp with eigenvalue −1. We are interested in finding a canonical basis for the minus space Mk!−(p) for certain levels. Using this result, along with previous works of Choi and Kim [CK13], we find a canonical basis for the space Mk!(p), and investigate its arithmetic properties. We also give another generalization of [CK13] to the cases of square-free integer levels.
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