ON THE MINUS PARTS OF CLASSICAL POINCARÉ SERIES

Let Sk(N) be the space of cusp forms of weight k for Γo(N). We show that Sk(N) is the direct sum of subspaces Sk⁺((N) and Sk⁻(N). Where Sk⁺(N) is the vector space of cusp forms of weight k for the group Γo⁺(N) generated by Γo(N) and WN and Sk⁻(N) is the subspace consisting of elements f in Sk(N) satisfying f|kWN = -f. We find generators spanning the space Sk⁻(N) from Poincare series and give all linear relations among such generators.

Abstract

1. Introduction and statement of results

2. Harmonic weak Maass forms

3. Proof of Theorem 1.1

References

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