If all zeros of a weakly holomorphic modular form in the fundamental domain lie on the lower boundary, then so do the zeros of its Serre derivative.
Gun,On the zeros of certain cusp forms, Math
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The Serre Derivatives and Zeros of Modular Forms
If all zeros of a weakly holomorphic modular form in the fundamental domain lie on the lower boundary, then so do the zeros of its Serre derivative.