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Darrin Doud

214 TMCB Department of Mathematics Brigham Young University Provo, UT 84602

phone: (801)422-1204 fax: (801)422-0504 e-mail:

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Two-divisibility of coefficients of certain weakly holomorphic modular forms

with Paul Jenkins and John Lopez

The Ramanujan Journal, 28, (2012), 89-111.

Abstract: We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly divisible by 2.

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GP program used in the paper

The program described in the paper to compute two-dissections of weakly holomorphic modular functions is written for the Pari/GP system and is available here.

Cited by:

• Nickolas Andersen and Paul Jenkins, Divisibility properties of coefficients of level p modular functions for genus zero primes, arXiv preprint, 2011.
• Seiichi Hanamoto, Three-divisibility of Fourier coefficients of weakly holomorphic modular forms, Ramanujan J., to appear.