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Rational decomposition of modular forms

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Abstract

We prove explicit formulas decomposing cusp forms of even weight for the modular group, in terms of generators having rational periods, and in terms of generators having rational Fourier coefficients. Using the Shimura correspondence, we also give a decomposition of Hecke cusp forms of half integral weight k+1/2 with k even in terms of forms with rational Fourier coefficients, given by Rankin–Cohen brackets of theta series with Eisenstein series.

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Authors and Affiliations

  1. Institute of Mathematics Simion Stoilow of the Romanian Academy, Bucharest, Romania

    Alexandru A. Popa

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  1. Alexandru A. Popa
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Correspondence to Alexandru A. Popa.

Additional information

This work was supported in part by the European Community’s Seventh Framework Programme under grant agreement PIRG05-GA-2009-248569.

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Popa, A.A. Rational decomposition of modular forms. Ramanujan J 26, 419–435 (2011). https://doi.org/10.1007/s11139-011-9301-6

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