Algebraic de Rham theory for weakly holomorphic modular forms of level one

Brown, Francis; Hain, Richard

doi:10.2140/ant.2018.12.723

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Algebraic de Rham theory for weakly holomorphic modular forms of level one

Francis Brown and Richard Hain

Vol. 12 (2018), No. 3, 723–750

DOI: 10.2140/ant.2018.12.723

Abstract

We establish an Eichler–Shimura isomorphism for weakly modular forms of level one. We do this by relating weakly modular forms with rational Fourier coefficients to the algebraic de Rham cohomology of the modular curve with twisted coefficients. This leads to formulae for the periods and quasiperiods of modular forms.

Keywords

weakly holomorphic modular form, algebraic de Rham cohomology

Mathematical Subject Classification 2010

Primary: 11F11

Secondary: 11F23, 11F25, 11F67

Milestones

Received: 3 August 2017

Revised: 22 December 2017

Accepted: 22 January 2018

Published: 12 June 2018

Authors

Francis Brown
All Souls College Oxford United Kingdom

Richard Hain
Department of Mathematics Duke University Durham, NC United States

Vol. 12, No. 3, 2018