Vol. 12, No. 3, 2018

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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

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.

weakly holomorphic modular form, algebraic de Rham cohomology
Mathematical Subject Classification 2010
Primary: 11F11
Secondary: 11F23, 11F25, 11F67
Received: 3 August 2017
Revised: 22 December 2017
Accepted: 22 January 2018
Published: 12 June 2018
Francis Brown
All Souls College
United Kingdom
Richard Hain
Department of Mathematics
Duke University
Durham, NC
United States