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arXiv · 1708.00652

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

Francis Brown·Richard Hain
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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 quasi-periods of modular forms.

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Francis Brown, Richard Hain. 2017-12-22. Algebraic de Rham theory for weakly holomorphic modular forms of level one. https://doi.org/10.2140/ant.2018.12.723

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