A CONGRUENCE PROPERTY OF FOURIER COEFFICIENTS FOR MODULAR FORMS
We investigate and propose solutions to some problems posed by Pacetti [16]. Indeed, specific sequences of integers linked to elliptic curves given on the field of rational numbers were of particular interest. These sequences are the coefficients ap, for primes p, of Fourier expansion of the modular forms, associated to the elliptic curves labeled 17a1 and 19a1, respectively, on John Cremona’s Table. Congruence properties of these coefficients were questioned. Based on Eichler-Shimura and Taylor-Wiles theorems, we prove a general congruence relation for coefficients ap. The result allows to compute and gives the distribution of the modular coefficients ap associated to elliptic curves grouped by isogeny classes.
elliptic curves, congruence modulo p, modular coefficients, modular form, isogeny classes.
Received: April 9, 2020; Accepted: June 18, 2020; Published: March 26, 2021
How to cite this article: Laurent Djerassem, Daniel Tieudjo and Marcel Tonga, A congruence property of Fourier coefficients for modular forms, JP Journal of Algebra, Number Theory and Applications 50(1) (2021), 1-17. DOI: 10.17654/NT050010001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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