Open Access
December 2014 Distinguishing eigenforms modulo a prime ideal
Sam Chow, Alexandru Ghitza
Funct. Approx. Comment. Math. 51(2): 363-377 (December 2014). DOI: 10.7169/facm/2014.51.2.8


Consider the Fourier expansions of two elements of a given space of modular forms. How many leading coefficients must agree in order to guarantee that the two expansions are the same? Sturm [20] gave an upper bound for modular forms of a given weight and level. This was adapted by Ram Murty [16] and Ghitza [5] to the case of two eigenforms of the same level but having potentially different weights. We consider their expansions modulo a prime ideal, presenting a new bound. In the process of analysing this bound, we generalise a result of Bach and Sorenson [2], who provide a practical upper bound for the least prime in an arithmetic progression.


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Sam Chow. Alexandru Ghitza. "Distinguishing eigenforms modulo a prime ideal." Funct. Approx. Comment. Math. 51 (2) 363 - 377, December 2014.


Published: December 2014
First available in Project Euclid: 26 November 2014

zbMATH: 1359.11034
MathSciNet: MR3282633
Digital Object Identifier: 10.7169/facm/2014.51.2.8

Primary: 11F11
Secondary: 11F25 , 11F33 , 11N13

Keywords: congruences , Fourier coefficients , Hecke operators , modular forms , primes in arithmetic progressions

Rights: Copyright © 2014 Adam Mickiewicz University

Vol.51 • No. 2 • December 2014
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