Functiones et Approximatio Commentarii Mathematici

Distinguishing eigenforms modulo a prime ideal

Sam Chow and Alexandru Ghitza

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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.

Article information

Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 363-377.

First available in Project Euclid: 26 November 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F25: Hecke-Petersson operators, differential operators (one variable) 11F33: Congruences for modular and $p$-adic modular forms [See also 14G20, 22E50] 11N13: Primes in progressions [See also 11B25]

modular forms Hecke operators Fourier coefficients congruences primes in arithmetic progressions


Chow, Sam; Ghitza, Alexandru. Distinguishing eigenforms modulo a prime ideal. Funct. Approx. Comment. Math. 51 (2014), no. 2, 363--377. doi:10.7169/facm/2014.51.2.8.

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