Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 51, Number 2 (2014), 363-377.
Distinguishing eigenforms modulo a prime ideal
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  gave an upper bound for modular forms of a given weight and level. This was adapted by Ram Murty  and Ghitza  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 , who provide a practical upper bound for the least prime in an arithmetic progression.
Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 363-377.
First available in Project Euclid: 26 November 2014
Permanent link to this document
Digital Object Identifier
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]
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. https://projecteuclid.org/euclid.facm/1417010859