Abstract
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.
Citation
Sam Chow. Alexandru Ghitza. "Distinguishing eigenforms modulo a prime ideal." Funct. Approx. Comment. Math. 51 (2) 363 - 377, December 2014. https://doi.org/10.7169/facm/2014.51.2.8
Information