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Consider the Fourier expansions of two elements of a given space of modularforms. How many leading coefficients must agree in order to guarantee that thetwo expansions are the same? Sturm gave an upper bound for modular forms of agiven weight and level. This was adapted by Ram Murty, Kohnen and Ghitza to thecase of two eigenforms of the same level but having potentially differentweights. We consider their expansions modulo a prime ideal, presenting a newbound. In the process of analysing this bound, we generalise a result of Bachand Sorenson, who provide a practical upper bound for the least prime in anarithmetic progression.

Distinguishing eigenforms modulo a prime ideal