Abstract
Given f(z), a modular form on a congruence subgroup (of the full modular group), we construct the function f(z;r,t) by summing over the terms of the Fourier expansion of f(z) with index congruent to r modulo t. In this paper, we determine a condition on the multiplier system of f(z) which guarantees that f(z;r,t) is itself a modular form on a (smaller) congruence subgroup.
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2000 Mathematics Subject Classification: Primary—11F11; Secondary—11F30
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Ludwick, K. Congruence Restricted Modular Forms. Ramanujan J 9, 341–356 (2005). https://doi.org/10.1007/s11139-005-1872-7
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DOI: https://doi.org/10.1007/s11139-005-1872-7