The Ramanujan Journal

, Volume 9, Issue 3, pp 341-356

Congruence Restricted Modular Forms

  • Kurt LudwickAffiliated withDepartment of Mathematics and Computer Science, Salisbury University Email author 

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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.


modular forms Fourier expansions multiplier systems