The Ramanujan Journal

, Volume 9, Issue 3, pp 341–356

Congruence Restricted Modular Forms


DOI: 10.1007/s11139-005-1872-7

Cite this article as:
Ludwick, K. Ramanujan J (2005) 9: 341. doi:10.1007/s11139-005-1872-7


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 formsFourier expansionsmultiplier systems

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceSalisbury UniversitySalisbury