Abstract
Bringmann et al. (Math. Ann., 355(3):1085–1121, 2013) and Guerzhoy (Proc. Am. Math. Soc., 136:3051–3059, 2008) studied the multiplicity two Hecke theory for weakly holomorphic modular forms on the full modular group. In this note, we consider a generalization of these results to congruence subgroups \(\Gamma _1(N)\) with a new form theory. Using this, we define new forms for harmonic weak Maass forms and study a level raising property modulo \(\ell \) for them.
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Acknowledgments
The authors appreciate for referee’s careful reading and helpful comments. The first author would like to thank KIAS for the support throughout associate membership program. Dohoon Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF2010-0022180).
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Choi, D., Lim, S. The spaces of new forms for harmonic weak Maalss forms and their level raising properties modulo \(\ell \) . Ramanujan J 37, 65–77 (2015). https://doi.org/10.1007/s11139-014-9557-8
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DOI: https://doi.org/10.1007/s11139-014-9557-8