JP Journal of Algebra, Number Theory and Applications
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Abstract: In this paper, we calculate the index in the modular
group, the parabolic class number, the genus, and signature of a family of
congruence subgroups of the
modular group. These subgroups arise naturally from the survival of modularity
under congruence restrictions of modular forms. In addition, we will show that
the index of these subgroups in the modular group is multiplicative and we will
reveal its connection with the number of inequivalent solutions to the quadratic
congruence
Keywords and phrases: modular forms, modular group, congruence subgroups, parabolic class number, genus, signature.
