Abstract
In this chapter we carry over to congruence groups of higher level the results of Chapter III. Again we shall represent modular forms by analytic expressions, namely by Eisenstein series of higher level. Here, in contrast to Chapter III, the integral dimension is not required to be even. This will lead to an important difference between forms for the homogeneous group Γ(N) and forms for the homogeneous group Γ[N], however, for their fields of automorphic functions one has KΓ(N) = KΓ[N]. As an application we discuss the construction of the field of modular functions for the principal congruence subgroup of level N.
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© 1974 Springer-Verlag Berlin Heidelberg
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Schoeneberg, B. (1974). Eisenstein Series of Higher Level. In: Elliptic Modular Functions. Die Grundlehren der mathematischen Wissenschaften, vol 203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65663-7_7
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DOI: https://doi.org/10.1007/978-3-642-65663-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65665-1
Online ISBN: 978-3-642-65663-7
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