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This article examines the Fourier expansions of certain non-classical p-adic modular forms of weight one: the eponymous generalised eigertforms of the title, so called because they lie in a generalised eigenspace for the Hecke operators. When this generalised eigenspace contains the theta series attached to a character of a real quadratic field K in which the prime p splits, the coefficients of the attendant generalised eigenform are expressed as p-adic logarithms of algebraic numbers belonging to an idoneous ring class field of K. This suggests an approach to
CitacióDarmon, H., Lauder, A., Rotger, V. Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields. "Advances in mathematics", 01 Octubre 2015, vol. 283, p. 130-142.