Classical Points of Low Weight in p-adic Families of Modular Forms

Eric David Stubley
We develop a new strategy for studying low weight specializations of p-adic families of ordinary modular forms. In the elliptic case, we give a new proof of a result of Ghate--Vatsal which states that a Hida family contains infinitely many classical eigenforms of weight one if and only if it has complex multiplication. Our strategy is designed to explicitly avoid use of the related facts that the Galois representation attached to a classical weight one...
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