Families of modular forms
The author gives a down-to-earth introduction to the theory of \(p\)-adic families of modular forms, and presents an elementary proof of \textit{D. Wan}'s result [Invent. Math. 133, No.~2, 449--463 (1998; Zbl 0907.11016)] that the Newton polygon of the \(U_p\)-operator acting on \(S_k(\Gamma_1(N_p))\) is bounded below by an explicit quadratic lower bound which is independent of \(k\) (Theorem 3).
scientific article; zbMATH DE number 2081346