Classical and Overconvergent Modular Forms of Higher Level, by Robert F. Coleman

This paper has appeared in J. Theor. Nombres Bordeaux 9 (1997), no. 2, 395-403, and so the dvi version has been removed. In this note we define a notion of overconvergent modular form of level $\Gamma_1(Np^n)$ where $N$ is a positive integer, $p$ is a prime, $(N,p)=1$ and $n\ge 1$ and generalize the main result of Classical and Overconvergent Modular Forms (Invent. Math. 124 (1996)). That is, we show that overconvergent forms of level $\Gamma_1(Np^n)$, weight $k$ and slope strictly less that $k-1$ are classical.

Robert F. Coleman <coleman@math.berkeley,edu>