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>