  We show that the action of Hecke operators away from $p$ on space of
($p$-adic) overconvergent modular forms is overconvergent in certain sense. As
a corollary, the action of Hecke algebra can be extended naturally to an action
of rigid functions on its generic fiber. This directly determines the
Hodge-Tate-Sen weights of Galois representation associated to an overconvergent
eigenform.
