On the action of Hecke operators on Drinfeld modular forms

In this paper we determine the explicit structure of the semisimple part of the Hecke algebra that acts on Drinfeld modular forms of full level modulo T . We use computations of the Hecke action modulo T to find Drinfeld modular forms that cannot be eigenforms. Finally, we conjecture that the Hecke algebra that acts on Drinfeld modular forms of full level is not smooth for large weight.