  We study the Eisenstein ideal of Drinfeld modular curves of small levels, and
the relation of the Eisenstein ideal to the cuspidal divisor group and the
component groups of Jacobians of Drinfeld modular curves. We prove that the
characteristic of the function field is an Eisenstein prime number when the
level is an arbitrary non square-free ideal of $\mathbb{F}_q[T]$ not equal to a
square of a prime.
