  We classify the irreducible, admissible, smooth, genuine mod p
representations of the metaplectic double cover of SL(2,F), where F is a p-adic
field and p is odd. We show, using a generalized Satake transform, that each
such representation is isomorphic to a certain explicit quotient of a compact
induction from a maximal compact subgroup by an action of a spherical Hecke
operator, and we define a parameter for the representation in terms of this
data. We show that our parameters distinguish genuine nonsupercuspidal
representations from genuine supercuspidals, and that every irreducible genuine
nonsupercuspidal representation is in fact an irreducible principal series
representation. In particular, the metaplectic double cover of p-adic SL(2) has
no genuine special mod p representations.
