Wadspurger has shown that the genuine automorphic cuspidal representations of the metaplectic cover S of SL_2 are divided naturally into packets, and that thse packets are indexed by the cuspidal automorphic representations of PGL_2. We construct packets of Lambda-adic modular forms of half integral weight, indexed by Lambda-adic forms on PGL_2. The elements of the Lambda-adic packets are nonzero, but they have specializations that vanish, owing to a trivial zero phenomenon and the sign of a complex root number. This is in contrast to the usual trivial zero phenomenon which arises from the vanishing of a p-adic factor.