 These three mock theta functions have different shadows, so unlike the case of Ramanujan's order 3 and order 5 functions, there are no linear relations between them and ordinary modular forms.The corresponding weak Maass forms are

where

and

is more or less the complementary error function.Under the metaplectic group, these three functions transform according to a certain 3-dimensional representation of the metaplectic group as follows

In other words, they are the components of a level 1 vector-valued harmonic weak Maass form of weight 1/2.