Modular forms of weight 1/2 are constructed directly as q-expansions following the explicit description given by Serre and Stark (see [SS77]).
For a space M of modular forms of weight 1/2, this returns the basis of the space as described by Serre and Stark. A list of tuples is returned; each tuple contains a character ψ and an integer t, and the corresponding modular form is the theta series defined as the sum over all integers n of ψ(n) q(t n2).