Weight Half Forms

Modular forms of weight \(1/2\) are constructed directly as \(q\)-expansions following the explicit description given by Serre and Stark (see [Serre and Stark, 1977]).

WeightOneHalfData(M): ModFrm -> List

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 \(\psi\) and an integer \(t\), and the corresponding modular form is the theta series defined as the sum over all integers \(n\) of \(\psi(n) q^{(t n^2)}\).