\(q\)-Expansions

We can associate a theta series to any pair of elements of a Brandt module, which give embeddings (with respect to any fixed module element) of the Brandt module in a space of weight \(2\) modular forms.

ThetaSeries(x, y, prec): ModBrdtElt, ModBrdtElt, RngIntElt -> RngSerElt

Returns the theta series associated to the pair \((x,y)\) of elements of a Brandt module, as an element of a power series ring.

qExpansionBasis(M, prec): ModBrdt, RngIntElt -> SeqEnum

A sequence of power series elements, to precision \(prec\), spanning the image of the theta functions associated to pairs in the Brandt module \(M\).