MAGMA package FastBases


Introduction

This Magma package has been designed for computing bases of the modular forms spaces M_k(Gamma_0(4),Q) for half-integral weights k. The basis modular forms are represented by their q-expansions up to a given precision. The main purpose is to be able to obtain a high precision. The algorithms are described in the paper "Fast computation of half-integral weight modular forms" by Ilker Inam and Gabor Wiese.

Download

Download the complete code, as well as the documentation and an example as a tar-file.

Files

FastBases.spec Package file.
FB_General.m Functions for various uses.
FB_Kohnen_Basis.m Functions for computing the Kohnen basis.
FB_Rankin_Cohen.m Functions for computing the Rankin-Cohen basis.
FB_Standard_Basis.m Functions for computing the standard basis.
FB_standard_forms.m Functions for computing some standard modular forms.
FB-Example.m An example illustrating the main functionality.
User-Guide.txt Short user guide..

Installation

It suffices to change to the directory containing the files of the package and to type in Magma:
AttachSpec("FastBases.spec");

Principal functions

FB_standard_basis(k,prec);
For any k half-integer or integer k, this function computes the q-expansions of the standard basis of the full space M_k(Gamma_0(4)) up to precision prec.

FB_Kohnen_basis(k,prec);
For a half-integer k = l+1/2 with l an integer at least 12, this function computes the q-expansions of the Kohnen basis of the plus space M_k^+(Gamma_0(4)) up to precision prec.

FB_RC_basis_plus(k,prec);
For a half-integer k = l+1/2 with l an even integer, this function computes the q-expansions of the Rankin-Cohen basis of the plus space M_k^+(Gamma_0(4)) up to precision prec.

FB_RC_basis_full(k,prec);
For a half-integer k = l+1/2 with l an odd integer, this function computes the q-expansions of the Rankin-Cohen basis of the full space M_k(Gamma_0(4)) up to precision prec.

FB_plus_subspace(C,k);
Given a half-integral or integral weight k and a basis C of q-expansions of weight k modular forms, this function computes a basis of the plus subspace spanned by the forms in C.


Last modification: 23 April 2020.