## Programs

MAGMA package *FastBases*

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.

MAGMA package *ArtinAlgebras*

This package contains functions for handling commutative algebras over fields
(e.g. matrix algebras), such as the computation of the decomposition of such
an algebra into a direct product of its localisations, and the computation of
an isomorphic affine algebra with few relations. Functions testing certain
properties (e.g. the Gorenstein property) are included. Some functions only
work over finite fields (for technical, not conceptual reasons).

MAGMA package *pAdicAlgebras*

This package contains functions for handling commutative matrix algebras
over p-adic rings.
It essentially computes the decomposition of the algebra as a direct product of its localisations
by using the Newton method to lift idempotents from the residue field.

MAGMA package *Weight1*

This package computes Katz modular forms of weight one over finite fields.
It is based on an algorithm by Edixhoven.

MAGMA package *HeckeAlgebra*

This package is designed for the computation of Hecke algebras
of modular forms over finite fields of characteristic p in the following cases:

- all eigenforms for a given level N, weight k and Dirichlet character
of modulus N,
- dihedral modular forms coming from the Hilbert class field of a quadratic number field,
- icosahedral modular forms (currently only in characteristic p=2) given by an
A5-polynomial.

MAGMA package *WeakCong*

The purpose of this Magma package is to compute whether Hecke eigenforms over Qbar_p belong to given Z_p-orbits
of Hecke eigenforms modulo powers of p.

*FastHeckeOperator* (by Georg Weber)

Fast computation of the Hecke operator T_p on weight 2 modular
symbols on \Gamma_0(N) for "small" N and "large" p.
The main function is written in C. A Magma interface is provided.
It should be easy to adapt this for Sage.

Last modification: 23 April 2020.