The first part of the functionality computes spaces of overconvergent modular forms at integer weights, extending the existing algorithm of Lauder to include the primes p=2,3.
The modifications to Lauder's implementation are described in the paper "Computing overconvergent forms for small primes".
Magma Code
The second part of the functionality computes spaces of overconvergent modular forms at the boundary of weight space. For simplicity, this is currently restricted to level 1, and the identity component of weight space.
The algorithm is described in the paper "Modular eigenforms at the boundary of weight space".
Magma Code
The third part of the functionality computes p-adic L-functions of real quadratic fields, and was written with Alan Lauder.
The algorithm is described in the paper "p-Adic L-functions of totally real fields".
Magma Code