The functions described here are very similar to those for Hilbert modular forms (see Chapter HILBERT MODULAR FORMS). Some further related intrinsics described there, such as HeckeEigenvalue, can also be applied to Bianchi modular forms.
In these computations it is typically very important to switch on the caching feature (see Section Caching Spaces of Modular Forms). This is because spaces of lower levels tend to be used repeatedly.
This computes the new subspace of a given space of Bianchi modular forms. The algorithm identifies the old spaces in M by comparing the Hecke action on M and spaces of lower levels. The algorithm assumes that the dimensions of old spaces are as expected. This has been extensively tested.
This returns a list of the Hecke-irreducible newform spaces in M, which is required to be a new space. The algorithm is the same as for Hilbert modular forms.
This constructs the newform associated to a Hecke-irreducible space M obtained from NewformDecomposition.