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Next: Admissible Representations of GL2(Qp)
Up: Arithmetic Geometry (Modular Forms)
Previous: Hilbert Modular Forms
Features:
- This new package computes spaces of modular forms over an arbitrary
imaginary quadratic field (referred to as Bianchi modular forms).
The function BianchiCuspForms creates the space of cuspidal forms
of weight 2 with given level and trivial character.
- These spaces have type ModFrmBianchi. The relevant verbose flag
is Bianchi.
- The computation of the space involves an expensive precomputation phase
which depends only on the field. Essentially, this consists of determining
the classes of perfect forms over the field. The results of this phase are
returned by VoronoiData, and this can later be passed in when creating
another space over the same field, to avoid repeating the precomputation.
- The space that is computed internally contains some Eisenstein series;
however, these are recognised by their eigenvalues and quotiented out.
- The HeckeOperator TI can be computed on these spaces, for an ideal
I that has odd order in the class group.
- The NewSubspace and its NewformDecomposition can be computed
(using generic code for dealing with Hecke modules that is also used for
Hilbert modular forms).
- The functionality is likely to be extended in subsequent releases.
Next: Admissible Representations of GL2(Qp)
Up: Arithmetic Geometry (Modular Forms)
Previous: Hilbert Modular Forms
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