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Brandt Modules
New Features:
- Brandt modules are now implemented for quaternion orders over
Fq[t]
,
- A new implementation of Brandt modules for quaternion orders over
Z
is included.
- Brandt modules are defined using the intrinsic BrandtModule, which
takes an order and an integer, which is the Eichler level.
- The algorithms efficiently handle the level: they do not explicitly
work with the ideal classes of the Eichler order, but only those of
the maximal order. (This is the same approach as in the algorithm
used to compute Hilbert modular forms.)
- The dimension of a Brandt module can be computed (without creating a module)
using either BrandtModuleDimension or BrandtModuleDimensionOfNewSubspace.
- The HeckeOperator of a Brandt module can be computed for any prime
not dividing the level.
- The common eigenvectors of the Hecke operators can be obtained efficiently
using HeckeEigenvectors. Eigenvalues at additional primes can be
then obtained using HeckeEigenvalue.
- The types ModBrdtNew and ModBrdtNewElt which have been introduced
for the new cases will revert to ModBrdt and ModBrdtElt in a
future release.
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