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Modular forms of weight 1 can be defined using the usual constructors.
For these spaces, the Dimension, the CuspidalSubspace and
EisensteinSubspace, EisensteinSeries, a qExpansionBasis,
and Hecke operators are available, as well as basic functionality such as
element arithmetic.
The algorithm used to determine spaces of weight 1 forms is as follows.
The Eisenstein series are constructed directly as q-expansions.
The cuspidal eigenforms correspond to Galois representations; those
corresponding to dihedral Galois representations are obtained explicitly
(from characters on ray class groups of quadratic fields). If the dihedral
forms span the full space of cusp forms, this is proved by comparing with
suitable spaces of integral weight forms; if not, a q-expansion basis
for the cuspidal space is obtained using the integral-weight spaces
(this is the most time-consuming part of the process).
For a space of weight 1, this returns the cuspidal eigenforms in M
corresponding to dihedral Galois representations, broken up according
to character. A list of tuples is returned; each tuple contains an
element of the DirichletCharacters of M, followed by a list
of eigenforms.
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