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Package sage :: Package modular :: Package modform :: Module modform :: Class ModularForms |
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HeckeModule
--+ |ModularFormsSpace
--+ |object
--+ | | |_uniqModularForms
--+ | ModularForms
ModularFormsWithCharacter
An ambient space of modular forms. Create using the command ModularForms(weight, group, character) INPUT: group -- a congruence subgroup (sage.modular.congroup.CongruenceSubgroup) weight -- an integer base_field -- a field (default rings.RationalField)
Method Summary | |
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__init__(self,
group,
weight,
base_field)
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__repr__(self)
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ambient_space(self)
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change_base(self,
F)
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cuspidal_subspace(self)
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dim_cuspidal(self)
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dim_eisenstein(self)
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dim_new_cuspidal(self)
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dim_new_eisenstein(self)
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dimension(self)
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eisenstein_params(self)
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eisenstein_series(self)
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eisenstein_subspace(self)
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is_ambient(self)
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modular_symbols(self)
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new_subspace(self)
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Set or get default initial precision for printing modular forms. | |
Compute q-expansion to precision prec of the linear combination of the basis for this space given by the vector. | |
vector_space(self)
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Inherited from object | |
x.__delattr__('name') <==> del x.name | |
x.__getattribute__('name') <==> x.name | |
x.__hash__() <==> hash(x) | |
helper for pickle | |
helper for pickle | |
x.__setattr__('name', value) <==> x.name = value | |
x.__str__() <==> str(x) | |
Inherited from ModularFormsSpace | |
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True if x is an element or subspace of self. | |
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This function returns a list of subspaces V(f_i,t) corresponding to newforms f_i of some level dividing the level of self, such that the direct sum of the subspaces equals self, if possible. | |
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This function returns a list of subspaces S(M,t) and E(M,t), corresponding to levels M dividing N and integers t dividing N/M, such that self is the direct sum of these spaces, if possible. | |
For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B. | |
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Inherited from HeckeModule | |
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Returns true if and only if only it is possible to split off a nontrivial generalized eigenspace of self as the kernel of some Hecke operator. | |
Returns true if and only if only it is possible to split off a nontrivial generalized eigenspace of self as the kernel of some Hecke operator of index coprime to the level. | |
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Instance Method Details |
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prec(self, set=None)Set or get default initial precision for printing modular forms. |
qexp(self, vector, prec)Compute q-expansion to precision prec of the linear combination of the basis for this space given by the vector. |
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