Home | Trees | Index | Help |
|
---|
Package sage :: Package modular :: Package modsym :: Module ambient :: Class ModularSymbolsAmbient_wtk_g0_Q |
|
Gens
--+ |HeckeModule
--+ |ModularSymbolsSpace
--+ |object
--+ | | |_uniqModularSymbolsAmbient
--+ |ModularSymbolsAmbient
--+ | ModularSymbolsAmbient_wtk_g0_Q
ModularSymbolsAmbient_wt2_g0_Q
Method Summary | |
---|---|
Initialize a space of modular symbols of weight k for Gamma_0(N), over Q. | |
__repr__(self)
| |
manin_symbols(self)
| |
Inherited from ModularSymbolsAmbient | |
| |
Coerce x into the modular symbols space. | |
| |
| |
| |
Given a vector v in self.vector_space(), return the corresponding vector in the ambient modular symbols space. | |
The boundary map to the corresponding space of boundary modular symbols. | |
Try to commit this modular symbols space to the database. | |
| |
The cuspidal subspace. | |
The t-th degeneracy map from self to modular symbols of the given level. | |
Returns the dimension of self. | |
| |
Creates and returns an element of self from a modular or sage symbol, if possible. | |
Returns the vector subspace of the vector space of the ambient space that defines self as a subspace of modular symbols. | |
Returns the factorization of the characteristic polynomial of the Hecke operator T_n of index n. | |
Returns the filename of self that should be used to store self in the database. | |
Returns the Hecke algebra associated to self. | |
Returns the intersection of self and other, which must both lie in a common ambient space of modular symbols. | |
Returns true if and only if self is an ambient space of modular symbols, i.e., created by specifying a group, weight, character, and sign, and not by using a decomposition or other command. | |
| |
| |
| |
Returns True if and only if self is a subspace of V. | |
Try to load the ambient space self from the database. | |
| |
| |
| |
| |
A list of Manin symbols that form a basis for the ambient space self. | |
Returns the new or p-new subspace of self. | |
| |
| |
Returns true if self is loaded and saved to disk. | |
Returns the subspace of this space of modular symbols. | |
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 ModularSymbolsSpace | |
Compare self and other. | |
| |
| |
Returns a basis for self. | |
| |
Returns an eigenvalue of T_n acting on self, where self must be new and non-splittable. | |
Return a_n, psi, i, where a_n is the n-th eigenvalue, psi : Z --> V is a map and i:V-->K is an isomorphism of V with a number field (or Q), such that the composition iso(psi(n)) is the eigenvalue of the n-th Hecke operator acting on a fixed element of self (which must be new and non-splittable). | |
The n-th generator of self. | |
Returns the group of this modular symbols space. | |
The matrix of the n-th Hecke operator acting on the basis for self. | |
Returns the n-th Hecke operator as a Matrix Function. | |
Returns the level of this modular symbols space. | |
The number of generators of self. | |
Return the projection map from the ambient space to self. | |
Returns the q-expansion to precision prec of a newform associated to self, where self must be new, cuspidal, and non-splittable. | |
Returns the sign of self. | |
Returns the Sturm bound for this space of modular symbols. | |
Returns the n-th Hecke operator T_n. | |
Returns the underlying vector space of self. | |
Returns the weight of this modular symbols space. | |
Inherited from HeckeModule | |
| |
| |
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. | |
| |
Inherited from Gens | |
| |
| |
| |
|
Instance Method Details |
---|
__init__(self,
N,
k,
sign=0)
|
Home | Trees | Index | Help |
|
---|
Generated by Epydoc 2.1 on Mon May 9 17:57:02 2005 | http://epydoc.sf.net |