Bases: sage.modular.hecke.morphism.HeckeModuleMorphism_matrix
A degeneracy map between Hecke modules of different levels.
EXAMPLES: We construct a number of degeneracy maps:
sage: M = ModularSymbols(33)
sage: d = M.degeneracy_map(11)
sage: d
Hecke module morphism degeneracy map corresponding to f(q) |--> f(q) defined by the matrix
[ 1 0 0]
[ 0 0 1]
[ 0 0 -1]
[ 0 1 -1]
[ 0 0 1]
[ 0 -1 1]
[-1 0 0]
[-1 0 0]
[-1 0 0]
Domain: Modular Symbols space of dimension 9 for Gamma_0(33) of weight ...
Codomain: Modular Symbols space of dimension 3 for Gamma_0(11) of weight ...
sage: d.t()
1
sage: d = M.degeneracy_map(11,3)
sage: d.t()
3
The parameter d must be a divisor of the quotient of the two levels:
sage: d = M.degeneracy_map(11,2)
...
ValueError: The level of self (=33) must be a divisor or multiple of level (=11), and t (=2) must be a divisor of the quotient.
Degeneracy maps can also go from lower level to higher level:
sage: M.degeneracy_map(66,2)
Hecke module morphism degeneracy map corresponding to f(q) |--> f(q^2) defined by the matrix
[ 2 0 0 0 0 0 1 0 0 0 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 -1]
[ 0 0 1 -1 0 -1 1 0 -1 2 0 0 0 -1 0 0 -1 1 2 -2 0 0 0 -1 1]
[ 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 -1 1 0 0 -1 1 0 0 0]
[ 0 0 0 0 0 0 0 0 0 2 -1 0 0 1 0 0 -1 1 0 0 1 0 -1 -1 1]
[ 0 -1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 -1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 -1 0 0 2 -1 0 0 1 0 0 0 -1 0 -1 1 -1 1]
[ 0 0 0 0 1 -1 0 1 -1 0 0 0 0 0 -1 2 0 0 0 0 1 0 1 0 0]
[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0]
[ 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 1 1 0 0 0]
Domain: Modular Symbols space of dimension 9 for Gamma_0(33) of weight ...
Codomain: Modular Symbols space of dimension 25 for Gamma_0(66) of weight ...
Return the divisor of the quotient of the two levels associated to the degeneracy map.
EXAMPLES:
sage: M = ModularSymbols(33)
sage: d = M.degeneracy_map(11,3)
sage: d.t()
3
sage: d = M.degeneracy_map(11,1)
sage: d.t()
1