Degeneracy maps

class sage.modular.hecke.degenmap.DegeneracyMap(matrix, domain, codomain, t)

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)
Traceback (most recent call last):
...
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 ...
t()

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

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