Implement degeneracy maps to make JH(22, [-1]).decomposition() work

[pjbruin]

In SageMath 7.5.rc0:

sage: JH(22, [-1]).decomposition()
Traceback (most recent call last):
...
NotImplementedError:

The thing that is not implemented is a degeneracy map between spaces of modular symbols.

See also #21799.

Depends on #21927

CC: @koffie

Component: modular forms

Issue created by migration from https://trac.sagemath.org/ticket/21798

[pjbruin]

Description changed:

--- 
+++ 
@@ -5,3 +5,5 @@
 ...
 ValueError: N (=22) should be a factor of the level                of this space (=11)

+See also #21799. +

[jdemeyer]

comment:2

The funny                  spacing in the error message should also be fixed.

[pjbruin]

comment:3

It seems the following is a more immediate example:

sage: ModularSymbols(GammaH(11, [-1]), 2).modular_symbols_of_level(22)
Traceback (most recent call last):
...
ValueError: N (=22) should be a factor of the level                of this space (=11)

This does work when replacing GammaH(11, [-1]) by Gamma1(11) or Gamma0(11).

[pjbruin]

comment:4

The above error is apparently deliberate, according to the following comment in the method sage.modular.modsym.ambient.ModularSymbolsAmbient_wtk_gamma_h.modular_symbols_of_level:

# We deliberately don't allow N to be a multiple of the level here,
# because there are many possibilities for what H could be at the
# higher level (and we don't implement the degeneracy raising maps
# anyway)

A canonical choice for the H at higher level N is to take the inverse image of H in (Z/*N*Z)^×. However, we then still have to implement the degeneracy maps. Doing this will require implementing the function sage.modular.arithgroup.congroup.degeneracy_coset_representatives_gamma_h and the method sage.modular.modsym.ambient.ModularSymbolsAmbient_wtk_gamma_h._degeneracy_raising_matrix_1.

[pjbruin]

comment:5

After #21927, the error occurs slightly later on, and a NotImplementedError is raised instead of a ValueError.

[pjbruin]

Dependencies: #21927

[pjbruin]

Description changed:

--- 
+++ 
@@ -1,9 +1,12 @@
+In SageMath 7.5.rc0:

sage: JH(22, [-1]).decomposition() Traceback (most recent call last): ... -ValueError: N (=22) should be a factor of the level of this space (=11) +NotImplementedError:

+The thing that is not implemented is a degeneracy map between spaces of modular symbols.
+
 See also #21799.

[pjbruin]

comment:7

A more immediate example:

sage: M = ModularSymbols(GammaH(22, [-1]), 2)
sage: N = ModularSymbols(GammaH(11, [-1]), 2)
sage: N.degeneracy_map(M, 1)
Traceback (most recent call last):
...
NotImplementedError: