Fix bug with pAutomorphicForms for weights larger than two

[mmasdeu]

The following code illustrates the bug:

sage: X = BruhatTitsQuotient(7,2)
sage: H = X.harmonic_cocycles(4,20)
sage: A = X.padic_automorphic_forms(4,20,overconvergent=True)
sage: f = A.lift(H.basis()[0]).modular_form(method='moments')
sage: T.<x> = Qq(7^2,20)
sage: a,b,c,d = X.embed_quaternion(X.get_units_of_order()[1]).change_ring(Qp(7,20)).list()
sage: (c*x + d)^4 * f(x) == f((a*x + b)/(c*x + d)) # Should return True
False

The problem arose because of the way distributions work, which get normalized even when the user wishes they weren't. I propose a fix to this.

CC: @roed314

Component: modular forms

Keywords: Bruhat Tits, Harmonic Cocycles, Overconvergent

Author: Marc Masdeu

Branch/Commit: 66bf400

Reviewer: Peter Graef

Issue created by migration from https://trac.sagemath.org/ticket/22634

[mmasdeu]

Branch: u/mmasdeu/22634-fix-bug-pautomorphicform

[mmasdeu]

New commits:

21e5565	Fixed bug when lifting p-automorphic forms of weight > 2.
ffcc45f	Added doctest to show that bug is fixed.

[mmasdeu]

Commit: ffcc45f

[sagetrac-pgraef]

comment:2

The bug still seems to occur in other cases, for example here

sage: X = BruhatTitsQuotient(7,2)
sage: H = X.harmonic_cocycles(4,20)
sage: A = X.padic_automorphic_forms(4,20,overconvergent=True)
sage: f = A.lift(H.basis()[1]).modular_form(method='moments')
sage: T.<x> = Qq(7^2,20)
sage: a,b,c,d = X.embed_quaternion(X.get_units_of_order()[1]).change_ring(Qp(7,20)).list()
sage: (c*x + d)^4 * f(x) - f((a*x + b)/(c*x + d))
(6*x + 3) + (6*x + 5)*7 + (x + 6)*7^2 + (2*x + 3)*7^3 + (3*x + 2)*7^4 + (6*x + 4)*7^5 + (x + 3)*7^6 + (4*x + 6)*7^7 + (5*x + 1)*7^8 + (6*x + 1)*7^9 + (3*x + 5)*7^10 + (x + 2)*7^11 + (5*x + 2)*7^12 + (5*x + 6)*7^13 + (4*x + 4)*7^14 + 5*7^15 + (4*x + 4)*7^16 + O(7^17)

or here

sage: X = BruhatTitsQuotient(3,5)
sage: H = X.harmonic_cocycles(4,20)
sage: A = X.padic_automorphic_forms(4,20,overconvergent=True)
sage: f = A.lift(H.basis()[0]).modular_form(method='moments')
sage: T.<x> = Qq(3^2,20)
sage: a,b,c,d = X.embed_quaternion(X.get_units_of_order()[1]).change_ring(Qp(3,20)).list()
sage: (c*x + d)^4 * f(x) - f((a*x + b)/(c*x + d))
3^3 + (x + 2)*3^5 + 2*x*3^6 + (x + 1)*3^7 + 2*3^8 + (x + 2)*3^9 + (2*x + 1)*3^10 + (2*x + 2)*3^12 + (x + 2)*3^14 + 2*x*3^15 + x*3^16 + O(3^17)

I tried to track down the problem, but didn't suceed. When evaluating the lift of the harmonic cocycle on random matrices, I just noticed that the values for the higher moments seem to be wrong.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

66bf400

Trac 22634: fixed one more bug.

[sagetrac-git]

Changed commit from ffcc45f to 66bf400

[mmasdeu]

comment:4

I tracked the error. I was trying to be extra careful in the lifting step and it turns out that it's not needed. The old code did not have this "functionality" and that's why it worked!

[sagetrac-pgraef]

comment:6

Works exactly as it should, everything looks perfect!

[sagetrac-pgraef]

Reviewer: Peter Graef

[vbraun]

Changed branch from u/mmasdeu/22634-fix-bug-pautomorphicform to 66bf400