Dimensions of eigenspaces for the Atkin-Lehner operator acting on modular forms

af34da7a-5b1a-45c9-aac1-252621303487 commented 14 years ago

This is a port of David Kohel's MAGMA code to compute dimensions of the eigenspaces for the Atkin-Lehner operators acting on spaces of cusp forms of weight 2 (see here for the original):

http://echidna.maths.usyd.edu.au/echidna/dbs/atkin-lehner/index.html

These methods do not rely on computing explicit bases of newforms, instead using formulae about the ramification points of the Atkin-Lehner operator.

These functions use the class number method qfbclassno() from Pari/GP.

NOTES: the functions for newforms are really slow right now (much slower than MAGMA).

The public methods supplied here are:

def modular_genusX0(self,w):
def atkin_lehner_eigenspace_dimensions(self):
def new_subspace_dimensionX0(self):
def atkin_lehner_new_eigenspace_dimension(self,w):
def old_subspace_dimension(self,M,R,w):
def atkin_lehner_new_eigenspace_dimensions(self):

Is this too many? the most important two are atkin_lehner_eigenspace_dimensions and atkin_lehner_new_eigenspace_dimension as those give the really important data about spaces of modular forms. We could make the others private if we wanted to and not lose (too) much.

Apply attachment: trac_9455_atkin_lehner_dim.patch

CC: @williamstein

Component: modular forms

Keywords: atkin lehner

Author: Lloyd Kilford

Branch/Commit: u/chapoton/9455 @ 05115d1

Issue created by migration from https://trac.sagemath.org/ticket/9455

af34da7a-5b1a-45c9-aac1-252621303487 commented 14 years ago

Code to implement dimensions of Atkin-Lehner eigenspaces for the ModularForms class

af34da7a-5b1a-45c9-aac1-252621303487 commented 14 years ago

comment:2

Attachment: atkin_lehner_decomposition_dimensions.sage.gz

af34da7a-5b1a-45c9-aac1-252621303487 commented 14 years ago

Description changed:

--- 
+++ 
@@ -5,3 +5,16 @@
 These methods do not rely on computing explicit bases of newforms, instead using formulae about the ramification points of the Atkin-Lehner operator. 

 These functions use the class number method qfbclassno() from Pari/GP.
+
+NOTES: the functions for newforms are really slow right now (much slower than MAGMA). 
+
+The public methods supplied here are:
+
+{{{def modular_genusX0(self,w):
+def atkin_lehner_eigenspace_dimensions(self):
+def new_subspace_dimensionX0(self):
+def atkin_lehner_new_eigenspace_dimension(self,w):
+def old_subspace_dimension(self,M,R,w):
+def atkin_lehner_new_eigenspace_dimensions(self):
+}}}
+Is this too many? the most important two are atkin_lehner_eigenspace_dimensions and atkin_lehner_new_eigenspace_dimension as those give the really important data about spaces of modular forms. We could make the others private if we wanted to and not lose (too) much.

fchapoton commented 11 years ago

Description changed:

--- 
+++ 
@@ -10,11 +10,12 @@

 The public methods supplied here are:

-{{{def modular_genusX0(self,w):
+```
+def modular_genusX0(self,w):
 def atkin_lehner_eigenspace_dimensions(self):
 def new_subspace_dimensionX0(self):
 def atkin_lehner_new_eigenspace_dimension(self,w):
 def old_subspace_dimension(self,M,R,w):
 def atkin_lehner_new_eigenspace_dimensions(self):
-}}}
+```
 Is this too many? the most important two are atkin_lehner_eigenspace_dimensions and atkin_lehner_new_eigenspace_dimension as those give the really important data about spaces of modular forms. We could make the others private if we wanted to and not lose (too) much.

fchapoton commented 11 years ago

comment:6

Attachment: trac_9455_atkin_lehner_dim.patch.gz

I have tried to maker a clean patch starting with the given file

Some doctests are still failing.

for the bot: apply only trac_9455_atkin_lehner_dim.patch

fchapoton commented 11 years ago

Changed keywords from none to atkin lehner

fchapoton commented 11 years ago

Description changed:

--- 
+++ 
@@ -19,3 +19,5 @@
 def atkin_lehner_new_eigenspace_dimensions(self):

Is this too many? the most important two are atkin_lehner_eigenspace_dimensions and atkin_lehner_new_eigenspace_dimension as those give the really important data about spaces of modular forms. We could make the others private if we wanted to and not lose (too) much. + +Apply attachment: trac_9455_atkin_lehner_dim.patch

fchapoton commented 10 years ago

New commits:

743dc9b trac 9455 dimensions of eigenspaces of Atkin Lehner operators

fchapoton commented 10 years ago

Branch: u/chapoton/9455

fchapoton commented 10 years ago

Commit: 743dc9b

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 743dc9b to 23a1cff

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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

`febd6dc`	`Merge branch 'u/chapoton/9455' of trac.sagemath.org:sage into 9455`
`23a1cff`	`trac #9455 pep8 cosmetic cleanup`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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

`5d01fc3`	`Merge branch 'u/chapoton/9455' into 6.5`
`758f137`	`trac #9455 make it work at last`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 23a1cff to 758f137

fchapoton commented 9 years ago

comment:14

Now all tests pass. But maybe this is too slow.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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

`6a1a30a`	`Merge branch 'u/chapoton/9455' into 6.6.b0`
`7fa13e9`	`trac #9455 details of doc`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 758f137 to 7fa13e9

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

`3efd2a1`	`trac #9455 a method in orders`
`adf5f43`	`trac #9455 Dimensions of eigenspaces for the Atkin-Lehner ops`
`929a08a`	`trac #9455 enhancements`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 7fa13e9 to 929a08a

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 929a08a to 1736e94

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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

1736e94 trac #9455 faster using libgap

fchapoton commented 9 years ago

Changed author from ljpk to L. J. P. Kilford

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

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

311782f trac #9455 fine tuning in order.py

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 9 years ago

Changed commit from 1736e94 to 311782f

fchapoton commented 9 years ago

Changed author from L. J. P. Kilford to Lloyd Kilford

11d1fc49-71a1-44e1-869f-76be013245a0 commented 8 years ago

comment:25

This needs some serious work.

Most of this new code is added via methods of Gamma0 modular forms space objects. However, these objects can have any weight, but the implementations here only work for weight 2, so you can type something like

 sage: ModularForms(1000003, 4).atkin_lehner_eigenspace_dimensions()

and it will silently return wrong output. More importantly, lots of these methods (e.g. atkin_lehner_ramification) are computing geometric properties of the underlying modular curves, so they belong in sage.modular.arithgroup.congroup_gamma0. Similarly, "primitive_ideal_number" should probably be a method of order objects, not a standalone function.

Many function names are mysterious or downright misleading, e.g. the method modular_genus_X0 is not actually computing the genus of anything in most cases.
The documentation is poor. What on earth is the "(M, R)-old subspace"? What are "cyclic ideals"? Docstrings for each method should explain what the arguments mean. The docstring for old_subspace_dimension(self, M, R, w) does not even mention Atkin--Lehner involutions!
Why is a line of code in the number fields module (in absolute_order_from_module_generators) deleted without explanation?

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 311782f to d984ba4

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

d984ba4 Merge branch 'u/chapoton/9455' into 7.1.b5

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from d984ba4 to 4ee1f8d

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

`0ad710b`	`Merge branch 'u/chapoton/9455' into 7.2.b4`
`4ee1f8d`	`trac 9455 fixing imports of gcd and factor`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

Changed commit from 4ee1f8d to 81c4d3a

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 8 years ago

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

81c4d3a Merge branch 'u/chapoton/9455' in 7.3.rc0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

Changed commit from 81c4d3a to f045a29

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 7 years ago

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

`1e3ce62`	`Merge branch 'u/chapoton/9455' in 7.6.b5`
`f045a29`	`trac 9455 py3 print`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 6 years ago

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

05115d1 Merge branch 'u/chapoton/9455' in 8.2.b8

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 6 years ago

Changed commit from f045a29 to 05115d1

sagemath / sage

Dimensions of eigenspaces for the Atkin-Lehner operator acting on modular forms #9455