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lalitkumarj / OMSCategory

Sage Category implementation of OMS
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Rank 1 examples failing #21

Open rharron opened 11 years ago

rharron commented 11 years ago

So, I uploaded a new examples file called Rank_1_examples.sage. It is set up to test a bunch of rank 1 examples (of OMSs) (i.e. start from a random symbol and get an eigensymbol, then compare to the classical modular form). Right now it makes it through the first example (X_0(11)), then crashes. sadface.

rpollack9974 commented 11 years ago

Mine crashes right away:

sage: dims_dict = load("working_copy/examples/data/dims_of_ord_cusp.sobj") sage: verify_rank_one(dims_dict)

Verifying rank one up to precision 10 Constructing 38 newforms. Constructing OMSs and verifying they match up.

Newform #1 (1, 11, 0) Finding non-Eisenstein prime

Non-Eisenstein prime = 2

AttributeError Traceback (most recent call last)

in () ----> 1 verify_rank_one(dims_dict) in verify_rank_one(input_dict, max_ell, prec, verbose) /Applications/sage-5.7/local/lib/python2.7/site-packages/sage/structure/factory.so in sage.structure.factory.UniqueFactory.**call** (sage/structure/factory.c:1036)() /Applications/sage-5.7/local/lib/python2.7/site-packages/sage/structure/factory.so in sage.structure.factory.UniqueFactory.create_key_and_extra_args (sage/structure/factory.c:1974)() /Applications/sage-5.7/local/lib/python2.7/site-packages/sage/modular/pollack_stevens/modsym_OMS_space.pyc in create_key(self, group, weight, sign, p, prec_cap, base, coefficients) 20 coeffcients = OverconvergentDistributions(weight, p, prec_cap, base, character) 21 if isinstance(group, (int, Integer)): ---> 22 p = coefficients.prime() 23 if group % p != 0: 24 group *= p AttributeError: 'NoneType' object has no attribute 'prime'
rharron commented 11 years ago

Sorry, I had fixed a typo on my computer, but forgotten to push. I've done that now.

rpollack9974 commented 11 years ago

just fixed a bug in this -- when killing off the Eisenstein bit you need to avoid the level or remember that you are not avoiding the level.

rharron commented 11 years ago

Ah right, I noticed right before going to bed last night and apparently did nothing about it.

rharron commented 11 years ago

It looks like it's working!

rharron commented 11 years ago

It worked for the first 36 newforms. I've uploaded the output of the test. The failure was in weight 4, level 9, p=7. This newform is CM, and in particular it's a_2 is 0.

rharron commented 11 years ago

So, for this 36th newform, I tried using Phi.hecke(p) - Phi to kill the Eisenstein part and it worked! I got an eigensymbol whose a_ell's matched up to 7^9. Using T_2 to kill Eisenstein left me with something that was a T_3 eigensymbol, but nothing else.

rpollack9974 commented 11 years ago

Ah! There are more Eisenstein series to worry about at level 3^2 * 7. You could take E_4 and 7-stabilize it to get an Eisenstein series of level Gamma_0(7) and then twist by the quadratic character of conductor 3 to get something new at level 3^2 * 7.

So in this example you have to apply both T_2 - 9 and T_2 + 9.

Confusing. I guess we need to look at the Eisenstein stuff more carefully...

rharron commented 11 years ago

I opened a new issue about figuring out the eisenstein series (#31).