Add rigorous Maass forms to the LMFDB

[davidlowryduda]

Woohoo!

Also thanks to David Roe.

[davidfarmer]

About the Fricke sign:

How about the Fricke sign (and Atkin-Lehner, if possible) is shown in all
cases, but (not computed rigorously) appears after that number, if appropriate?

[davidlowryduda]

Maybe we have enough precision to compute the Fricke/Atkin-Lehner eigenvalues accurately enough so that, invoking the fact that those exist and are +1 or -1, we have them rigorously?

This is almost always true. But I want to make sure that I implement that correctly and handle the error bounds correctly. It's a bit of a different way of working with error than I had been. I'll modify the data later after I've worked that out. And when I can't guarantee it rigorously, I'll add the heuristic in.

The previous "interesting" Maass forms should be removed from the 'some interesting" list.

I'll do that as soon as this PR is approved.

[davidlowryduda]

@davidfarmer @AndrewVSutherland I've also added in RCS knowls and a portrait knowl.

I think this PR is ready.

[AndrewVSutherland]

I've copied the data to proddb. Does anyone (including @arbooker @davidfarmer @jenpaulhus @jvoight @jwj61) have any remaining concerns or comments on this PR? I'd like to merge it tomorrow if we think it is ready (but happy to wait if there are people who want to review it that need more time).

[AndrewVSutherland]

Question for @davidlowryduda from @arbooker: "The Hecke eigenvalue data seems to be limited to about 8 decimal places of precision, even for level 1 (where we have much more accurate data). Is that by choice?"

Andy also noted that we need to delete the top/bottom knowls for the old Maass form data so that we don't get duplicates on the list of interesting Maass forms (I can take care of that).

[jwj61]

The first browse button I clicked was level 4 (because I don't know much about Maass forms) and got no results. Do we really want square levels in the browse area?

[AndrewVSutherland]

No, we should remove non-squarefree levels from the browse list

[davidlowryduda]

The first browse button I clicked was level 4 (because I don't know much about Maass forms) and got no results. Do we really want square levels in the browse area?

No, we should remove non-squarefree levels from the browse list

You're right! I've removed them now.

[davidlowryduda]

Question for @davidlowryduda from @arbooker: "The Hecke eigenvalue data seems to be limited to about 8 decimal places of precision, even for level 1 (where we have much more accurate data). Is that by choice?"

Andy also noted that we need to delete the top/bottom knowls for the old Maass form data so that we don't get duplicates on the list of interesting Maass forms (I can take care of that).

On the pages, I show only the first 8 or so digits for presentation reasons. All the digits (i.e. whatever we have) is available from the downloads on the right. I've added a short disclaimer for that.

Closely related: I also updated the coefficients and errors for level 1 earlier today (so @AndrewVSutherland didn't put it on proddb yet). Previously I'd stored only up to double precision, but now I store more when we have it.

[jenpaulhus]

I know very little about Maass forms so I mainly just clicked around to see if I could break anything or see anything weird.

Neither of the two things below necessarily need to happen before this PR is merged, but mentioning them now.

(1) It might be good to have the spectral parameters cut off at a certain length on the individual pages so that if your browser screen isn't very wide, you can still fit them in and not force a lot of white space at the top. Instead of showing the whole spectral parameter, you can click a button to see it all or to copy it. I believe Edgar originally coded this for somewhere else, but it's on the groups pages (eg: Permutation Group presentation part way down the page here https://beta.lmfdb.org/Groups/Abstract/1679616.oq) Here's an example of a long spectral parameter:
https://blue.lmfdb.xyz/ModularForm/GL2/Q/Maass/1.0.1.46.1

(2) There was also something strange when I looked at the pages on my phone. A few entries in the tables on the individual pages were not LaTeXing. I don't know what that's about. I've attached a screenshot. It happened for many pages, not just this one.

[davidlowryduda]

Thanks!

(1) It might be good to have the spectral parameters cut off at a certain length on the individual pages so that if your browser screen isn't very wide, you can still fit them in and not force a lot of white space at the top. Instead of showing the whole spectral parameter, you can click a button to see it all or to copy it. I believe Edgar originally coded this for somewhere else, but it's on the groups pages (eg: Permutation Group presentation part way down the page here https://beta.lmfdb.org/Groups/Abstract/1679616.oq) Here's an example of a long spectral parameter: https://blue.lmfdb.xyz/ModularForm/GL2/Q/Maass/1.0.1.46.1

Good idea. I've now pushed a change where I now use the same functionality that you pointed to. When the spectral parameter is very long, I truncate it and add a raw-toggle where the full value can be seen and copied.

(2) There was also something strange when I looked at the pages on my phone. A few entries in the tables on the individual pages were not LaTeXing. I don't know what that's about. I've attached a screenshot. It happened for many pages, not just this one.

I have no clue!

[AndrewVSutherland]

@jenpaulhus I think the latex display problems are likely inside katex and something we have no control over.

I see the same issue on my iPhone when I use Safari, but if I switch to Chrome the coefficients are displayed correctly.

[AndrewVSutherland]

The maass_rigor tables have been copied to proddb, I think this PR is ready to merge. If anyone has any remaining concerns, please raise them now! Unless there are any objections I will merge this tomorrow.

[AndrewVSutherland]

@davidlowryduda @roed314 rigorous Maass forms are up on beta, please let me know if anyone spots anything amiss!

[roed314]

I deleted the old top/bottom knowls. I'll keep looking to see if I spot anything else wrong.