Display partial information on classical modular form pages

[AndrewVSutherland]

Edited per the discussion below

In cases where the coefficients of the Q-expansion are too large to reasonably display, as on

http://beta.lmfdb.org/ModularForm/GL2/Q/holomorphic/23/38/1/ http://beta.lmfdb.org/ModularForm/GL2/Q/holomorphic/23/38/1/a

for example, don't display the q-expansion but just give information about the coefficient field (a link to the field if it is in the LMFDB, and if not, at least its degree and perhaps a defining polynomial for it).

We can instead provide a link for downloading whatever coefficient data we have available for those who want it.

For cases where we only know the dimensions of the Hecke orbits that make up the decomposition of the space and perhaps some other partial information (e.g. the coefficient field or its degree), we could display this and note that the coefficients are not yet available. This would be friendlier then a long list of "Hecke orbit space not in database" entries (we currently hide these space to avoid displaying them).

I am marking this as critical because, as it stands, many of the current pages (not just the two examples above) cannot be reasonably rendered and take very long to load. This is something we could easily fix even before filling out and verifying all the modular form data we would like to have available (see the discussion at #1248).

This more flexible approach would also allows us to have modular forms pages in cases where we have only numerical data but still want to include the L-function in the LMFDB (as noted in #1237 (comment)).

[sehlen]

It does not make sense to restrict to a_2 as this might vanish. Moreover,
it might not be of the form alpha where Q(alpha) is the coefficient field
in the data that we computed. We have to distinguish several cases and I
would rather vote for hiding the q-expansion by default in those cases.

On Tue, May 17, 2016, 08:56 Andrew Sutherland notifications@github.com
wrote:

In cases where the coefficients of the Q-expansion are too large to
reasonably display, as on

http://beta.lmfdb.org/ModularForm/GL2/Q/holomorphic/23/38/1/
http://beta.lmfdb.org/ModularForm/GL2/Q/holomorphic/23/38/1/a

for example, only display the first two coefficients (e.g. q+_a_2 q^2+...)
and give information about the coefficient field (a link to the field if it
is in the LMFDB, and if not, at least its degree and perhaps a defining
polynomial for it). I note that the coefficient field is not always Q(
a), but when it is not it can usually be compactly described as Q(
_a_2,b) for some reasonably simple b). We could then provide a link
for downloading whatever coefficient data we have available for those who
want it.

For cases where we only know the dimensions of the Hecke orbits that make
up the decomposition of the space and perhaps some other partial
information (e.g. the coefficient field or its degree), we could display
this and note that the coefficients are not yet available. This would be
friendlier then a long list of "Hecke orbit space not in database" entries
(we currently hide these space to avoid displaying them).

I am marking this as critical because, as it stands, many of the current
pages (not just the two examples above) cannot be reasonably rendered and
take very long to load. This is something we could easily fix even before
filling out and verifying all the modular form data we would like to have
available (see the discussion at #1248
#1248).

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#1385

[sehlen]

But there is another issue with this, namely that pages take long to load
(before they get the chance to render) because the record is large. Please
assign me and I can offer a fix for both issues today or tomorrow for
people to test.

On Tue, May 17, 2016, 09:03 Stephan Ehlen stephan@die-ehlens.de wrote:

It does not make sense to restrict to a_2 as this might vanish. Moreover,
it might not be of the form alpha where Q(alpha) is the coefficient field
in the data that we computed. We have to distinguish several cases and I
would rather vote for hiding the q-expansion by default in those cases.

On Tue, May 17, 2016, 08:56 Andrew Sutherland notifications@github.com
wrote:

In cases where the coefficients of the Q-expansion are too large to
reasonably display, as on

http://beta.lmfdb.org/ModularForm/GL2/Q/holomorphic/23/38/1/
http://beta.lmfdb.org/ModularForm/GL2/Q/holomorphic/23/38/1/a

for example, only display the first two coefficients (e.g. q+_a_2 q^2+...)
and give information about the coefficient field (a link to the field if it
is in the LMFDB, and if not, at least its degree and perhaps a defining
polynomial for it). I note that the coefficient field is not always Q(
a), but when it is not it can usually be compactly described as Q(
_a_2,b) for some reasonably simple b). We could then provide a link
for downloading whatever coefficient data we have available for those who
want it.

For cases where we only know the dimensions of the Hecke orbits that make
up the decomposition of the space and perhaps some other partial
information (e.g. the coefficient field or its degree), we could display
this and note that the coefficients are not yet available. This would be
friendlier then a long list of "Hecke orbit space not in database" entries
(we currently hide these space to avoid displaying them).

I am marking this as critical because, as it stands, many of the current
pages (not just the two examples above) cannot be reasonably rendered and
take very long to load. This is something we could easily fix even before
filling out and verifying all the modular form data we would like to have
available (see the discussion at #1248
#1248).

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#1385

[AndrewVSutherland]

@sehlen (#1385 (comment)) Good point, and I think you are right that we don't want to complicate things. So for the moment we could just have two cases

• Display everything as we do now (coefficients and information about the coefficient field)
• Display no coefficients (with a download button if they are available) and give information about the coefficient field (its dimension, and a link to its LMFDB page if there is one or a defining polynomial if not)

Does that sound reasonable? (If so I can amend the issue description)

[sehlen]

@AndrewVSutherland Absolutely, that's exactly what I wanted to (will) do.

[sehlen]

See my proposal at #1386 (comment) and my branch https://github.com/sehlen/lmfdb/tree/cleanup_bugfix_efficiency for testing this.

[sehlen]

Updated, see my pull request #1409