Hi Neil, You might look at https://www.lmfdb.org . It's a very large database of information about L-function and modular forms. Victor On Fri, Jan 29, 2021 at 1:16 PM Neil Sloane <njasloane@gmail.com> wrote:

In the Feb 2021 Notices of AMS, there is an article by Aaron Pollack about modular forms associated with exceptional groups. The coeffts of the modular form associated with E_8 are famously connected with the densest sphere packing in 8-D (and the Theory Of Everything), so naturally I was interested in this. The first reference in the article is to

Walter L. Baily, Jr., An Exceptional Arithmetic Group and its Eisenstein Series, Annals of Mathematics , May, 1970, Vol. 91, No. 3 (May, 1970), pp. 512-549 : https://www.jstor.org/stable/1970636

and Baily's last theorem there shows that the Fourier coefficients of the various Eisenstein series associated with this group (which is connected with E_7) are rational numbers. But no numbers are given (this is the Annals, after all). And that is just the first of 20 references. So what are the values of these Fourier coefficients?

I also looked at Baily's book "Intro. Lectures on Automorphic Forms" which has a chapter on Fourier coeffts, but again there were no numbers given. Do we have any experts on automorphic forms on the list?

Best regards Neil

Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun