Characteristic polynomials of
T2 on Sk(SL2(Z))
The characteristic polynomial of T2
acting on Sk(SL2(Z)) for all k<=3000.
Notes:
- Here is a list of the charpolys at level 1 of T_2 as a single PARI-readable file
for all weights < 800: all.gp.bz2 (11 MB). This
file is bzipped, so you'll have to decompress it with bunzip2.
If you make the stack have size at least 512MB (use allocatemem() a few times),
this complete file should read into PARI in under a minute. Decompressing from
bzip2 in the first place will take less than a minute, and after decompression
the file is 26MB.
- Alex Ghitza has used used Sage to check that the characteristic polynomial
of T2 is irreducible for all k<=4096.
- Seth Kleinerman has used Magma to check that the characteristic polynomial
of T2 is irreducible for k<=3000, except k=2796.
- Kevin Buzzard computed T2 for weights k<=2048. William Stein
computed T2 for the remaining weights k<=3000 using
meccah and neron.
All mistakes are the responsibility of William Stein.