Hi all
I already sent this to sage-nt but didn't get a response, so I try
again: Can someone maybe have a look at one of the tickets above
(in particular #17909)?
They are for modular forms for Hecke triangle groups.
In particular this includes (classical) modular forms for SL2(Z)
and for the Theta subgroup (see the readme for more information).
I no longer work in academics (I'm a software developer now)
but the code might be useful for others (e.g. in the classical cases)
and in my opinion it would be a pity if the functionality got lost in
the ticket graveyard...
I didn't expect a fast review but the tickets are there since
quite a while already... :-)
#17909: Rankin Cohen brackets (also for quasi forms) and more
decomposition methods for quasi forms
#17943: Depends on #17909 (but I could make it separate I guess).
Here I tried to make some experimental code (conversions
from numerical coefficients to exact forms) more robust
and fixed some bugs
#18043: I tried my best to add support for HyperbolicPlane(), it could
certainly be improved by someone familiar with the
HyperbolicPlane code...
So if someone has time or is interested, it's appreciated. :-)
Best
Jonas
--------
PS
I would be interested in generalizing the implementation to Jacobi
forms if someone has the time to help me with the algebraic structure.
PPS
Using appropriate subspaces it's quite easy to find some differential
equations satisfied by the forms (e.g. E2). For instance I found:
n=4
E2.derivative(4) == -3/2*E2^2*E2.derivative(2) + 5/2*E2*E2.derivative(3)
+ 9/4*E2*E2.derivative()^2 -3*E2.derivative()*E2.derivative(2)
n=5 (non-arithmetic)
E2^3*E2.derivative(2) == E2^2*E2.derivative(3) + 3/2 *
E2^2*E2.derivative()^2 + 4*E2*E2.derivative()*E2.derivative(2) -20/3 *
E2.derivative()*E2.derivative(3) -22/3*E2.derivative()^3 +
40/9*E2.derivative(2)^2
Maybe that's of interest to someone...
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