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I plan to use this page to make available various useful little scripts and tables of data that I and other people have worked out in connection with the explicit calculation of spaces of automorphic forms. These scripts are written in various combinations of Sage, PARI/GP and Magma. (The first two are open source and free; the latter is not open source and not free.)

These scripts exist in two versions. The most up-to-date is a Sage version,
which will soon be available as a part of Sage. A slightly older Sage version
can be downloaded from here: `overconvergent.py`. Examples of its use can be
found in the slides for a talk I gave at the
Heilbronn Institute in August 2008.

The original versions, in PARI/GP, are available below. These scripts all run
happily in the antiquated GP/PARI version 2.1.6 on
`crackpipe.ma.ic.ac.uk`, and should work on any more recent versions
too. To use them, just download the script and save it, and run the GP
interpreter on them by typing `gp hijikata_padic.gp` (for instance).
This will load the script into GP and print full documentation of all the
functions in each module.

`hijikata_padic.gp`, which calculates the characteristic power series of the U_p operator by taking a p-adic limit in the trace formula. Valid for any p and N, and returns a power series over weight space; assumes trivial character at p. Based on`hijikata.gp`by William Stein.`hijikata_verbose.gp`is a minimally modified version of William Stein's`hijikata.gp`which returns its results in a symbolic form.`umatrix_small_p.gp`calculates the matrix of the U operator acting on overconvergent forms of tame level 1 and weight 0, when p is 2, 3, 5, 7 or 13. The calculation is "longhand", without using Kolberg's recurrences. Also includes code to calculate the T_l operators for primes l =/= p; this bit has not been very carefully checked.`umatrix_recurrence.gp`calculates the matrix of the U operator using Kolberg's recurrences; this is much faster than the above, but less full-featured, and p = 13 is not implemented yet. It also includes functions to calculate the norm of U regarded as an operator from S_{0}(r_{1}) to S_{0}(r_{2}) for various r_{1}< r_{2}, which were used in the calculations for my note on the norm of the U operator.

These programs are intended to accompany my paper "Explicit calculations of automorphic forms on unitary groups". They calculate automorphic forms for the unitary group in 3 variables attached to Q(sqrt(-7)).

- Classical forms of level 1:
`level1.zip`. This is a suite of programs, mostly in Sage but using the Sage interface to Magma at one point, for computing the space of automorphic forms of level G(Z-hat). The code included can compute the Hecke operators at any split prime, and there is also experimental code for non-split primes. Users without access to Magma can still compute at 2, 3 and 11 with the pre-calculated data included.*(To do: reimplement the Magma-based parts in GAP, which is included with Sage.)* - Classical forms of level 2:
`level2.zip`. Written entirely in Magma. Level 2 here means a certain parahoric subgroup of G(Z_2) (not the Iwahori).

Last updated 2008-10-16