MECCAH: Computation Log

Note: There is a lot that MECCAH is used for that does not appear here...

April 2005 Christian Meyer

Recently I finished my thesis, entitled "A dictionary of modular
threefolds" and dealing with modularity of Calabi-Yau threefolds. I
made extensive use of MECCAH to produce a large table of integer
coefficients of weight four newforms for \Gamma_0(N) for N<=2430
(incomplete for large N).  I am attaching the thesis. It contains (at
the end of chapter 1) also my experiences concerning computing time
and memory.

The table was created between June 2003 and November 2004.  
Here is the table.  Each line contains a level and the first 25 coefficients
(up to a97}) of a certain cusp form of this level. In my thesis I
numbered the occurring newforms according to their appearance in this
list.  Whenever possible, I also mentioned the notation you started.

April 2005 William Stein and Grigor Grigorov
Modular symbols computations giving lower bounds on Shafarevich-Tate
groups of elliptic curves as an application of results of Grigorov's
Ph.D.  thesis.
April 12, 2005 Aaron Silberstein
From: Aaron Michael Silberstein 
To: William Stein 
Date: 2005-04-12 03:13 pm

Hi William,

I just wanted to let you know that I'm using Meccah to do more 
calculations for an upcoming paper of Keith Conrad, Brian Conrad, and 
Harald Helfgott.

Thanks for making this all available to me.

November 2004 Edray Goins (Purdue) I'm computing the complete list of d-digit palindromes which are also d-digit palindromes for some base other than base 10. This list is in the range 1 < d < 27. I've written code in Mathematica which takes as an input two d-digit numbers N1 and N2, generates a list of d-digit palindromes N such that N1 < N < N2, and returns those N which are palindromes for some base other than 10. I'm using MECCAH to check several ranges {N1, N2} at once; I only need to check d = 17, 19, 21, 23, and 25 digits.
November 2004 Edray Goins (Purdue) I'm using gridMathematica (a parallelized version of Mathematica) to do a lengthy computation that requires a lot of computational power. The computation will use up to eight nodes total; several nodes will be at Purdue University, but MECCAH will be used for anywhere from two to six nodes from time to time. I plan to do most of the computation during the Thanksgiving break.
June -- Septmeber 2004 Samit Dasgupta Computations of elliptic units for real quadratic fields [pdf]
June -- August 2004 William Stein (and students) Verification of the full BSD conjecture for certain elliptic curves
July -- August 2004 Jennifer Sinnott Tables of Elliptic Curves over Number Fields
April 2004 Curt McMullen During the last couple of months I have used meccah intensively to study a problem in billiards and moduli space. Click here to read more.
April 2004 Samit Dasgupta Generating gross-stark units for my Ph.D. thesis
February 2004 Allan Steel Building tables of irreducible polynomials over GF(2) of the form x^n + g(x), where g is of minimal degree [e.g.: x^11425 + x + 1]
February 2004 Seth Kleinerman Computation of multiple of order of torsion subgroup of many modular abelian varieties.
February 2004 William Stein Computation of arithmetic information about every weight 2 newform on Gamma_0(N) of level at most 7500.
January 2004 Kartik Venkatram Some calculations involving collections of rational points on elliptic curves, particularly the Hamming minimal weight of the elements of ideals generated by such elements (an analogue of Reed-Solomon techniques).
2003-2004 David Dumas Big calculations of holonomy representations of complex projective structures on punctured tori (see also the Neron note).
November 2003 William Stein Creating the new Modular Forms Database
November 2003 Aaron Silberstein Research about "prime polynomials". See this paper, or this much more up-to-date version.
2002 William Stein and Mark Watkins A huge table of elliptic curves
Summer 2002 Stanley Sawyer Some computations related to biological evolution.