HECKE: Modular forms software for MAGMA

William A. Stein

The MAGMA version of HECKE is now the only one that I actively support, and is much more developed than the C++ version. It comes standard with MAGMA. However, you can obtain the MAGMA source code for this package and documentation from this web page without purchasing MAGMA.

The links below are to my personal local MAGMA development directory, and you are welcome to browse through them.

Frequently Asked Questions

1. Question: (August 12, 2001)  CyclotomicField() won't take a value > 32768 !! Moreover, neither will CyclotomicPolynomial!! This is a shame, because at the end of the day if one wants to deal with Dirichlet characters one is using barely any of the arithmetic of cyclotomic fields. I guess what I'm saying is: I see no reason why I can't, at the end of the day, compute the dimension of S_2(N,chi) where N is a random 10-digit prime and chi is, say, a character of order N-1. The dimension will be independent of which character I choose, by Galois theory, but I (personally) cannot construct any of them within magma. On the other hand, an "ad hoc" construction of the bare bones of Dirichlet characters would work no problem. This is a minor annoyance, because the very reason I'm working within magma and not pari is that I had assumed that I would not have to implement any of the theory of Dirichlet characters!! Answer:   An alternative is to create a dirichlet character over the approximate complex numbers. (Note, the following code will only work in the absolutely newest version of the MAGMA. If you don't have it, make these modifications.)

   > C := ComplexField();
   > e := Exp(2*Pi(C)*C.1/33012);
   > G := DirichletGroup(33013,C,e,33012);
   > DimensionCuspForms(eps,2);
   0
   > DimensionCuspForms(eps,3);
   5501.000000000000000000000000 + 5.135246190230402938987214200 E-29*i
   // that's clearly 5501.
   > DimensionCuspForms(eps,7);
   16506
   > DimensionCuspForms(eps,5);
   11004.00000000000000000000000 - 5.135246190230402938987214200 E-29*i
   

   
   
   
2. Buying MAGMA:
   

   On Friday 17 August 2001 03:04 pm, you wrote:
   > Hi.  I'm told there have been various weird
   > issues obstructing the purchase of MAGMA here, due
   > to something with licensing agreement.
   
   Answers to some of your questions can be found at
   
       http://www.maths.usyd.edu.au:8000/u/magma/
   
   At 
   
       http://www.maths.usyd.edu.au:8000/u/magma/Ordering/Pricing.html
   
   it says that a 3-year Sun institutional license costs $1000.  (It used
   to be $3000 for 3-years, so...)
   
   It also says:
   
      "In the case of the PC version, a special rate is available for
       individuals acquiring a subscription for private use (just as is the
       case with journal subscriptions). A fully-featured student version is
       also available for PCs."
   
   In the past, I've heard that the "special rate" was $200 for a 3-year
   license.  The student rate is $100.  Thus, if you want MAGMA for a
   Linux PC or Windows computer, you can get it quite cheaply.  For a Sun
   version, you'll have to get the 3-year $1000 institution license.
   
   > I was told the university legal dept might have to be consulted,
   > which I want to avoid because they drag their feet, so I'd be just
   > as happy to make a direct purchase.  Is there a suitable person "in
   > charge" of MAGMA with whom I could discuss such things?
   
   John Cannon ([email protected]), who is a group theorist at the
   University of Sydney "is MAGMA".  (His wife and postdocs like David
   Kohel also help out.)
   
   > For example, the idiots here in the purchasing dept said that the
   > Univ of Sydney won't accept credit card purchases of MAGMA, which I
   > find rather hard to believe.
   
   I can't comment on this, except to say "Australia not the USA, so make
   no assumptions, and MAGMA is not a company."
   
   > So I'd like to get in touch with someone higher-up in MAGMA-land to
   > find out what the real story is for getting oneself a copy of this
   
   John Cannon is at the top of MAGMA-land.  You could also write to
   David Kohel ([email protected]), who you must know by now, who
   can help out extensively.
   
   Best regards,
     William