[was@form dsw]$ [was@form dsw]$ Magma V2.9-3      Fri May 24 2002 18:12:54    [Seed = 232754131]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
>  M := ModularSymbols(127,4,-1);C := CS(M);time D := SortDecomposition(ND(C));
Time: 0.200
>  A,B,C := Explode(D);
> K := HeckeEigenvalueField(C);
> time CK := BaseExtend(C,K);
Time: 0.020
> t2 := HeckeOperator(CK,2);
> Parent(t2);

>> );
   ^
User error: bad syntax
> Parent(t2);
Full Matrix Algebra of degree 17 over K
> fcp(t2);

[Interrupt twice in half a second; exiting]

Total time: 14.199 seconds, Total memory usage: 8.26MB
[was@form dsw]$ me
Magma V2.9-3      Fri May 24 2002 18:38:53    [Seed = 298053077]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/magma/local/emacs.m"

Loading "/home/was/magma/local/init.m"
> time M := ModularSymbols(567,4,-1); 
Time: 3.020
> time D := DC(M,5);
D;
Time: 123.210
> [
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 3,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 2,
Modular symbols space of level 567, weight 4, and dimension 1,
Modular symbols space of level 567, weight 4, and dimension 3,
Modular symbols space of level 567, weight 4, and dimension 2,
Modular symbols space of level 567, weight 4, and dimension 6,
Modular symbols space of level 567, weight 4, and dimension 2,
Modular symbols space of level 567, weight 4, and dimension 5,
Modular symbols space of level 567, weight 4, and dimension 1,
Modular symbols space of level 567, weight 4, and dimension 2,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 3,
Modular symbols space of level 567, weight 4, and dimension 6,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 6,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 6,
Modular symbols space of level 567, weight 4, and dimension 8,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 8,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 4,
Modular symbols space of level 567, weight 4, and dimension 6,
Modular symbols space of level 567, weight 4, and dimension 3,
Modular symbols space of level 567, weight 4, and dimension 3,
Modular symbols space of level 567, weight 4, and dimension 6,
Modular symbols space of level 567, weight 4, and dimension 8,
Modular symbols space of level 567, weight 4, and dimension 5,
Modular symbols space of level 567, weight 4, and dimension 5,
Modular symbols space of level 567, weight 4, and dimension 8,
Modular symbols space of level 567, weight 4, and dimension 8,
Modular symbols space of level 567, weight 4, and dimension 8,
Modular symbols space of level 567, weight 4, and dimension 9,
Modular symbols space of level 567, weight 4, and dimension 9,
Modular symbols space of level 567, weight 4, and dimension 12
]
> 
> 
> f := D[#D];
> factor(567);
[ <3, 4>, <7, 1> ]
1
> f;
Modular symbols space of level 567, weight 4, and dimension 12
> t13 := DualHeckeOperator(f,13);f13 := CharacteristicPolynomial(t13);
> f13;
x^12 - 174*x^11 - 585*x^10 + 1427092*x^9 - 37260225*x^8 - 4109741982*x^7 + 126990431385*x^6 + 5305634575416*x^5 - 118492885726992*x^4 - 3711372569040128*x^3 + 26385141936830208*x^2 + 1121235198200838144*x + 6516572507993214976
> Determinant(t13);
6516572507993214976
> factor($1);
[ <2, 12>, <39886841, 2> ]
> factormod(f13,13);
[
<$.1 + 9, 2>,
<$.1 + 10, 2>,
<$.1^4 + 11*$.1^3 + 5*$.1^2 + 2*$.1 + 6, 2>
]
1
> g := Newforms("81k4A")[1];
> Coefficient(g,13);
-49
> -49 mod 13;
3
> 567/81;
7
> t7 := DualHeckeOperator(f,7);f7 := CharacteristicPolynomial(t7);
> f7;
x^12 - 84*x^11 + 3234*x^10 - 75460*x^9 + 1188495*x^8 - 13311144*x^7 + 108707676*x^6 - 652246056*x^5 + 2853576495*x^4 - 8877793540*x^3 + 18643366434*x^2 - 23727920916*x + 13841287201
> factormod(f7,13);
[
<$.1 + 6, 12>
]
1
> 
> M := ModularSymbols(127,4,-1);
> D := DC(M,3);
> D;
[
Modular symbols space of level 127, weight 4, and dimension 1,
Modular symbols space of level 127, weight 4, and dimension 13,
Modular symbols space of level 127, weight 4, and dimension 17
]
> 
> 
> f := CharacteristicPolynomial9DualHeckeOperator(D[3],2));
> factormod(f,43);

factormod(
f: [108921173/194418336 -89790623/27774048 -181801051/27774048 ...,
p: 43
)
In file "/home/was/magma/local/init.m", line 110, column 46:
>>    return Factorization(PolynomialRing(GF(p))!f);    
                                                ^
Runtime error in '!': Illegal coercion
> f := CharacteristicPolynomial9DualHeckeOperator(D[3],2));

>> f := CharacteristicPolynomial9DualHeckeOperator(D[3],2));
                                                          ^
User error: bad syntax
> f := CharacteristicPolynomial9DualHeckeOperator(D[3],2));

>> f := CharacteristicPolynomial(DualHeckeOperator(D[3],2));
                                                          ^
User error: bad syntax
> > f := CharacteristicPolynomial(DualHeckeOperator(D[3],2));
> factormod(f,43);
[
<$.1 + 1, 1>,
<$.1^3 + 8*$.1^2 + 2*$.1 + 22, 1>,
<$.1^4 + 26*$.1^3 + 26*$.1^2 + 4*$.1 + 20, 1>,
<$.1^9 + 42*$.1^8 + 41*$.1^7 + 3*$.1^6 + 5*$.1^5 + 26*$.1^4 + 30*$.1^3 + 42*$.1^2 + 27, 1>
]
1
> factormod(f,43);
[
<$.1 + 1, 1>,
<$.1^3 + 8*$.1^2 + 2*$.1 + 22, 1>,
<$.1^4 + 26*$.1^3 + 26*$.1^2 + 4*$.1 + 20, 1>,
<$.1^9 + 42*$.1^8 + 41*$.1^7 + 3*$.1^6 + 5*$.1^5 + 26*$.1^4 + 30*$.1^3 + 42*$.1^2 + 27, 1>
]
1
> laod "~/magma/local/init.m";

>> laod ~/magma/local/init.m";
         ^
User error: bad syntax
> laod "~/magma/local/init.m";

>> load "~/magma/local/init.m";
        ^
User error: bad syntax
> > load "~/magma/local/init.m";
Loading "/home/was/magma/local/init.m"
> factormod(f,43);
[
<x + 1, 1>,
<x^3 + 8*x^2 + 2*x + 22, 1>,
<x^4 + 26*x^3 + 26*x^2 + 4*x + 20, 1>,
<x^9 + 42*x^8 + 41*x^7 + 3*x^6 + 5*x^5 + 26*x^4 + 30*x^3 + 42*x^2 + 27, 1>
]
1
> f7;
x^12 - 84*x^11 + 3234*x^10 - 75460*x^9 + 1188495*x^8 - 13311144*x^7 + 108707676*x^6 - 652246056*x^5 + 2853576495*x^4 - 8877793540*x^3 + 18643366434*x^2 - 23727920916*x + 13841287201
> SetColumns(70);
> f7;
x^12 - 84*x^11 + 3234*x^10 - 75460*x^9 + 1188495*x^8 - 13311144*x^7 + 
    108707676*x^6 - 652246056*x^5 + 2853576495*x^4 - 8877793540*x^3 + 
    18643366434*x^2 - 23727920916*x + 13841287201
> factormod(f7,13);
[
    <x + 6, 12>
]
1
>