[was@ecstasy pq]$ [was@ecstasy pq]$ Magma V2.7-1      Fri Sep 15 2000 16:28:37 on ecstasy  [Seed = 1069828122]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/modsym/init-magma.m"

C               IndexGamma0     R               factormod       padiccharpoly
CS              MS              Tn              fcp             qexp
DC              ND              Z               fn              x
ES              NS              charpoly        idxG0
F               Q               ellap           modcharpoly
> M:=ModularSymbols(11*17);
> e:=WindingElement(M);
> e;
-1*{oo, 0}
> wp:=AtkinLehner(M,11);
> wq:=AtkinLehner(M,17);
> e*wp;
{-2/11, -3/17}
> e*wq;
-1*{-2/11, -3/17}
> e*wp in CuspidalSubspace(M);
false
> (e*wp+e) in CuspidalSubspace(M);
false
> (e*wp-e) in CuspidalSubspace(M);
false
> RationalPeriodMapping;

>> RationalPeriodMapping;
   ^
User error: Identifier 'RationalPeriodMapping' has not been declared or assigned
> J:=CuspidalSubspace(M);
> SubgroupOfTorus(J,e);
Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
Mapping from: Lattice of rank 1 and degree 34 to Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
> SubgroupOfTorus(J,e*wp);
Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
Mapping from: Lattice of rank 1 and degree 34 to Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
> SubgroupOfTorus(J,e*wp-e);
Abelian Group isomorphic to Z/15
Defined on 1 generator
Relations:
15*$.1 = 0
Mapping from: Lattice of rank 1 and degree 34 to Abelian Group isomorphic to Z/15
Defined on 1 generator
Relations:
15*$.1 = 0
> SubgroupOfTorus(J,e*wp+e);
Abelian Group isomorphic to Z/8
Defined on 1 generator
Relations:
8*$.1 = 0
Mapping from: Lattice of rank 1 and degree 34 to Abelian Group isomorphic to Z/8
Defined on 1 generator
Relations:
8*$.1 = 0
> SubgroupOfTorus(J,[e*wp,e]);
Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
Mapping from: Lattice of rank 2 and degree 34 to Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
> SubgroupOfTorus(J,[e*wq,e]);
Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
Mapping from: Lattice of rank 2 and degree 34 to Abelian Group isomorphic to Z/240
Defined on 1 generator
Relations:
240*$.1 = 0
> 240 div 15;
16
> 17+1
> ;
18
> 240 div 18
> ;
13
> 240 div 8;
30
> load "/home/was/modsym/period.m";
Loading "/home/was/modsym/period.m"

In file "/home/was/modsym/period.m", line 75, column 1:
>> intrinsic DualModularSymbol(M::ModSym) -> Map
   ^
User error: Illegal intrinsic
> phi:=ScaledRationalPeriodMapping(J);
> phi(e);

>> phi(e);
      ^
Runtime error in map application: Element is not in the domain of the map
> V:=VectorSpace(M); V!Eltseq(e);
(0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
> phi(V!Eltseq(e));
(0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0)
> phi:=ScaledRationalPeriodMapping(J);

>> phi:=ScaledRationalPeriodMapping(J);
        ^
User error: Identifier 'ScaledRationalPeriodMapping' has not been declared or assigned
>  phi:=ScaledRationalPeriodMap(J);
> phi(V!Eltseq(e));

>> phi(V!Eltseq(e));
      ^
Runtime error in procedure call: Attempting to call something that is not callable
>  phi:=ScaledRationalPeriodMap(J);
> e*phi;

>> e*phi;
    ^
Runtime error in '*': Bad argument types
Argument types given: ModSymElt, ModMatFldElt
> a:=V!Eltseq(e) * phi;
(-1/30 -1/15 23/240 1/30 -31/240 1/15 1/30 0 -31/240 -1/30 1/15 0 -1/16 -7/240 1/15 1/240 -7/240 -1/16 -1/8 17/240 1/15 1/15 1/240 -7/240 1/30 7/240 -1/10 -1/240 1/16 23/240 -3/80 11/48 -1/16 -1/16)
> b:=V!Eltseq(e*wp) * phi;
(1/30 1/15 247/240 -1/30 -239/240 14/15 -1/30 0 -239/240 1/30 -1/15 -1 -1/16 -23/240 -1/15 -31/240 -23/240 -17/16 -1/8 193/240 -1/15 14/15 -31/240 -23/240 -1/30 23/240 1/10 31/240 1/16 7/240 -67/80 43/48 -1/16 -1/16)
> V!Eltseq(e-e*wp) * phi;
(-1/15 -2/15 -14/15 1/15 13/15 -13/15 1/15 0 13/15 -1/15 2/15 1 0 1/15 2/15 2/15 1/15 1 0 -11/15 2/15 -13/15 2/15 1/15 1/15 -1/15 -1/5 -2/15 0 1/15 4/5 -2/3 0 0)
> a:=V!Eltseq(e) * phi;
> b:=V!Eltseq(e*wp) * phi;
> a;
(-1/30 -1/15 23/240 1/30 -31/240 1/15 1/30 0 -31/240 -1/30 1/15 0 -1/16 -7/240 1/15 1/240 -7/240 -1/16 -1/8 17/240 1/15 1/15 1/240 -7/240 1/30 7/240 -1/10 -1/240 1/16 23/240 -3/80 11/48 -1/16 -1/16)
> b;
(1/30 1/15 247/240 -1/30 -239/240 14/15 -1/30 0 -239/240 1/30 -1/15 -1 -1/16 -23/240 -1/15 -31/240 -23/240 -17/16 -1/8 193/240 -1/15 14/15 -31/240 -23/240 -1/30 23/240 1/10 31/240 1/16 7/240 -67/80 43/48 -1/16 -1/16)
> -1*a;
(1/30 1/15 -23/240 -1/30 31/240 -1/15 -1/30 0 31/240 1/30 -1/15 0 1/16 7/240 -1/15 -1/240 7/240 1/16 1/8 -17/240 -1/15 -1/15 -1/240 7/240 -1/30 -7/240 1/10 1/240 -1/16 -23/240 3/80 -11/48 1/16 1/16)
> SubgroupOfTorus(J,[e*wp-17*e]);
Abelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
5*$.1 = 0
Mapping from: Lattice of rank 1 and degree 34 to Abelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
5*$.1 = 0
> #SubgroupOfTorus(J,[e*wp-17*e]);
5
> [a : #SubgroupOfTorus(J,[e*wp-a*e]) eq 1  | GCD(a,240) eq 1];

>> [a : #SubgroupOfTorus(J,[e*wp-a*e]) eq 1  | GCD(a,240) eq 1];
        ^
User error: bad syntax
> [a : a in [2..240] | GCD(a,240) eq 1 and #SubgroupOfTorus(J,[e*wp-a*e]) eq 1];
[ 209 ]
> factor(209);
[ <11, 1>, <19, 1> ]
1
> [a : a in [2..240] | GCD(a,240) eq 1 and #SubgroupOfTorus(J,[e*wq-a*e]) eq 1];
[ 31 ]
> M33:=MS(3*11);
> J33:=CS(M33);
> e33:=WindingElement(M33);
> w3:=AtkinLehner(M33,3); w11:=AtkinLehner(M33,11);
> SubgroupOfTorus(J33,[e33,e33*w3,e33*w11]);
> SubgroupOfTorus(J33,[e33,e33*w3,e33*w11]);
Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0
Mapping from: Lattice of rank 1 and degree 6 to Abelian Group isomorphic to Z/10
Defined on 1 generator
Relations:
10*$.1 = 0
> [a : a in [2..10] | GCD(a,10) eq 1 and #SubgroupOfTorus(J33,[e33*w3-a*e33]) eq 1];
[]
> [a : a in [2..10] | GCD(a,10) eq 1 and #SubgroupOfTorus(J33,[e33*w11-a*e33]) eq 1];
[ 9 ]
> [a : a in [2..10] | #SubgroupOfTorus(J33,[e33*w3-a*e33]) eq 1];
[]
> [a : a in [1..15] | #SubgroupOfTorus(J33,[e33*w3-a*e33]) eq 1];
[ 1, 11 ]
> NS:=NewSubspace(J);
> SubgroupOfTorus(NS,e);
Abelian Group isomorphic to Z/12
Defined on 1 generator
Relations:
12*$.1 = 0
Mapping from: Lattice of rank 1 and degree 26 to Abelian Group isomorphic to Z/12
Defined on 1 generator
Relations:
12*$.1 = 0
> 240 div 12;
20
> 209^2 mod 240;
1
> factor(240);
[ <2, 4>, <3, 1>, <5, 1> ]
1
> 31^2 mod 240;
1
>