CoCalc Shared Fileswww / cgi-bin / old_logs / logfile_magma-12-23-03.txt
Author: William A. Stein

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Thu Nov 27 13:45:57 2003

Input: 1+1

Output: Magma V2.10-6     Thu Nov 27 2003 13:45:54 on modular  [Seed = 217412972]
-------------------------------------

2

Total time: 2.979 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Thu Nov 27 17:12:30 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2*

(a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))]
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,0);

Output: Magma V2.10-6     Thu Nov 27 2003 17:12:27 on modular  [Seed = 1503662226]
-------------------------------------

>> Eigenvalues(M);
^

>> Eigenspace(M,1);
^
User error: Identifier 'M' has not been declared or assigned

>> Eigenspace(M,0);
^
User error: Identifier 'M' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Thu Nov 27 17:12:40 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2*

(a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))];
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,0);

Output: Magma V2.10-6     Thu Nov 27 2003 17:12:37 on modular  [Seed = 1637361844]
-------------------------------------

{
<1, 1>,
<(1/3*a - 3)/(a - 5), 1>,
<(1/6*a - 5/3)/(a - 5), 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-2*a + 6)/(a + 2)         -2/(a - 1))
Vector space of degree 3, dimension 0 over Univariate rational function field
over Rational Field

Total time: 2.989 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Thu Nov 27 17:13:40 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2*

(a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))];
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,(1/3*a - 3)/(a - 5));
Eigenspace(M,(1/6*a - 5/3)/(a - 5));

Output: Magma V2.10-6     Thu Nov 27 2003 17:13:37 on modular  [Seed = 1788027515]
-------------------------------------

{
<1, 1>,
<(1/3*a - 3)/(a - 5), 1>,
<(1/6*a - 5/3)/(a - 5), 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-2*a + 6)/(a + 2)         -2/(a - 1))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                       1 (-1/2*a + 3/2)/(a - 1/2)   (-1/2*a - 1)/(a - 1/2))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(   1 -1/3 -2/3)

Total time: 2.909 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Thu Nov 27 17:19:05 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(3*a-4)/(5*(a-4)),2*(3*a-4)/(5*(a-4)),4*(a+2)/(5*(4-a)),(a+2)/(5*(4-a)),2*(4*a-7)

/(5*(a-4)),2*(a+2)/(5*(4-a)),(a-1)/(a-4),(a-1)/(a-4),(a+2)/(4-a)];
Eigenvalues(M);
Eigenspace(M,1);

Output: Magma V2.10-6     Thu Nov 27 2003 17:19:02 on modular  [Seed = 2072132653]
-------------------------------------

{
<0, 1>,
<1, 1>,
<(1/5*a - 8/5)/(a - 4), 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-2*a + 6)/(a + 2)         -2/(a - 1))

Total time: 2.999 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Thu Nov 27 17:20:00 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(3*a-4)/(5*(a-4)),2*(3*a-4)/(5*(a-4)),4*(a+2)/(5*(4-a)),(a+2)/(5*(4-a)),2*(4*a-7)

/(5*(a-4)),2*(a+2)/(5*(4-a)),(a-1)/(a-4),(a-1)/(a-4),(a+2)/(4-a)];
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,0);
Eigenspace(M,(1/5*a - 8/5)/(a - 4));

Output: Magma V2.10-6     Thu Nov 27 2003 17:19:57 on modular  [Seed = 2222834441]
-------------------------------------

{
<0, 1>,
<1, 1>,
<(1/5*a - 8/5)/(a - 4), 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-2*a + 6)/(a + 2)         -2/(a - 1))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(   1 -1/3 -2/3)
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                       1 (-1/2*a + 3/2)/(a - 1/2)   (-1/2*a - 1)/(a - 1/2))

Total time: 2.959 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Thu Nov 27 17:24:13 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(2*a-7)/(3*(a-5)),(3*a-4)/(3*(a-5)),2*(a+2)/(3*(5-a)),(a+2)/(6*(5-a)),(3*a-8)/(2*

(a-5)),(a+2)/(3*(5-a)),5*(a-1)/(6*(a-5)),5*(a-1)/(6*(a-5)),2*(a+5)/(3*(5-a))];
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,(1/3*a - 3)/(a - 5));
Eigenspace(M,(1/6*a - 5/3)/(a - 5));

Output: Magma V2.10-6     Thu Nov 27 2003 17:24:10 on modular  [Seed = 2506937119]
-------------------------------------

{
<1, 1>,
<(1/3*a - 3)/(a - 5), 1>,
<(1/6*a - 5/3)/(a - 5), 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-2*a + 6)/(a + 2)         -2/(a - 1))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                       1 (-1/2*a + 3/2)/(a - 1/2)   (-1/2*a - 1)/(a - 1/2))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(   1 -1/3 -2/3)

Total time: 3.079 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Thu Nov 27 20:49:32 2003

Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(MOdularSymbols(56,2,+1))))); #A;
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),+110)));
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),-110)));
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),+54)));
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),-54)));

Output: Magma V2.10-6     Thu Nov 27 2003 20:49:29 on modular  [Seed = 417435343]
-------------------------------------

>> A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(MOdu
^
User error: Identifier 'MOdularSymbols' has not been declared or assigned

>> uspidalSubspace(MOdularSymbols(56,2,+1))))); #A;
^
User error: Identifier 'A' has not been declared or assigned

>> al(DualHeckeOperator(A[2],109)),+110)));
^
User error: Identifier 'A' has not been declared or assigned

>> al(DualHeckeOperator(A[2],109)),-110)));
^
User error: Identifier 'A' has not been declared or assigned

>> al(DualHeckeOperator(A[2],53)),+54)));
^
User error: Identifier 'A' has not been declared or assigned

>> al(DualHeckeOperator(A[2],53)),-54)));
^
User error: Identifier 'A' has not been declared or assigned

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Thu Nov 27 20:49:56 2003

Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A;
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),+110)));
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],109)),-110)));
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),+54)));
Factorization(Numerator(Evaluate(CharacteristicPolynomial(DualHeckeOperator(A[2],53)),-54)));

Output: Magma V2.10-6     Thu Nov 27 2003 20:49:52 on modular  [Seed = 300451759]
-------------------------------------

2
[ <2, 3>, <3, 1>, <5, 1> ]
[ <2, 2>, <5, 2> ]
[ <2, 4>, <3, 1> ]
[ <2, 2>, <3, 1>, <5, 1> ]

Total time: 3.609 seconds, Total memory usage: 2.79MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Thu Nov 27 21:02:20 2003

Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A;
56*109; C;
E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1);
CongruenceGroupAnemic(A[2],Parent(Newform(E)),200);
56*53; D;
E:=EllipticCurve(EllipticCurveDatabase(),2968,4,1);
CongruenceGroupAnemic(A[2],Parent(Newform(E)),200);

Output: Magma V2.10-6     Thu Nov 27 2003 21:02:16 on modular  [Seed = 3710144011]
-------------------------------------

2
6104

>> 56*109; C;
^
User error: Identifier 'C' has not been declared or assigned
Abelian Group of order 1
2968

>> 56*53; D;
^
User error: Identifier 'D' has not been declared or assigned
Abelian Group isomorphic to Z/3
Defined on 1 generator
Relations:
3*$.1 = 0 Total time: 4.279 seconds, Total memory usage: 5.09MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 21:07:13 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A; 56*109; C; E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1); CongruenceGroupAnemic(A[1],Parent(Newform(E)),200); Output: Magma V2.10-6 Thu Nov 27 2003 21:07:09 on modular [Seed = 3426049663] ------------------------------------- 2 6104 >> 56*109; C; ^ User error: Identifier 'C' has not been declared or assigned Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0

Total time: 4.119 seconds, Total memory usage: 4.50MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Thu Nov 27 21:07:59 2003

Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A;
56*109; C;
E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1);
CongruenceGroupAnemic(A[1],Parent(Newform(E)),200);

Output: Magma V2.10-6     Thu Nov 27 2003 21:07:55 on modular  [Seed = 3292354113]
-------------------------------------

2
6104

>> 56*109; C;
^
User error: Identifier 'C' has not been declared or assigned
Abelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
5*$.1 = 0 Total time: 4.159 seconds, Total memory usage: 4.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Thu Nov 27 21:09:03 2003 Input: A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(56,2,+1))))); #A; 56*109; C; E:=EllipticCurve(EllipticCurveDatabase(),6104,3,1); CongruenceGroupAnemic(A[1],Parent(Newform(E)),200); Output: Magma V2.10-6 Thu Nov 27 2003 21:08:58 on modular [Seed = 3124964350] ------------------------------------- 2 6104 >> 56*109; C; ^ User error: Identifier 'C' has not been declared or assigned Abelian Group isomorphic to Z/5 Defined on 1 generator Relations: 5*$.1 = 0

Total time: 4.219 seconds, Total memory usage: 4.50MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Thu Nov 27 21:37:11 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
f0:=2*(x^2+y^2)+x-y-16;
f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192;
f2:=640*(x^6+y^6)+1552*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2)+73*(x-y)-81905;
I:=ideal<P|f0,f1,f2>;
B:=GroebnerBasis(I);
B;
Factorization(2749936217096833768575);
Bn:=GroebnerBasis(ChangeRing(I,GF(2430902559671)));
Bn;
PP:=ChangeRing(P,GF(2430902559671));
Factorization(PP!(y^2 + 1852361963659*y + 840678110478));

Output: Magma V2.10-6     Thu Nov 27 2003 21:37:07 on modular  [Seed = 2089154514]
-------------------------------------

[
x^2 + 3*x + y^3 + 5*y^2 + 2614760142323078757143*y + 550651912315588962426,
x*y + 2*x + 2*y^3 + 8*y^2 + 2479584067549323745715*y +
1530544330223333986239,
5*x + 2*y^3 + 8*y^2 + 2479584067549323745712*y + 1101303824631177924868,
y^4 + y^3 + 4*y^2 + 2626616282958524270696*y + 2208607045947985918918,
3*y^3 + 12*y^2 + 2344407992775568734288*y + 1946020167765167937252,
15*y^2 + 588128861636802099900*y + 1924284781875100852290,
2749936217096833768575
]
[ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <35159, 1>, <2430902559671, 1> ]
[
x + 2430902559670*y + 578540596012,
y^2 + 1852361963659*y + 840678110478
]
[
<y^2 + 1852361963659*y + 840678110478, 1>
]

Total time: 2.999 seconds, Total memory usage: 1.93MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Thu Nov 27 21:40:18 2003

Input: // Allan
f := SwinnertonDyerPolynomial(5);
g := SwinnertonDyerPolynomial(6);
time L:=Factorization(f*g);
#L;

Output: Magma V2.10-6     Thu Nov 27 2003 21:40:14 on modular  [Seed = 1872160156]
-------------------------------------

Time: 0.660
2

Total time: 3.729 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Thu Nov 27 21:40:30 2003

Input: // Allan
f := SwinnertonDyerPolynomial(5);
g := SwinnertonDyerPolynomial(6);
time L:=Factorization(f*g);
#L;
L;

Output: Magma V2.10-6     Thu Nov 27 2003 21:40:26 on modular  [Seed = 1738468736]
-------------------------------------

Time: 0.660
2
[
<$.1^32 - 448*$.1^30 + 84864*$.1^28 - 9028096*$.1^26 + 602397952*$.1^24 - 26625650688*$.1^22 + 801918722048*$.1^20 - 16665641517056*$.1^18 +
239210760462336*$.1^16 - 2349014746136576*$.1^14 +
15459151516270592*$.1^12 - 65892492886671360*$.1^10 +
172580952324702208*$.1^8 - 255690851718529024*$.1^6 +
183876928237731840*$.1^4 - 44660812492570624*$.1^2 + 2000989041197056,
1>,
<$.1^64 - 1312*$.1^62 + 792048*$.1^60 - 293134944*$.1^58 +
74737287288*$.1^56 - 13981172308896*$.1^54 + 1995413247403984*$.1^52 - 223010452468129504*$.1^50 + 19875965471079809820*$.1^48 - 1431186296399427673760*$.1^46 + 84041236543621002233072*$.1^44 - 4051269676739248306877664*$.1^42 + 161038437520893531719546696*$.1^40 - 5292590468585153795497272608*$.1^38 +
143976257181996292530653998416*$.1^36 - 3240853899326109989616514647392*$.1^34 +
60261059130667890854325275719238*$.1^32 - 922739669127277027441017551584608*$.1^30 +
11582497564629879101390954172990800*$.1^28 - 118444912349891951852181962142375200*$.1^26 +
978878175154164215599705915851796296*$.1^24 - 6471399892949448329687739464771529952*$.1^22 +
33785494292069713784801456649105169648*$.1^20 - 137048942135190916858196960829292680864*$.1^18 +
423140580409718469187953106123559340828*$.1^16 - 968316307427310602872375357706532108000*$.1^14 +
1585722240968892813653220405983168716752*$.1^12 - 1771080720430629161685158978892152599456*$.1^10 +
1258829468814790188483900997578812102776*$.1^8 - 511762449216265420619809586571618679392*$.1^6 +
100392008259975194458539996111340080624*$.1^4 - 8316202966928528723117528333532208416*$.1^2 +
198828783273803025550632280753863681, 1>
]

Total time: 3.720 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Nov 27 21:41:44 2003

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-6     Thu Nov 27 2003 21:41:41 on modular  [Seed = 1471077839]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.949 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Nov 27 21:42:04 2003

Input: for

Output: Magma V2.10-6     Thu Nov 27 2003 21:42:01 on modular  [Seed = 1203686851]
-------------------------------------

>> for;
^

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host gb1000.math.kyushu-u.ac.jp. (133.5.165.4)
Time: Thu Nov 27 21:42:15 2003

Input: for

Output: Magma V2.10-6     Thu Nov 27 2003 21:42:12 on modular  [Seed = 1069987398]
-------------------------------------

>> for;
^

Total time: 3.019 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host mac174.sm.luth.se. (130.240.15.174)
Time: Fri Nov 28 11:24:42 2003

Input: "Replace this by some code, then click [PARI] or [MAGMA]!"

Output: Magma V2.10-6     Fri Nov 28 2003 11:24:38 on modular  [Seed = 1370036455]
-------------------------------------

Replace this by some code, then click [PARI] or [MAGMA]!

Total time: 2.959 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:20:59 2003

Input: C:=DoublyCirculantQRCode(7);

Output: Magma V2.10-6     Fri Nov 28 2003 12:20:56 on modular  [Seed = 4228137076]
-------------------------------------

Total time: 3.049 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:21:16 2003

Input: C:=DoublyCirculantQRCode(7);
C;

Output: Magma V2.10-6     Fri Nov 28 2003 12:21:13 on modular  [Seed = 3827064733]
-------------------------------------

[14, 7, 3] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 1 1 1 0 1 0 0]
[0 1 0 0 0 0 0 0 1 1 1 0 1 0]
[0 0 1 0 0 0 0 0 0 1 1 1 0 1]
[0 0 0 1 0 0 0 1 0 0 1 1 1 0]
[0 0 0 0 1 0 0 0 1 0 0 1 1 1]
[0 0 0 0 0 1 0 1 0 1 0 0 1 1]
[0 0 0 0 0 0 1 1 1 0 1 0 0 1]

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:22:54 2003

Input: C:=DoublyCirculantQRCode(11);
C;

Output: Magma V2.10-6     Fri Nov 28 2003 12:22:50 on modular  [Seed = 3960756215]
-------------------------------------

[22, 11, 7] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1]
[0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 0]
[0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1]
[0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1]
[0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 0 1]
[0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1]

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:24:07 2003

Input: C:=DoublyCirculantQRCode(13);
C;

Output: Magma V2.10-6     Fri Nov 28 2003 12:24:04 on modular  [Seed = 3576524305]
-------------------------------------

[26, 13, 6] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1 0]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1]

Total time: 3.069 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:24:47 2003

Input: C:=DoublyCirculantQRCode(17);
C;

Output: Magma V2.10-6     Fri Nov 28 2003 12:24:44 on modular  [Seed = 3710215793]
-------------------------------------

[34, 17] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1]

Total time: 3.059 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:25:22 2003

Input: C:=DoublyCirculantQRCode(17);
C;
MinimalDistance(C);

Output: Magma V2.10-6     Fri Nov 28 2003 12:25:19 on modular  [Seed = 3375460934]
-------------------------------------

[34, 17] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1]

>> MinimalDistance(C);;
^
User error: Identifier 'MinimalDistance' has not been declared or assigned

Total time: 3.089 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:26:25 2003

Input: C:=DoublyCirculantQRCode(17);
C;
MinimumDistance(C);

Output: Magma V2.10-6     Fri Nov 28 2003 12:26:22 on modular  [Seed = 2974354431]
-------------------------------------

[34, 17] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0 1]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0 1]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1]
6

Total time: 3.079 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:27:10 2003

Input: C:=DoublyCirculantQRCode(19);
C;
MinimumDistance(C);

Output: Magma V2.10-6     Fri Nov 28 2003 12:27:06 on modular  [Seed = 3108045731]
-------------------------------------

[38, 19] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1]
[0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1]
[0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0]
[0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 0 1 1 0 1]
7

Total time: 3.059 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:27:44 2003

Input: C:=DoublyCirculantQRCode(23);
C;
MinimumDistance(C);

Output: Magma V2.10-6     Fri Nov 28 2003 12:27:41 on modular  [Seed = 2706971484]
-------------------------------------

[46, 23] Linear Code over GF(2)
Generator matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1
0 1 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 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0
1 0 1 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 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0
0 1 0 1 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 1 1 1 1 1 0 1 0 1 1 0 0 1 1
0 0 1 0 1 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 1 1 1 1 1 0 1 0 1 1 0 0 1
1 0 0 1 0 1]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0
1 1 0 0 1 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 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0
0 1 1 0 0 1]
[0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1 1
0 0 1 1 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 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0 1
1 0 0 1 1 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 1 0 1 0 0 0 0 1 1 1 1 1 0 1 0
1 1 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0 1
0 1 1 0 0 1]
[0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1 0
1 0 1 1 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1 1
0 1 0 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1 1
1 0 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1 1
1 1 0 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 1
1 1 1 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1
1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0
1 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0 0
0 1 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0 0
0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 0
0 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1
0 0 0 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0
1 0 0 0 0 1]
7

Total time: 3.059 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:28:15 2003

Input: C:=DoublyCirculantQRCode(29);
C;
MinimumDistance(C);

Output: Magma V2.10-6     Fri Nov 28 2003 12:28:11 on modular  [Seed = 2840662898]
-------------------------------------

[58, 29] Linear Code over GF(2)
Generator matrix:
[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 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0
0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1]
[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 0 0 0 1 1 1 0 0 1 1 1 1 0 1
0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 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 0 0 0 1 1 1 0 0 1 1 1 1 0
1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1 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 0 0 0 1 1 1 0 0 1 1 1 1
0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 1]
[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 1 0 0 1 1 1 0 0 1 1 1
1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1]
[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 1 1 0 0 1 1 1 0 0 1 1
1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 1]
[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 1 1 1 0 0 1 1 1 0 0 1
1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1]
[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 1 1 1 1 0 0 1 1 1 0 0
1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 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 1 1 1 1 0 0 1 1 1 0
0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1]
[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 1 0 1 1 1 1 0 0 1 1 1
0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 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 1 0 1 1 1 1 0 0 1 1
1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 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 1 0 1 1 1 1 0 0 1
1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0]
[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 1 0 1 1 1 1 0 0
1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1]
[0 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 1 0 0 0 1 0 1 1 1 1 0
0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0 0]
[0 0 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 1 0 0 0 1 0 1 1 1 1
0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 0]
[0 0 0 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 1 0 0 0 1 0 1 1 1
1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1]
[0 0 0 0 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 1 0 0 1 0 0 0 1 0 1 1
1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0]
[0 0 0 0 0 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 1 0 0 1 0 0 0 1 0 1
1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0 0]
[0 0 0 0 0 0 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 1 0 0 1 0 0 0 1 0
1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1 0]
[0 0 0 0 0 0 0 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 1 0 0 1 0 0 0 1
0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0
1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0
0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 1 0
0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 1
0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 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 1 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0
1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 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 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0
0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 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 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0 1
0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 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 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 0
1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 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 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 0
0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1]
12

Total time: 3.029 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:28:49 2003

Input: C:=DoublyCirculantQRCode(31);
C;
MinimumDistance(C);

Output: Magma V2.10-6     Fri Nov 28 2003 12:28:46 on modular  [Seed = 2439588655]
-------------------------------------

[62, 31] Linear Code over GF(2)
Generator matrix:
[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 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1
1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 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 0 0 0 0 0 0 1 1 1 0 1 1 0 1
1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 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 0 0 0 0 0 0 1 1 1 0 1 1 0
1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1]
[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 0 0 0 1 0 0 1 1 1 0 1 1
0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 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 0 0 0 1 0 0 1 1 1 0 1
1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 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 0 0 0 1 0 0 1 1 1 0
1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1]
[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 1 0 0 1 0 0 1 1 1
0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 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 1 0 0 1 0 0 1 1
1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 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 1 0 0 1 0 0 1
1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 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 1 0 0 1 0 0
1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1 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 1 0 0 1 0
0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 1]
[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 1 0 0 0 0 1 0 0 1
0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1]
[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 1 1 0 0 0 0 1 0 0
1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0 1]
[0 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 1 1 1 0 0 0 0 1 0
0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1 0]
[0 0 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 1 1 1 0 0 0 0 1
0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0 1]
[0 0 0 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 1 0 1 1 1 0 0 0 0
1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1 0]
[0 0 0 0 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 1 0 1 1 1 0 0 0
0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0 1]
[0 0 0 0 0 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 1 0 1 0 1 1 1 0 0
0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 0]
[0 0 0 0 0 0 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 1 0 1 0 1 1 1 0
0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0]
[0 0 0 0 0 0 0 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 1 0 1 0 1 1 1
0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0]
[0 0 0 0 0 0 0 0 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 1 0 1 0 1 1
1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 1
1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0
1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 1
0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 1 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 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 0
1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 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 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1
0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 0 1 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 0 0 1 0 0 0 0 1 0 1 1 1 1 0 0 0
1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 1 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 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0
0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 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 0 0 0 0 0 1 0 0 0 1 1 0 1 1 1 1 0
0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 1 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 0 0 0 0 0 1 0 1 0 1 1 0 1 1 1 1
0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1 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 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1
1 0 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1]
7

Total time: 3.189 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 12:29:44 2003

Input: C:=DoublyCirculantQRCode(37);
C;
MinimumDistance(C);

Output: Magma V2.10-6     Fri Nov 28 2003 12:29:41 on modular  [Seed = 2590122991]
-------------------------------------

[74, 37] Linear Code over GF(2)
Generator matrix:
[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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1]
[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 0 0 0 0 0 0 0 0 0 0 0 1 1 1
0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 1 1
1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1]
[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 0 0 0 0 0 0 0 0 0 1 0 1
1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1]
[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 0 0 0 0 0 0 0 0 1 1 0
1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 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 0 0 0 0 0 0 0 0 1 1
0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 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 0 0 0 0 0 0 0 0 1
1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1]
[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 0 0 0 0 0 1 0 0
1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 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 0 0 0 0 0 1 0
0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1]
[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 0 0 0 1 0 1
0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1]
[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 0 0 1 1 0
1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1]
[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 0 1 1 1
0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1]
[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 1 1 1
1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0]
[0 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 1 1
1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0]
[0 0 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 1
1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0]
[0 0 0 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
1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1]
[0 0 0 0 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 1 0 0
0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 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 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0
0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 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 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1
0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1
1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1
1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 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 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1
1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0
1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 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 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0
1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0
0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1
0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1
1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1]
12

Total time: 3.169 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:26:17 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=1366076058403;
f1:=2590764387755;
f2:=3192785289108;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:26:13 on modular  [Seed = 868982553]
-------------------------------------

[]
27
[]
36

Total time: 3.269 seconds, Total memory usage: 1.94MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:27:04 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=1237559558535;
f1:=4618476257611;
f2:=1771339940640;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:27:00 on modular  [Seed = 200517392]
-------------------------------------

[ <366427174246, 936139050903, 0>, <729572566429, 2655705066073, 0>,
<799473895704, 2681189646640, 0>, <1408904790141, 246104236481, 0>,
<2825450335113, 961623631470, 0>, <3329120936973, 2565788990989, 0>,
<3581194270392, 2540304410422, 0>, <4301697223593, 1850269596000, 0>,
<4528551981581, 1965670251651, 0> ]
[
<x + 3225642079929, 1>,
<x + 4344863146065, 1>
]
[
<x^2 + 5159149924412*x + 871909337570, 1>
]
[
<x + 3225642079929, 1>,
<x + 4344863146065, 1>
]
[
<x^2 + 5159149924412*x + 871909337570, 1>
]
[
<x + 1290363504238, 1>,
<x + 3875819471506, 1>
]
[
<x^2 + 5159149924412*x + 871909337570, 1>
]
[
<x + 1290363504238, 1>,
<x + 3875819471506, 1>
]
[
<x + 3225642079929, 1>,
<x + 4344863146065, 1>
]
[
<x + 1290363504238, 1>,
<x + 3875819471506, 1>
]
27
[ <111999871605, 4899443106346, 3257828155161>, <219250367204, 2184697719270,
3477945283971>, <821787457239, 441403113397, 4365987944593>, <2226239470925,
2896939759078, 1856574669973>, <2419571365379, 2129255421068, 4712633972520>,
<5136348054734, 3851055761470, 4199423147954> ]
[
<x + 1348749859592, 1>,
<x + 3635190611304, 1>,
<x + 5084598341797, 1>
]
[
<x + 1348749859592, 2>,
<x + 3635190611304, 2>,
<x + 5084598341797, 2>
]
[
<x + 1348749859592, 1>,
<x + 3635190611304, 1>,
<x + 5084598341797, 1>
]
[
<x + 1348749859592, 2>,
<x + 3635190611304, 2>,
<x + 5084598341797, 2>
]
[
<x + 2096213381504, 1>,
<x^2 + 510604777655*x + 1568343686432, 1>
]
[
<x + 2096213381504, 2>,
<x^2 + 510604777655*x + 1568343686432, 2>
]
[
<x + 2096213381504, 1>,
<x^2 + 510604777655*x + 1568343686432, 1>
]
[
<x + 2096213381504, 2>,
<x^2 + 510604777655*x + 1568343686432, 2>
]
[
<x + 2096213381504, 1>,
<x^2 + 510604777655*x + 1568343686432, 1>
]
[
<x + 2096213381504, 2>,
<x^2 + 510604777655*x + 1568343686432, 2>
]
[
<x + 1348749859592, 1>,
<x + 3635190611304, 1>,
<x + 5084598341797, 1>
]
[
<x + 1348749859592, 2>,
<x + 3635190611304, 2>,
<x + 5084598341797, 2>
]
36

Total time: 3.399 seconds, Total memory usage: 1.94MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:27:26 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=5200520646404;
f1:=1150349096740;
f2:=4237089101808;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:27:23 on modular  [Seed = 66826215]
-------------------------------------

[ <3370307863942, 5011329312978, 0>, <3721693715583, 3443373886111, 0>,
<3843195007561, 2480493387997, 0> ]
[
<x^2 + 1727877202782*x + 2834633576045, 1>
]
[
<x^2 + 1727877202782*x + 2834633576045, 1>
]
[
<x^2 + 1727877202782*x + 2834633576045, 1>
]
27
[]
36

Total time: 3.349 seconds, Total memory usage: 1.94MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:27:51 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=2327136090767;
f1:=2647590640482;
f2:=4900698753729;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:27:48 on modular  [Seed = 467908560]
-------------------------------------

[]
27
[]
36

Total time: 3.259 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:28:32 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=1388631197972;
f1:=5181403620092;
f2:=908395318285;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:28:28 on modular  [Seed = 334217136]
-------------------------------------

[ <542463558561, 2113471712437, 0>, <896193300545, 2307476134461, 0>,
<4028941434437, 1046650446645, 0> ]
[
<x + 2890855371327, 1>,
<x + 3434183048851, 1>
]
[
<x + 2890855371327, 1>,
<x + 3434183048851, 1>
]
[
<x + 2890855371327, 1>,
<x + 3434183048851, 1>
]
27
[]
36

Total time: 3.399 seconds, Total memory usage: 1.94MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:28:51 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=4748886167107;
f1:=725507982392;
f2:=3499950548075;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:28:48 on modular  [Seed = 3943909220]
-------------------------------------

[]
27
[]
36

Total time: 3.279 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:29:22 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=2591961607789;
f1:=36769060797;
f2:=2811170238233;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:29:19 on modular  [Seed = 3793374834]
-------------------------------------

[]
27
[]
36

Total time: 3.299 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:29:37 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=2591961607789;
f1:=36769060797;
f2:=2811170238233;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:29:34 on modular  [Seed = 4194455963]
-------------------------------------

[]
27
[]
36

Total time: 3.229 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:30:03 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=1446741701307;
f1:=3194847765863;
f2:=3304559678408;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:30:00 on modular  [Seed = 4060764597]
-------------------------------------

[]
27
[ <1441432152364, 5075630842515, 1564835826223>, <4419698336419, 5158967442712,
3600217769814>, <5074066098303, 700598301859, 302544697506> ]
[
<x + 921755665109, 1>,
<x + 2151093725129, 1>,
<x + 3267103807690, 1>
]
[
<x + 921755665109, 2>,
<x + 2151093725129, 2>,
<x + 3267103807690, 2>
]
[
<x + 921755665109, 1>,
<x + 2151093725129, 1>,
<x + 3267103807690, 1>
]
[
<x + 921755665109, 2>,
<x + 2151093725129, 2>,
<x + 3267103807690, 2>
]
[
<x + 921755665109, 1>,
<x + 2151093725129, 1>,
<x + 3267103807690, 1>
]
[
<x + 921755665109, 2>,
<x + 2151093725129, 2>,
<x + 3267103807690, 2>
]
36

Total time: 3.499 seconds, Total memory usage: 1.99MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:30:26 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=5057832268023;
f1:=2457454435757;
f2:=5009798957119;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:30:23 on modular  [Seed = 3275450515]
-------------------------------------

[]
27
[]
36

Total time: 3.339 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:31:07 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=3908044323274;
f1:=474141643354;
f2:=3392077099935;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:31:04 on modular  [Seed = 3676532956]
-------------------------------------

[]
27
[ <1432718350231, 2577269460898, 1249229038910>, <4398886853922, 1664548382069,
4886036004408>, <5103591382933, 1225780450576, 4799931543768> ]
[
<x^3 + 2641081244385*x^2 + 3076286913866*x + 5096177323634, 1>
]
[
<x^3 + 2641081244385*x^2 + 3076286913866*x + 5096177323634, 2>
]
[
<x^3 + 2641081244385*x^2 + 3076286913866*x + 5096177323634, 1>
]
[
<x^3 + 2641081244385*x^2 + 3076286913866*x + 5096177323634, 2>
]
[
<x^3 + 2641081244385*x^2 + 3076286913866*x + 5096177323634, 1>
]
[
<x^3 + 2641081244385*x^2 + 3076286913866*x + 5096177323634, 2>
]
36

Total time: 3.339 seconds, Total memory usage: 1.99MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:31:28 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=5359564472347;
f1:=1557625926929;
f2:=2432895672430;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:31:24 on modular  [Seed = 3542841536]
-------------------------------------

[]
27
[ <2822438931716, 5357631023947, 1632327600978>, <3877337861163, 4930213235167,
4744243650287>, <4235419794207, 647352327972, 4558625335821> ]
[
<x + 1498140510295, 1>,
<x^2 + 5020303757163*x + 1898378452966, 1>
]
[
<x + 1498140510295, 2>,
<x^2 + 5020303757163*x + 1898378452966, 2>
]
[
<x + 1498140510295, 1>,
<x^2 + 5020303757163*x + 1898378452966, 1>
]
[
<x + 1498140510295, 2>,
<x^2 + 5020303757163*x + 1898378452966, 2>
]
[
<x + 1498140510295, 1>,
<x^2 + 5020303757163*x + 1898378452966, 1>
]
[
<x + 1498140510295, 2>,
<x^2 + 5020303757163*x + 1898378452966, 2>
]
36

Total time: 3.269 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:31:56 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=69275895431;
f1:=2558966378446;
f2:=2889492328518;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:31:53 on modular  [Seed = 2874343517]
-------------------------------------

[]
27
[ <1444534880264, 638408936802, 3517999112870>, <4292471587785, 2719758364766,
1257974476022>, <5198190119037, 2109430991975, 691624704651> ]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
36

Total time: 3.279 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:32:07 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=69275895431;
f1:=2558966378446;
f2:=2889492328518;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:32:04 on modular  [Seed = 2740652136]
-------------------------------------

[]
27
[ <1444534880264, 638408936802, 3517999112870>, <4292471587785, 2719758364766,
1257974476022>, <5198190119037, 2109430991975, 691624704651> ]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
36

Total time: 3.329 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:32:27 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=69275895431;
f1:=2558966378446;
f2:=2889492328518;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:32:23 on modular  [Seed = 3141734508]
-------------------------------------

[]
27
[ <1444534880264, 638408936802, 3517999112870>, <4292471587785, 2719758364766,
1257974476022>, <5198190119037, 2109430991975, 691624704651> ]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
[
<x + 2378804489129, 1>,
<x^2 + 2170358328726*x + 1805901505640, 1>
]
[
<x + 2378804489129, 2>,
<x^2 + 2170358328726*x + 1805901505640, 2>
]
36

Total time: 3.319 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:32:46 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=2188720769727;
f1:=2489747699477;
f2:=2101389220360;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:32:43 on modular  [Seed = 3008043031]
-------------------------------------

[]
27
[ <2633972796332, 389071919784, 2945581151314>, <3337747150862, 3103654715067,
4108440050501>, <4963476639892, 1974871658692, 3881175385271> ]
[
<x^3 + 4064137455642*x^2 + 4898178637757*x + 619635547627, 1>
]
[
<x^3 + 4064137455642*x^2 + 4898178637757*x + 619635547627, 2>
]
[
<x^3 + 4064137455642*x^2 + 4898178637757*x + 619635547627, 1>
]
[
<x^3 + 4064137455642*x^2 + 4898178637757*x + 619635547627, 2>
]
[
<x^3 + 4064137455642*x^2 + 4898178637757*x + 619635547627, 1>
]
[
<x^3 + 4064137455642*x^2 + 4898178637757*x + 619635547627, 2>
]
36

Total time: 3.319 seconds, Total memory usage: 1.99MB

************** MAGMA *****************
Host encserver1.math.ucalgary.ca. (136.159.61.73)
Time: Fri Nov 28 13:33:08 2003

Input: p:= 5467598293543;
K:=GF(p);
P<x,y,z>:=PolynomialRing(K,3);

f0:=5050278591955;
f1:=4076806917888;
f2:=1296058978637;
f3:=0;

poly1:=8*((f2+3*y^2*x-(f3+y^3)^2/4)*(f3+y^3)/2-f1-3*y*x^2);
poly2:=64*((f2+3*y^2*x-(f3+y^3)^2/4)^2/4-f0-x^3);
poly3:=-3*y^4*x^2-120*y^2*x+24*y^2*x^3*z+96*x^2*y*f3+16+96*z*x^2-48*z^2*
x^4-64*x^3*f2;
poly4:=-3*x^2*y^5-40*x*y^3+24*x^3*y^3*z-48*y-96*x^2*y*z-48*x^4*z^2*y+24
*x^2*f3*y^2+32*x*f3+96*x^3*f3*z-64*x^4*f1;
poly5:=x^2*y^6+24*x*y^4-24*x^3*y^4*z-16*x^2*y^3*f3+144*y^2-288*x^2*y^2*z
-192*x*y*f3+144*x^4*z^2*y^2+192*x^3*z*y*f3+64*x^2*f3^2-256*x^5*f0-
256*x^5*z^3;

I1:=ideal<P|poly1,poly2,z>;
V1:=Variety(I1);
V1;

for v in V1 do
s1:=(f3+v[2]^3)/2;
s0:=(f2+3*v[2]^2*v[1]-s1^2)/2;
S:=x^2+s1*x+s0;
Factorization(S);
end for;

VarietySizeOverAlgebraicClosure(I1);

I2:=ideal<P|poly3,poly4,poly5>;
V2:=Variety(I2);
V2;

for v in V2 do
if v[1] ne 0 then
u2:=v[1];
u1:=v[2];
u0:=v[3];
U:=u2*x^2+u1*x+u0;
s2:=(3*u1*u2^2)/(2*u2^3);
s1:=-(-3*u1^2*u2/4-1-3*u0*u2^2)/(2*u2^3);
s0:=-(u1^3/8+3*u1/u2/2-3*u0*u1*u2/2-f3)/(2*u2^3);
S:=x^3+s2*x^2+s1*x+s0;
Factorization(S);
Factorization(x^4+f3*x^3+f2*x^2+f1*x+f0+U^3);
end if;
end for;

VarietySizeOverAlgebraicClosure(I2);

Output: Magma V2.10-6     Fri Nov 28 2003 13:33:05 on modular  [Seed = 2339577861]
-------------------------------------

[]
27
[ <790394822678, 4568695114671, 3434700804444>, <2154255580542, 3238405308559,
5381764533926>, <2522947890323, 3128096163856, 2118731248716> ]
[
<x^3 + 4013362799520*x^2 + 4105869545090*x + 4645673207537, 1>
]
[
<x^3 + 4013362799520*x^2 + 4105869545090*x + 4645673207537, 2>
]
[
<x^3 + 4013362799520*x^2 + 4105869545090*x + 4645673207537, 1>
]
[
<x^3 + 4013362799520*x^2 + 4105869545090*x + 4645673207537, 2>
]
[
<x^3 + 4013362799520*x^2 + 4105869545090*x + 4645673207537, 1>
]
[
<x^3 + 4013362799520*x^2 + 4105869545090*x + 4645673207537, 2>
]
36

Total time: 3.319 seconds, Total memory usage: 1.95MB

************** MAGMA *****************
Host pcp238458pcs.elictc01.md.comcast.net. (68.55.164.65)
Time: Fri Nov 28 16:03:21 2003

Input: F:=GF(97);
a:=F!87;
b:=F!46;
E:=EllipticCurve([0,0,0,a,b]);
order(E);

Output: Magma V2.10-6     Fri Nov 28 2003 16:03:18 on modular  [Seed = 2808029404]
-------------------------------------

>> order(E);;
^
User error: Identifier 'order' has not been declared or assigned

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host pcp238458pcs.elictc01.md.comcast.net. (68.55.164.65)
Time: Fri Nov 28 16:03:39 2003

Input: F:=GF(97);
a:=F!87;
b:=F!46;
E:=EllipticCurve([0,0,0,a,b]);
Order(E);

Output: Magma V2.10-6     Fri Nov 28 2003 16:03:36 on modular  [Seed = 3209115898]
-------------------------------------

111

Total time: 2.979 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Fri Nov 28 18:09:47 2003

Input: sqrt{4}

Output: Magma V2.10-6     Fri Nov 28 2003 18:09:44 on modular  [Seed = 2874360191]
-------------------------------------

>> sqrt{4}
^

Total time: 2.939 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:26:02 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do
print([N,i,(2),CP(DH(A[i],2)),(3),CP(DH(A[i],3)),(5),CP(DH(A[i],5)),(7),CP(DH(A[i],7)),(11),CP(DH(A[i],11)),(13),CP(DH(A[i],13))]);
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 03:25:55 on modular  [Seed = 3409751231]
-------------------------------------

[
364,
1,
2,
$.1, 3,$.1 + 2,
5,
$.1 - 1, 7,$.1 + 1,
11,
$.1 + 4, 13,$.1 - 1
]
[
364,
2,
2,
$.1, 3,$.1,
5,
$.1 + 3, 7,$.1 - 1,
11,
$.1 + 2, 13,$.1 + 1
]
[
364,
3,
2,
$.1^2, 3,$.1^2 - 6,
5,
$.1^2 + 2*$.1 - 5,
7,
$.1^2 + 2*$.1 + 1,
11,
$.1^2 - 8*$.1 + 10,
13,
$.1^2 + 2*$.1 + 1
]
[
364,
4,
2,
$.1^2, 3,$.1^2 - 2*$.1 - 2, 5,$.1^2 - 3,
7,
$.1^2 - 2*$.1 + 1,
11,
$.1^2 - 6*$.1 + 6,
13,
$.1^2 - 2*$.1 + 1
]

Total time: 6.919 seconds, Total memory usage: 3.67MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:33:30 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
print([N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]);
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 03:33:23 on modular  [Seed = 2790375442]
-------------------------------------

[
364,
1,
2,
$.1, 3,$.1 + 2,
5,
$.1 - 1, 7,$.1 + 1,
11,
$.1 + 4, 13,$.1 - 1
]
[
364,
2,
2,
$.1, 3,$.1,
5,
$.1 + 3, 7,$.1 - 1,
11,
$.1 + 2, 13,$.1 + 1
]
[
364,
3,
2,
$.1^2, 3,$.1^2 - 6,
5,
$.1^2 + 2*$.1 - 5,
7,
$.1^2 + 2*$.1 + 1,
11,
$.1^2 - 8*$.1 + 10,
13,
$.1^2 + 2*$.1 + 1
]
[
364,
4,
2,
$.1^2, 3,$.1^2 - 2*$.1 - 2, 5,$.1^2 - 3,
7,
$.1^2 - 2*$.1 + 1,
11,
$.1^2 - 6*$.1 + 6,
13,
$.1^2 - 2*$.1 + 1
]

Total time: 6.819 seconds, Total memory usage: 3.67MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:36:38 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; print B;
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 03:36:30 on modular  [Seed = 2824850753]
-------------------------------------

[
364,
1,
2,
$.1, 3,$.1 + 2,
5,
$.1 - 1, 7,$.1 + 1,
11,
$.1 + 4, 13,$.1 - 1
]
[
364,
2,
2,
$.1, 3,$.1,
5,
$.1 + 3, 7,$.1 - 1,
11,
$.1 + 2, 13,$.1 + 1
]
[
364,
3,
2,
$.1^2, 3,$.1^2 - 6,
5,
$.1^2 + 2*$.1 - 5,
7,
$.1^2 + 2*$.1 + 1,
11,
$.1^2 - 8*$.1 + 10,
13,
$.1^2 + 2*$.1 + 1
]
[
364,
4,
2,
$.1^2, 3,$.1^2 - 2*$.1 - 2, 5,$.1^2 - 3,
7,
$.1^2 - 2*$.1 + 1,
11,
$.1^2 - 6*$.1 + 6,
13,
$.1^2 - 2*$.1 + 1
]

Total time: 6.739 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:39:56 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
print [B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 03:39:50 on modular  [Seed = 3192511119]
-------------------------------------

[
364,
1,
2,
$.1, 3,$.1 + 2,
5,
$.1 - 1, 7,$.1 + 1,
11,
$.1 + 4, 13,$.1 - 1
]
[
364,
2,
2,
$.1, 3,$.1,
5,
$.1 + 3, 7,$.1 - 1,
11,
$.1 + 2, 13,$.1 + 1
]
[
364,
3,
2,
$.1^2, 3,$.1^2 - 6,
5,
$.1^2 + 2*$.1 - 5,
7,
$.1^2 + 2*$.1 + 1,
11,
$.1^2 - 8*$.1 + 10,
13,
$.1^2 + 2*$.1 + 1
]
[
364,
4,
2,
$.1^2, 3,$.1^2 - 2*$.1 - 2, 5,$.1^2 - 3,
7,
$.1^2 - 2*$.1 + 1,
11,
$.1^2 - 6*$.1 + 6,
13,
$.1^2 - 2*$.1 + 1
]

Total time: 6.659 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:41:21 2003

Input: print [1,2,3,4,5,6,7,8,9,10,11,12,13,14];

Output: Magma V2.10-6     Sat Nov 29 2003 03:41:18 on modular  [Seed = 2407066438]
-------------------------------------

[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]

Total time: 2.939 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:41:38 2003

Input: print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];

Output: Magma V2.10-6     Sat Nov 29 2003 03:41:35 on modular  [Seed = 2539713359]
-------------------------------------

>> print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];;
^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.919 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:44:24 2003

Input: R<x>:=PolynomialRing(Q);
print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];

Output: Magma V2.10-6     Sat Nov 29 2003 03:44:21 on modular  [Seed = 2641034911]
-------------------------------------

>> R<x>:=PolynomialRing(Q);
^
User error: Identifier 'Q' has not been declared or assigned

>> print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];;
^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:44:49 2003

Input: R<x>:=PolynomialRing(Integer);
print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];

Output: Magma V2.10-6     Sat Nov 29 2003 03:44:46 on modular  [Seed = 1687357308]
-------------------------------------

>> R<x>:=PolynomialRing(Integer);
^
User error: Identifier 'Integer' has not been declared or assigned

>> print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];;
^
User error: Identifier 'x' has not been declared or assigned

Total time: 2.939 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:46:16 2003

Input: R<x>:=PolynomialRing(RationalField());
print [x+1,2,3,4,5,6,7,8,9,10,11,12,13,14];

Output: Magma V2.10-6     Sat Nov 29 2003 03:46:13 on modular  [Seed = 1771965146]
-------------------------------------

[
x + 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14
]

Total time: 2.929 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:46:44 2003

Input: R<x>:=PolynomialRing(RationalField());
print [1,2,3,4,5,6,7,8,9,10,11,12,13,14];

Output: Magma V2.10-6     Sat Nov 29 2003 03:46:41 on modular  [Seed = 1904612070]
-------------------------------------

[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 ]

Total time: 2.919 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:54:00 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "B[1]"; printf "B[2]"; printf "B[3]"; printf "B[4]"; printf "B[5]"; printf "B[6]"; printf "B[7]"; printf "B[8]"; printf "B[9]"; printf "B[10]"; printf "B[11]"; printf "B[12]"; printf "B[13]"; printf "B[14]";
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 03:53:53 on modular  [Seed = 1270622860]
-------------------------------------

B[1]B[2]B[3]B[4]B[5]B[6]B[7]B[8]B[9]B[10]B[11]B[12]B[13]B[14]B[1]B[2]B[3]B[4]B[\
5]B[6]B[7]B[8]B[9]B[10]B[11]B[12]B[13]B[14]B[1]B[2]B[3]B[4]B[5]B[6]B[7]B[8]B[9]\
B[10]B[11]B[12]B[13]B[14]B[1]B[2]B[3]B[4]B[5]B[6]B[7]B[8]B[9]B[10]B[11]B[12]B[1\
3]B[14]
Total time: 6.869 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 03:59:27 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf B[1]; printf B[2]; printf B[3]; printf B[4]; printf B[5]; printf B[6]; printf B[7]; printf B[8]; printf B[9]; printf B[10]; printf B[11]; printf B[12]; printf B[13]; printf B[14];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 03:59:20 on modular  [Seed = 1538014165]
-------------------------------------

>> printf B[1]; printf B[2]; printf B[3]; printf B[4]; printf B[5]; printf B[6
^
Runtime error in printf: Argument 1 should be a format string

Total time: 6.929 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:00:56 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
print B[1]; print B[2]; print B[3]; print B[4]; print B[5]; print B[6]; print B[7]; print B[8]; print B[9]; print B[10]; print B[11]; print B[12]; print B[13]; print B[14];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:00:49 on modular  [Seed = 735867916]
-------------------------------------

364
1
2
$.1 3$.1 + 2
5
$.1 - 1 7$.1 + 1
11
$.1 + 4 13$.1 - 1
364
2
2
$.1 3$.1
5
$.1 + 3 7$.1 - 1
11
$.1 + 2 13$.1 + 1
364
3
2
$.1^2 3$.1^2 - 6
5
$.1^2 + 2*$.1 - 5
7
$.1^2 + 2*$.1 + 1
11
$.1^2 - 8*$.1 + 10
13
$.1^2 + 2*$.1 + 1
364
4
2
$.1^2 3$.1^2 - 2*$.1 - 2 5$.1^2 - 3
7
$.1^2 - 2*$.1 + 1
11
$.1^2 - 6*$.1 + 6
13
$.1^2 - 2*$.1 + 1

Total time: 6.919 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:07:56 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:07:49 on modular  [Seed = 1436683220]
-------------------------------------

364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 -
1364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 +
1364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 -
3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1
Total time: 7.369 seconds, Total memory usage: 3.67MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:08:38 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%on",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:08:31 on modular  [Seed = 1571422262]
-------------------------------------

364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 -
1n364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 +
1n364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1n364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 -
3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1n
Total time: 7.099 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:09:04 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%on",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:08:57 on modular  [Seed = 634550376]
-------------------------------------

364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 -
1n364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 +
1n364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1n364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 -
3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1n
Total time: 6.869 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:11:08 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; print [N,i];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:11:01 on modular  [Seed = 918645751]
-------------------------------------

[ 364, 1 ]
2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[ 364, 2 ]
2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1[ 364, 3 ]
2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 +
10,13,$.1^2 + 2*$.1 + 1[ 364, 4 ]
2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 +
6,13,$.1^2 - 2*$.1 + 1
Total time: 6.969 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:12:50 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=364;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:12:43 on modular  [Seed = 1070097232]
-------------------------------------

364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[]
364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1[]
364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1[]
364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1[]

Total time: 7.059 seconds, Total memory usage: 3.77MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:15:25 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [364..365] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:15:17 on modular  [Seed = 4245332284]
-------------------------------------

364,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[]
364,2,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 1,11,$.1 + 2,13,$.1 + 1[]
364,3,2,$.1^2,3,$.1^2 - 6,5,$.1^2 + 2*$.1 - 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 10,13,$.1^2 + 2*$.1 + 1[]
364,4,2,$.1^2,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 2*$.1 + 1[]
365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x +
6,13,x^2 - 12[]
365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[]
365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x
+ 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 -
16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3
+ 9*x^2 - 28*x - 4[]
365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 -
14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 -
352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x -
3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[]
365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x +
3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x +
32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 -
7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 +
7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8
- 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[]

Total time: 8.319 seconds, Total memory usage: 3.97MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:16:56 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [361..365] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:16:41 on modular  [Seed = 3325139547]
-------------------------------------

361,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 - 3,11,$.1 + 5,13,$.1[]
361,2,2,$.1,3,$.1 - 2,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 - 4[]
361,3,2,$.1^2 - 5,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 361,4,2,$.1^2 - 5,3,$.1^2 + 4*$.1 + 4,5,$.1^2 -$.1 - 1,7,$.1^2 + 2*$.1 -
4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 + 3*$.1 - 9[]
361,5,2,$.1^2 -$.1 - 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1
+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 + 2*$.1 + 1[]
361,6,2,$.1^2 +$.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1
+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 - 2*$.1 + 1[]
361,7,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 + 37[]
361,8,2,$.1^3 - 3*$.1^2 + 3,3,$.1^3 - 3*$.1^2 + 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 - 37[]
361,9,2,$.1^4 - 5*$.1^2 + 5,3,$.1^4 - 5*$.1^2 + 5,5,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,7,$.1^4 + 8*$.1^3 + 14*$.1^2 - 8*$.1 + 1,11,$.1^4 + 10*$.1^3 +
35*$.1^2 + 50*$.1 + 25,13,$.1^4 - 10*$.1^2 + 5[]
362,1,2,x + 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x - 4[]
362,2,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x + 1,13,x + 4[]
362,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + x - 1,7,x^2 + 3*x + 1,11,x^2 + 2*x
- 4,13,x^2 + 7*x + 11[]
362,4,2,x^2 - 2*x + 1,3,x^2 - 2*x - 1,5,x^2 - 4*x + 2,7,x^2 - 8,11,x^2 + 10*x +
23,13,x^2 - 8*x + 14[]
362,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 4*x^4 - 2*x^3 + 17*x^2 -
x - 17,5,x^5 - 18*x^3 + 8*x^2 + 56*x - 48,7,x^5 - 5*x^4 - 9*x^3 + 61*x^2 -
136,11,x^5 - 4*x^4 - 4*x^3 + 13*x^2 + 5*x - 9,13,x^5 - 10*x^4 + 22*x^3 + 20*x^2
- 48*x + 16[]
362,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 13*x^3 + 3*x^2 + 38*x -
28,5,x^5 + x^4 - 17*x^3 - 16*x^2 + 68*x + 72,7,x^5 - 6*x^4 - 3*x^3 + 51*x^2 -
6*x - 109,11,x^5 - 4*x^4 - 23*x^3 + 139*x^2 - 214*x + 84,13,x^5 + 5*x^4 - 31*x^3
- 90*x^2 + 328*x + 8[]
363,1,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x - 2[]
363,2,2,x - 2,3,x + 1,5,x - 4,7,x + 1,11,x,13,x - 2[]
363,3,2,x + 2,3,x + 1,5,x - 4,7,x - 1,11,x,13,x + 2[]
363,4,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 3[]
363,5,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x +
1,11,x^2,13,x^2 + 4*x - 1[]
363,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x +
1,11,x^2,13,x^2 - 4*x - 1[]
363,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 20,11,x^2,13,x^2[]
363,8,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 6*x +
9,11,x^2,13,x^2 - 8*x + 11[]
363,9,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x +
9,11,x^2,13,x^2 + 8*x + 11[]
363,10,2,x^4 - 7*x^2 + 4,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 15*x^2
+ 16*x + 64,7,x^4 - 7*x^2 + 4,11,x^4,13,x^4 - 51*x^2 + 576[]
364,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x + 4,13,x - 1[]
364,2,2,x,3,x,5,x + 3,7,x - 1,11,x + 2,13,x + 1[]
364,3,2,x^2,3,x^2 - 6,5,x^2 + 2*x - 5,7,x^2 + 2*x + 1,11,x^2 - 8*x + 10,13,x^2 +
2*x + 1[]
364,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 6*x + 6,13,x^2 -
2*x + 1[]
365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x +
6,13,x^2 - 12[]
365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[]
365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x
+ 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 -
16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3
+ 9*x^2 - 28*x - 4[]
365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 -
14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 -
352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x -
3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[]
365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x +
3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x +
32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 -
7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 +
7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8
- 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[]

Total time: 14.479 seconds, Total memory usage: 5.09MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:18:15 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [361..368] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sat Nov 29 2003 04:17:52 on modular  [Seed = 3459880426]
-------------------------------------

361,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 - 3,11,$.1 + 5,13,$.1[]
361,2,2,$.1,3,$.1 - 2,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 - 4[]
361,3,2,$.1^2 - 5,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 361,4,2,$.1^2 - 5,3,$.1^2 + 4*$.1 + 4,5,$.1^2 -$.1 - 1,7,$.1^2 + 2*$.1 -
4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 + 3*$.1 - 9[]
361,5,2,$.1^2 -$.1 - 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1
+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 + 2*$.1 + 1[]
361,6,2,$.1^2 +$.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1
+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 - 2*$.1 + 1[]
361,7,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 + 37[]
361,8,2,$.1^3 - 3*$.1^2 + 3,3,$.1^3 - 3*$.1^2 + 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 - 37[]
361,9,2,$.1^4 - 5*$.1^2 + 5,3,$.1^4 - 5*$.1^2 + 5,5,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,7,$.1^4 + 8*$.1^3 + 14*$.1^2 - 8*$.1 + 1,11,$.1^4 + 10*$.1^3 +
35*$.1^2 + 50*$.1 + 25,13,$.1^4 - 10*$.1^2 + 5[]
362,1,2,x + 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x - 4[]
362,2,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x + 1,13,x + 4[]
362,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + x - 1,7,x^2 + 3*x + 1,11,x^2 + 2*x
- 4,13,x^2 + 7*x + 11[]
362,4,2,x^2 - 2*x + 1,3,x^2 - 2*x - 1,5,x^2 - 4*x + 2,7,x^2 - 8,11,x^2 + 10*x +
23,13,x^2 - 8*x + 14[]
362,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 4*x^4 - 2*x^3 + 17*x^2 -
x - 17,5,x^5 - 18*x^3 + 8*x^2 + 56*x - 48,7,x^5 - 5*x^4 - 9*x^3 + 61*x^2 -
136,11,x^5 - 4*x^4 - 4*x^3 + 13*x^2 + 5*x - 9,13,x^5 - 10*x^4 + 22*x^3 + 20*x^2
- 48*x + 16[]
362,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 13*x^3 + 3*x^2 + 38*x -
28,5,x^5 + x^4 - 17*x^3 - 16*x^2 + 68*x + 72,7,x^5 - 6*x^4 - 3*x^3 + 51*x^2 -
6*x - 109,11,x^5 - 4*x^4 - 23*x^3 + 139*x^2 - 214*x + 84,13,x^5 + 5*x^4 - 31*x^3
- 90*x^2 + 328*x + 8[]
363,1,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x - 2[]
363,2,2,x - 2,3,x + 1,5,x - 4,7,x + 1,11,x,13,x - 2[]
363,3,2,x + 2,3,x + 1,5,x - 4,7,x - 1,11,x,13,x + 2[]
363,4,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 3[]
363,5,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x +
1,11,x^2,13,x^2 + 4*x - 1[]
363,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x +
1,11,x^2,13,x^2 - 4*x - 1[]
363,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 20,11,x^2,13,x^2[]
363,8,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 6*x +
9,11,x^2,13,x^2 - 8*x + 11[]
363,9,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x +
9,11,x^2,13,x^2 + 8*x + 11[]
363,10,2,x^4 - 7*x^2 + 4,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 15*x^2
+ 16*x + 64,7,x^4 - 7*x^2 + 4,11,x^4,13,x^4 - 51*x^2 + 576[]
364,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x + 4,13,x - 1[]
364,2,2,x,3,x,5,x + 3,7,x - 1,11,x + 2,13,x + 1[]
364,3,2,x^2,3,x^2 - 6,5,x^2 + 2*x - 5,7,x^2 + 2*x + 1,11,x^2 - 8*x + 10,13,x^2 +
2*x + 1[]
364,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 6*x + 6,13,x^2 -
2*x + 1[]
365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x +
6,13,x^2 - 12[]
365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[]
365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x
+ 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 -
16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3
+ 9*x^2 - 28*x - 4[]
365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 -
14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 -
352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x -
3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[]
365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x +
3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x +
32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 -
7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 +
7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8
- 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[]
366,1,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x + 2[]
366,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 6,13,x[]
366,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x + 3,13,x + 1[]
366,4,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 2,13,x - 4[]
366,5,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x + 1,13,x + 5[]
366,6,2,x - 1,3,x - 1,5,x - 1,7,x - 1,11,x + 1,13,x + 5[]
366,7,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x - 4[]
366,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 17,7,x^2 + 3*x - 2,11,x^2 - 3*x -
2,13,x^2 - 7*x + 8[]
367,1,2,x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 61*x^6 + 197*x^5 + 212*x^4 -
66*x^3 - 132*x^2 - 12*x + 13,3,x^11 + 6*x^10 + 3*x^9 - 41*x^8 - 64*x^7 + 64*x^6
+ 158*x^5 - 9*x^4 - 118*x^3 - 14*x^2 + 24*x - 1,5,x^11 + 8*x^10 + 7*x^9 - 85*x^8
- 191*x^7 + 190*x^6 + 791*x^5 + 247*x^4 - 815*x^3 - 687*x^2 - 128*x + 5,7,x^11 +
7*x^10 - 13*x^9 - 186*x^8 - 277*x^7 + 859*x^6 + 2780*x^5 + 1778*x^4 - 1871*x^3 -
2671*x^2 - 799*x + 25,11,x^11 + 10*x^10 - 12*x^9 - 313*x^8 - 120*x^7 + 3196*x^6
+ 661*x^5 - 11246*x^4 + 2768*x^3 + 5371*x^2 - 892*x - 743,13,x^11 + 5*x^10 -
48*x^9 - 277*x^8 + 569*x^7 + 4656*x^6 + 745*x^5 - 22685*x^4 - 14329*x^3 +
25989*x^2 - 1682*x - 2621[]
367,2,2,x^19 - 9*x^18 + 11*x^17 + 123*x^16 - 372*x^15 - 469*x^14 + 2884*x^13 -
550*x^12 - 10042*x^11 + 8029*x^10 + 17059*x^9 - 20350*x^8 - 12836*x^7 +
20779*x^6 + 2682*x^5 - 7739*x^4 + 63*x^3 + 899*x^2 - 27*x - 29,3,x^19 - 4*x^18 -
35*x^17 + 149*x^16 + 486*x^15 - 2260*x^14 - 3442*x^13 + 18203*x^12 + 13108*x^11
- 84580*x^10 - 25304*x^9 + 229397*x^8 + 19212*x^7 - 348172*x^6 - 3000*x^5 +
262144*x^4 + 15968*x^3 - 68672*x^2 - 21504*x - 1792,5,x^19 - 6*x^18 - 43*x^17 +
309*x^16 + 595*x^15 - 6046*x^14 - 2461*x^13 + 58707*x^12 - 5347*x^11 -
322649*x^10 + 48332*x^9 + 1052323*x^8 + 41520*x^7 - 1950148*x^6 - 697328*x^5 +
1640832*x^4 + 1181408*x^3 - 153984*x^2 - 315520*x - 68864,7,x^19 - x^18 -
68*x^17 + 93*x^16 + 1821*x^15 - 3162*x^14 - 24162*x^13 + 51825*x^12 +
161877*x^11 - 438685*x^10 - 465321*x^9 + 1870316*x^8 + 63387*x^7 - 3600393*x^6 +
1757269*x^5 + 2308835*x^4 - 1465397*x^3 - 561533*x^2 + 257949*x + 75177,11,x^19
- 4*x^18 - 120*x^17 + 545*x^16 + 5632*x^15 - 29392*x^14 - 128435*x^13 +
812306*x^12 + 1363286*x^11 - 12382021*x^10 - 2606314*x^9 + 102742747*x^8 -
71962574*x^7 - 413796744*x^6 + 565237368*x^5 + 539820496*x^4 - 1225061216*x^3 +
173670080*x^2 + 608625792*x - 263379712,13,x^19 - 5*x^18 - 99*x^17 + 398*x^16 +
4006*x^15 - 11816*x^14 - 82529*x^13 + 167855*x^12 + 890309*x^11 - 1326823*x^10 -
4991303*x^9 + 6366113*x^8 + 13486540*x^7 - 17861951*x^6 - 12151477*x^5 +
22331038*x^4 - 6313452*x^3 - 683605*x^2 + 175252*x - 2548[]

Errors: /home/mfd/gomagma: line 2: 23466 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 04:18:46 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [361..367] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 04:18:24 on modular  [Seed = 3609234643]
-------------------------------------

361,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 - 3,11,$.1 + 5,13,$.1[]
361,2,2,$.1,3,$.1 - 2,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 - 4[]
361,3,2,$.1^2 - 5,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 - 4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 361,4,2,$.1^2 - 5,3,$.1^2 + 4*$.1 + 4,5,$.1^2 -$.1 - 1,7,$.1^2 + 2*$.1 -
4,11,$.1^2 - 6*$.1 + 4,13,$.1^2 + 3*$.1 - 9[]
361,5,2,$.1^2 -$.1 - 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1
+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 + 2*$.1 + 1[]
361,6,2,$.1^2 +$.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 6*$.1
+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 - 2*$.1 + 1[]
361,7,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 + 37[]
361,8,2,$.1^3 - 3*$.1^2 + 3,3,$.1^3 - 3*$.1^2 + 1,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 - 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 - 37[]
361,9,2,$.1^4 - 5*$.1^2 + 5,3,$.1^4 - 5*$.1^2 + 5,5,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,7,$.1^4 + 8*$.1^3 + 14*$.1^2 - 8*$.1 + 1,11,$.1^4 + 10*$.1^3 +
35*$.1^2 + 50*$.1 + 25,13,$.1^4 - 10*$.1^2 + 5[]
362,1,2,x + 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x - 4[]
362,2,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x + 1,13,x + 4[]
362,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + x - 1,7,x^2 + 3*x + 1,11,x^2 + 2*x
- 4,13,x^2 + 7*x + 11[]
362,4,2,x^2 - 2*x + 1,3,x^2 - 2*x - 1,5,x^2 - 4*x + 2,7,x^2 - 8,11,x^2 + 10*x +
23,13,x^2 - 8*x + 14[]
362,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 4*x^4 - 2*x^3 + 17*x^2 -
x - 17,5,x^5 - 18*x^3 + 8*x^2 + 56*x - 48,7,x^5 - 5*x^4 - 9*x^3 + 61*x^2 -
136,11,x^5 - 4*x^4 - 4*x^3 + 13*x^2 + 5*x - 9,13,x^5 - 10*x^4 + 22*x^3 + 20*x^2
- 48*x + 16[]
362,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 13*x^3 + 3*x^2 + 38*x -
28,5,x^5 + x^4 - 17*x^3 - 16*x^2 + 68*x + 72,7,x^5 - 6*x^4 - 3*x^3 + 51*x^2 -
6*x - 109,11,x^5 - 4*x^4 - 23*x^3 + 139*x^2 - 214*x + 84,13,x^5 + 5*x^4 - 31*x^3
- 90*x^2 + 328*x + 8[]
363,1,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x - 2[]
363,2,2,x - 2,3,x + 1,5,x - 4,7,x + 1,11,x,13,x - 2[]
363,3,2,x + 2,3,x + 1,5,x - 4,7,x - 1,11,x,13,x + 2[]
363,4,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 3[]
363,5,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x +
1,11,x^2,13,x^2 + 4*x - 1[]
363,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x +
1,11,x^2,13,x^2 - 4*x - 1[]
363,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 20,11,x^2,13,x^2[]
363,8,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 6*x +
9,11,x^2,13,x^2 - 8*x + 11[]
363,9,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x +
9,11,x^2,13,x^2 + 8*x + 11[]
363,10,2,x^4 - 7*x^2 + 4,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 15*x^2
+ 16*x + 64,7,x^4 - 7*x^2 + 4,11,x^4,13,x^4 - 51*x^2 + 576[]
364,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x + 4,13,x - 1[]
364,2,2,x,3,x,5,x + 3,7,x - 1,11,x + 2,13,x + 1[]
364,3,2,x^2,3,x^2 - 6,5,x^2 + 2*x - 5,7,x^2 + 2*x + 1,11,x^2 - 8*x + 10,13,x^2 +
2*x + 1[]
364,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 6*x + 6,13,x^2 -
2*x + 1[]
365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 6*x + 6,11,x^2 + 6*x +
6,13,x^2 - 12[]
365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + x^2 - 16*x + 13[]
365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 + 6*x^4 + 7*x^3 - 9*x^2 - 8*x
+ 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 + 2*x^3 - 15*x^2 -
16*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x - 278,13,x^5 + 9*x^4 + 24*x^3
+ 9*x^2 - 28*x - 4[]
365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 - 16*x - 3,3,x^7 - 2*x^6 -
14*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 - 53*x^4 + 148*x^3 + 196*x^2 -
352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3 + 112*x^2 - 11*x -
3,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 - 1084*x^2 + 736*x - 27[]
365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 - 46*x^3 - 41*x^2 + 25*x +
3,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 + 163*x^2 - 163*x +
32,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 -
7*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 + 1736*x^2 + 496*x - 1312,11,x^8 +
7*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 - 2867*x^2 - 7633*x + 9702,13,x^8
- 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 + 244*x^2 - 643*x - 74[]
366,1,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x + 2[]
366,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 6,13,x[]
366,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x + 3,13,x + 1[]
366,4,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 2,13,x - 4[]
366,5,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x + 1,13,x + 5[]
366,6,2,x - 1,3,x - 1,5,x - 1,7,x - 1,11,x + 1,13,x + 5[]
366,7,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x - 4[]
366,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 17,7,x^2 + 3*x - 2,11,x^2 - 3*x -
2,13,x^2 - 7*x + 8[]
367,1,2,x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 61*x^6 + 197*x^5 + 212*x^4 -
66*x^3 - 132*x^2 - 12*x + 13,3,x^11 + 6*x^10 + 3*x^9 - 41*x^8 - 64*x^7 + 64*x^6
+ 158*x^5 - 9*x^4 - 118*x^3 - 14*x^2 + 24*x - 1,5,x^11 + 8*x^10 + 7*x^9 - 85*x^8
- 191*x^7 + 190*x^6 + 791*x^5 + 247*x^4 - 815*x^3 - 687*x^2 - 128*x + 5,7,x^11 +
7*x^10 - 13*x^9 - 186*x^8 - 277*x^7 + 859*x^6 + 2780*x^5 + 1778*x^4 - 1871*x^3 -
2671*x^2 - 799*x + 25,11,x^11 + 10*x^10 - 12*x^9 - 313*x^8 - 120*x^7 + 3196*x^6
+ 661*x^5 - 11246*x^4 + 2768*x^3 + 5371*x^2 - 892*x - 743,13,x^11 + 5*x^10 -
48*x^9 - 277*x^8 + 569*x^7 + 4656*x^6 + 745*x^5 - 22685*x^4 - 14329*x^3 +
25989*x^2 - 1682*x - 2621[]
367,2,2,x^19 - 9*x^18 + 11*x^17 + 123*x^16 - 372*x^15 - 469*x^14 + 2884*x^13 -
550*x^12 - 10042*x^11 + 8029*x^10 + 17059*x^9 - 20350*x^8 - 12836*x^7 +
20779*x^6 + 2682*x^5 - 7739*x^4 + 63*x^3 + 899*x^2 - 27*x - 29,3,x^19 - 4*x^18 -
35*x^17 + 149*x^16 + 486*x^15 - 2260*x^14 - 3442*x^13 + 18203*x^12 + 13108*x^11
- 84580*x^10 - 25304*x^9 + 229397*x^8 + 19212*x^7 - 348172*x^6 - 3000*x^5 +
262144*x^4 + 15968*x^3 - 68672*x^2 - 21504*x - 1792,5,x^19 - 6*x^18 - 43*x^17 +
309*x^16 + 595*x^15 - 6046*x^14 - 2461*x^13 + 58707*x^12 - 5347*x^11 -
322649*x^10 + 48332*x^9 + 1052323*x^8 + 41520*x^7 - 1950148*x^6 - 697328*x^5 +
1640832*x^4 + 1181408*x^3 - 153984*x^2 - 315520*x - 68864,7,x^19 - x^18 -
68*x^17 + 93*x^16 + 1821*x^15 - 3162*x^14 - 24162*x^13 + 51825*x^12 +
161877*x^11 - 438685*x^10 - 465321*x^9 + 1870316*x^8 + 63387*x^7 - 3600393*x^6 +
1757269*x^5 + 2308835*x^4 - 1465397*x^3 - 561533*x^2 + 257949*x + 75177,11,x^19
- 4*x^18 - 120*x^17 + 545*x^16 + 5632*x^15 - 29392*x^14 - 128435*x^13 +
812306*x^12 + 1363286*x^11 - 12382021*x^10 - 2606314*x^9 + 102742747*x^8 -
71962574*x^7 - 413796744*x^6 + 565237368*x^5 + 539820496*x^4 - 1225061216*x^3 +
173670080*x^2 + 608625792*x - 263379712,13,x^19 - 5*x^18 - 99*x^17 + 398*x^16 +
4006*x^15 - 11816*x^14 - 82529*x^13 + 167855*x^12 + 890309*x^11 - 1326823*x^10 -
4991303*x^9 + 6366113*x^8 + 13486540*x^7 - 17861951*x^6 - 12151477*x^5 +
22331038*x^4 - 6313452*x^3 - 683605*x^2 + 175252*x - 2548[]

Total time: 21.159 seconds, Total memory usage: 6.39MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 06:46:22 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [11..20] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 06:46:17 on modular  [Seed = 1036682582]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
14,1,2,x + 1,3,x + 2,5,x,7,x - 1,11,x,13,x + 4[]
15,1,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 4,13,x + 2[]
17,1,2,x + 1,3,x,5,x + 2,7,x - 4,11,x,13,x + 2[]
19,1,2,x,3,x + 2,5,x - 3,7,x + 1,11,x - 3,13,x + 4[]
20,1,2,x,3,x + 2,5,x + 1,7,x - 2,11,x,13,x - 2[]

Total time: 4.049 seconds, Total memory usage: 4.09MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 06:46:35 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [11..20] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 06:46:31 on modular  [Seed = 99794288]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
14,1,2,x + 1,3,x + 2,5,x,7,x - 1,11,x,13,x + 4[]
15,1,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 4,13,x + 2[]
17,1,2,x + 1,3,x,5,x + 2,7,x - 4,11,x,13,x + 2[]
19,1,2,x,3,x + 2,5,x - 3,7,x + 1,11,x - 3,13,x + 4[]
20,1,2,x,3,x + 2,5,x + 1,7,x - 2,11,x,13,x - 2[]

Total time: 4.159 seconds, Total memory usage: 4.09MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 06:49:02 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [20..40] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 06:48:54 on modular  [Seed = 317041366]
-------------------------------------

20,1,2,$.1,3,$.1 + 2,5,$.1 + 1,7,$.1 - 2,11,$.1,13,$.1 - 2[]
21,1,2,x + 1,3,x - 1,5,x + 2,7,x + 1,11,x - 4,13,x + 2[]
23,1,2,x^2 + x - 1,3,x^2 - 5,5,x^2 + 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 6*x +
4,13,x^2 - 6*x + 9[]
24,1,2,x,3,x + 1,5,x + 2,7,x,11,x - 4,13,x + 2[]
26,1,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x - 6,13,x - 1[]
26,2,2,x - 1,3,x + 3,5,x + 1,7,x - 1,11,x + 2,13,x + 1[]
27,1,2,x,3,x,5,x,7,x + 1,11,x,13,x - 5[]
29,1,2,x^2 + 2*x - 1,3,x^2 - 2*x - 1,5,x^2 + 2*x + 1,7,x^2 - 8,11,x^2 - 2*x -
1,13,x^2 + 2*x - 7[]
30,1,2,x + 1,3,x - 1,5,x + 1,7,x + 4,11,x,13,x - 2[]
31,1,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 - 4*x
+ 4,13,x^2 + 2*x - 4[]
32,1,2,x,3,x,5,x + 2,7,x,11,x,13,x - 6[]
33,1,2,x - 1,3,x + 1,5,x + 2,7,x - 4,11,x - 1,13,x + 2[]
34,1,2,x - 1,3,x + 2,5,x,7,x + 4,11,x - 6,13,x - 2[]
35,1,2,x,3,x - 1,5,x + 1,7,x - 1,11,x + 3,13,x - 5[]
35,2,2,x^2 + x - 4,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - x -
4,13,x^2 - 5*x + 2[]
36,1,2,x,3,x,5,x,7,x + 4,11,x,13,x - 2[]
37,1,2,x + 2,3,x + 3,5,x + 2,7,x + 1,11,x + 5,13,x + 2[]
37,2,2,x,3,x - 1,5,x,7,x + 1,11,x - 3,13,x + 4[]
38,1,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 6,13,x - 5[]
38,2,2,x - 1,3,x + 1,5,x + 4,7,x - 3,11,x - 2,13,x + 1[]
39,1,2,x - 1,3,x + 1,5,x - 2,7,x + 4,11,x - 4,13,x - 1[]
39,2,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 + 4*x + 4,13,x^2
+ 2*x + 1[]
40,1,2,x,3,x,5,x - 1,7,x + 4,11,x - 4,13,x + 2[]

Total time: 7.539 seconds, Total memory usage: 4.93MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 06:51:39 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [40..80] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 06:51:21 on modular  [Seed = 3809760440]
-------------------------------------

40,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 + 4,11,$.1 - 4,13,$.1 + 2[]
41,1,2,x^3 + x^2 - 5*x - 1,3,x^3 - 4*x + 2,5,x^3 + 2*x^2 - 4*x - 4,7,x^3 - 6*x^2
+ 8*x - 2,11,x^3 - 2*x^2 - 20*x + 50,13,x^3 + 2*x^2 - 12*x - 8[]
42,1,2,x - 1,3,x + 1,5,x + 2,7,x + 1,11,x + 4,13,x - 6[]
43,1,2,x + 2,3,x + 2,5,x + 4,7,x,11,x - 3,13,x + 5[]
43,2,2,x^2 - 2,3,x^2 - 2,5,x^2 - 4*x + 2,7,x^2 + 4*x + 2,11,x^2 + 2*x - 7,13,x^2
- 2*x - 7[]
44,1,2,x,3,x - 1,5,x + 3,7,x - 2,11,x + 1,13,x + 4[]
45,1,2,x - 1,3,x,5,x + 1,7,x,11,x - 4,13,x + 2[]
46,1,2,x + 1,3,x,5,x - 4,7,x + 4,11,x - 2,13,x + 2[]
47,1,2,x^4 - x^3 - 5*x^2 + 5*x - 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 + 2*x^3 -
16*x^2 - 16*x + 48,7,x^4 - 4*x^3 - 7*x^2 + 44*x - 43,11,x^4 + 6*x^3 - 4*x^2 -
56*x - 48,13,x^4 - 8*x^3 + 56*x + 48[]
48,1,2,x,3,x - 1,5,x + 2,7,x,11,x + 4,13,x + 2[]
49,1,2,x - 1,3,x,5,x,7,x,11,x - 4,13,x[]
50,1,2,x + 1,3,x - 1,5,x,7,x - 2,11,x + 3,13,x + 4[]
50,2,2,x - 1,3,x + 1,5,x,7,x + 2,11,x + 3,13,x - 4[]
51,1,2,x,3,x - 1,5,x - 3,7,x + 4,11,x + 3,13,x + 1[]
51,2,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2,11,x^2 + x - 4,13,x^2 -
5*x + 2[]
52,1,2,x,3,x,5,x - 2,7,x + 2,11,x + 2,13,x + 1[]
53,1,2,x + 1,3,x + 3,5,x,7,x + 4,11,x,13,x + 3[]
53,2,2,x^3 + x^2 - 3*x - 1,3,x^3 - 3*x^2 - x + 1,5,x^3 + 2*x^2 - 4*x - 4,7,x^3 -
4*x^2 + 4,11,x^3 + 4*x^2 - 4*x - 20,13,x^3 - 3*x^2 + 3*x - 1[]
54,1,2,x + 1,3,x,5,x - 3,7,x + 1,11,x + 3,13,x + 4[]
54,2,2,x - 1,3,x,5,x + 3,7,x + 1,11,x - 3,13,x + 4[]
55,1,2,x - 1,3,x,5,x - 1,7,x,11,x + 1,13,x - 2[]
55,2,2,x^2 - 2*x - 1,3,x^2 - 8,5,x^2 + 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 2*x +
1,13,x^2 + 8*x + 8[]
56,1,2,x,3,x - 2,5,x + 4,7,x - 1,11,x,13,x[]
56,2,2,x,3,x,5,x - 2,7,x + 1,11,x + 4,13,x - 2[]
57,1,2,x + 2,3,x + 1,5,x + 3,7,x + 5,11,x - 1,13,x - 2[]
57,2,2,x - 1,3,x - 1,5,x + 2,7,x,11,x,13,x - 6[]
57,3,2,x + 2,3,x - 1,5,x - 1,7,x - 3,11,x + 3,13,x + 6[]
58,1,2,x + 1,3,x + 3,5,x + 3,7,x + 2,11,x + 1,13,x - 3[]
58,2,2,x - 1,3,x + 1,5,x - 1,7,x + 2,11,x + 3,13,x + 1[]
59,1,2,x^5 - 9*x^3 + 2*x^2 + 16*x - 8,3,x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 13*x -
1,5,x^5 - 2*x^4 - 14*x^3 + 23*x^2 + 19*x + 1,7,x^5 - 2*x^4 - 16*x^3 + 43*x^2 +
13*x - 71,11,x^5 + 2*x^4 - 24*x^3 - 24*x^2 + 128*x - 64,13,x^5 - 8*x^4 + 88*x^2
- 48*x - 224[]
61,1,2,x + 1,3,x + 2,5,x + 3,7,x - 1,11,x + 5,13,x - 1[]
61,2,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 + x^2 - 9*x - 13,7,x^3
+ 3*x^2 - x - 1,11,x^3 - 13*x^2 + 53*x - 67,13,x^3 + 9*x^2 + 11*x - 37[]
62,1,2,x - 1,3,x,5,x + 2,7,x,11,x,13,x - 2[]
62,2,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 + 6*x +
6,13,x^2 + 2*x - 26[]
63,1,2,x - 1,3,x,5,x - 2,7,x + 1,11,x + 4,13,x + 2[]
63,2,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2 - 2*x + 1,11,x^2 - 12,13,x^2 - 4*x + 4[]
64,1,2,x,3,x,5,x - 2,7,x,11,x,13,x + 6[]
65,1,2,x + 1,3,x + 2,5,x + 1,7,x + 4,11,x - 2,13,x + 1[]
65,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 6*x +
6,13,x^2 - 2*x + 1[]
65,3,2,x^2 + 2*x - 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 4*x - 4,11,x^2 - 4*x +
2,13,x^2 + 2*x + 1[]
66,1,2,x + 1,3,x - 1,5,x,7,x - 2,11,x + 1,13,x + 4[]
66,2,2,x - 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x + 6[]
66,3,2,x - 1,3,x - 1,5,x + 4,7,x + 2,11,x - 1,13,x - 4[]
67,1,2,x - 2,3,x + 2,5,x - 2,7,x + 2,11,x + 4,13,x - 2[]
67,2,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 + 6*x + 9,7,x^2 + x - 11,11,x^2 -
5,13,x^2 + 7*x + 1[]
67,3,2,x^2 + x - 1,3,x^2 - x - 1,5,x^2 - 4*x - 1,7,x^2 - x - 1,11,x^2 - 2*x +
1,13,x^2 + x - 1[]
68,1,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 + 2*x - 2,11,x^2 + 6*x + 6,13,x^2 -
4*x - 8[]
69,1,2,x - 1,3,x - 1,5,x,7,x + 2,11,x - 4,13,x + 6[]
69,2,2,x^2 - 5,3,x^2 + 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 2*x - 4,11,x^2 - 8*x +
16,13,x^2 - 20[]
70,1,2,x - 1,3,x,5,x + 1,7,x + 1,11,x - 4,13,x + 6[]
71,1,2,x^3 - 5*x + 3,3,x^3 + x^2 - 8*x - 3,5,x^3 + 3*x^2 - 2*x - 7,7,x^3 - 2*x^2
- 16*x + 24,11,x^3 + 2*x^2 - 16*x - 24,13,x^3 - 12*x^2 + 48*x - 64[]
71,2,2,x^3 + x^2 - 4*x - 3,3,x^3 - x^2 - 4*x + 3,5,x^3 - 5*x^2 - 2*x + 25,7,x^3
- 2*x^2 - 16*x + 24,11,x^3 - 20*x + 24,13,x^3 + 6*x^2 - 8*x - 56[]
72,1,2,x,3,x,5,x - 2,7,x,11,x + 4,13,x + 2[]
73,1,2,x - 1,3,x,5,x - 2,7,x - 2,11,x + 2,13,x + 6[]
73,2,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 + 3*x + 1,7,x^2 + 6*x + 9,11,x^2 +
3*x + 1,13,x^2 - x - 11[]
73,3,2,x^2 - x - 3,3,x^2 - x - 3,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 7*x +
9,13,x^2 + x - 3[]
74,1,2,x^2 + 2*x + 1,3,x^2 - 3*x - 1,5,x^2 + x - 3,7,x^2 - 2*x - 12,11,x^2 + x -
3,13,x^2 + x - 3[]
74,2,2,x^2 - 2*x + 1,3,x^2 + x - 1,5,x^2 - x - 11,7,x^2 + 2*x - 4,11,x^2 + 5*x +
5,13,x^2 - x - 11[]
75,1,2,x - 2,3,x + 1,5,x,7,x + 3,11,x - 2,13,x - 1[]
75,2,2,x - 1,3,x - 1,5,x,7,x,11,x + 4,13,x - 2[]
75,3,2,x + 2,3,x - 1,5,x,7,x - 3,11,x - 2,13,x + 1[]
76,1,2,x,3,x - 2,5,x + 1,7,x + 3,11,x - 5,13,x + 4[]
77,1,2,x,3,x + 3,5,x + 1,7,x + 1,11,x + 1,13,x + 4[]
77,2,2,x - 1,3,x - 2,5,x + 2,7,x + 1,11,x - 1,13,x - 4[]
77,3,2,x,3,x - 1,5,x - 3,7,x - 1,11,x + 1,13,x + 4[]
77,4,2,x^2 - 5,3,x^2 - 2*x - 4,5,x^2 + 4*x + 4,7,x^2 - 2*x + 1,11,x^2 + 2*x +
1,13,x^2 - 2*x - 4[]
78,1,2,x + 1,3,x + 1,5,x - 2,7,x - 4,11,x + 4,13,x - 1[]
79,1,2,x + 1,3,x + 1,5,x + 3,7,x + 1,11,x + 2,13,x - 3[]
79,2,2,x^5 - 6*x^3 + 8*x - 1,3,x^5 - x^4 - 12*x^3 + 8*x^2 + 24*x - 16,5,x^5 -
7*x^4 + 9*x^3 + 27*x^2 - 65*x + 31,7,x^5 + 5*x^4 - 6*x^3 - 52*x^2 - 56*x -
16,11,x^5 - 2*x^4 - 35*x^3 + 34*x^2 + 185*x + 106,13,x^5 + 3*x^4 - 23*x^3 -
123*x^2 - 197*x - 103[]
80,1,2,x,3,x,5,x - 1,7,x - 4,11,x + 4,13,x + 2[]
80,2,2,x,3,x - 2,5,x + 1,7,x + 2,11,x,13,x - 2[]

Total time: 18.260 seconds, Total memory usage: 7.05MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sat Nov 29 07:00:46 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [80..110] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 07:00:23 on modular  [Seed = 4161752525]
-------------------------------------

80,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 - 4,11,$.1 + 4,13,$.1 + 2[]
80,2,2,$.1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 2,11,$.1,13,$.1 - 2[]
81,1,2,x^2 - 3,3,x^2,5,x^2 - 3,7,x^2 - 4*x + 4,11,x^2 - 12,13,x^2 + 2*x + 1[]
82,1,2,x + 1,3,x + 2,5,x + 2,7,x + 4,11,x + 2,13,x - 4[]
82,2,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 8,7,x^2 + 4*x + 2,11,x^2 - 18,13,x^2[]
83,1,2,x + 1,3,x + 1,5,x + 2,7,x + 3,11,x - 3,13,x + 6[]
83,2,2,x^6 - x^5 - 9*x^4 + 7*x^3 + 20*x^2 - 12*x - 8,3,x^6 - x^5 - 10*x^4 +
5*x^3 + 30*x^2 - 4*x - 25,5,x^6 - 2*x^5 - 20*x^4 + 28*x^3 + 104*x^2 - 64*x -
160,7,x^6 - 3*x^5 - 22*x^4 + 55*x^3 + 154*x^2 - 228*x - 409,11,x^6 + 3*x^5 -
26*x^4 - 83*x^3 + 66*x^2 + 156*x - 113,13,x^6 - 14*x^5 + 44*x^4 + 108*x^3 -
488*x^2 - 288*x + 992[]
84,1,2,x,3,x + 1,5,x - 4,7,x + 1,11,x - 2,13,x + 6[]
84,2,2,x,3,x - 1,5,x,7,x - 1,11,x + 6,13,x - 2[]
85,1,2,x - 1,3,x - 2,5,x + 1,7,x + 2,11,x - 2,13,x - 2[]
85,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 + 4*x + 2,11,x^2 +
8*x + 14,13,x^2 - 8[]
85,3,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 + 2*x - 2,11,x^2 - 6*x +
6,13,x^2 + 8*x + 16[]
86,1,2,x^2 + 2*x + 1,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 - 4*x + 4,11,x^2,13,x^2
- 4*x + 4[]
86,2,2,x^2 - 2*x + 1,3,x^2 - x - 1,5,x^2 + 3*x + 1,7,x^2 - 20,11,x^2 + 4*x -
16,13,x^2 - 20[]
87,1,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x - 1,11,x^2 - 4*x
- 1,13,x^2 + 2*x - 19[]
87,2,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 16*x + 8,7,x^3 -
4*x^2 - x + 8,11,x^3 + 8*x^2 + 15*x + 4,13,x^3 - 4*x^2 - 7*x + 26[]
88,1,2,x,3,x + 3,5,x + 3,7,x + 2,11,x + 1,13,x[]
88,2,2,x^2,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2 + 2*x - 16,11,x^2 + 2*x +
1,13,x^2 + 2*x - 16[]
89,1,2,x + 1,3,x + 1,5,x + 1,7,x + 4,11,x + 2,13,x - 2[]
89,2,2,x - 1,3,x - 2,5,x + 2,7,x - 2,11,x + 4,13,x - 2[]
89,3,2,x^5 + x^4 - 10*x^3 - 10*x^2 + 21*x + 17,3,x^5 + 3*x^4 - 4*x^3 - 16*x^2 -
9*x - 1,5,x^5 + x^4 - 14*x^3 - 14*x^2 + 29*x + 13,7,x^5 - 8*x^4 + 10*x^3 +
36*x^2 - 68*x + 28,11,x^5 - 6*x^4 - 20*x^3 + 112*x^2 + 80*x - 112,13,x^5 -
28*x^3 - 56*x^2 + 16[]
90,1,2,x + 1,3,x,5,x - 1,7,x - 2,11,x - 6,13,x + 4[]
90,2,2,x - 1,3,x,5,x + 1,7,x - 2,11,x + 6,13,x + 4[]
90,3,2,x - 1,3,x,5,x - 1,7,x + 4,11,x,13,x - 2[]
91,1,2,x + 2,3,x,5,x + 3,7,x + 1,11,x + 6,13,x + 1[]
91,2,2,x,3,x + 2,5,x + 3,7,x - 1,11,x,13,x - 1[]
91,3,2,x^2 - 2,3,x^2 - 2,5,x^2 - 6*x + 7,7,x^2 - 2*x + 1,11,x^2 - 18,13,x^2 +
2*x + 1[]
91,4,2,x^3 - x^2 - 4*x + 2,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 - 2*x^2 - 3*x + 2,7,x^3
+ 3*x^2 + 3*x + 1,11,x^3 - 2*x^2 - 6*x + 8,13,x^3 - 3*x^2 + 3*x - 1[]
92,1,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x + 1[]
92,2,2,x,3,x + 3,5,x + 2,7,x + 4,11,x - 2,13,x + 5[]
93,1,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 4*x - 1,7,x^2 + 4*x - 1,11,x^2 +
6*x + 4,13,x^2 + 2*x - 4[]
93,2,2,x^3 - 4*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 -
4*x^2 - x + 8,11,x^3 + 2*x^2 - 20*x + 16,13,x^3 - 4*x^2 - 16*x + 56[]
94,1,2,x - 1,3,x,5,x,7,x,11,x - 2,13,x + 4[]
94,2,2,x^2 + 2*x + 1,3,x^2 - 8,5,x^2 - 4*x + 2,7,x^2 + 4*x - 4,11,x^2 - 8*x +
14,13,x^2 + 4*x + 2[]
95,1,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3
- 16*x + 16,11,x^3 + 8*x^2 + 8*x - 16,13,x^3 - 8*x^2 + 12*x - 4[]
95,2,2,x^4 + 2*x^3 - 6*x^2 - 8*x + 9,3,x^4 - 2*x^3 - 8*x^2 + 16*x - 4,5,x^4 +
4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 4*x^3 - 16*x^2 + 48*x + 32,11,x^4 - 4*x^3 -
16*x^2 + 32*x + 48,13,x^4 - 2*x^3 - 24*x^2 + 32*x + 20[]
96,1,2,x,3,x - 1,5,x - 2,7,x + 4,11,x - 4,13,x + 2[]
96,2,2,x,3,x + 1,5,x - 2,7,x - 4,11,x + 4,13,x + 2[]
97,1,2,x^3 + 4*x^2 + 3*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x +
1,7,x^3 + 7*x^2 + 14*x + 7,11,x^3 + 7*x^2 + 14*x + 7,13,x^3 + 2*x^2 - x - 1[]
97,2,2,x^4 - 3*x^3 - x^2 + 6*x - 1,3,x^4 - 5*x^2 - x + 4,5,x^4 - x^3 - 4*x^2 + x
+ 2,7,x^4 - 3*x^3 - 6*x^2 + 23*x - 16,11,x^4 - 5*x^3 - 14*x^2 + 47*x + 92,13,x^4
+ 6*x^3 - 29*x^2 - 167*x - 122[]
98,1,2,x + 1,3,x - 2,5,x,7,x,11,x,13,x - 4[]
98,2,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 8,7,x^2,11,x^2 + 4*x + 4,13,x^2[]
99,1,2,x + 1,3,x,5,x + 4,7,x + 2,11,x + 1,13,x + 2[]
99,2,2,x - 1,3,x,5,x - 4,7,x + 2,11,x - 1,13,x + 2[]
99,3,2,x + 1,3,x,5,x - 2,7,x - 4,11,x + 1,13,x + 2[]
99,4,2,x - 2,3,x,5,x + 1,7,x + 2,11,x + 1,13,x - 4[]
100,1,2,x,3,x - 2,5,x,7,x + 2,11,x,13,x + 2[]
101,1,2,x,3,x + 2,5,x + 1,7,x + 2,11,x + 2,13,x - 1[]
101,2,2,x^7 - 13*x^5 + 2*x^4 + 47*x^3 - 16*x^2 - 43*x + 14,3,x^7 - 4*x^6 - 7*x^5
+ 38*x^4 + 4*x^3 - 96*x^2 + 13*x + 68,5,x^7 + 3*x^6 - 13*x^5 - 33*x^4 + 48*x^3 +
94*x^2 - 43*x - 67,7,x^7 - 2*x^6 - 25*x^5 + 66*x^4 + 90*x^3 - 326*x^2 + 165*x +
14,11,x^7 - 8*x^6 - x^5 + 114*x^4 - 72*x^3 - 554*x^2 + 213*x + 878,13,x^7 + x^6
- 45*x^5 - 59*x^4 + 664*x^3 + 1066*x^2 - 3203*x - 6001[]
102,1,2,x + 1,3,x + 1,5,x + 4,7,x + 2,11,x,13,x + 6[]
102,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[]
102,3,2,x - 1,3,x - 1,5,x + 2,7,x,11,x + 4,13,x + 2[]
103,1,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 +
3*x + 1,13,x^2 + 3*x - 9[]
103,2,2,x^6 - 4*x^5 - x^4 + 17*x^3 - 9*x^2 - 16*x + 11,3,x^6 - 13*x^4 + 40*x^2 -
8*x - 16,5,x^6 - 3*x^5 - 11*x^4 + 34*x^3 + 12*x^2 - 40*x - 16,7,x^6 + 2*x^5 -
18*x^4 - 26*x^3 + 74*x^2 + 66*x + 1,11,x^6 + x^5 - 41*x^4 - 68*x^3 + 416*x^2 +
968*x + 272,13,x^6 + x^5 - 28*x^4 + 53*x^3 + 20*x^2 - 103*x + 55[]
104,1,2,x,3,x - 1,5,x + 1,7,x - 5,11,x + 2,13,x + 1[]
104,2,2,x^2,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2 + x - 4,11,x^2 + 2*x - 16,13,x^2
- 2*x + 1[]
105,1,2,x - 1,3,x - 1,5,x - 1,7,x - 1,11,x,13,x + 6[]
105,2,2,x^2 - 5,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x -
16,13,x^2 - 20[]
106,1,2,x + 1,3,x + 1,5,x + 4,7,x,11,x + 4,13,x - 1[]
106,2,2,x + 1,3,x - 2,5,x - 1,7,x + 2,11,x - 5,13,x + 4[]
106,3,2,x - 1,3,x - 1,5,x,7,x + 4,11,x,13,x - 5[]
106,4,2,x - 1,3,x + 2,5,x - 3,7,x - 2,11,x + 3,13,x + 4[]
107,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 - 4*x
- 1,13,x^2 + 12*x + 36[]
107,2,2,x^7 + x^6 - 10*x^5 - 7*x^4 + 29*x^3 + 12*x^2 - 20*x - 8,3,x^7 - 3*x^6 -
9*x^5 + 29*x^4 + 14*x^3 - 69*x^2 + 12*x + 29,5,x^7 - 5*x^6 - 9*x^5 + 64*x^4 -
28*x^3 - 152*x^2 + 192*x - 64,7,x^7 - 4*x^6 - 23*x^5 + 114*x^4 - 32*x^3 -
360*x^2 + 448*x - 128,11,x^7 + 2*x^6 - 41*x^5 - 95*x^4 + 361*x^3 + 950*x^2 +
519*x + 47,13,x^7 - 18*x^6 + 98*x^5 + x^4 - 1649*x^3 + 4855*x^2 - 3548*x -
1244[]
108,1,2,x,3,x,5,x,7,x - 5,11,x,13,x + 7[]
109,1,2,x - 1,3,x,5,x - 3,7,x - 2,11,x - 1,13,x[]
109,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 5*x -
13,7,x^3 + x^2 - 16*x + 13,11,x^3 + 13*x^2 + 54*x + 71,13,x^3 + x^2 - 16*x +
13[]
109,3,2,x^4 + x^3 - 5*x^2 - 4*x + 3,3,x^4 - 4*x^3 - x^2 + 15*x - 8,5,x^4 - x^3 -
5*x^2 + 4*x + 3,7,x^4 + 3*x^3 - 10*x^2 - 23*x - 2,11,x^4 - 12*x^3 + 33*x^2 +
47*x - 177,13,x^4 + 7*x^3 - 10*x^2 - 93*x + 16[]
110,1,2,x + 1,3,x - 1,5,x + 1,7,x - 5,11,x - 1,13,x - 2[]
110,2,2,x - 1,3,x - 1,5,x + 1,7,x + 1,11,x + 1,13,x - 2[]
110,3,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 1,13,x + 6[]
110,4,2,x^2 + 2*x + 1,3,x^2 + x - 8,5,x^2 - 2*x + 1,7,x^2 - x - 8,11,x^2 + 2*x +
1,13,x^2 - 4*x + 4[]

Total time: 22.149 seconds, Total memory usage: 7.83MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sat Nov 29 07:12:30 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [110..130] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 07:12:08 on modular  [Seed = 2807043549]
-------------------------------------

110,1,2,$.1 + 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 5,11,$.1 - 1,13,$.1 - 2[]
110,2,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 1,13,$.1 - 2[]
110,3,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1 - 3,11,$.1 - 1,13,$.1 + 6[]
110,4,2,$.1^2 + 2*$.1 + 1,3,$.1^2 +$.1 - 8,5,$.1^2 - 2*$.1 + 1,7,$.1^2 -$.1 -
8,11,$.1^2 + 2*$.1 + 1,13,$.1^2 - 4*$.1 + 4[]
111,1,2,x^3 - 3*x^2 - x + 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 4*x +
20,7,x^3 + 4*x^2 - 8*x - 16,11,x^3 - 4*x^2 - 16*x + 32,13,x^3 + 2*x^2 - 20*x -
8[]
111,2,2,x^4 - 6*x^2 + 2*x + 5,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 2*x^3 -
8*x^2 + 4,7,x^4 - 4*x^3 - 16*x^2 + 64*x - 16,11,x^4 - 32*x^2 - 32*x + 64,13,x^4
- 4*x^3 - 32*x^2 + 144*x - 80[]
112,1,2,x,3,x + 2,5,x + 4,7,x + 1,11,x,13,x[]
112,2,2,x,3,x,5,x - 2,7,x - 1,11,x - 4,13,x - 2[]
112,3,2,x,3,x - 2,5,x,7,x + 1,11,x,13,x + 4[]
113,1,2,x + 1,3,x - 2,5,x - 2,7,x,11,x,13,x - 2[]
113,2,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 - 8*x + 16,11,x^2 + 4*x -
8,13,x^2 + 4*x - 8[]
113,3,2,x^3 + 2*x^2 - x - 1,3,x^3 + 5*x^2 + 6*x + 1,5,x^3 + x^2 - 9*x - 1,7,x^3
+ 10*x^2 + 31*x + 29,11,x^3 - 2*x^2 - 15*x - 13,13,x^3 + 8*x^2 + 5*x - 43[]
113,4,2,x^3 + 2*x^2 - 5*x - 9,3,x^3 + x^2 - 4*x - 1,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 6*x^2 + 3*x + 9,11,x^3 - 2*x^2 - 3*x + 3,13,x^3 - 8*x^2 + 17*x - 7[]
114,1,2,x + 1,3,x + 1,5,x,7,x - 4,11,x - 4,13,x[]
114,2,2,x - 1,3,x + 1,5,x - 2,7,x,11,x + 4,13,x - 2[]
114,3,2,x - 1,3,x - 1,5,x,7,x + 4,11,x,13,x + 4[]
115,1,2,x - 2,3,x,5,x + 1,7,x - 1,11,x - 2,13,x + 2[]
115,2,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 +
2*x - 4,13,x^2 + 8*x + 11[]
115,3,2,x^4 - 2*x^3 - 4*x^2 + 5*x + 2,3,x^4 + 2*x^3 - 7*x^2 - 8*x + 16,5,x^4 -
4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 3*x^3 - 14*x^2 - 52*x - 32,11,x^4 - 4*x^3 -
16*x^2 + 40*x + 32,13,x^4 - 41*x^2 + 212[]
116,1,2,x,3,x - 1,5,x - 3,7,x + 4,11,x - 3,13,x - 5[]
116,2,2,x,3,x - 2,5,x + 2,7,x - 4,11,x + 6,13,x - 2[]
116,3,2,x,3,x + 3,5,x - 3,7,x - 4,11,x + 1,13,x + 3[]
117,1,2,x + 1,3,x,5,x + 2,7,x + 4,11,x + 4,13,x - 1[]
117,2,2,x^2 - 3,3,x^2,5,x^2,7,x^2 - 4*x + 4,11,x^2 - 12,13,x^2 - 2*x + 1[]
117,3,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 8,7,x^2 - 8,11,x^2 - 4*x + 4,13,x^2 + 2*x +
1[]
118,1,2,x + 1,3,x + 1,5,x + 3,7,x + 1,11,x + 2,13,x + 2[]
118,2,2,x + 1,3,x - 2,5,x - 2,7,x + 3,11,x - 1,13,x - 3[]
118,3,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 6[]
118,4,2,x - 1,3,x - 2,5,x + 2,7,x + 3,11,x + 1,13,x + 3[]
119,1,2,x^4 + x^3 - 5*x^2 - x + 3,3,x^4 - 2*x^3 - 7*x^2 + 12*x - 1,5,x^4 - 2*x^3
- 7*x^2 + 4*x + 3,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 20*x^2 + 8*x
+ 48,13,x^4 - 8*x^3 - 16*x^2 + 216*x - 368[]
119,2,2,x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 14*x - 17,3,x^5 + 2*x^4 - 11*x^3 - 12*x^2
+ 31*x - 12,5,x^5 - 23*x^3 + 18*x^2 + 131*x - 178,7,x^5 + 5*x^4 + 10*x^3 +
10*x^2 + 5*x + 1,11,x^5 + 2*x^4 - 44*x^3 - 40*x^2 + 496*x - 192,13,x^5 - 2*x^4 -
40*x^3 + 56*x^2 + 352*x - 544[]
120,1,2,x,3,x - 1,5,x + 1,7,x - 4,11,x,13,x + 6[]
120,2,2,x,3,x - 1,5,x - 1,7,x,11,x + 4,13,x - 6[]
121,1,2,x,3,x + 1,5,x + 3,7,x,11,x,13,x[]
121,2,2,x - 1,3,x - 2,5,x - 1,7,x + 2,11,x,13,x - 1[]
121,3,2,x + 1,3,x - 2,5,x - 1,7,x - 2,11,x,13,x + 1[]
121,4,2,x - 2,3,x + 1,5,x - 1,7,x - 2,11,x,13,x + 4[]
122,1,2,x + 1,3,x + 2,5,x - 1,7,x + 5,11,x + 3,13,x + 3[]
122,2,2,x^2 + 2*x + 1,3,x^2 - x - 3,5,x^2,7,x^2 - 5*x + 3,11,x^2 - 2*x -
12,13,x^2 - 6*x - 4[]
122,3,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + x^2 - 5*x + 2,5,x^3 - x^2 - 12*x +
16,7,x^3 - 4*x^2 - 10*x + 41,11,x^3 + 7*x^2 + 10*x - 4,13,x^3 + x^2 - 6*x - 4[]
123,1,2,x,3,x + 1,5,x + 2,7,x + 4,11,x - 5,13,x + 4[]
123,2,2,x + 2,3,x - 1,5,x + 4,7,x + 2,11,x + 3,13,x + 6[]
123,3,2,x^2 - 2,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 2*x -
1,13,x^2 - 4*x - 14[]
123,4,2,x^3 - x^2 - 4*x + 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 2*x +
4,7,x^3 - 2*x^2 - 14*x + 32,11,x^3 + 4*x^2 + x - 4,13,x^3 - 8*x^2 + 14*x + 4[]
124,1,2,x,3,x,5,x - 1,7,x - 3,11,x - 6,13,x + 4[]
124,2,2,x,3,x + 2,5,x + 3,7,x + 1,11,x + 6,13,x - 2[]
125,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2,7,x^2 + 6*x + 9,11,x^2 + 6*x +
9,13,x^2 + 3*x - 9[]
125,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2,7,x^2 - 6*x + 9,11,x^2 + 6*x +
9,13,x^2 - 3*x - 9[]
125,3,2,x^4 - 8*x^2 + 11,3,x^4 - 7*x^2 + 11,5,x^4,7,x^4 - 13*x^2 + 11,11,x^4 -
8*x^3 + 24*x^2 - 32*x + 16,13,x^4 - 32*x^2 + 176[]
126,1,2,x + 1,3,x,5,x - 2,7,x + 1,11,x - 4,13,x - 6[]
126,2,2,x - 1,3,x,5,x,7,x - 1,11,x,13,x + 4[]
127,1,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 + 3*x^2
- 3,11,x^3 - 21*x - 37,13,x^3 + 3*x^2 - 18*x - 37[]
127,2,2,x^7 - 2*x^6 - 8*x^5 + 15*x^4 + 17*x^3 - 28*x^2 - 11*x + 15,3,x^7 - 3*x^6
- 12*x^5 + 39*x^4 + 26*x^3 - 128*x^2 + 64*x + 16,5,x^7 - 8*x^6 + 11*x^5 + 53*x^4
- 146*x^3 + 32*x^2 + 128*x - 48,7,x^7 + 3*x^6 - 20*x^5 - 41*x^4 + 114*x^3 +
64*x^2 - 112*x - 16,11,x^7 - 28*x^5 - 17*x^4 + 88*x^3 - 37*x^2 - 5*x + 3,13,x^7
+ x^6 - 69*x^5 - 38*x^4 + 1515*x^3 + 52*x^2 - 10416*x + 5383[]
128,1,2,x,3,x + 2,5,x + 2,7,x + 4,11,x - 2,13,x + 2[]
128,2,2,x,3,x - 2,5,x - 2,7,x + 4,11,x + 2,13,x - 2[]
128,3,2,x,3,x - 2,5,x + 2,7,x - 4,11,x + 2,13,x + 2[]
128,4,2,x,3,x + 2,5,x - 2,7,x - 4,11,x - 2,13,x - 2[]
129,1,2,x,3,x + 1,5,x + 2,7,x + 2,11,x + 5,13,x - 3[]
129,2,2,x - 1,3,x - 1,5,x - 2,7,x,11,x,13,x + 2[]
129,3,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 1,7,x^2 - 2*x - 7,11,x^2 -
6*x + 7,13,x^2 + 10*x + 25[]
129,4,2,x^3 + 2*x^2 - 5*x - 8,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 4*x^2 - x -
2,7,x^3 - 4*x^2 - 3*x + 10,11,x^3 - x^2 - 19*x - 25,13,x^3 - 9*x^2 + 27*x - 27[]
130,1,2,x + 1,3,x + 2,5,x - 1,7,x + 4,11,x + 6,13,x - 1[]
130,2,2,x - 1,3,x - 2,5,x + 1,7,x + 4,11,x + 2,13,x + 1[]
130,3,2,x - 1,3,x,5,x - 1,7,x,11,x,13,x - 1[]

Total time: 21.549 seconds, Total memory usage: 7.15MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sat Nov 29 07:19:56 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [130..150] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sat Nov 29 2003 07:19:33 on modular  [Seed = 3041002498]
-------------------------------------

130,1,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 1[]
130,2,2,$.1 - 1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[]
130,3,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1,13,$.1 - 1[]
131,1,2,x,3,x + 1,5,x + 2,7,x + 1,11,x,13,x + 3[]
131,2,2,x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 +
16*x - 32,3,x^10 - x^9 - 22*x^8 + 24*x^7 + 157*x^6 - 184*x^5 - 403*x^4 + 533*x^3
+ 222*x^2 - 390*x + 67,5,x^10 - 4*x^9 - 26*x^8 + 116*x^7 + 155*x^6 - 988*x^5 +
138*x^4 + 2384*x^3 - 763*x^2 - 1856*x + 8,7,x^10 - x^9 - 46*x^8 + 36*x^7 +
701*x^6 - 376*x^5 - 3971*x^4 + 929*x^3 + 7566*x^2 + 738*x - 1213,11,x^10 - 2*x^9
- 48*x^8 + 76*x^7 + 829*x^6 - 1032*x^5 - 6248*x^4 + 6058*x^3 + 19601*x^2 -
12860*x - 17852,13,x^10 - 11*x^9 - 4*x^8 + 386*x^7 - 1069*x^6 - 1056*x^5 +
5897*x^4 - 2717*x^3 - 6108*x^2 + 4764*x - 31[]
132,1,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x - 6[]
132,2,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x + 2[]
133,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2 + 9*x +
19,13,x^2 - 2*x + 1[]
133,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x -
1,13,x^2 + 2*x + 1[]
133,3,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 + 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 5*x
+ 3,13,x^2 + 4*x - 9[]
133,4,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 - x + 4,5,x^3 + 2*x^2 - 5*x -
2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 7*x^2 + 11*x - 4,13,x^3 + 2*x^2 - 5*x - 2[]
134,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - 3*x^2 - 2*x +
3,7,x^3 - 20*x + 8,11,x^3 + x^2 - 16*x + 9,13,x^3 - 11*x^2 + 30*x - 9[]
134,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 -
12*x - 8,11,x^3 + 3*x^2 - 24*x - 53,13,x^3 + 3*x^2 - 18*x - 3[]
135,1,2,x + 2,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 5[]
135,2,2,x - 2,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 5[]
135,3,2,x^2 + x - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 12,11,x^2 - 2*x -
12,13,x^2 - 6*x - 4[]
135,4,2,x^2 - x - 3,3,x^2,5,x^2 + 2*x + 1,7,x^2 - 2*x - 12,11,x^2 + 2*x -
12,13,x^2 - 6*x - 4[]
136,1,2,x,3,x - 2,5,x,7,x,11,x - 2,13,x + 6[]
136,2,2,x,3,x + 2,5,x + 2,7,x + 2,11,x + 6,13,x - 2[]
136,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 4,11,x^2 - 2*x -
4,13,x^2 - 20[]
137,1,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,5,x^4 + 2*x^3 -
12*x^2 - 23*x + 1,7,x^4 + 13*x^3 + 60*x^2 + 116*x + 79,11,x^4 - x^3 - 38*x^2 +
76*x + 101,13,x^4 + 8*x^3 + 10*x^2 - 49*x - 101[]
137,2,2,x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7,3,x^7 - 3*x^6 - 8*x^5 + 26*x^4
+ 11*x^3 - 58*x^2 + 16*x + 14,5,x^7 + 2*x^6 - 18*x^5 - 21*x^4 + 103*x^3 + 26*x^2
- 188*x + 88,7,x^7 - 15*x^6 + 80*x^5 - 168*x^4 + 43*x^3 + 300*x^2 - 352*x +
112,11,x^7 + 3*x^6 - 26*x^5 - 140*x^4 - 219*x^3 - 92*x^2 + 24*x + 16,13,x^7 -
12*x^6 + 32*x^5 + 85*x^4 - 351*x^3 - 202*x^2 + 876*x + 488[]
138,1,2,x + 1,3,x + 1,5,x + 2,7,x + 2,11,x + 6,13,x + 2[]
138,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[]
138,3,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x + 2[]
138,4,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 20,11,x^2 + 6*x +
4,13,x^2 - 20[]
139,1,2,x - 1,3,x - 2,5,x + 1,7,x - 3,11,x - 5,13,x + 7[]
139,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 8*x^2 + 19*x +
13,7,x^3 - 7*x + 7,11,x^3 + 7*x^2 - 49,13,x^3 - x^2 - 16*x - 13[]
139,3,2,x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8,3,x^7 + 2*x^6 -
15*x^5 - 25*x^4 + 56*x^3 + 52*x^2 - 56*x - 16,5,x^7 - 11*x^6 + 36*x^5 + 2*x^4 -
211*x^3 + 319*x^2 - 55*x - 83,7,x^7 + 5*x^6 - 8*x^5 - 82*x^4 - 155*x^3 - 109*x^2
- 31*x - 3,11,x^7 - 2*x^6 - 36*x^5 + 82*x^4 + 186*x^3 - 314*x^2 - 294*x +
229,13,x^7 - 6*x^6 - 2*x^5 + 64*x^4 - 108*x^3 + 38*x^2 + 6*x - 1[]
140,1,2,x,3,x - 3,5,x + 1,7,x + 1,11,x + 5,13,x + 3[]
140,2,2,x,3,x - 1,5,x - 1,7,x - 1,11,x - 3,13,x + 1[]
141,1,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 3,13,x + 4[]
141,2,2,x + 1,3,x + 1,5,x,7,x - 4,11,x,13,x - 6[]
141,3,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[]
141,4,2,x - 2,3,x - 1,5,x + 1,7,x + 3,11,x - 1,13,x + 2[]
141,5,2,x + 2,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x - 2[]
141,6,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x +
8,13,x^2 + 6*x - 8[]
142,1,2,x + 1,3,x + 1,5,x + 2,7,x + 1,11,x + 2,13,x + 3[]
142,2,2,x + 1,3,x,5,x - 2,7,x,11,x - 6,13,x - 4[]
142,3,2,x + 1,3,x - 3,5,x - 2,7,x + 3,11,x + 6,13,x + 5[]
142,4,2,x - 1,3,x - 1,5,x,7,x + 1,11,x,13,x + 1[]
142,5,2,x - 1,3,x + 3,5,x + 4,7,x + 3,11,x,13,x - 1[]
143,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x + 1,13,x + 1[]
143,2,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 - 16*x^2 + 8*x
+ 16,7,x^4 - 6*x^3 + x^2 + 44*x - 61,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 +
4*x^3 + 6*x^2 + 4*x + 1[]
143,3,2,x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12,3,x^6 - 3*x^5 - 11*x^4 + 33*x^3
+ 25*x^2 - 91*x + 28,5,x^6 - x^5 - 26*x^4 + 32*x^3 + 152*x^2 - 256*x + 96,7,x^6
- 4*x^5 - 23*x^4 + 66*x^3 + 187*x^2 - 210*x - 448,11,x^6 + 6*x^5 + 15*x^4 +
20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[]
144,1,2,x,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[]
144,2,2,x,3,x,5,x,7,x - 4,11,x,13,x - 2[]
145,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x + 6,13,x - 2[]
145,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 +
4*x - 4,13,x^2 + 4*x + 4[]
145,3,2,x^3 - 3*x^2 - x + 5,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 6*x^2 - 4*x - 8[]
145,4,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 4*x^2 + 4,11,x^3 - 2*x^2 - 8*x - 4,13,x^3 + 2*x^2 - 12*x - 8[]
146,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 8*x + 4,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 -
8*x^2 + 16*x - 2,11,x^3 - 2*x^2 - 28*x + 72,13,x^3 - 4*x^2 + 2[]
146,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 8*x^2 + 4*x + 4,5,x^4 - 2*x^3 -
14*x^2 + 26*x + 2,7,x^4 - 22*x^2 + 6*x + 2,11,x^4 - 24*x^2 - 16*x + 80,13,x^4 +
4*x^3 - 38*x^2 - 106*x + 314[]
147,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[]
147,2,2,x - 2,3,x + 1,5,x - 2,7,x,11,x + 2,13,x + 1[]
147,3,2,x - 2,3,x - 1,5,x + 2,7,x,11,x + 2,13,x - 1[]
147,4,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 2,7,x^2,11,x^2 + 4*x +
4,13,x^2 + 8*x + 14[]
147,5,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2,11,x^2 + 4*x +
4,13,x^2 - 8*x + 14[]
148,1,2,x,3,x + 1,5,x + 4,7,x + 3,11,x - 5,13,x[]
148,2,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - x - 4,13,x^2 -
4*x + 4[]
149,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x -
13,7,x^3 + 5*x^2 + 6*x + 1,11,x^3 + 5*x^2 - 8*x + 1,13,x^3 + 3*x^2 - 4*x - 13[]
149,2,2,x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x
+ 39,3,x^9 - 6*x^8 + 55*x^6 - 67*x^5 - 125*x^4 + 235*x^3 - 6*x^2 - 117*x +
27,5,x^9 + x^8 - 25*x^7 - 4*x^6 + 202*x^5 - 83*x^4 - 529*x^3 + 305*x^2 + 392*x -
221,7,x^9 - 3*x^8 - 34*x^7 + 117*x^6 + 208*x^5 - 916*x^4 + 144*x^3 + 1056*x^2 -
128*x - 64,11,x^9 - 5*x^8 - 33*x^7 + 202*x^6 + 66*x^5 - 1503*x^4 + 997*x^3 +
2817*x^2 - 3392*x + 981,13,x^9 - 7*x^8 - 28*x^7 + 277*x^6 - 152*x^5 - 2028*x^4 +
3072*x^3 + 32*x^2 - 512*x - 64[]

Errors: /home/mfd/gomagma: line 2: 24023 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sat Nov 29 07:20:45 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [130..150] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sat Nov 29 2003 07:20:22 on modular  [Seed = 2222142688]
-------------------------------------

130,1,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 1[]
130,2,2,$.1 - 1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[]
130,3,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1,13,$.1 - 1[]
131,1,2,x,3,x + 1,5,x + 2,7,x + 1,11,x,13,x + 3[]
131,2,2,x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 +
16*x - 32,3,x^10 - x^9 - 22*x^8 + 24*x^7 + 157*x^6 - 184*x^5 - 403*x^4 + 533*x^3
+ 222*x^2 - 390*x + 67,5,x^10 - 4*x^9 - 26*x^8 + 116*x^7 + 155*x^6 - 988*x^5 +
138*x^4 + 2384*x^3 - 763*x^2 - 1856*x + 8,7,x^10 - x^9 - 46*x^8 + 36*x^7 +
701*x^6 - 376*x^5 - 3971*x^4 + 929*x^3 + 7566*x^2 + 738*x - 1213,11,x^10 - 2*x^9
- 48*x^8 + 76*x^7 + 829*x^6 - 1032*x^5 - 6248*x^4 + 6058*x^3 + 19601*x^2 -
12860*x - 17852,13,x^10 - 11*x^9 - 4*x^8 + 386*x^7 - 1069*x^6 - 1056*x^5 +
5897*x^4 - 2717*x^3 - 6108*x^2 + 4764*x - 31[]
132,1,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x - 6[]
132,2,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x + 2[]
133,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2 + 9*x +
19,13,x^2 - 2*x + 1[]
133,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x -
1,13,x^2 + 2*x + 1[]
133,3,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 + 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 5*x
+ 3,13,x^2 + 4*x - 9[]
133,4,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 - x + 4,5,x^3 + 2*x^2 - 5*x -
2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 7*x^2 + 11*x - 4,13,x^3 + 2*x^2 - 5*x - 2[]
134,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - 3*x^2 - 2*x +
3,7,x^3 - 20*x + 8,11,x^3 + x^2 - 16*x + 9,13,x^3 - 11*x^2 + 30*x - 9[]
134,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 -
12*x - 8,11,x^3 + 3*x^2 - 24*x - 53,13,x^3 + 3*x^2 - 18*x - 3[]
135,1,2,x + 2,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 5[]
135,2,2,x - 2,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 5[]
135,3,2,x^2 + x - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 12,11,x^2 - 2*x -
12,13,x^2 - 6*x - 4[]
135,4,2,x^2 - x - 3,3,x^2,5,x^2 + 2*x + 1,7,x^2 - 2*x - 12,11,x^2 + 2*x -
12,13,x^2 - 6*x - 4[]
136,1,2,x,3,x - 2,5,x,7,x,11,x - 2,13,x + 6[]
136,2,2,x,3,x + 2,5,x + 2,7,x + 2,11,x + 6,13,x - 2[]
136,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 4,11,x^2 - 2*x -
4,13,x^2 - 20[]
137,1,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,5,x^4 + 2*x^3 -
12*x^2 - 23*x + 1,7,x^4 + 13*x^3 + 60*x^2 + 116*x + 79,11,x^4 - x^3 - 38*x^2 +
76*x + 101,13,x^4 + 8*x^3 + 10*x^2 - 49*x - 101[]
137,2,2,x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7,3,x^7 - 3*x^6 - 8*x^5 + 26*x^4
+ 11*x^3 - 58*x^2 + 16*x + 14,5,x^7 + 2*x^6 - 18*x^5 - 21*x^4 + 103*x^3 + 26*x^2
- 188*x + 88,7,x^7 - 15*x^6 + 80*x^5 - 168*x^4 + 43*x^3 + 300*x^2 - 352*x +
112,11,x^7 + 3*x^6 - 26*x^5 - 140*x^4 - 219*x^3 - 92*x^2 + 24*x + 16,13,x^7 -
12*x^6 + 32*x^5 + 85*x^4 - 351*x^3 - 202*x^2 + 876*x + 488[]
138,1,2,x + 1,3,x + 1,5,x + 2,7,x + 2,11,x + 6,13,x + 2[]
138,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[]
138,3,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x + 2[]
138,4,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 20,11,x^2 + 6*x +
4,13,x^2 - 20[]
139,1,2,x - 1,3,x - 2,5,x + 1,7,x - 3,11,x - 5,13,x + 7[]
139,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 8*x^2 + 19*x +
13,7,x^3 - 7*x + 7,11,x^3 + 7*x^2 - 49,13,x^3 - x^2 - 16*x - 13[]
139,3,2,x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8,3,x^7 + 2*x^6 -
15*x^5 - 25*x^4 + 56*x^3 + 52*x^2 - 56*x - 16,5,x^7 - 11*x^6 + 36*x^5 + 2*x^4 -
211*x^3 + 319*x^2 - 55*x - 83,7,x^7 + 5*x^6 - 8*x^5 - 82*x^4 - 155*x^3 - 109*x^2
- 31*x - 3,11,x^7 - 2*x^6 - 36*x^5 + 82*x^4 + 186*x^3 - 314*x^2 - 294*x +
229,13,x^7 - 6*x^6 - 2*x^5 + 64*x^4 - 108*x^3 + 38*x^2 + 6*x - 1[]
140,1,2,x,3,x - 3,5,x + 1,7,x + 1,11,x + 5,13,x + 3[]
140,2,2,x,3,x - 1,5,x - 1,7,x - 1,11,x - 3,13,x + 1[]
141,1,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 3,13,x + 4[]
141,2,2,x + 1,3,x + 1,5,x,7,x - 4,11,x,13,x - 6[]
141,3,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[]
141,4,2,x - 2,3,x - 1,5,x + 1,7,x + 3,11,x - 1,13,x + 2[]
141,5,2,x + 2,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x - 2[]
141,6,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x +
8,13,x^2 + 6*x - 8[]
142,1,2,x + 1,3,x + 1,5,x + 2,7,x + 1,11,x + 2,13,x + 3[]
142,2,2,x + 1,3,x,5,x - 2,7,x,11,x - 6,13,x - 4[]
142,3,2,x + 1,3,x - 3,5,x - 2,7,x + 3,11,x + 6,13,x + 5[]
142,4,2,x - 1,3,x - 1,5,x,7,x + 1,11,x,13,x + 1[]
142,5,2,x - 1,3,x + 3,5,x + 4,7,x + 3,11,x,13,x - 1[]
143,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x + 1,13,x + 1[]
143,2,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 - 16*x^2 + 8*x
+ 16,7,x^4 - 6*x^3 + x^2 + 44*x - 61,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 +
4*x^3 + 6*x^2 + 4*x + 1[]
143,3,2,x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12,3,x^6 - 3*x^5 - 11*x^4 + 33*x^3
+ 25*x^2 - 91*x + 28,5,x^6 - x^5 - 26*x^4 + 32*x^3 + 152*x^2 - 256*x + 96,7,x^6
- 4*x^5 - 23*x^4 + 66*x^3 + 187*x^2 - 210*x - 448,11,x^6 + 6*x^5 + 15*x^4 +
20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[]
144,1,2,x,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[]
144,2,2,x,3,x,5,x,7,x - 4,11,x,13,x - 2[]
145,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x + 6,13,x - 2[]
145,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 +
4*x - 4,13,x^2 + 4*x + 4[]
145,3,2,x^3 - 3*x^2 - x + 5,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 6*x^2 - 4*x - 8[]
145,4,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 4*x^2 + 4,11,x^3 - 2*x^2 - 8*x - 4,13,x^3 + 2*x^2 - 12*x - 8[]
146,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 8*x + 4,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 -
8*x^2 + 16*x - 2,11,x^3 - 2*x^2 - 28*x + 72,13,x^3 - 4*x^2 + 2[]
146,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 8*x^2 + 4*x + 4,5,x^4 - 2*x^3 -
14*x^2 + 26*x + 2,7,x^4 - 22*x^2 + 6*x + 2,11,x^4 - 24*x^2 - 16*x + 80,13,x^4 +
4*x^3 - 38*x^2 - 106*x + 314[]
147,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[]
147,2,2,x - 2,3,x + 1,5,x - 2,7,x,11,x + 2,13,x + 1[]
147,3,2,x - 2,3,x - 1,5,x + 2,7,x,11,x + 2,13,x - 1[]
147,4,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 2,7,x^2,11,x^2 + 4*x +
4,13,x^2 + 8*x + 14[]
147,5,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2,11,x^2 + 4*x +
4,13,x^2 - 8*x + 14[]
148,1,2,x,3,x + 1,5,x + 4,7,x + 3,11,x - 5,13,x[]
148,2,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - x - 4,13,x^2 -
4*x + 4[]
149,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x -
13,7,x^3 + 5*x^2 + 6*x + 1,11,x^3 + 5*x^2 - 8*x + 1,13,x^3 + 3*x^2 - 4*x - 13[]
149,2,2,x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x
+ 39,3,x^9 - 6*x^8 + 55*x^6 - 67*x^5 - 125*x^4 + 235*x^3 - 6*x^2 - 117*x +
27,5,x^9 + x^8 - 25*x^7 - 4*x^6 + 202*x^5 - 83*x^4 - 529*x^3 + 305*x^2 + 392*x -
221,7,x^9 - 3*x^8 - 34*x^7 + 117*x^6 + 208*x^5 - 916*x^4 + 144*x^3 + 1056*x^2 -
128*x - 64,11,x^9 - 5*x^8 - 33*x^7 + 202*x^6 + 66*x^5 - 1503*x^4 + 997*x^3 +
2817*x^2 - 3392*x + 981,13,x^9 - 7*x^8 - 28*x^7 + 277*x^6 - 152*x^5 - 2028*x^4 +
3072*x^3 + 32*x^2 - 512*x - 64[]

Errors: /home/mfd/gomagma: line 2: 24038 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sat Nov 29 07:25:15 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [130..148] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 07:24:52 on modular  [Seed = 2472819941]
-------------------------------------

130,1,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 1[]
130,2,2,$.1 - 1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[]
130,3,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1,13,$.1 - 1[]
131,1,2,x,3,x + 1,5,x + 2,7,x + 1,11,x,13,x + 3[]
131,2,2,x^10 - 18*x^8 + 2*x^7 + 111*x^6 - 18*x^5 - 270*x^4 + 28*x^3 + 232*x^2 +
16*x - 32,3,x^10 - x^9 - 22*x^8 + 24*x^7 + 157*x^6 - 184*x^5 - 403*x^4 + 533*x^3
+ 222*x^2 - 390*x + 67,5,x^10 - 4*x^9 - 26*x^8 + 116*x^7 + 155*x^6 - 988*x^5 +
138*x^4 + 2384*x^3 - 763*x^2 - 1856*x + 8,7,x^10 - x^9 - 46*x^8 + 36*x^7 +
701*x^6 - 376*x^5 - 3971*x^4 + 929*x^3 + 7566*x^2 + 738*x - 1213,11,x^10 - 2*x^9
- 48*x^8 + 76*x^7 + 829*x^6 - 1032*x^5 - 6248*x^4 + 6058*x^3 + 19601*x^2 -
12860*x - 17852,13,x^10 - 11*x^9 - 4*x^8 + 386*x^7 - 1069*x^6 - 1056*x^5 +
5897*x^4 - 2717*x^3 - 6108*x^2 + 4764*x - 31[]
132,1,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x - 6[]
132,2,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x + 2[]
133,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2 + 9*x +
19,13,x^2 - 2*x + 1[]
133,2,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x -
1,13,x^2 + 2*x + 1[]
133,3,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 + 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 5*x
+ 3,13,x^2 + 4*x - 9[]
133,4,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 - x + 4,5,x^3 + 2*x^2 - 5*x -
2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 7*x^2 + 11*x - 4,13,x^3 + 2*x^2 - 5*x - 2[]
134,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - 3*x^2 - 2*x +
3,7,x^3 - 20*x + 8,11,x^3 + x^2 - 16*x + 9,13,x^3 - 11*x^2 + 30*x - 9[]
134,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 -
12*x - 8,11,x^3 + 3*x^2 - 24*x - 53,13,x^3 + 3*x^2 - 18*x - 3[]
135,1,2,x + 2,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 5[]
135,2,2,x - 2,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 5[]
135,3,2,x^2 + x - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 12,11,x^2 - 2*x -
12,13,x^2 - 6*x - 4[]
135,4,2,x^2 - x - 3,3,x^2,5,x^2 + 2*x + 1,7,x^2 - 2*x - 12,11,x^2 + 2*x -
12,13,x^2 - 6*x - 4[]
136,1,2,x,3,x - 2,5,x,7,x,11,x - 2,13,x + 6[]
136,2,2,x,3,x + 2,5,x + 2,7,x + 2,11,x + 6,13,x - 2[]
136,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 4,11,x^2 - 2*x -
4,13,x^2 - 20[]
137,1,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,5,x^4 + 2*x^3 -
12*x^2 - 23*x + 1,7,x^4 + 13*x^3 + 60*x^2 + 116*x + 79,11,x^4 - x^3 - 38*x^2 +
76*x + 101,13,x^4 + 8*x^3 + 10*x^2 - 49*x - 101[]
137,2,2,x^7 - 10*x^5 + 28*x^3 + 3*x^2 - 19*x - 7,3,x^7 - 3*x^6 - 8*x^5 + 26*x^4
+ 11*x^3 - 58*x^2 + 16*x + 14,5,x^7 + 2*x^6 - 18*x^5 - 21*x^4 + 103*x^3 + 26*x^2
- 188*x + 88,7,x^7 - 15*x^6 + 80*x^5 - 168*x^4 + 43*x^3 + 300*x^2 - 352*x +
112,11,x^7 + 3*x^6 - 26*x^5 - 140*x^4 - 219*x^3 - 92*x^2 + 24*x + 16,13,x^7 -
12*x^6 + 32*x^5 + 85*x^4 - 351*x^3 - 202*x^2 + 876*x + 488[]
138,1,2,x + 1,3,x + 1,5,x + 2,7,x + 2,11,x + 6,13,x + 2[]
138,2,2,x + 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[]
138,3,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x + 2[]
138,4,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 20,11,x^2 + 6*x +
4,13,x^2 - 20[]
139,1,2,x - 1,3,x - 2,5,x + 1,7,x - 3,11,x - 5,13,x + 7[]
139,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 8*x^2 + 19*x +
13,7,x^3 - 7*x + 7,11,x^3 + 7*x^2 - 49,13,x^3 - x^2 - 16*x - 13[]
139,3,2,x^7 - x^6 - 11*x^5 + 8*x^4 + 35*x^3 - 10*x^2 - 32*x - 8,3,x^7 + 2*x^6 -
15*x^5 - 25*x^4 + 56*x^3 + 52*x^2 - 56*x - 16,5,x^7 - 11*x^6 + 36*x^5 + 2*x^4 -
211*x^3 + 319*x^2 - 55*x - 83,7,x^7 + 5*x^6 - 8*x^5 - 82*x^4 - 155*x^3 - 109*x^2
- 31*x - 3,11,x^7 - 2*x^6 - 36*x^5 + 82*x^4 + 186*x^3 - 314*x^2 - 294*x +
229,13,x^7 - 6*x^6 - 2*x^5 + 64*x^4 - 108*x^3 + 38*x^2 + 6*x - 1[]
140,1,2,x,3,x - 3,5,x + 1,7,x + 1,11,x + 5,13,x + 3[]
140,2,2,x,3,x - 1,5,x - 1,7,x - 1,11,x - 3,13,x + 1[]
141,1,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 3,13,x + 4[]
141,2,2,x + 1,3,x + 1,5,x,7,x - 4,11,x,13,x - 6[]
141,3,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[]
141,4,2,x - 2,3,x - 1,5,x + 1,7,x + 3,11,x - 1,13,x + 2[]
141,5,2,x + 2,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x - 2[]
141,6,2,x^2 + x - 4,3,x^2 + 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x +
8,13,x^2 + 6*x - 8[]
142,1,2,x + 1,3,x + 1,5,x + 2,7,x + 1,11,x + 2,13,x + 3[]
142,2,2,x + 1,3,x,5,x - 2,7,x,11,x - 6,13,x - 4[]
142,3,2,x + 1,3,x - 3,5,x - 2,7,x + 3,11,x + 6,13,x + 5[]
142,4,2,x - 1,3,x - 1,5,x,7,x + 1,11,x,13,x + 1[]
142,5,2,x - 1,3,x + 3,5,x + 4,7,x + 3,11,x,13,x - 1[]
143,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x + 1,13,x + 1[]
143,2,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 7*x^2 + 4*x + 1,5,x^4 - 16*x^2 + 8*x
+ 16,7,x^4 - 6*x^3 + x^2 + 44*x - 61,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 +
4*x^3 + 6*x^2 + 4*x + 1[]
143,3,2,x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12,3,x^6 - 3*x^5 - 11*x^4 + 33*x^3
+ 25*x^2 - 91*x + 28,5,x^6 - x^5 - 26*x^4 + 32*x^3 + 152*x^2 - 256*x + 96,7,x^6
- 4*x^5 - 23*x^4 + 66*x^3 + 187*x^2 - 210*x - 448,11,x^6 + 6*x^5 + 15*x^4 +
20*x^3 + 15*x^2 + 6*x + 1,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[]
144,1,2,x,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[]
144,2,2,x,3,x,5,x,7,x - 4,11,x,13,x - 2[]
145,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x + 6,13,x - 2[]
145,2,2,x^2 + 2*x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 +
4*x - 4,13,x^2 + 4*x + 4[]
145,3,2,x^3 - 3*x^2 - x + 5,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 6*x^2 - 4*x - 8[]
145,4,2,x^3 - x^2 - 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 4*x^2 + 4,11,x^3 - 2*x^2 - 8*x - 4,13,x^3 + 2*x^2 - 12*x - 8[]
146,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 8*x + 4,5,x^3 + 2*x^2 - 4*x - 6,7,x^3 -
8*x^2 + 16*x - 2,11,x^3 - 2*x^2 - 28*x + 72,13,x^3 - 4*x^2 + 2[]
146,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 8*x^2 + 4*x + 4,5,x^4 - 2*x^3 -
14*x^2 + 26*x + 2,7,x^4 - 22*x^2 + 6*x + 2,11,x^4 - 24*x^2 - 16*x + 80,13,x^4 +
4*x^3 - 38*x^2 - 106*x + 314[]
147,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[]
147,2,2,x - 2,3,x + 1,5,x - 2,7,x,11,x + 2,13,x + 1[]
147,3,2,x - 2,3,x - 1,5,x + 2,7,x,11,x + 2,13,x - 1[]
147,4,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 2,7,x^2,11,x^2 + 4*x +
4,13,x^2 + 8*x + 14[]
147,5,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2,11,x^2 + 4*x +
4,13,x^2 - 8*x + 14[]
148,1,2,x,3,x + 1,5,x + 4,7,x + 3,11,x - 5,13,x[]
148,2,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2 - x - 4,11,x^2 - x - 4,13,x^2 -
4*x + 4[]

Total time: 21.689 seconds, Total memory usage: 8.47MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 07:35:31 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [148..160] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 07:35:14 on modular  [Seed = 1822146959]
-------------------------------------

148,1,2,$.1,3,$.1 + 1,5,$.1 + 4,7,$.1 + 3,11,$.1 - 5,13,$.1[]
148,2,2,$.1^2,3,$.1^2 + $.1 - 4,5,$.1^2 - 4*$.1 + 4,7,$.1^2 - $.1 - 4,11,$.1^2 -
$.1 - 4,13,$.1^2 - 4*$.1 + 4[] 149,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 3*x^2 - 4*x - 13,7,x^3 + 5*x^2 + 6*x + 1,11,x^3 + 5*x^2 - 8*x + 1,13,x^3 + 3*x^2 - 4*x - 13[] 149,2,2,x^9 + x^8 - 15*x^7 - 12*x^6 + 75*x^5 + 48*x^4 - 137*x^3 - 76*x^2 + 68*x + 39,3,x^9 - 6*x^8 + 55*x^6 - 67*x^5 - 125*x^4 + 235*x^3 - 6*x^2 - 117*x + 27,5,x^9 + x^8 - 25*x^7 - 4*x^6 + 202*x^5 - 83*x^4 - 529*x^3 + 305*x^2 + 392*x - 221,7,x^9 - 3*x^8 - 34*x^7 + 117*x^6 + 208*x^5 - 916*x^4 + 144*x^3 + 1056*x^2 - 128*x - 64,11,x^9 - 5*x^8 - 33*x^7 + 202*x^6 + 66*x^5 - 1503*x^4 + 997*x^3 + 2817*x^2 - 3392*x + 981,13,x^9 - 7*x^8 - 28*x^7 + 277*x^6 - 152*x^5 - 2028*x^4 + 3072*x^3 + 32*x^2 - 512*x - 64[] 150,1,2,x + 1,3,x + 1,5,x,7,x - 2,11,x - 2,13,x - 6[] 150,2,2,x - 1,3,x + 1,5,x,7,x - 4,11,x,13,x + 2[] 150,3,2,x - 1,3,x - 1,5,x,7,x + 2,11,x - 2,13,x + 6[] 151,1,2,x^3 + 2*x^2 - x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 7*x^2 + 14*x + 7,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 5*x^2 - x - 13,13,x^3 + x^2 - 16*x + 13[] 151,2,2,x^3 - 5*x + 3,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 5*x^2 - 2*x + 25,7,x^3 + 6*x^2 + 12*x + 8,11,x^3 + x^2 - 20*x + 25,13,x^3 + 2*x^2 - 32*x - 24[] 151,3,2,x^6 - x^5 - 7*x^4 + 3*x^3 + 13*x^2 + 3*x - 1,3,x^6 + 5*x^5 - 4*x^4 - 51*x^3 - 68*x^2 - 12*x + 8,5,x^6 - 6*x^5 + 5*x^4 + 16*x^3 - 8*x^2 - 12*x - 1,7,x^6 - 3*x^5 - 33*x^4 + 119*x^3 + 200*x^2 - 1100*x + 1000,11,x^6 - 8*x^5 + 14*x^4 + 23*x^3 - 64*x^2 - 7*x + 49,13,x^6 + x^5 - 40*x^4 - x^3 + 236*x^2 - 36*x - 328[] 152,1,2,x,3,x + 2,5,x + 1,7,x + 3,11,x + 3,13,x + 4[] 152,2,2,x,3,x - 1,5,x,7,x - 3,11,x - 2,13,x - 1[] 152,3,2,x^3,3,x^3 - x^2 - 10*x + 8,5,x^3 - x^2 - 10*x + 8,7,x^3 - 4*x^2 - 5*x + 16,11,x^3 + 5*x^2 - 2*x - 8,13,x^3 - 5*x^2 - 2*x + 8[] 153,1,2,x + 2,3,x,5,x + 1,7,x + 2,11,x + 3,13,x + 5[] 153,2,2,x - 2,3,x,5,x - 1,7,x + 2,11,x - 3,13,x + 5[] 153,3,2,x - 1,3,x,5,x - 2,7,x - 4,11,x,13,x + 2[] 153,4,2,x,3,x,5,x + 3,7,x + 4,11,x - 3,13,x + 1[] 153,5,2,x^2 - x - 4,3,x^2,5,x^2 + 3*x - 2,7,x^2,11,x^2 - x - 4,13,x^2 - 5*x + 2[] 154,1,2,x + 1,3,x,5,x + 4,7,x + 1,11,x + 1,13,x - 2[] 154,2,2,x + 1,3,x - 2,5,x - 2,7,x + 1,11,x - 1,13,x + 4[] 154,3,2,x - 1,3,x,5,x - 2,7,x + 1,11,x + 1,13,x - 2[] 154,4,2,x^2 - 2*x + 1,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 - 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + 2*x - 4[] 155,1,2,x,3,x + 1,5,x + 1,7,x,11,x + 4,13,x + 6[] 155,2,2,x + 1,3,x - 2,5,x + 1,7,x - 4,11,x - 4,13,x[] 155,3,2,x + 2,3,x + 1,5,x - 1,7,x + 2,11,x - 2,13,x + 6[] 155,4,2,x^4 + x^3 - 8*x^2 - 4*x + 12,3,x^4 + x^3 - 9*x^2 - 9*x - 2,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 12*x^2 - 4*x + 16,11,x^4 + 6*x^3 - 16*x^2 - 124*x - 144,13,x^4 - 16*x^3 + 84*x^2 - 156*x + 64[] 155,5,2,x^4 - x^3 - 6*x^2 + 4*x + 4,3,x^4 - x^3 - 5*x^2 + 3*x + 4,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 2*x^3 - 20*x^2 + 52*x - 32,11,x^4 + 4*x^3 - 8*x^2 - 12*x + 16,13,x^4 - 10*x^3 + 20*x^2 + 52*x - 136[] 156,1,2,x,3,x + 1,5,x + 4,7,x + 2,11,x + 4,13,x - 1[] 156,2,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x - 1[] 157,1,2,x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 7*x + 1,3,x^5 + 7*x^4 + 15*x^3 + 7*x^2 - 8*x - 5,5,x^5 + 3*x^4 - 12*x^3 - 39*x^2 - x + 25,7,x^5 + 3*x^4 - 15*x^3 - 26*x^2 + 61*x + 17,11,x^5 + 14*x^4 + 64*x^3 + 91*x^2 - 20*x + 1,13,x^5 + 7*x^4 + 9*x^3 - 32*x^2 - 89*x - 59[] 157,2,2,x^7 - 5*x^6 + 2*x^5 + 21*x^4 - 22*x^3 - 21*x^2 + 27*x - 1,3,x^7 - 5*x^6 - x^5 + 31*x^4 - 20*x^3 - 45*x^2 + 44*x - 4,5,x^7 + x^6 - 16*x^5 + 3*x^4 + 73*x^3 - 87*x^2 + 8*x + 16,7,x^7 - x^6 - 16*x^5 + 19*x^4 + 56*x^3 - 75*x^2 + 19*x - 1,11,x^7 - 10*x^6 + 28*x^5 - 9*x^4 - 44*x^3 + 33*x^2 + 8*x - 8,13,x^7 + 5*x^6 - 16*x^5 - 63*x^4 + 128*x^3 + 187*x^2 - 407*x + 113[] 158,1,2,x + 1,3,x + 1,5,x + 1,7,x + 3,11,x - 4,13,x + 7[] 158,2,2,x + 1,3,x - 1,5,x - 3,7,x + 1,11,x,13,x - 5[] 158,3,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 1[] 158,4,2,x - 1,3,x - 2,5,x + 2,7,x,11,x + 4,13,x - 2[] 158,5,2,x - 1,3,x + 3,5,x + 3,7,x + 3,11,x + 2,13,x + 5[] 158,6,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2 + 4*x + 4,7,x^2 - 8*x + 16,11,x^2,13,x^2 - 4*x - 20[] 159,1,2,x^4 - 3*x^3 - x^2 + 7*x - 3,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 2*x^3 - 11*x^2 + 32*x - 21,7,x^4 + 4*x^3 - 7*x^2 - 44*x - 43,11,x^4 - 6*x^3 - 28*x^2 + 232*x - 336,13,x^4 + 6*x^3 - 9*x^2 - 70*x + 1[] 159,2,2,x^5 - 10*x^3 + 22*x + 5,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 - 19*x^3 + 6*x^2 + 67*x - 2,7,x^5 - 4*x^4 - 23*x^3 + 92*x^2 + 117*x - 472,11,x^5 - 2*x^4 - 28*x^3 + 72*x^2 + 16*x - 64,13,x^5 - 8*x^4 - 13*x^3 + 136*x^2 + 101*x - 110[] 160,1,2,x,3,x + 2,5,x + 1,7,x + 2,11,x + 4,13,x + 6[] 160,2,2,x,3,x - 2,5,x + 1,7,x - 2,11,x - 4,13,x + 6[] 160,3,2,x^2,3,x^2 - 8,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 - 32,13,x^2 + 4*x + 4[] Total time: 17.389 seconds, Total memory usage: 7.25MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 07:44:16 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [160..170] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 07:44:01 on modular [Seed = 1102506673] ------------------------------------- 160,1,2,$.1,3,$.1 + 2,5,$.1 + 1,7,$.1 + 2,11,$.1 + 4,13,$.1 + 6[] 160,2,2,$.1,3,$.1 - 2,5,$.1 + 1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 6[] 160,3,2,$.1^2,3,$.1^2 - 8,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 8,11,$.1^2 - 32,13,$.1^2
+ 4*$.1 + 4[] 161,1,2,x + 1,3,x,5,x - 2,7,x - 1,11,x - 4,13,x - 6[] 161,2,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x - 4,7,x^2 + 2*x + 1,11,x^2 - 20,13,x^2 + 4*x - 1[] 161,3,2,x^3 + x^2 - 5*x - 1,3,x^3 - 2*x^2 - 2*x + 2,5,x^3 - 2*x^2 - 2*x + 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 4*x^2 + 4,13,x^3 - 2*x^2 - 12*x + 8[] 161,4,2,x^5 - 2*x^4 - 9*x^3 + 17*x^2 + 16*x - 27,3,x^5 - 13*x^3 + 38*x + 10,5,x^5 + 4*x^4 - 14*x^3 - 54*x^2 + 52*x + 168,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 + 4*x^4 - 28*x^3 - 148*x^2 - 160*x - 48,13,x^5 + 6*x^4 - 9*x^3 - 46*x^2 + 12*x + 56[] 162,1,2,x + 1,3,x,5,x + 3,7,x + 4,11,x,13,x + 1[] 162,2,2,x + 1,3,x,5,x,7,x - 2,11,x - 3,13,x - 2[] 162,3,2,x - 1,3,x,5,x,7,x - 2,11,x + 3,13,x - 2[] 162,4,2,x - 1,3,x,5,x - 3,7,x + 4,11,x,13,x + 1[] 163,1,2,x,3,x,5,x + 4,7,x - 2,11,x + 6,13,x - 4[] 163,2,2,x^5 + 5*x^4 + 3*x^3 - 15*x^2 - 16*x + 3,3,x^5 + 5*x^4 + x^3 - 23*x^2 - 28*x - 9,5,x^5 + 9*x^4 + 23*x^3 + 12*x^2 - x - 1,7,x^5 + 6*x^4 - 5*x^3 - 48*x^2 + 18*x - 1,11,x^5 - 2*x^4 - 26*x^3 + 57*x^2 - 32*x + 3,13,x^5 + 14*x^4 + 73*x^3 + 173*x^2 + 179*x + 61[] 163,3,2,x^7 - 3*x^6 - 5*x^5 + 19*x^4 - 23*x^2 + 4*x + 6,3,x^7 - x^6 - 11*x^5 + 13*x^4 + 26*x^3 - 39*x^2 + 16*x - 2,5,x^7 - 11*x^6 + 41*x^5 - 44*x^4 - 73*x^3 + 199*x^2 - 136*x + 24,7,x^7 - 21*x^5 - 18*x^4 + 104*x^3 + 115*x^2 - 136*x - 158,11,x^7 - 2*x^6 - 20*x^5 + 67*x^4 - 34*x^3 - 49*x^2 + 20*x + 12,13,x^7 - 10*x^6 + 11*x^5 + 149*x^4 - 493*x^3 + 311*x^2 + 402*x - 334[] 164,1,2,x^4,3,x^4 - 2*x^3 - 10*x^2 + 22*x - 2,5,x^4 - 4*x^3 - 8*x^2 + 44*x - 36,7,x^4 - 22*x^2 + 26*x + 38,11,x^4 - 4*x^3 - 18*x^2 + 18*x + 54,13,x^4 - 40*x^2 - 48*x + 144[] 165,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 4*x - 4,11,x^2 + 2*x + 1,13,x^2 - 32[] 165,2,2,x^2 - 3,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 2*x + 1,13,x^2 - 4*x - 8[] 165,3,2,x^3 + x^2 - 5*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 16*x + 16,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 2*x^2 - 12*x - 8[] 166,1,2,x + 1,3,x + 1,5,x + 2,7,x - 1,11,x + 5,13,x + 2[] 166,2,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 - 3*x + 1,7,x^2 + 3*x + 1,11,x^2 - 6*x + 4,13,x^2 - 3*x + 1[] 166,3,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 6*x + 4,5,x^3 + x^2 - 5*x + 2,7,x^3 - 2*x^2 - 14*x - 13,11,x^3 - 5*x^2 + 2*x + 4,13,x^3 + 9*x^2 + 23*x + 14[] 167,1,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + 2*x + 1,7,x^2 + 5*x + 5,11,x^2,13,x^2 + 5*x + 5[] 167,2,2,x^12 - 2*x^11 - 17*x^10 + 33*x^9 + 103*x^8 - 189*x^7 - 277*x^6 + 447*x^5 + 363*x^4 - 433*x^3 - 205*x^2 + 120*x + 9,3,x^12 - 3*x^11 - 22*x^10 + 71*x^9 + 145*x^8 - 552*x^7 - 243*x^6 + 1577*x^5 - 122*x^4 - 1737*x^3 + 384*x^2 + 599*x - 91,5,x^12 - 4*x^11 - 41*x^10 + 152*x^9 + 648*x^8 - 2136*x^7 - 4816*x^6 + 13568*x^5 + 15616*x^4 - 37632*x^3 - 12544*x^2 + 33792*x - 9216,7,x^12 - 11*x^11 + 4*x^10 + 335*x^9 - 965*x^8 - 2308*x^7 + 11629*x^6 - 1491*x^5 - 39468*x^4 + 30443*x^3 + 38438*x^2 - 37689*x - 1557,11,x^12 - 77*x^10 - 12*x^9 + 2080*x^8 + 500*x^7 - 24675*x^6 - 6388*x^5 + 127975*x^4 + 29620*x^3 - 237953*x^2 - 23960*x + 86192,13,x^12 - 9*x^11 - 47*x^10 + 642*x^9 - 396*x^8 - 12320*x^7 + 32400*x^6 + 35904*x^5 - 180288*x^4 + 58880*x^3 + 179456*x^2 - 38912*x - 37888[] 168,1,2,x,3,x + 1,5,x - 2,7,x - 1,11,x,13,x - 6[] 168,2,2,x,3,x - 1,5,x - 2,7,x + 1,11,x,13,x + 2[] 169,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 3,7,x^2,11,x^2,13,x^2[] 169,2,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3 + 3*x^2 - 4*x - 13,11,x^3 + 8*x^2 + 19*x + 13,13,x^3[] 169,3,2,x^3 - 2*x^2 - x + 1,3,x^3 + 2*x^2 - x - 1,5,x^3 - 4*x^2 + 3*x + 1,7,x^3 - 3*x^2 - 4*x + 13,11,x^3 - 8*x^2 + 19*x - 13,13,x^3[] 170,1,2,x + 1,3,x + 2,5,x + 1,7,x - 2,11,x - 6,13,x - 2[] 170,2,2,x + 1,3,x - 3,5,x + 1,7,x - 2,11,x + 4,13,x + 3[] 170,3,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 5[] 170,4,2,x + 1,3,x + 2,5,x - 1,7,x + 2,11,x + 2,13,x + 6[] 170,5,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x + 1[] 170,6,2,x^2 - 2*x + 1,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 + 8*x + 16,13,x^2 - 5*x + 2[] Total time: 14.729 seconds, Total memory usage: 6.70MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:15:59 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [170..180] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:15:42 on modular [Seed = 333756300] ------------------------------------- 170,1,2,$.1 + 1,3,$.1 + 2,5,$.1 + 1,7,$.1 - 2,11,$.1 - 6,13,$.1 - 2[] 170,2,2,$.1 + 1,3,$.1 - 3,5,$.1 + 1,7,$.1 - 2,11,$.1 + 4,13,$.1 + 3[] 170,3,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 2,11,$.1,13,$.1 - 5[] 170,4,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 6[] 170,5,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 2,11,$.1,13,$.1 + 1[] 170,6,2,$.1^2 - 2*$.1 + 1,3,$.1^2 + $.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 2*$.1 - 16,11,$.1^2 + 8*$.1 + 16,13,$.1^2 - 5*$.1 + 2[] 171,1,2,x + 1,3,x,5,x - 2,7,x,11,x,13,x - 6[] 171,2,2,x - 2,3,x,5,x + 1,7,x - 3,11,x - 3,13,x + 6[] 171,3,2,x - 2,3,x,5,x - 3,7,x + 5,11,x + 1,13,x - 2[] 171,4,2,x,3,x,5,x + 3,7,x + 1,11,x + 3,13,x + 4[] 171,5,2,x^4 - 9*x^2 + 12,3,x^4,5,x^4 - 15*x^2 + 48,7,x^4 - 2*x^3 - 15*x^2 + 16*x + 64,11,x^4 - 27*x^2 + 108,13,x^4 - 8*x^3 + 24*x^2 - 32*x + 16[] 172,1,2,x,3,x + 2,5,x,7,x + 4,11,x + 3,13,x + 1[] 172,2,2,x^2,3,x^2 - 4*x + 2,5,x^2 - 2,7,x^2 - 2,11,x^2 - 2*x - 7,13,x^2 + 6*x + 1[] 173,1,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 6*x^3 + 10*x^2 + 3*x - 1,5,x^4 + x^3 - 5*x^2 - 7*x - 1,7,x^4 + 9*x^3 + 27*x^2 + 31*x + 11,11,x^4 + 5*x^3 - 11*x^2 - 65*x - 31,13,x^4 + 5*x^3 - 30*x^2 - 200*x - 275[] 173,2,2,x^10 - x^9 - 16*x^8 + 16*x^7 + 85*x^6 - 80*x^5 - 175*x^4 + 136*x^3 + 138*x^2 - 71*x - 25,3,x^10 - 8*x^9 + 11*x^8 + 59*x^7 - 165*x^6 - 55*x^5 + 484*x^4 - 202*x^3 - 390*x^2 + 169*x + 113,5,x^10 - x^9 - 29*x^8 + 41*x^7 + 253*x^6 - 452*x^5 - 548*x^4 + 1344*x^3 - 544*x^2 - 128*x + 64,7,x^10 - 11*x^9 + 20*x^8 + 168*x^7 - 704*x^6 + 235*x^5 + 2126*x^4 - 1607*x^3 - 2023*x^2 + 1319*x + 577,11,x^10 - 5*x^9 - 34*x^8 + 188*x^7 + 194*x^6 - 1935*x^5 + 1554*x^4 + 2983*x^3 - 2373*x^2 - 1687*x - 25,13,x^10 - x^9 - 63*x^8 + 59*x^7 + 1259*x^6 - 1496*x^5 - 9134*x^4 + 13207*x^3 + 14308*x^2 - 19944*x + 5285[] 174,1,2,x + 1,3,x + 1,5,x - 3,7,x + 3,11,x - 6,13,x[] 174,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x + 4,13,x - 6[] 174,3,2,x + 1,3,x - 1,5,x + 3,7,x - 5,11,x - 6,13,x + 4[] 174,4,2,x - 1,3,x + 1,5,x - 1,7,x - 1,11,x - 6,13,x + 4[] 174,5,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x + 2,13,x[] 175,1,2,x,3,x + 1,5,x,7,x + 1,11,x + 3,13,x + 5[] 175,2,2,x - 2,3,x - 1,5,x,7,x + 1,11,x + 3,13,x - 1[] 175,3,2,x + 2,3,x + 1,5,x,7,x - 1,11,x + 3,13,x + 1[] 175,4,2,x^2 - x - 4,3,x^2 - x - 4,5,x^2,7,x^2 - 2*x + 1,11,x^2 - x - 4,13,x^2 + 5*x + 2[] 175,5,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 4*x - 1,13,x^2 + 2*x - 4[] 175,6,2,x^2 + x - 1,3,x^2 - 2*x - 4,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x - 1,13,x^2 - 2*x - 4[] 176,1,2,x,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x[] 176,2,2,x,3,x - 1,5,x - 1,7,x - 2,11,x + 1,13,x - 4[] 176,3,2,x,3,x + 1,5,x + 3,7,x + 2,11,x - 1,13,x + 4[] 176,4,2,x^2,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 - 2*x - 16,11,x^2 - 2*x + 1,13,x^2 + 2*x - 16[] 177,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - 5,7,x^2 + 7*x + 11,11,x^2 - 5,13,x^2 + 8*x + 11[] 177,2,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - x - 1,11,x^2 - 4*x - 1,13,x^2 + 2*x + 1[] 177,3,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 6*x + 9,7,x^2 + 7*x + 11,11,x^2 + 2*x - 19,13,x^2 - 45[] 177,4,2,x^3 - 4*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 - 9*x^2 + 23*x - 16,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 - 4*x^2 - 7*x + 26[] 178,1,2,x + 1,3,x - 2,5,x - 2,7,x,11,x,13,x + 4[] 178,2,2,x - 1,3,x - 1,5,x - 3,7,x + 4,11,x + 6,13,x - 2[] 178,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 1,5,x^2 + 2*x - 7,7,x^2 + 4*x + 4,11,x^2 + 4*x - 4,13,x^2 + 4*x + 4[] 178,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 8*x + 4,5,x^3 + x^2 - 8*x - 4,7,x^3 - 10*x + 8,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 2*x^2 - 18*x - 44[] 179,1,2,x - 2,3,x,5,x - 3,7,x + 4,11,x - 4,13,x + 1[] 179,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3 + 4*x^2 + 3*x - 1,11,x^3 + 3*x^2 - 4*x + 1,13,x^3 + 11*x^2 + 38*x + 41[] 179,3,2,x^11 + 3*x^10 - 14*x^9 - 45*x^8 + 59*x^7 + 225*x^6 - 58*x^5 - 427*x^4 - 76*x^3 + 240*x^2 + 56*x - 16,3,x^11 - 25*x^9 + 5*x^8 + 219*x^7 - 98*x^6 - 781*x^5 + 589*x^4 + 901*x^3 - 1000*x^2 + 185*x - 9,5,x^11 - 3*x^10 - 28*x^9 + 65*x^8 + 310*x^7 - 499*x^6 - 1680*x^5 + 1613*x^4 + 4325*x^3 - 1977*x^2 - 4019*x + 663,7,x^11 - 8*x^10 - 19*x^9 + 281*x^8 - 202*x^7 - 2904*x^6 + 4160*x^5 + 12464*x^4 - 18560*x^3 - 26624*x^2 + 25728*x + 27392,11,x^11 + 9*x^10 - 24*x^9 - 359*x^8 + 4*x^7 + 5052*x^6 + 2592*x^5 - 32352*x^4 - 15552*x^3 + 94144*x^2 + 21504*x - 95488,13,x^11 - 24*x^10 + 206*x^9 - 583*x^8 - 1712*x^7 + 14840*x^6 - 30091*x^5 + 2233*x^4 + 47058*x^3 - 11030*x^2 - 30872*x - 7499[] 180,1,2,x,3,x,5,x - 1,7,x - 2,11,x,13,x - 2[] Total time: 16.819 seconds, Total memory usage: 7.37MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:22:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [180..190] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:21:39 on modular [Seed = 3876603365] ------------------------------------- 180,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 - 2,11,$.1,13,$.1 - 2[] 181,1,2,x^5 + 3*x^4 - x^3 - 7*x^2 - 2*x + 1,3,x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 9*x - 1,5,x^5 + 5*x^4 - 5*x^3 - 55*x^2 - 88*x - 43,7,x^5 + 2*x^4 - 19*x^3 - 42*x^2 + 66*x + 149,11,x^5 + 20*x^4 + 153*x^3 + 554*x^2 + 936*x + 575,13,x^5 + 2*x^4 - 40*x^3 - 53*x^2 + 222*x + 293[] 181,2,2,x^9 - 3*x^8 - 9*x^7 + 29*x^6 + 23*x^5 - 84*x^4 - 23*x^3 + 89*x^2 + 8*x - 27,3,x^9 - 3*x^8 - 15*x^7 + 46*x^6 + 63*x^5 - 213*x^4 - 32*x^3 + 272*x^2 - 144*x + 16,5,x^9 - x^8 - 24*x^7 + 28*x^6 + 170*x^5 - 181*x^4 - 441*x^3 + 340*x^2 + 326*x - 3,7,x^9 - 2*x^8 - 26*x^7 + 42*x^6 + 152*x^5 - 195*x^4 - 331*x^3 + 259*x^2 + 268*x - 31,11,x^9 - 24*x^8 + 221*x^7 - 898*x^6 + 832*x^5 + 5259*x^4 - 15404*x^3 + 5356*x^2 + 22256*x - 19056,13,x^9 + 8*x^8 - 17*x^7 - 333*x^6 - 1035*x^5 - 252*x^4 + 4742*x^3 + 10438*x^2 + 9148*x + 2993[] 182,1,2,x + 1,3,x - 1,5,x - 4,7,x + 1,11,x + 1,13,x - 1[] 182,2,2,x + 1,3,x - 3,5,x,7,x - 1,11,x + 5,13,x + 1[] 182,3,2,x - 1,3,x,5,x - 2,7,x + 1,11,x - 4,13,x + 1[] 182,4,2,x - 1,3,x - 3,5,x + 4,7,x + 1,11,x - 1,13,x + 1[] 182,5,2,x - 1,3,x - 1,5,x,7,x - 1,11,x + 3,13,x - 1[] 183,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x - 1,11,x^2 + 2*x - 1,13,x^2 + 6*x + 9[] 183,2,2,x^3 - x^2 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 6*x^2 + 12*x - 8,7,x^3 - 16*x - 16,11,x^3 - 2*x^2 - 4*x + 4,13,x^3 - 6*x^2 - 4*x + 40[] 183,3,2,x^6 - 11*x^4 + 2*x^3 + 31*x^2 - 10*x - 17,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 2*x^5 - 23*x^4 + 28*x^3 + 144*x^2 - 80*x - 144,7,x^6 - 2*x^5 - 25*x^4 + 60*x^3 + 128*x^2 - 432*x + 288,11,x^6 + 8*x^5 - 5*x^4 - 110*x^3 - 68*x^2 + 8*x + 4,13,x^6 - 6*x^5 - 23*x^4 + 116*x^3 + 168*x^2 - 464*x - 608[] 184,1,2,x,3,x + 1,5,x + 2,7,x + 4,11,x + 2,13,x - 7[] 184,2,2,x,3,x,5,x,7,x - 4,11,x - 6,13,x + 2[] 184,3,2,x,3,x - 3,5,x,7,x + 2,11,x,13,x + 5[] 184,4,2,x,3,x + 1,5,x + 4,7,x - 2,11,x + 4,13,x + 5[] 184,5,2,x^2,3,x^2 + x - 4,5,x^2 - 4*x + 4,7,x^2,11,x^2 - 2*x - 16,13,x^2 - 5*x + 2[] 185,1,2,x - 1,3,x + 2,5,x + 1,7,x + 2,11,x,13,x + 2[] 185,2,2,x + 2,3,x - 1,5,x + 1,7,x + 5,11,x - 3,13,x + 2[] 185,3,2,x,3,x + 1,5,x - 1,7,x + 3,11,x + 5,13,x - 4[] 185,4,2,x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 11*x - 12,3,x^5 - 3*x^4 - 6*x^3 + 20*x^2 + 4*x - 22,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 - 11*x^4 + 32*x^3 + 32*x^2 - 268*x + 302,11,x^5 + 5*x^4 - 8*x^3 - 48*x^2 + 16*x + 96,13,x^5 - 4*x^4 - 28*x^3 + 60*x^2 + 148*x - 256[] 185,5,2,x^5 - 8*x^3 + 2*x^2 + 11*x - 2,3,x^5 + x^4 - 8*x^3 - 4*x^2 + 4*x + 2,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - 7*x^4 + 6*x^3 + 24*x^2 - 2,11,x^5 - 7*x^4 - 12*x^3 + 144*x^2 - 176*x - 32,13,x^5 - 2*x^4 - 20*x^3 + 20*x^2 + 76*x - 88[] 186,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x - 3,13,x - 3[] 186,2,2,x + 1,3,x - 1,5,x - 3,7,x + 2,11,x - 5,13,x + 7[] 186,3,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x + 3,13,x + 1[] 186,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2 - 2*x - 16,11,x^2 + x - 4,13,x^2 - 3*x - 2[] 187,1,2,x - 2,3,x,5,x - 4,7,x + 5,11,x + 1,13,x - 4[] 187,2,2,x,3,x - 1,5,x - 3,7,x - 2,11,x - 1,13,x - 2[] 187,3,2,x^2 - 4*x + 4,3,x^2 + x - 4,5,x^2 - x - 4,7,x^2 - 3*x - 2,11,x^2 - 2*x + 1,13,x^2[] 187,4,2,x^2 + 2*x - 2,3,x^2 - 3,5,x^2 + 4*x + 1,7,x^2 + 4*x + 4,11,x^2 - 2*x + 1,13,x^2 + 10*x + 22[] 187,5,2,x^3 + 2*x^2 - 2*x - 2,3,x^3 + 3*x^2 - x - 5,5,x^3 + 7*x^2 + 13*x + 5,7,x^3 - 16*x + 16,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 30*x - 2[] 187,6,2,x^4 - x^3 - 6*x^2 + 2*x + 2,3,x^4 - x^3 - 11*x^2 + 9*x + 20,5,x^4 - 3*x^3 - 3*x^2 + 9*x - 2,7,x^4,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 2*x^3 - 28*x^2 - 90*x - 36[] 188,1,2,x^2,3,x^2 - x - 3,5,x^2,7,x^2 - 5*x + 3,11,x^2 - 2*x - 12,13,x^2 - 4*x + 4[] 188,2,2,x^2,3,x^2 + 3*x + 1,5,x^2 + 2*x - 4,7,x^2 + 7*x + 11,11,x^2 + 4*x - 16,13,x^2 + 4*x - 16[] 189,1,2,x + 2,3,x,5,x + 1,7,x + 1,11,x + 4,13,x + 2[] 189,2,2,x,3,x,5,x - 3,7,x - 1,11,x - 6,13,x + 4[] 189,3,2,x - 2,3,x,5,x - 1,7,x + 1,11,x - 4,13,x + 2[] 189,4,2,x,3,x,5,x + 3,7,x - 1,11,x + 6,13,x + 4[] 189,5,2,x^2 - 3,3,x^2,5,x^2 - 3,7,x^2 - 2*x + 1,11,x^2 - 3,13,x^2 - 4*x + 4[] 189,6,2,x^2 - 7,3,x^2,5,x^2 - 7,7,x^2 + 2*x + 1,11,x^2 - 7,13,x^2 + 4*x + 4[] 190,1,2,x + 1,3,x + 1,5,x + 1,7,x + 1,11,x,13,x + 3[] 190,2,2,x - 1,3,x + 3,5,x + 1,7,x + 5,11,x + 4,13,x + 1[] 190,3,2,x - 1,3,x - 1,5,x - 1,7,x + 1,11,x,13,x + 1[] 190,4,2,x^2 + 2*x + 1,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + x - 4,11,x^2 - 8*x + 16,13,x^2 + x - 38[] Total time: 19.180 seconds, Total memory usage: 7.53MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:28:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [190..200] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:27:58 on modular [Seed = 4093859147] ------------------------------------- 190,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1,13,$.1 + 3[] 190,2,2,$.1 - 1,3,$.1 + 3,5,$.1 + 1,7,$.1 + 5,11,$.1 + 4,13,$.1 + 1[] 190,3,2,$.1 - 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1,13,$.1 + 1[] 190,4,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + $.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 + $.1 - 4,11,$.1^2 - 8*$.1 + 16,13,$.1^2 + $.1 - 38[] 191,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 + x - 1,7,x^2 + x - 1,11,x^2 + x - 1,13,x^2 + 7*x + 1[] 191,2,2,x^14 - 23*x^12 + x^11 + 205*x^10 - 13*x^9 - 895*x^8 + 35*x^7 + 1993*x^6 + 103*x^5 - 2135*x^4 - 465*x^3 + 853*x^2 + 374*x + 41,3,x^14 - 2*x^13 - 30*x^12 + 58*x^11 + 334*x^10 - 630*x^9 - 1667*x^8 + 3160*x^7 + 3418*x^6 - 7088*x^5 - 1483*x^4 + 5142*x^3 - 940*x^2 - 122*x + 5,5,x^14 - x^13 - 48*x^12 + 63*x^11 + 860*x^10 - 1339*x^9 - 6923*x^8 + 11842*x^7 + 23938*x^6 - 41166*x^5 - 31785*x^4 + 51275*x^3 + 6610*x^2 - 21509*x + 5527,7,x^14 - 3*x^13 - 71*x^12 + 236*x^11 + 1872*x^10 - 7064*x^9 - 21808*x^8 + 101248*x^7 + 85248*x^6 - 691840*x^5 + 303360*x^4 + 1703424*x^3 - 2363392*x^2 + 942080*x - 69632,11,x^14 + 3*x^13 - 103*x^12 - 332*x^11 + 3764*x^10 + 13152*x^9 - 56816*x^8 - 222400*x^7 + 288512*x^6 + 1458688*x^5 + 131840*x^4 - 2122240*x^3 - 254976*x^2 + 892928*x - 167936,13,x^14 - 19*x^13 + 62*x^12 + 949*x^11 - 7606*x^10 + 503*x^9 + 166303*x^8 - 478782*x^7 - 645034*x^6 + 5011874*x^5 - 6716001*x^4 - 1704311*x^3 + 7511848*x^2 - 1293835*x - 1553539[] 192,1,2,x,3,x + 1,5,x + 2,7,x + 4,11,x + 4,13,x - 2[] 192,2,2,x,3,x - 1,5,x - 2,7,x,11,x + 4,13,x - 2[] 192,3,2,x,3,x - 1,5,x + 2,7,x - 4,11,x - 4,13,x - 2[] 192,4,2,x,3,x + 1,5,x - 2,7,x,11,x - 4,13,x - 2[] 193,1,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - 5,7,x^2 + x - 11,11,x^2 - 3*x - 9,13,x^2 + 6*x + 9[] 193,2,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,3,x^5 + 5*x^4 - x^3 - 27*x^2 - 10*x + 23,5,x^5 + 8*x^4 + 15*x^3 - 26*x^2 - 106*x - 83,7,x^5 + 10*x^4 + 27*x^3 + 5*x^2 - 25*x - 11,11,x^5 + 10*x^4 + 5*x^3 - 162*x^2 - 162*x + 729,13,x^5 - 2*x^4 - 45*x^3 + 50*x^2 + 350*x - 23[] 193,3,2,x^8 - 2*x^7 - 9*x^6 + 18*x^5 + 21*x^4 - 44*x^3 - 11*x^2 + 27*x + 1,3,x^8 - 5*x^7 - 2*x^6 + 40*x^5 - 37*x^4 - 48*x^3 + 36*x^2 + 31*x + 4,5,x^8 - 8*x^7 + 16*x^6 + 8*x^5 - 35*x^4 + x^3 + 16*x^2 - x - 2,7,x^8 - 5*x^7 - 10*x^6 + 62*x^5 - 9*x^4 - 71*x^3 + 28*x^2 + 17*x - 8,11,x^8 - 9*x^7 + 8*x^6 + 121*x^5 - 279*x^4 - 301*x^3 + 1067*x^2 - 333*x - 4,13,x^8 + 4*x^7 - 18*x^6 - 70*x^5 + 49*x^4 + 307*x^3 + 144*x^2 - 199*x - 118[] 194,1,2,x - 1,3,x,5,x - 4,7,x + 4,11,x - 4,13,x + 4[] 194,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 2*x^3 - 9*x^2 + 18*x + 1,5,x^4 + 2*x^3 - 15*x^2 - 26*x + 27,7,x^4 - 6*x^3 + 7*x^2 + 10*x - 13,11,x^4 - 2*x^3 - 9*x^2 + 2*x + 9,13,x^4 - 4*x^3 - 20*x^2 + 80*x - 16[] 194,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 9*x^2 + 18*x - 7,5,x^4 + 2*x^3 - 5*x^2 - 6*x + 7,7,x^4 - 2*x^3 - 19*x^2 + 62*x - 49,11,x^4 + 2*x^3 - 41*x^2 - 66*x + 193,13,x^4 - 4*x^3 - 20*x^2 + 48*x + 112[] 195,1,2,x - 2,3,x + 1,5,x - 1,7,x - 3,11,x + 1,13,x + 1[] 195,2,2,x - 2,3,x - 1,5,x + 1,7,x + 1,11,x - 5,13,x + 1[] 195,3,2,x + 1,3,x - 1,5,x - 1,7,x,11,x - 4,13,x - 1[] 195,4,2,x - 2,3,x - 1,5,x - 1,7,x + 3,11,x + 5,13,x - 1[] 195,5,2,x^3 - 7*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - x^2 - 16*x - 16,11,x^3 - x^2 - 16*x - 16,13,x^3 - 3*x^2 + 3*x - 1[] 196,1,2,x,3,x - 1,5,x - 3,7,x,11,x + 3,13,x - 2[] 196,2,2,x,3,x + 1,5,x + 3,7,x,11,x + 3,13,x + 2[] 196,3,2,x^2,3,x^2 - 8,5,x^2 - 2,7,x^2,11,x^2 - 8*x + 16,13,x^2 - 18[] 197,1,2,x + 2,3,x,5,x,7,x + 3,11,x - 4,13,x + 2[] 197,2,2,x^5 - 5*x^3 + x^2 + 3*x - 1,3,x^5 + 8*x^4 + 18*x^3 - x^2 - 38*x - 25,5,x^5 + 4*x^4 - 8*x^3 - 37*x^2 + 16*x + 85,7,x^5 + 10*x^4 + 27*x^3 - 9*x^2 - 97*x - 53,11,x^5 + 8*x^4 + x^3 - 68*x^2 + 22*x + 59,13,x^5 + 8*x^4 - 18*x^3 - 163*x^2 + 188*x + 493[] 197,3,2,x^10 - 15*x^8 + x^7 + 78*x^6 - 7*x^5 - 165*x^4 + 15*x^3 + 123*x^2 - 9*x - 26,3,x^10 - 10*x^9 + 29*x^8 + 17*x^7 - 227*x^6 + 316*x^5 + 184*x^4 - 784*x^3 + 646*x^2 - 175*x + 2,5,x^10 - 2*x^9 - 26*x^8 + 59*x^7 + 180*x^6 - 465*x^5 - 194*x^4 + 804*x^3 - 200*x^2 - 176*x + 32,7,x^10 - 11*x^9 + 25*x^8 + 100*x^7 - 420*x^6 - 24*x^5 + 1485*x^4 - 1136*x^3 - 496*x^2 + 384*x + 64,11,x^10 - 2*x^9 - 48*x^8 + 128*x^7 + 590*x^6 - 1633*x^5 - 2727*x^4 + 6561*x^3 + 5866*x^2 - 7319*x - 5906,13,x^10 - 8*x^9 - 14*x^8 + 189*x^7 - 28*x^6 - 1145*x^5 + 116*x^4 + 2160*x^3 - 352*x^2 - 1264*x + 448[] 198,1,2,x + 1,3,x,5,x,7,x - 2,11,x - 1,13,x - 2[] 198,2,2,x + 1,3,x,5,x - 4,7,x + 2,11,x + 1,13,x - 4[] 198,3,2,x + 1,3,x,5,x + 2,7,x + 4,11,x - 1,13,x + 6[] 198,4,2,x - 1,3,x,5,x,7,x - 2,11,x + 1,13,x - 2[] 198,5,2,x - 1,3,x,5,x,7,x - 2,11,x - 1,13,x + 4[] 199,1,2,x^2 + x - 1,3,x^2 - 4*x + 4,5,x^2 - 6*x + 9,7,x^2,11,x^2 + 6*x + 4,13,x^2 - 2*x - 19[] 199,2,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 + 2*x^3 - x^2 - 2*x + 1,5,x^4 + 5*x^3 + 4*x^2 - 10*x - 11,7,x^4 + 3*x^3 - 10*x^2 + 6*x - 1,11,x^4 + 7*x^3 + 10*x^2 - 6*x - 11,13,x^4 - 14*x^2 + 25*x - 11[] 199,3,2,x^10 - 5*x^9 - 4*x^8 + 51*x^7 - 32*x^6 - 154*x^5 + 151*x^4 + 168*x^3 - 168*x^2 - 54*x + 27,3,x^10 + 4*x^9 - 19*x^8 - 88*x^7 + 73*x^6 + 552*x^5 + 200*x^4 - 784*x^3 - 480*x^2 + 96*x + 64,5,x^10 + x^9 - 26*x^8 - 26*x^7 + 216*x^6 + 219*x^5 - 607*x^4 - 571*x^3 + 317*x^2 + 156*x - 63,7,x^10 + 3*x^9 - 41*x^8 - 135*x^7 + 504*x^6 + 2027*x^5 - 1160*x^4 - 10173*x^3 - 8697*x^2 + 1110*x + 497,11,x^10 - 17*x^9 + 84*x^8 + 80*x^7 - 1875*x^6 + 4370*x^5 + 4696*x^4 - 27992*x^3 + 16544*x^2 + 42144*x - 45504,13,x^10 - 60*x^8 - 21*x^7 + 1174*x^6 + 364*x^5 - 9433*x^4 - 593*x^3 + 30585*x^2 - 5033*x - 26803[] 200,1,2,x,3,x - 2,5,x,7,x - 2,11,x + 4,13,x - 4[] 200,2,2,x,3,x + 3,5,x,7,x - 2,11,x - 1,13,x - 4[] 200,3,2,x,3,x,5,x,7,x - 4,11,x - 4,13,x - 2[] 200,4,2,x,3,x - 3,5,x,7,x + 2,11,x - 1,13,x + 4[] 200,5,2,x,3,x + 2,5,x,7,x + 2,11,x + 4,13,x + 4[] Total time: 16.959 seconds, Total memory usage: 7.28MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:36:31 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [200..210] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:36:08 on modular [Seed = 3508948600] ------------------------------------- 200,1,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 + 4,13,$.1 - 4[] 200,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 - 1,13,$.1 - 4[] 200,3,2,$.1,3,$.1,5,$.1,7,$.1 - 4,11,$.1 - 4,13,$.1 - 2[] 200,4,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 - 1,13,$.1 + 4[] 200,5,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 + 4,13,$.1 + 4[] 201,1,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x,13,x - 4[] 201,2,2,x + 2,3,x + 1,5,x,7,x,11,x + 6,13,x - 4[] 201,3,2,x + 1,3,x - 1,5,x + 1,7,x + 5,11,x + 4,13,x + 4[] 201,4,2,x^3 - 3*x^2 - x + 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - x^2 - 3*x + 1,7,x^3 - x^2 - 5*x + 1,11,x^3 - 10*x^2 + 24*x + 4,13,x^3 + 8*x^2 + 12*x + 4[] 201,5,2,x^5 - 8*x^3 + 13*x + 2,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 + 3*x^4 - 9*x^3 - 19*x^2 + 10*x + 16,7,x^5 - 7*x^4 + 3*x^3 + 63*x^2 - 128*x + 64,11,x^5 - 20*x^3 - 4*x^2 + 56*x - 32,13,x^5 - 10*x^4 + 20*x^3 + 36*x^2 - 88*x - 32[] 202,1,2,x + 1,3,x,5,x - 2,7,x - 1,11,x - 4,13,x[] 202,2,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 - 6*x - 17,7,x^3 + 3*x^2 - 18*x - 37,11,x^3 + 9*x^2 + 24*x + 17,13,x^3 + 3*x^2 - 36*x - 127[] 202,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + x^3 - 8*x^2 + x + 8,5,x^4 - 3*x^3 - 4*x^2 + 7*x - 2,7,x^4 - 2*x^3 - 9*x^2 + 3*x + 13,11,x^4 - x^3 - 28*x^2 + 39*x - 8,13,x^4 - x^3 - 16*x^2 - 19*x - 4[] 203,1,2,x - 1,3,x - 2,5,x - 2,7,x - 1,11,x + 4,13,x + 2[] 203,2,2,x + 2,3,x + 1,5,x + 4,7,x - 1,11,x - 2,13,x - 4[] 203,3,2,x + 1,3,x + 1,5,x - 1,7,x - 1,11,x + 5,13,x + 5[] 203,4,2,x^2 + 2*x + 1,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 + 2*x + 1,11,x^2 + x - 4,13,x^2 - 5*x + 2[] 203,5,2,x^2 - 4*x + 4,3,x^2 - 2*x - 1,5,x^2 - 8,7,x^2 + 2*x + 1,11,x^2 + 4*x - 4,13,x^2 - 8*x + 8[] 203,6,2,x^3 + x^2 - 3*x - 1,3,x^3 + 3*x^2 - x - 5,5,x^3 + 5*x^2 + 3*x - 5,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 5*x^2 - 5*x - 1,13,x^3 + 15*x^2 + 75*x + 125[] 203,7,2,x^5 - 2*x^4 - 8*x^3 + 14*x^2 + 9*x - 6,3,x^5 + 2*x^4 - 10*x^3 - 18*x^2 + 11*x + 2,5,x^5 - 5*x^4 - 3*x^3 + 29*x^2 + 6*x - 24,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - 3*x^4 - 39*x^3 + 117*x^2 + 270*x - 648,13,x^5 - 15*x^4 + 53*x^3 + 147*x^2 - 1082*x + 1432[] 204,1,2,x,3,x + 1,5,x + 1,7,x - 4,11,x - 3,13,x - 3[] 204,2,2,x,3,x - 1,5,x - 1,7,x,11,x - 5,13,x + 5[] 205,1,2,x + 1,3,x - 2,5,x + 1,7,x - 2,11,x - 6,13,x - 2[] 205,2,2,x - 1,3,x - 2,5,x - 1,7,x - 2,11,x,13,x + 4[] 205,3,2,x + 1,3,x,5,x - 1,7,x + 4,11,x,13,x + 2[] 205,4,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 3*x - 9,11,x^2 + 8*x + 11,13,x^2 + 3*x - 9[] 205,5,2,x^2 + x - 3,3,x^2 + 6*x + 9,5,x^2 - 2*x + 1,7,x^2 + 3*x - 1,11,x^2 + 6*x + 9,13,x^2 + x - 29[] 205,6,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 2*x^2 - 5*x + 2,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 9*x^2 + 23*x + 14,11,x^3 - 4*x^2 - 7*x + 26,13,x^3 + 3*x^2 - x - 2[] 205,7,2,x^3 - 4*x - 1,3,x^3 - 2*x^2 - 5*x + 2,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - x^2 - 5*x - 2,11,x^3 - 4*x^2 - x + 8,13,x^3 - x^2 - 15*x + 28[] 206,1,2,x + 1,3,x - 2,5,x - 4,7,x,11,x + 6,13,x + 2[] 206,2,2,x^2 + 2*x + 1,3,x^2 - x - 7,5,x^2 - x - 7,7,x^2 + 3*x - 5,11,x^2 - 8*x + 16,13,x^2 - 2*x - 28[] 206,3,2,x^2 + 2*x + 1,3,x^2 + 3*x - 1,5,x^2 + 5*x + 3,7,x^2 - 5*x + 3,11,x^2,13,x^2 - 6*x - 4[] 206,4,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 5*x^2 + 12*x - 5,5,x^4 - 7*x^2 + 6*x - 1,7,x^4 - 2*x^3 - 17*x^2 + 50*x - 31,11,x^4 - 4*x^3 - 24*x^2 + 48*x + 80,13,x^4 - 28*x^2 - 48*x - 16[] 207,1,2,x + 1,3,x,5,x,7,x + 2,11,x + 4,13,x + 6[] 207,2,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 8,13,x^2[] 207,3,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 8,13,x^2[] 207,4,2,x^2 - 5,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 8*x + 16,13,x^2 - 20[] 207,5,2,x^2 - x - 1,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 - 6*x + 4,13,x^2 - 6*x + 9[] 208,1,2,x,3,x + 1,5,x + 1,7,x + 5,11,x - 2,13,x + 1[] 208,2,2,x,3,x,5,x - 2,7,x - 2,11,x - 2,13,x + 1[] 208,3,2,x,3,x - 3,5,x + 1,7,x + 1,11,x - 2,13,x + 1[] 208,4,2,x,3,x + 1,5,x + 3,7,x - 1,11,x + 6,13,x - 1[] 208,5,2,x^2,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 - x - 4,11,x^2 - 2*x - 16,13,x^2 - 2*x + 1[] 209,1,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x - 2[] 209,2,2,x^2 - 2,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2 + 4*x + 2,11,x^2 + 2*x + 1,13,x^2 + 4*x - 14[] 209,3,2,x^5 - 2*x^4 - 6*x^3 + 10*x^2 + 5*x - 4,3,x^5 - x^4 - 9*x^3 + 11*x^2 + 7*x - 1,5,x^5 + 5*x^4 - 3*x^3 - 33*x^2 - 9*x + 19,7,x^5 - 6*x^4 - x^3 + 62*x^2 - 119*x + 64,11,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,13,x^5 - 4*x^4 - 9*x^3 + 26*x^2 + 37*x + 2[] 209,4,2,x^7 + x^6 - 14*x^5 - 10*x^4 + 59*x^3 + 27*x^2 - 66*x - 30,3,x^7 - 2*x^6 - 14*x^5 + 28*x^4 + 46*x^3 - 100*x^2 - 17*x + 64,5,x^7 - 2*x^6 - 20*x^5 + 34*x^4 + 88*x^3 - 156*x^2 + 57*x - 6,7,x^7 - 10*x^6 + 17*x^5 + 86*x^4 - 185*x^3 - 316*x^2 + 394*x + 512,11,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,13,x^7 + 4*x^6 - 51*x^5 - 194*x^4 + 639*x^3 + 2082*x^2 - 2550*x - 5716[] 210,1,2,x + 1,3,x + 1,5,x + 1,7,x + 1,11,x + 4,13,x + 2[] 210,2,2,x + 1,3,x - 1,5,x - 1,7,x - 1,11,x,13,x - 2[] 210,3,2,x - 1,3,x + 1,5,x - 1,7,x - 1,11,x - 4,13,x + 2[] 210,4,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x,13,x - 2[] 210,5,2,x - 1,3,x - 1,5,x - 1,7,x + 1,11,x + 4,13,x + 2[] Total time: 21.779 seconds, Total memory usage: 8.34MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:42:15 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [210..220] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 08:41:52 on modular [Seed = 2740207330] ------------------------------------- 210,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 210,2,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,3,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1 - 1,11,$.1 - 4,13,$.1 + 2[] 210,4,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,5,2,$.1 - 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 211,1,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - x - 1,11,x^2 + 6*x + 9,13,x^2 - 8*x + 11[] 211,2,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 - x - 4,5,x^3 + 5*x^2 + 2*x - 4,7,x^3 + 3*x^2 - x - 2,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 - x^2 - 21*x + 37[] 211,3,2,x^3 + 2*x^2 - x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 8*x^2 + 19*x + 13,7,x^3 - 2*x^2 - 15*x + 29,11,x^3 + 2*x^2 - 29*x - 71,13,x^3 + 3*x^2 - 4*x + 1[] 211,4,2,x^9 + x^8 - 14*x^7 - 11*x^6 + 66*x^5 + 36*x^4 - 123*x^3 - 38*x^2 + 72*x + 8,3,x^9 + x^8 - 20*x^7 - 17*x^6 + 128*x^5 + 80*x^4 - 292*x^3 - 72*x^2 + 224*x - 32,5,x^9 - 15*x^8 + 83*x^7 - 189*x^6 + 63*x^5 + 377*x^4 - 410*x^3 + 10*x^2 + 51*x - 3,7,x^9 + 2*x^8 - 35*x^7 - 57*x^6 + 322*x^5 + 200*x^4 - 984*x^3 + 352*x^2 + 384*x - 192,11,x^9 - 13*x^8 + 31*x^7 + 235*x^6 - 1233*x^5 + 671*x^4 + 5452*x^3 - 9568*x^2 + 3705*x - 333,13,x^9 + 4*x^8 - 37*x^7 - 52*x^6 + 480*x^5 - 186*x^4 - 1768*x^3 + 2169*x^2 + 272*x - 931[] 212,1,2,x,3,x - 2,5,x - 2,7,x,11,x + 4,13,x + 2[] 212,2,2,x,3,x + 1,5,x + 2,7,x + 2,11,x - 2,13,x + 7[] 212,3,2,x^3,3,x^3 + 3*x^2 - 3*x - 7,5,x^3 - 12*x - 12,7,x^3 - 6*x^2 + 28,11,x^3 - 6*x^2 - 12*x + 84,13,x^3 - 15*x^2 + 75*x - 125[] 213,1,2,x - 1,3,x - 1,5,x - 2,7,x - 2,11,x,13,x + 2[] 213,2,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 6*x + 9,11,x^2 + 4*x - 1,13,x^2 + 5*x - 5[] 213,3,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 + 3*x - 1[] 213,4,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 + 8*x + 11,13,x^2 + x - 11[] 213,5,2,x^4 - 3*x^3 - 2*x^2 + 7*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 3*x^3 - 5*x^2 - 4*x + 4,7,x^4 - 6*x^3 + 7*x^2 + 6*x - 4,11,x^4 - 2*x^3 - 15*x^2 + 36*x - 16,13,x^4 - 5*x^3 - 11*x^2 + 40*x + 4[] 214,1,2,x + 1,3,x - 1,5,x + 4,7,x + 2,11,x + 3,13,x + 1[] 214,2,2,x + 1,3,x + 2,5,x + 1,7,x - 4,11,x + 6,13,x + 4[] 214,3,2,x - 1,3,x - 1,5,x,7,x - 2,11,x + 3,13,x + 1[] 214,4,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x + 2,13,x - 4[] 214,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 4*x + 1,7,x^2 + 2*x - 2,11,x^2 - 2*x - 2,13,x^2 - 2*x - 2[] 214,6,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 + 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 2*x - 2[] 215,1,2,x,3,x,5,x + 1,7,x + 2,11,x + 1,13,x + 1[] 215,2,2,x^3 + 2*x^2 - 3*x - 3,3,x^3 - x^2 - 4*x + 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 3*x^2 - 6*x - 7,11,x^3 - 9*x^2 + 107,13,x^3 + 2*x^2 - 16*x - 8[] 215,3,2,x^5 - 2*x^4 - 7*x^3 + 13*x^2 + 5*x - 4,3,x^5 + x^4 - 16*x^3 - 7*x^2 + 64*x - 16,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - 5*x^4 - 14*x^3 + 97*x^2 - 58*x - 160,11,x^5 + 6*x^4 + x^3 - 43*x^2 - 59*x - 12,13,x^5 - 5*x^4 - 50*x^3 + 284*x^2 + 224*x - 2000[] 215,4,2,x^6 - 3*x^5 - 5*x^4 + 17*x^3 + 3*x^2 - 17*x - 3,3,x^6 - 4*x^5 - 5*x^4 + 30*x^3 - 20*x^2 + 1,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,7,x^6 - 8*x^5 + x^4 + 92*x^3 - 72*x^2 - 194*x - 31,11,x^6 - 41*x^4 + 12*x^3 + 322*x^2 + 88*x - 93,13,x^6 - 6*x^5 - 20*x^4 + 104*x^3 + 144*x^2 - 352*x - 448[] 216,1,2,x,3,x,5,x + 4,7,x + 3,11,x + 4,13,x - 1[] 216,2,2,x,3,x,5,x + 1,7,x - 3,11,x - 5,13,x - 4[] 216,3,2,x,3,x,5,x - 1,7,x - 3,11,x + 5,13,x - 4[] 216,4,2,x,3,x,5,x - 4,7,x + 3,11,x - 4,13,x - 1[] 217,1,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 9*x - 9,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 6*x^2 + 3*x - 19,13,x^3 + 3*x^2 - 18*x - 37[] 217,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 27*x + 27,13,x^3 + 3*x^2 - 24*x + 1[] 217,3,2,x^4 - 5*x^2 + x + 1,3,x^4 - 3*x^3 - 2*x^2 + 9*x - 4,5,x^4 - 4*x^3 + x^2 + 5*x - 2,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 23*x^2 + 81*x - 68,13,x^4 + x^3 - 18*x^2 - 37*x - 2[] 217,4,2,x^5 - 3*x^4 - 5*x^3 + 16*x^2 + 6*x - 19,3,x^5 - 3*x^4 - 6*x^3 + 15*x^2 + 8*x - 16,5,x^5 - 17*x^3 - 5*x^2 + 56*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 13*x^3 + 39*x^2 + 48*x + 8,13,x^5 + 3*x^4 - 14*x^3 - 47*x^2 - 36*x - 4[] 218,1,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x - 3,13,x + 4[] 218,2,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 - 2*x - 1,7,x^2 + 4*x + 2,11,x^2 + 2*x - 7,13,x^2 + 8*x + 8[] 218,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2 - 2*x + 1,13,x^2 - 4*x - 8[] 218,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x + 4,11,x^2 + 6*x + 4,13,x^2 - 3*x - 9[] 218,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 3*x + 8,5,x^3 + 3*x^2 - 6*x - 12,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 3*x^2 - 6*x + 12,13,x^3 - 9*x^2 + 15*x + 16[] 219,1,2,x - 1,3,x + 1,5,x + 4,7,x - 2,11,x + 4,13,x + 2[] 219,2,2,x + 2,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x + 2[] 219,3,2,x,3,x - 1,5,x + 3,7,x + 4,11,x,13,x + 4[] 219,4,2,x^4 - x^3 - 6*x^2 + 4*x + 4,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 9*x^3 + 25*x^2 - 21*x + 2,7,x^4 + 4*x^3 - 8*x^2 - 12*x + 16,11,x^4 - 2*x^3 - 20*x^2 + 52*x - 32,13,x^4 - 6*x^3 - 4*x^2 + 12*x + 8[] 219,5,2,x^6 + x^5 - 9*x^4 - 5*x^3 + 20*x^2 + 4*x - 4,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 5*x^5 - 7*x^4 + 49*x^3 + 20*x^2 - 128*x - 64,7,x^6 - 8*x^5 + 4*x^4 + 92*x^3 - 216*x^2 + 160*x - 32,11,x^6 + 2*x^5 - 40*x^4 - 20*x^3 + 336*x^2 - 240*x + 32,13,x^6 - 4*x^5 - 28*x^4 + 108*x^3 + 88*x^2 - 240*x + 32[] Errors: /home/mfd/gomagma: line 2: 24258 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:43:11 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [210..218] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:42:52 on modular [Seed = 2874947222] ------------------------------------- 210,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 210,2,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,3,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1 - 1,11,$.1 - 4,13,$.1 + 2[] 210,4,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 1,11,$.1,13,$.1 - 2[] 210,5,2,$.1 - 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1 + 4,13,$.1 + 2[] 211,1,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - x - 1,11,x^2 + 6*x + 9,13,x^2 - 8*x + 11[] 211,2,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 - x - 4,5,x^3 + 5*x^2 + 2*x - 4,7,x^3 + 3*x^2 - x - 2,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 - x^2 - 21*x + 37[] 211,3,2,x^3 + 2*x^2 - x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 8*x^2 + 19*x + 13,7,x^3 - 2*x^2 - 15*x + 29,11,x^3 + 2*x^2 - 29*x - 71,13,x^3 + 3*x^2 - 4*x + 1[] 211,4,2,x^9 + x^8 - 14*x^7 - 11*x^6 + 66*x^5 + 36*x^4 - 123*x^3 - 38*x^2 + 72*x + 8,3,x^9 + x^8 - 20*x^7 - 17*x^6 + 128*x^5 + 80*x^4 - 292*x^3 - 72*x^2 + 224*x - 32,5,x^9 - 15*x^8 + 83*x^7 - 189*x^6 + 63*x^5 + 377*x^4 - 410*x^3 + 10*x^2 + 51*x - 3,7,x^9 + 2*x^8 - 35*x^7 - 57*x^6 + 322*x^5 + 200*x^4 - 984*x^3 + 352*x^2 + 384*x - 192,11,x^9 - 13*x^8 + 31*x^7 + 235*x^6 - 1233*x^5 + 671*x^4 + 5452*x^3 - 9568*x^2 + 3705*x - 333,13,x^9 + 4*x^8 - 37*x^7 - 52*x^6 + 480*x^5 - 186*x^4 - 1768*x^3 + 2169*x^2 + 272*x - 931[] 212,1,2,x,3,x - 2,5,x - 2,7,x,11,x + 4,13,x + 2[] 212,2,2,x,3,x + 1,5,x + 2,7,x + 2,11,x - 2,13,x + 7[] 212,3,2,x^3,3,x^3 + 3*x^2 - 3*x - 7,5,x^3 - 12*x - 12,7,x^3 - 6*x^2 + 28,11,x^3 - 6*x^2 - 12*x + 84,13,x^3 - 15*x^2 + 75*x - 125[] 213,1,2,x - 1,3,x - 1,5,x - 2,7,x - 2,11,x,13,x + 2[] 213,2,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 6*x + 9,11,x^2 + 4*x - 1,13,x^2 + 5*x - 5[] 213,3,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 + 3*x - 1[] 213,4,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 + 8*x + 11,13,x^2 + x - 11[] 213,5,2,x^4 - 3*x^3 - 2*x^2 + 7*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 3*x^3 - 5*x^2 - 4*x + 4,7,x^4 - 6*x^3 + 7*x^2 + 6*x - 4,11,x^4 - 2*x^3 - 15*x^2 + 36*x - 16,13,x^4 - 5*x^3 - 11*x^2 + 40*x + 4[] 214,1,2,x + 1,3,x - 1,5,x + 4,7,x + 2,11,x + 3,13,x + 1[] 214,2,2,x + 1,3,x + 2,5,x + 1,7,x - 4,11,x + 6,13,x + 4[] 214,3,2,x - 1,3,x - 1,5,x,7,x - 2,11,x + 3,13,x + 1[] 214,4,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x + 2,13,x - 4[] 214,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 4*x + 1,7,x^2 + 2*x - 2,11,x^2 - 2*x - 2,13,x^2 - 2*x - 2[] 214,6,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 + 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 2*x - 2[] 215,1,2,x,3,x,5,x + 1,7,x + 2,11,x + 1,13,x + 1[] 215,2,2,x^3 + 2*x^2 - 3*x - 3,3,x^3 - x^2 - 4*x + 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 3*x^2 - 6*x - 7,11,x^3 - 9*x^2 + 107,13,x^3 + 2*x^2 - 16*x - 8[] 215,3,2,x^5 - 2*x^4 - 7*x^3 + 13*x^2 + 5*x - 4,3,x^5 + x^4 - 16*x^3 - 7*x^2 + 64*x - 16,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - 5*x^4 - 14*x^3 + 97*x^2 - 58*x - 160,11,x^5 + 6*x^4 + x^3 - 43*x^2 - 59*x - 12,13,x^5 - 5*x^4 - 50*x^3 + 284*x^2 + 224*x - 2000[] 215,4,2,x^6 - 3*x^5 - 5*x^4 + 17*x^3 + 3*x^2 - 17*x - 3,3,x^6 - 4*x^5 - 5*x^4 + 30*x^3 - 20*x^2 + 1,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,7,x^6 - 8*x^5 + x^4 + 92*x^3 - 72*x^2 - 194*x - 31,11,x^6 - 41*x^4 + 12*x^3 + 322*x^2 + 88*x - 93,13,x^6 - 6*x^5 - 20*x^4 + 104*x^3 + 144*x^2 - 352*x - 448[] 216,1,2,x,3,x,5,x + 4,7,x + 3,11,x + 4,13,x - 1[] 216,2,2,x,3,x,5,x + 1,7,x - 3,11,x - 5,13,x - 4[] 216,3,2,x,3,x,5,x - 1,7,x - 3,11,x + 5,13,x - 4[] 216,4,2,x,3,x,5,x - 4,7,x + 3,11,x - 4,13,x - 1[] 217,1,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 9*x - 9,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 6*x^2 + 3*x - 19,13,x^3 + 3*x^2 - 18*x - 37[] 217,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 27*x + 27,13,x^3 + 3*x^2 - 24*x + 1[] 217,3,2,x^4 - 5*x^2 + x + 1,3,x^4 - 3*x^3 - 2*x^2 + 9*x - 4,5,x^4 - 4*x^3 + x^2 + 5*x - 2,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 23*x^2 + 81*x - 68,13,x^4 + x^3 - 18*x^2 - 37*x - 2[] 217,4,2,x^5 - 3*x^4 - 5*x^3 + 16*x^2 + 6*x - 19,3,x^5 - 3*x^4 - 6*x^3 + 15*x^2 + 8*x - 16,5,x^5 - 17*x^3 - 5*x^2 + 56*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 13*x^3 + 39*x^2 + 48*x + 8,13,x^5 + 3*x^4 - 14*x^3 - 47*x^2 - 36*x - 4[] 218,1,2,x - 1,3,x + 2,5,x + 3,7,x + 4,11,x - 3,13,x + 4[] 218,2,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 - 2*x - 1,7,x^2 + 4*x + 2,11,x^2 + 2*x - 7,13,x^2 + 8*x + 8[] 218,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2 - 2*x + 1,13,x^2 - 4*x - 8[] 218,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x + 4,11,x^2 + 6*x + 4,13,x^2 - 3*x - 9[] 218,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 3*x + 8,5,x^3 + 3*x^2 - 6*x - 12,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 3*x^2 - 6*x + 12,13,x^3 - 9*x^2 + 15*x + 16[] Total time: 18.959 seconds, Total memory usage: 7.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 08:49:40 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [218..226] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 08:49:21 on modular [Seed = 3092194360] ------------------------------------- 218,1,2,$.1 - 1,3,$.1 + 2,5,$.1 + 3,7,$.1 + 4,11,$.1 - 3,13,$.1 + 4[] 218,2,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + 4*$.1 + 2,5,$.1^2 - 2*$.1 - 1,7,$.1^2 +
4*$.1 + 2,11,$.1^2 + 2*$.1 - 7,13,$.1^2 + 8*$.1 + 8[] 218,3,2,$.1^2 - 2*$.1 + 1,3,$.1^2 + 2*$.1 - 2,5,$.1^2 - 3,7,$.1^2 - 6*$.1 +
6,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 - 8[]
218,4,2,$.1^2 - 2*$.1 + 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 + 4*$.1 + 4,11,$.1^2 + 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[]
218,5,2,$.1^3 + 3*$.1^2 + 3*$.1 + 1,3,$.1^3 - 3*$.1^2 - 3*$.1 + 8,5,$.1^3 + 3*$.1^2 - 6*$.1 - 12,7,$.1^3 - 6*$.1^2 + 12*$.1 - 8,11,$.1^3 - 3*$.1^2 - 6*$.1 + 12,13,$.1^3 - 9*$.1^2 + 15*$.1 + 16[]
219,1,2,x - 1,3,x + 1,5,x + 4,7,x - 2,11,x + 4,13,x + 2[]
219,2,2,x + 2,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x + 2[]
219,3,2,x,3,x - 1,5,x + 3,7,x + 4,11,x,13,x + 4[]
219,4,2,x^4 - x^3 - 6*x^2 + 4*x + 4,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 -
9*x^3 + 25*x^2 - 21*x + 2,7,x^4 + 4*x^3 - 8*x^2 - 12*x + 16,11,x^4 - 2*x^3 -
20*x^2 + 52*x - 32,13,x^4 - 6*x^3 - 4*x^2 + 12*x + 8[]
219,5,2,x^6 + x^5 - 9*x^4 - 5*x^3 + 20*x^2 + 4*x - 4,3,x^6 - 6*x^5 + 15*x^4 -
20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 5*x^5 - 7*x^4 + 49*x^3 + 20*x^2 - 128*x -
64,7,x^6 - 8*x^5 + 4*x^4 + 92*x^3 - 216*x^2 + 160*x - 32,11,x^6 + 2*x^5 - 40*x^4
- 20*x^3 + 336*x^2 - 240*x + 32,13,x^6 - 4*x^5 - 28*x^4 + 108*x^3 + 88*x^2 -
240*x + 32[]
220,1,2,x,3,x + 2,5,x - 1,7,x + 4,11,x + 1,13,x + 4[]
220,2,2,x,3,x - 2,5,x - 1,7,x,11,x - 1,13,x[]
221,1,2,x - 1,3,x - 2,5,x - 2,7,x - 2,11,x + 6,13,x + 1[]
221,2,2,x + 1,3,x,5,x - 4,7,x + 2,11,x - 6,13,x + 1[]
221,3,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + x - 1,11,x^2 + 3*x -
9,13,x^2 + 2*x + 1[]
221,4,2,x^2 - 5,3,x^2 - 2*x - 4,5,x^2 + 2*x - 4,7,x^2 - 4*x + 4,11,x^2 - 4*x +
4,13,x^2 + 2*x + 1[]
221,5,2,x^2 + x - 5,3,x^2 - x - 5,5,x^2 + 2*x + 1,7,x^2 + 5*x + 1,11,x^2 - 3*x -
3,13,x^2 + 2*x + 1[]
221,6,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 - x - 4,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 +
9*x^2 + 23*x + 16,11,x^3 + 7*x^2 + 11*x + 4,13,x^3 - 3*x^2 + 3*x - 1[]
221,7,2,x^6 - x^5 - 9*x^4 + 6*x^3 + 19*x^2 - 5*x - 3,3,x^6 - x^5 - 11*x^4 +
12*x^3 + 28*x^2 - 36*x + 4,5,x^6 + 2*x^5 - 15*x^4 - 16*x^3 + 60*x^2 - 16*x -
12,7,x^6 - 7*x^5 - 7*x^4 + 112*x^3 - 56*x^2 - 400*x + 208,11,x^6 + x^5 - 19*x^4
- 8*x^3 + 88*x^2 + 16*x - 48,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x +
1[]
222,1,2,x + 1,3,x + 1,5,x - 2,7,x,11,x + 4,13,x - 6[]
222,2,2,x + 1,3,x + 1,5,x + 4,7,x - 3,11,x - 5,13,x - 3[]
222,3,2,x + 1,3,x - 1,5,x - 4,7,x + 1,11,x + 1,13,x + 3[]
222,4,2,x - 1,3,x + 1,5,x,7,x - 3,11,x - 1,13,x - 1[]
222,5,2,x - 1,3,x - 1,5,x,7,x + 1,11,x - 3,13,x + 1[]
223,1,2,x^2 + 2*x - 1,3,x^2 + 2*x - 1,5,x^2 + 4*x + 2,7,x^2 - 2,11,x^2 - 2*x -
1,13,x^2 - 4*x + 2[]
223,2,2,x^4 + 4*x^3 + 2*x^2 - 5*x - 3,3,x^4 - 4*x^2 + x + 1,5,x^4 + 3*x^3 - x^2
- 7*x - 3,7,x^4 + 6*x^3 - 31*x - 3,11,x^4 + 10*x^3 + 24*x^2 - 21*x - 83,13,x^4 +
9*x^3 + 13*x^2 - 19*x - 31[]
223,3,2,x^12 - 7*x^11 + 6*x^10 + 57*x^9 - 122*x^8 - 105*x^7 + 430*x^6 - 73*x^5 -
499*x^4 + 242*x^3 + 143*x^2 - 52*x - 19,3,x^12 - 27*x^10 + 7*x^9 + 263*x^8 -
131*x^7 - 1091*x^6 + 816*x^5 + 1600*x^4 - 1752*x^3 + 128*x^2 + 288*x - 64,5,x^12
- 7*x^11 - 11*x^10 + 157*x^9 - 97*x^8 - 1096*x^7 + 1354*x^6 + 2692*x^5 -
3952*x^4 - 1744*x^3 + 3200*x^2 - 512*x - 128,7,x^12 - 2*x^11 - 35*x^10 + 55*x^9
+ 385*x^8 - 527*x^7 - 1444*x^6 + 2034*x^5 + 1158*x^4 - 2761*x^3 + 1299*x^2 -
174*x + 2,11,x^12 - 6*x^11 - 53*x^10 + 329*x^9 + 919*x^8 - 6597*x^7 - 4941*x^6 +
58510*x^5 - 14616*x^4 - 213896*x^3 + 167520*x^2 + 204800*x - 194048,13,x^12 -
x^11 - 81*x^10 + 89*x^9 + 2061*x^8 - 2766*x^7 - 17434*x^6 + 27992*x^5 +
28880*x^4 - 34320*x^3 - 26304*x^2 - 1216*x + 896[]
224,1,2,x,3,x + 2,5,x,7,x + 1,11,x + 4,13,x + 4[]
224,2,2,x,3,x - 2,5,x,7,x - 1,11,x - 4,13,x + 4[]
224,3,2,x^2,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 - 2*x + 1,11,x^2 + 4*x -
16,13,x^2 - 6*x + 4[]
224,4,2,x^2,3,x^2 - 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 2*x + 1,11,x^2 - 4*x -
16,13,x^2 - 6*x + 4[]
225,1,2,x,3,x,5,x,7,x + 5,11,x,13,x + 5[]
225,2,2,x,3,x,5,x,7,x - 5,11,x,13,x - 5[]
225,3,2,x + 1,3,x,5,x,7,x,11,x - 4,13,x - 2[]
225,4,2,x - 2,3,x,5,x,7,x - 3,11,x + 2,13,x + 1[]
225,5,2,x + 2,3,x,5,x,7,x + 3,11,x + 2,13,x - 1[]
225,6,2,x^2 - 5,3,x^2,5,x^2,7,x^2,11,x^2,13,x^2[]
226,1,2,x - 1,3,x + 2,5,x + 4,7,x,11,x + 4,13,x + 2[]
226,2,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 + 4*x + 2,7,x^2 + 4*x - 4,11,x^2 + 8*x +
16,13,x^2 - 4*x + 4[]
226,3,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 4*x + 4,7,x^2,11,x^2 - 4*x -
8,13,x^2 + 4*x - 8[]
226,4,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 6*x^2 + 12*x - 4,5,x^4 -
4*x^3 - 4*x^2 + 16*x - 4,7,x^4 + 4*x^3 - 4*x^2 - 16*x + 16,11,x^4 - 20*x^2 +
80,13,x^4 - 4*x^3 - 24*x^2 + 96*x - 64[]

Total time: 18.139 seconds, Total memory usage: 7.55MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 09:26:37 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [226..234] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 09:26:19 on modular  [Seed = 1470153916]
-------------------------------------

226,1,2,$.1 - 1,3,$.1 + 2,5,$.1 + 4,7,$.1,11,$.1 + 4,13,$.1 + 2[]
226,2,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2,5,$.1^2 + 4*$.1 + 2,7,$.1^2 + 4*$.1 - 4,11,$.1^2 + 8*$.1 + 16,13,$.1^2 - 4*$.1 + 4[] 226,3,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2*$.1 - 2,5,$.1^2 - 4*$.1 + 4,7,$.1^2,11,$.1^2 - 4*$.1 - 8,13,$.1^2 + 4*$.1 - 8[]
226,4,2,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,3,$.1^4 - 2*$.1^3 - 6*$.1^2 + 12*$.1 - 4,5,$.1^4 - 4*$.1^3 - 4*$.1^2 + 16*$.1 - 4,7,$.1^4 + 4*$.1^3 - 4*$.1^2 - 16*$.1 + 16,11,$.1^4 - 20*$.1^2 + 80,13,$.1^4 - 4*$.1^3 - 24*$.1^2 + 96*$.1 -
64[]
227,1,2,x^2 - 2,3,x^2 + 4*x + 4,5,x^2 - 2,7,x^2 + 2*x - 7,11,x^2 - 2*x -
7,13,x^2 + 8*x + 8[]
227,2,2,x^2 - 5,3,x^2 - 3*x + 1,5,x^2 + 4*x + 4,7,x^2 - 7*x + 11,11,x^2 - x -
1,13,x^2 + 2*x - 4[]
227,3,2,x^2 - 2*x + 1,3,x^2 + x - 7,5,x^2 - 4*x + 4,7,x^2 - 3*x - 5,11,x^2 - 5*x
- 1,13,x^2 - 2*x - 28[]
227,4,2,x^3 + 2*x^2 - x - 1,3,x^3 - x^2 - 2*x + 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3
+ 6*x^2 + 5*x - 13,11,x^3 + x^2 - 16*x - 29,13,x^3 + 9*x^2 + 27*x + 27[]
227,5,2,x^10 - 17*x^8 - 3*x^7 + 98*x^6 + 40*x^5 - 218*x^4 - 148*x^3 + 136*x^2 +
144*x + 32,3,x^10 - x^9 - 17*x^8 + 8*x^7 + 99*x^6 - 8*x^5 - 210*x^4 + 5*x^3 +
152*x^2 - 20*x - 4,5,x^10 - 7*x^9 - 18*x^8 + 205*x^7 - 66*x^6 - 1746*x^5 +
1594*x^4 + 5648*x^3 - 5408*x^2 - 5712*x + 5472,7,x^10 - 37*x^8 + 3*x^7 + 422*x^6
- 37*x^5 - 1575*x^4 - 216*x^3 + 2014*x^2 + 774*x - 265,11,x^10 + 3*x^9 - 64*x^8
- 165*x^7 + 1442*x^6 + 2675*x^5 - 14456*x^4 - 11754*x^3 + 61970*x^2 - 14195*x -
38209,13,x^10 - 23*x^9 + 191*x^8 - 505*x^7 - 2032*x^6 + 17104*x^5 - 37704*x^4 -
11504*x^3 + 184640*x^2 - 292992*x + 151808[]
228,1,2,x,3,x + 1,5,x - 2,7,x,11,x - 2,13,x - 2[]
228,2,2,x,3,x + 1,5,x + 3,7,x - 1,11,x + 5,13,x + 6[]
228,3,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 3*x - 6,7,x^2 - x - 8,11,x^2 + 3*x -
6,13,x^2 - 4*x + 4[]
229,1,2,x + 1,3,x - 1,5,x + 3,7,x - 2,11,x + 3,13,x + 6[]
229,2,2,x^6 + 4*x^5 - 12*x^3 - 3*x^2 + 9*x - 1,3,x^6 + 6*x^5 + 7*x^4 - 17*x^3 -
36*x^2 - 6*x + 13,5,x^6 + 3*x^5 - 12*x^4 - 39*x^3 + 19*x^2 + 121*x + 79,7,x^6 +
5*x^5 - 16*x^4 - 127*x^3 - 155*x^2 + 213*x + 386,11,x^6 + 22*x^5 + 190*x^4 +
815*x^3 + 1815*x^2 + 1996*x + 853,13,x^6 - x^5 - 34*x^4 + 121*x^3 - 111*x^2 -
21*x + 46[]
229,3,2,x^11 - 5*x^10 - 4*x^9 + 50*x^8 - 26*x^7 - 165*x^6 + 152*x^5 + 193*x^4 -
207*x^3 - 50*x^2 + 52*x + 1,3,x^11 - 3*x^10 - 19*x^9 + 60*x^8 + 109*x^7 -
402*x^6 - 133*x^5 + 987*x^4 - 332*x^3 - 572*x^2 + 288*x - 16,5,x^11 - 28*x^9 +
3*x^8 + 204*x^7 - 23*x^6 - 397*x^5 + 238*x^3 + 21*x^2 - 44*x - 7,7,x^11 - x^10 -
33*x^9 + 26*x^8 + 342*x^7 - 293*x^6 - 1477*x^5 + 1416*x^4 + 2679*x^3 - 2815*x^2
- 1556*x + 1736,11,x^11 - 27*x^10 + 288*x^9 - 1447*x^8 + 2508*x^7 + 7057*x^6 -
38171*x^5 + 44023*x^4 + 51012*x^3 - 149100*x^2 + 103664*x - 22384,13,x^11 +
7*x^10 - 28*x^9 - 203*x^8 + 311*x^7 + 1849*x^6 - 1432*x^5 - 6708*x^4 + 1776*x^3
+ 8528*x^2 + 1984*x - 128[]
230,1,2,x^2 + 2*x + 1,3,x^2 + x - 5,5,x^2 + 2*x + 1,7,x^2 - x - 5,11,x^2 - 3*x -
3,13,x^2 - 7*x + 7[]
230,2,2,x^2 + 2*x + 1,3,x^2 - 3*x - 1,5,x^2 - 2*x + 1,7,x^2 - 3*x - 1,11,x^2 +
7*x + 9,13,x^2 - 3*x - 1[]
230,3,2,x^2 - 2*x + 1,3,x^2 - x - 1,5,x^2 - 2*x + 1,7,x^2 - x - 1,11,x^2 - x -
11,13,x^2 + 3*x - 29[]
230,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 9*x + 12,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 3*x^2 - 21*x + 64,11,x^3 - 3*x^2 - 39*x + 144,13,x^3 + x^2 - 15*x -
18[]
231,1,2,x + 1,3,x + 1,5,x + 2,7,x - 1,11,x + 1,13,x - 6[]
231,2,2,x^2 + x - 5,3,x^2 + 2*x + 1,5,x^2 - 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 2*x
+ 1,13,x^2 - 2*x + 1[]
231,3,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 2*x
+ 1,13,x^2 + 2*x - 19[]
231,4,2,x^3 - 6*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 15*x + 2,7,x^3 + 3*x^2 +
3*x + 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 15*x + 2[]
231,5,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 - 7*x +
26,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 4*x^2 - 27*x - 94[]
232,1,2,x,3,x + 1,5,x + 3,7,x - 2,11,x + 3,13,x + 5[]
232,2,2,x,3,x - 1,5,x - 1,7,x - 2,11,x - 3,13,x + 1[]
232,3,2,x^2,3,x^2 + 2*x - 1,5,x^2 + 2*x - 7,7,x^2 + 8*x + 16,11,x^2 + 2*x -
1,13,x^2 + 2*x - 31[]
232,4,2,x^3,3,x^3 - 2*x^2 - 5*x + 8,5,x^3 - 4*x^2 - 3*x + 10,7,x^3,11,x^3 -
2*x^2 - 29*x + 80,13,x^3 - 4*x^2 - 19*x + 2[]
233,1,2,x - 1,3,x + 2,5,x - 2,7,x - 4,11,x - 6,13,x - 6[]
233,2,2,x^7 + 2*x^6 - 6*x^5 - 10*x^4 + 10*x^3 + 8*x^2 - 7*x + 1,3,x^7 + 8*x^6 +
18*x^5 - 3*x^4 - 44*x^3 - 20*x^2 + 12*x + 1,5,x^7 + 3*x^6 - 15*x^5 - 40*x^4 +
41*x^3 + 79*x^2 - 29*x - 43,7,x^7 + 17*x^6 + 112*x^5 + 351*x^4 + 494*x^3 +
157*x^2 - 182*x - 41,11,x^7 - x^6 - 37*x^5 + 34*x^4 + 402*x^3 - 271*x^2 - 1242*x
+ 471,13,x^7 + 12*x^6 + 4*x^5 - 464*x^4 - 2100*x^3 - 2956*x^2 - 753*x + 687[]
233,3,2,x^11 + 2*x^10 - 16*x^9 - 30*x^8 + 91*x^7 + 158*x^6 - 213*x^5 - 349*x^4 +
152*x^3 + 290*x^2 + 41*x - 19,3,x^11 - 10*x^10 + 28*x^9 + 29*x^8 - 277*x^7 +
394*x^6 + 162*x^5 - 716*x^4 + 250*x^3 + 312*x^2 - 138*x - 29,5,x^11 + x^10 -
35*x^9 - 20*x^8 + 429*x^7 + 109*x^6 - 2119*x^5 - 265*x^4 + 3880*x^3 + 336*x^2 -
1280*x - 128,7,x^11 - 15*x^10 + 72*x^9 - 53*x^8 - 514*x^7 + 1169*x^6 + 434*x^5 -
3161*x^4 + 1712*x^3 + 1552*x^2 - 1056*x - 144,11,x^11 + 5*x^10 - 23*x^9 -
164*x^8 - 92*x^7 + 1161*x^6 + 3112*x^5 + 2905*x^4 + 272*x^3 - 1248*x^2 - 720*x -
108,13,x^11 - 4*x^10 - 50*x^9 + 188*x^8 + 557*x^7 - 2440*x^6 - 237*x^5 +
6067*x^4 - 766*x^3 - 4762*x^2 + 247*x + 687[]
234,1,2,x + 1,3,x,5,x + 2,7,x + 2,11,x + 4,13,x + 1[]
234,2,2,x + 1,3,x,5,x - 1,7,x - 1,11,x - 2,13,x + 1[]
234,3,2,x - 1,3,x,5,x - 2,7,x + 2,11,x - 4,13,x + 1[]
234,4,2,x - 1,3,x,5,x + 2,7,x - 4,11,x - 4,13,x - 1[]
234,5,2,x - 1,3,x,5,x - 3,7,x + 1,11,x + 6,13,x - 1[]

Total time: 18.119 seconds, Total memory usage: 7.48MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 09:34:18 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [234..240] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 09:34:00 on modular  [Seed = 719174418]
-------------------------------------

234,1,2,$.1 + 1,3,$.1,5,$.1 + 2,7,$.1 + 2,11,$.1 + 4,13,$.1 + 1[]
234,2,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 - 1,11,$.1 - 2,13,$.1 + 1[]
234,3,2,$.1 - 1,3,$.1,5,$.1 - 2,7,$.1 + 2,11,$.1 - 4,13,$.1 + 1[]
234,4,2,$.1 - 1,3,$.1,5,$.1 + 2,7,$.1 - 4,11,$.1 - 4,13,$.1 - 1[]
234,5,2,$.1 - 1,3,$.1,5,$.1 - 3,7,$.1 + 1,11,$.1 + 6,13,$.1 - 1[]
235,1,2,x + 1,3,x + 1,5,x + 1,7,x - 1,11,x - 3,13,x - 3[]
235,2,2,x - 2,3,x - 2,5,x + 1,7,x + 2,11,x,13,x - 3[]
235,3,2,x + 1,3,x + 1,5,x - 1,7,x - 1,11,x + 3,13,x + 3[]
235,4,2,x^5 + 4*x^4 - 12*x^2 - 4*x + 7,3,x^5 + 5*x^4 + 3*x^3 - 13*x^2 - 13*x +
1,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 5*x^4 - 17*x^3 - 83*x^2 +
61*x + 227,11,x^5 + x^4 - 46*x^3 - 72*x^2 + 368*x + 656,13,x^5 + 11*x^4 + 18*x^3
- 156*x^2 - 632*x - 656[]
235,5,2,x^7 - x^6 - 10*x^5 + 8*x^4 + 28*x^3 - 17*x^2 - 19*x + 2,3,x^7 - x^6 -
15*x^5 + 13*x^4 + 57*x^3 - 37*x^2 - 42*x - 8,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 23*x^5 - 53*x^4 + 91*x^3 + 29*x^2 -
66*x + 16,11,x^7 - x^6 - 46*x^5 + 40*x^4 + 512*x^3 - 80*x^2 - 1408*x -
256,13,x^7 - 2*x^6 - 35*x^5 + 36*x^4 + 128*x^3 - 96*x^2 - 96*x + 32[]
236,1,2,x,3,x - 1,5,x - 3,7,x + 1,11,x - 6,13,x + 4[]
236,2,2,x,3,x + 1,5,x + 1,7,x + 3,11,x + 2,13,x[]
236,3,2,x^3,3,x^3 - 9*x + 1,5,x^3 + 4*x^2 + x - 3,7,x^3 - 8*x^2 + 15*x +
3,11,x^3 - 2*x^2 - 16*x + 8,13,x^3 - 4*x^2 - 12*x + 24[]
237,1,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 6*x +
7,13,x^2 + 2*x - 7[]
237,2,2,x^4 + 3*x^3 - x^2 - 5*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 +
4*x^3 - x^2 - 14*x - 9,7,x^4 + 2*x^3 - 20*x^2 - 40*x - 16,11,x^4 + 8*x^3 +
11*x^2 - 42*x - 89,13,x^4 + 6*x^3 - 21*x^2 - 74*x + 141[]
237,3,2,x^7 - 2*x^6 - 11*x^5 + 22*x^4 + 30*x^3 - 65*x^2 - 2*x + 23,3,x^7 - 7*x^6
+ 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,5,x^7 + 2*x^6 - 25*x^5 - 32*x^4 +
191*x^3 + 102*x^2 - 416*x + 32,7,x^7 - 4*x^6 - 23*x^5 + 98*x^4 + 12*x^3 -
264*x^2 + 48*x + 128,11,x^7 - 2*x^6 - 42*x^5 + 40*x^4 + 416*x^3 - 52*x^2 - 611*x
+ 116,13,x^7 - 6*x^6 - 16*x^5 + 194*x^4 - 528*x^3 + 616*x^2 - 315*x + 58[]
238,1,2,x + 1,3,x,5,x + 2,7,x + 1,11,x + 2,13,x[]
238,2,2,x + 1,3,x - 2,5,x - 4,7,x - 1,11,x + 4,13,x + 4[]
238,3,2,x - 1,3,x - 2,5,x,7,x + 1,11,x + 2,13,x + 2[]
238,4,2,x - 1,3,x + 2,5,x + 4,7,x - 1,11,x + 6,13,x + 2[]
238,5,2,x - 1,3,x,5,x - 2,7,x - 1,11,x,13,x + 2[]
238,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 2*x + 1,11,x^2 -
6*x + 4,13,x^2 - 4*x - 16[]
239,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 4*x^2 + 3*x - 1,7,x^3
+ 3*x^2 + 3*x + 1,11,x^3 + x^2 - 2*x - 1,13,x^3 + 7*x^2 + 14*x + 7[]
239,2,2,x^17 - 28*x^15 + x^14 + 319*x^13 - 17*x^12 - 1903*x^11 + 91*x^10 +
6377*x^9 - 125*x^8 - 11967*x^7 - 233*x^6 + 11733*x^5 + 503*x^4 - 5015*x^3 -
94*x^2 + 609*x + 49,3,x^17 - 3*x^16 - 35*x^15 + 110*x^14 + 468*x^13 - 1573*x^12
- 2977*x^11 + 11197*x^10 + 8880*x^9 - 42041*x^8 - 8213*x^7 + 80809*x^6 -
11957*x^5 - 70374*x^4 + 23710*x^3 + 20383*x^2 - 9684*x + 592,5,x^17 - 6*x^16 -
44*x^15 + 311*x^14 + 647*x^13 - 6439*x^12 - 1715*x^11 + 66664*x^10 - 47987*x^9 -
345487*x^8 + 500506*x^7 + 707930*x^6 - 1708498*x^5 + 168922*x^4 + 1466245*x^3 -
775724*x^2 - 64969*x + 43871,7,x^17 - 5*x^16 - 77*x^15 + 393*x^14 + 2276*x^13 -
12292*x^12 - 31088*x^11 + 193664*x^10 + 166432*x^9 - 1590464*x^8 + 251392*x^7 +
6211328*x^6 - 5164544*x^5 - 8086528*x^4 + 10784768*x^3 - 540672*x^2 - 1900544*x
- 262144,11,x^17 + x^16 - 123*x^15 - 202*x^14 + 6056*x^13 + 13619*x^12 -
149697*x^11 - 427543*x^10 + 1893660*x^9 + 6787983*x^8 - 10803586*x^7 -
53477248*x^6 + 15048164*x^5 + 195019206*x^4 + 50388863*x^3 - 305552905*x^2 -
115295798*x + 151629817,13,x^17 - 15*x^16 - 30*x^15 + 1407*x^14 - 3250*x^13 -
47272*x^12 + 199728*x^11 + 647712*x^10 - 4205376*x^9 - 2052928*x^8 +
38764288*x^7 - 25163008*x^6 - 147311616*x^5 + 180070400*x^4 + 144123904*x^3 -
224333824*x^2 + 9224192*x + 11583488[]
240,1,2,x,3,x + 1,5,x + 1,7,x + 4,11,x,13,x + 6[]
240,2,2,x,3,x + 1,5,x - 1,7,x,11,x - 4,13,x - 6[]
240,3,2,x,3,x + 1,5,x + 1,7,x - 4,11,x,13,x - 2[]
240,4,2,x,3,x - 1,5,x - 1,7,x,11,x - 4,13,x + 2[]

Total time: 18.079 seconds, Total memory usage: 7.16MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 09:40:29 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [240..248] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 09:40:08 on modular  [Seed = 32936361]
-------------------------------------

240,1,2,$.1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 4,11,$.1,13,$.1 + 6[]
240,2,2,$.1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 - 4,13,$.1 - 6[]
240,3,2,$.1,3,$.1 + 1,5,$.1 + 1,7,$.1 - 4,11,$.1,13,$.1 - 2[]
240,4,2,$.1,3,$.1 - 1,5,$.1 - 1,7,$.1,11,$.1 - 4,13,$.1 + 2[]
241,1,2,x^7 + 4*x^6 - 14*x^4 - 10*x^3 + 6*x^2 + 3*x - 1,3,x^7 + 3*x^6 - 5*x^5 -
19*x^4 - 4*x^3 + 14*x^2 + 8*x + 1,5,x^7 + 8*x^6 + 12*x^5 - 50*x^4 - 165*x^3 -
93*x^2 + 137*x + 127,7,x^7 + 7*x^6 - 3*x^5 - 98*x^4 - 138*x^3 + 127*x^2 + 260*x
+ 61,11,x^7 + 18*x^6 + 117*x^5 + 283*x^4 - 137*x^3 - 1559*x^2 - 1281*x +
1069,13,x^7 + x^6 - 48*x^5 - 62*x^4 + 533*x^3 + 860*x^2 + 13*x - 1[]
241,2,2,x^12 - 3*x^11 - 14*x^10 + 44*x^9 + 65*x^8 - 219*x^7 - 123*x^6 + 444*x^5
+ 105*x^4 - 328*x^3 - 45*x^2 + 18*x - 1,3,x^12 - x^11 - 25*x^10 + 25*x^9 +
224*x^8 - 210*x^7 - 888*x^6 + 725*x^5 + 1540*x^4 - 960*x^3 - 992*x^2 + 400*x +
64,5,x^12 - 6*x^11 - 14*x^10 + 134*x^9 - 68*x^8 - 797*x^7 + 1301*x^6 + 497*x^5 -
2193*x^4 + 1071*x^3 + 339*x^2 - 347*x + 62,7,x^12 - 3*x^11 - 33*x^10 + 96*x^9 +
245*x^8 - 854*x^7 + 263*x^6 + 855*x^5 - 588*x^4 - 131*x^3 + 200*x^2 - 53*x +
4,11,x^12 - 22*x^11 + 177*x^10 - 553*x^9 - 215*x^8 + 5545*x^7 - 12739*x^6 +
9811*x^5 + 3100*x^4 - 9672*x^3 + 5900*x^2 - 1460*x + 128,13,x^12 + 5*x^11 -
62*x^10 - 296*x^9 + 1425*x^8 + 6470*x^7 - 15049*x^6 - 64645*x^5 + 69802*x^4 +
288472*x^3 - 90512*x^2 - 441248*x - 52672[]
242,1,2,x + 1,3,x + 2,5,x + 3,7,x - 2,11,x,13,x - 5[]
242,2,2,x - 1,3,x + 2,5,x + 3,7,x + 2,11,x,13,x + 5[]
242,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 + 6*x + 6,11,x^2,13,x^2 +
6*x + 9[]
242,4,2,x^2 + 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 4*x +
4,11,x^2,13,x^2 - 2*x - 4[]
242,5,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2,13,x^2 -
6*x + 9[]
242,6,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 + 4*x +
4,11,x^2,13,x^2 + 2*x - 4[]
243,1,2,x,3,x,5,x,7,x + 4,11,x,13,x + 7[]
243,2,2,x,3,x,5,x,7,x - 5,11,x,13,x - 2[]
243,3,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2 + 2*x + 1,11,x^2 - 12,13,x^2 - 10*x +
25[]
243,4,2,x^2 - 6,3,x^2,5,x^2 - 6,7,x^2 - 4*x + 4,11,x^2 - 6,13,x^2 + 2*x + 1[]
243,5,2,x^3 + 3*x^2 - 3,3,x^3,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 + 3*x^2 - 6*x -
17,11,x^3 + 3*x^2 - 18*x - 3,13,x^3 + 3*x^2 - 6*x - 17[]
243,6,2,x^3 - 3*x^2 + 3,3,x^3,5,x^3 - 6*x^2 + 9*x - 3,7,x^3 + 3*x^2 - 6*x -
17,11,x^3 - 3*x^2 - 18*x + 3,13,x^3 + 3*x^2 - 6*x - 17[]
244,1,2,x,3,x,5,x + 3,7,x + 3,11,x + 1,13,x - 1[]
244,2,2,x^4,3,x^4 - 12*x^2 + 4*x + 16,5,x^4 - 5*x^3 + x^2 + 13*x + 2,7,x^4 + x^3
- 9*x^2 - 9*x - 2,11,x^4 + x^3 - 23*x^2 + 41*x - 18,13,x^4 - 5*x^3 - 3*x^2 +
17*x + 6[]
245,1,2,x + 2,3,x - 3,5,x + 1,7,x,11,x - 1,13,x - 3[]
245,2,2,x,3,x + 1,5,x - 1,7,x,11,x + 3,13,x + 5[]
245,3,2,x + 2,3,x + 3,5,x - 1,7,x,11,x - 1,13,x + 3[]
245,4,2,x^2 - 2,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2,11,x^2 + 6*x + 1,13,x^2 +
6*x + 7[]
245,5,2,x^2 + x - 4,3,x^2 - x - 4,5,x^2 + 2*x + 1,7,x^2,11,x^2 - x - 4,13,x^2 +
5*x + 2[]
245,6,2,x^2 - 2*x - 1,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2,11,x^2 - 4*x -
4,13,x^2 - 4*x - 4[]
245,7,2,x^2 - 2,3,x^2 - 2*x - 1,5,x^2 - 2*x + 1,7,x^2,11,x^2 + 6*x + 1,13,x^2 -
6*x + 7[]
245,8,2,x^2 - 2*x - 1,3,x^2 - 2*x - 1,5,x^2 - 2*x + 1,7,x^2,11,x^2 - 4*x -
4,13,x^2 + 4*x - 4[]
246,1,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x + 4,13,x + 4[]
246,2,2,x + 1,3,x + 1,5,x - 3,7,x + 2,11,x - 2,13,x - 1[]
246,3,2,x + 1,3,x - 1,5,x + 2,7,x - 2,11,x - 4,13,x - 4[]
246,4,2,x + 1,3,x - 1,5,x - 3,7,x - 2,11,x + 6,13,x + 1[]
246,5,2,x - 1,3,x + 1,5,x - 1,7,x - 2,11,x - 2,13,x + 7[]
246,6,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x + 1[]
246,7,2,x - 1,3,x - 1,5,x + 2,7,x - 4,11,x + 4,13,x - 2[]
247,1,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 4*x + 4,11,x^2 + 6*x
+ 4,13,x^2 - 2*x + 1[]
247,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 - 6*x
+ 1,11,x^3 - 9*x - 9,13,x^3 - 3*x^2 + 3*x - 1[]
247,3,2,x^4 + 3*x^3 - 2*x^2 - 9*x - 4,3,x^4 + x^3 - 6*x^2 - 3*x + 8,5,x^4 +
8*x^3 + 19*x^2 + 13*x - 1,7,x^4 + 2*x^3 - 11*x^2 - 23*x - 1,11,x^4 + 5*x^3 -
9*x^2 - 66*x - 55,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[]
247,4,2,x^5 - 4*x^4 + 12*x^2 - 5*x - 5,3,x^5 - 3*x^4 - 4*x^3 + 11*x^2 + 6*x -
4,5,x^5 - 3*x^4 - 8*x^3 + 17*x^2 + 18*x + 4,7,x^5 + x^4 - 12*x^3 + x^2 + 12*x +
4,11,x^5 + 2*x^4 - 39*x^3 - 51*x^2 + 338*x + 428,13,x^5 + 5*x^4 + 10*x^3 +
10*x^2 + 5*x + 1[]
247,5,2,x^5 - 9*x^3 - x^2 + 19*x + 4,3,x^5 - 3*x^4 - 8*x^3 + 25*x^2 - 16,5,x^5 -
2*x^4 - 15*x^3 + 25*x^2 + 9*x - 2,7,x^5 - 4*x^4 - 15*x^3 + 47*x^2 + 59*x -
32,11,x^5 - 7*x^4 + 9*x^3 + 8*x^2 - 11*x - 4,13,x^5 - 5*x^4 + 10*x^3 - 10*x^2 +
5*x - 1[]
248,1,2,x,3,x + 2,5,x - 1,7,x + 3,11,x + 2,13,x + 2[]
248,2,2,x,3,x + 2,5,x - 2,7,x,11,x - 2,13,x - 4[]
248,3,2,x,3,x,5,x + 3,7,x + 3,11,x - 2,13,x + 4[]
248,4,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 3*x - 6,7,x^2 - x - 8,11,x^2 + 4*x +
4,13,x^2 - 2*x - 32[]
248,5,2,x^3,3,x^3 - 2*x^2 - 6*x + 8,5,x^3 + 3*x^2 - 4*x - 4,7,x^3 - 5*x^2 - 8*x
+ 44,11,x^3 - 8*x^2 + 6*x + 44,13,x^3 - 2*x^2 - 14*x + 32[]

Total time: 20.190 seconds, Total memory usage: 7.82MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 09:46:25 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [248..256] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 09:46:06 on modular  [Seed = 283614814]
-------------------------------------

248,1,2,$.1,3,$.1 + 2,5,$.1 - 1,7,$.1 + 3,11,$.1 + 2,13,$.1 + 2[]
248,2,2,$.1,3,$.1 + 2,5,$.1 - 2,7,$.1,11,$.1 - 2,13,$.1 - 4[]
248,3,2,$.1,3,$.1,5,$.1 + 3,7,$.1 + 3,11,$.1 - 2,13,$.1 + 4[]
248,4,2,$.1^2,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - 3*$.1 - 6,7,$.1^2 - $.1 - 8,11,$.1^2
+ 4*$.1 + 4,13,$.1^2 - 2*$.1 - 32[] 248,5,2,$.1^3,3,$.1^3 - 2*$.1^2 - 6*$.1 + 8,5,$.1^3 + 3*$.1^2 - 4*$.1 -
4,7,$.1^3 - 5*$.1^2 - 8*$.1 + 44,11,$.1^3 - 8*$.1^2 + 6*$.1 + 44,13,$.1^3 - 2*$.1^2 - 14*$.1 + 32[] 249,1,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 3,13,x - 2[] 249,2,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 3,13,x + 6[] 249,3,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 6*x + 7,7,x^2 + 4*x + 4,11,x^2 + 6*x + 1,13,x^2[] 249,4,2,x^4 - 2*x^3 - 4*x^2 + 8*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 - 6*x^3 + 8*x^2 - 1,7,x^4 - 8*x^2 - 4*x + 4,11,x^4 - 4*x^3 - 14*x^2 + 32*x + 37,13,x^4 + 6*x^3 + 4*x^2 - 24*x - 28[] 249,5,2,x^5 + 3*x^4 - 4*x^3 - 14*x^2 - 3*x + 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 2*x^4 - 12*x^3 - 10*x^2 + 43*x - 22,7,x^5 - 8*x^4 + 12*x^3 + 36*x^2 - 92*x + 32,11,x^5 - 4*x^4 - 14*x^3 + 4*x^2 + 13*x - 4,13,x^5 - 4*x^4 - 24*x^3 + 144*x^2 - 220*x + 104[] 250,1,2,x^2 + 2*x + 1,3,x^2 + 3*x + 1,5,x^2,7,x^2 + x - 11,11,x^2 + 6*x + 4,13,x^2 - 2*x - 4[] 250,2,2,x^2 + 2*x + 1,3,x^2 - 2*x - 4,5,x^2,7,x^2 + x - 1,11,x^2 - 9*x + 19,13,x^2 + 3*x + 1[] 250,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 4,5,x^2,7,x^2 - x - 1,11,x^2 - 9*x + 19,13,x^2 - 3*x + 1[] 250,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2,7,x^2 - x - 11,11,x^2 + 6*x + 4,13,x^2 + 2*x - 4[] 251,1,2,x^4 + 2*x^3 - x^2 - 2*x + 1,3,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,5,x^4 + 3*x^3 - 2*x^2 - 2*x + 1,7,x^4 + 3*x^3 - 5*x^2 - 19*x - 11,11,x^4 + 3*x^3 - 4*x - 1,13,x^4 + 12*x^3 + 48*x^2 + 77*x + 41[] 251,2,2,x^17 - 2*x^16 - 28*x^15 + 54*x^14 + 317*x^13 - 582*x^12 - 1867*x^11 + 3178*x^10 + 6186*x^9 - 9216*x^8 - 11921*x^7 + 13680*x^6 + 13752*x^5 - 9400*x^4 - 8800*x^3 + 1920*x^2 + 2240*x + 256,3,x^17 - 38*x^15 + 5*x^14 + 582*x^13 - 142*x^12 - 4602*x^11 + 1445*x^10 + 20039*x^9 - 6280*x^8 - 48174*x^7 + 10424*x^6 + 63091*x^5 - 3260*x^4 - 41362*x^3 - 5377*x^2 + 10587*x + 3164,5,x^17 - 3*x^16 - 54*x^15 + 168*x^14 + 1118*x^13 - 3641*x^12 - 11152*x^11 + 38721*x^10 + 56108*x^9 - 215683*x^8 - 141507*x^7 + 649211*x^6 + 155977*x^5 - 1041793*x^4 - 22991*x^3 + 813550*x^2 - 51713*x - 228857,7,x^17 - 3*x^16 - 71*x^15 + 203*x^14 + 2030*x^13 - 5579*x^12 - 29805*x^11 + 80756*x^10 + 235362*x^9 - 668242*x^8 - 922654*x^7 + 3176896*x^6 + 1056610*x^5 - 7921027*x^4 + 3243764*x^3 + 7315324*x^2 - 7772692*x + 2209789,11,x^17 + x^16 - 122*x^15 - 152*x^14 + 5977*x^13 + 9162*x^12 - 151560*x^11 - 278496*x^10 + 2100848*x^9 + 4542848*x^8 - 15007296*x^7 - 38411776*x^6 + 41462784*x^5 + 139814400*x^4 + 18051072*x^3 - 84443136*x^2 - 11018240*x + 10657792,13,x^17 - 22*x^16 + 106*x^15 + 985*x^14 - 11180*x^13 + 18658*x^12 + 166344*x^11 - 636123*x^10 - 596895*x^9 + 5242340*x^8 - 1749194*x^7 - 16832410*x^6 + 11584495*x^5 + 21090650*x^4 - 16505080*x^3 - 6409715*x^2 + 5938307*x - 504874[] 252,1,2,x,3,x,5,x + 4,7,x + 1,11,x + 2,13,x + 6[] 252,2,2,x,3,x,5,x,7,x - 1,11,x - 6,13,x - 2[] 253,1,2,x^3 - 3*x^2 + 3,3,x^3 - 3*x^2 + 3,5,x^3 - 3*x^2 + 3,7,x^3 - 3*x^2 + 3,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 - 6*x - 17[] 253,2,2,x^3 + x^2 - 4*x + 1,3,x^3 + 5*x^2 + 4*x - 5,5,x^3 + 5*x^2 + 4*x - 5,7,x^3 + 3*x^2 - 10*x + 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + x^2 - 4*x + 1[] 253,3,2,x^5 + 4*x^4 - 14*x^2 - 13*x - 1,3,x^5 + 5*x^4 + 3*x^3 - 10*x^2 - 4*x + 1,5,x^5 + 3*x^4 - 14*x^3 - 43*x^2 - 12*x + 16,7,x^5 + 3*x^4 - 20*x^3 - 71*x^2 - 6*x + 92,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 + 15*x^4 + 83*x^3 + 208*x^2 + 232*x + 89[] 253,4,2,x^6 - 3*x^5 - 4*x^4 + 16*x^3 - 3*x^2 - 10*x + 1,3,x^6 - 7*x^5 + 11*x^4 + 18*x^3 - 56*x^2 + 33*x - 4,5,x^6 - 3*x^5 - 12*x^4 + 25*x^3 + 38*x^2 - 40*x - 32,7,x^6 + x^5 - 18*x^4 + 7*x^3 + 70*x^2 - 92*x + 32,11,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,13,x^6 + 3*x^5 - 33*x^4 - 94*x^3 + 226*x^2 + 783*x + 502[] 254,1,2,x + 1,3,x,5,x + 1,7,x + 3,11,x - 1,13,x + 2[] 254,2,2,x - 1,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[] 254,3,2,x - 1,3,x + 2,5,x,7,x - 4,11,x,13,x - 6[] 254,4,2,x - 1,3,x + 2,5,x + 3,7,x + 1,11,x + 3,13,x + 4[] 254,5,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 + x - 4,7,x^2 - x - 4,11,x^2 + 7*x + 8,13,x^2 + 2*x - 16[] 254,6,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + 2*x^4 - 10*x^3 - 16*x^2 + 10*x + 16,5,x^5 + x^4 - 20*x^3 - 18*x^2 + 54*x + 54,7,x^5 - 3*x^4 - 20*x^3 + 40*x^2 + 96*x - 32,11,x^5 - x^4 - 44*x^3 + 72*x^2 + 480*x - 1056,13,x^5 - 10*x^4 + 40*x^3 - 80*x^2 + 80*x - 32[] 255,1,2,x^2 - x - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 13,11,x^2 - 10*x + 25,13,x^2 + 6*x - 4[] 255,2,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 5,11,x^2 - 2*x - 19,13,x^2 - 6*x + 4[] 255,3,2,x^3 - 4*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 4*x^2 - x + 8,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 - 4*x^2 - 16*x + 56[] 255,4,2,x^4 - x^3 - 8*x^2 + 7*x + 9,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 4*x^3 - 17*x^2 + 80*x - 64,11,x^4 - 2*x^3 - 31*x^2 + 112*x - 96,13,x^4 + 2*x^3 - 48*x^2 - 120*x + 208[] 256,1,2,x,3,x,5,x + 4,7,x,11,x,13,x + 4[] 256,2,2,x,3,x + 2,5,x,7,x,11,x + 6,13,x[] 256,3,2,x,3,x,5,x - 4,7,x,11,x,13,x - 4[] 256,4,2,x,3,x - 2,5,x,7,x,11,x - 6,13,x[] 256,5,2,x^2,3,x^2 - 8,5,x^2,7,x^2,11,x^2 - 8,13,x^2[] Total time: 19.180 seconds, Total memory usage: 8.02MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 09:54:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [256..264] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 09:53:43 on modular [Seed = 3793055605] ------------------------------------- 256,1,2,$.1,3,$.1,5,$.1 + 4,7,$.1,11,$.1,13,$.1 + 4[] 256,2,2,$.1,3,$.1 + 2,5,$.1,7,$.1,11,$.1 + 6,13,$.1[] 256,3,2,$.1,3,$.1,5,$.1 - 4,7,$.1,11,$.1,13,$.1 - 4[] 256,4,2,$.1,3,$.1 - 2,5,$.1,7,$.1,11,$.1 - 6,13,$.1[] 256,5,2,$.1^2,3,$.1^2 - 8,5,$.1^2,7,$.1^2,11,$.1^2 - 8,13,$.1^2[] 257,1,2,x^7 + 3*x^6 - 3*x^5 - 11*x^4 + 3*x^3 + 10*x^2 - x - 1,3,x^7 + 5*x^6 + x^5 - 22*x^4 - 17*x^3 + 15*x^2 + 8*x - 4,5,x^7 + x^6 - 15*x^5 - 5*x^4 + 52*x^3 - 35*x^2 - 2*x + 4,7,x^7 + 18*x^6 + 125*x^5 + 410*x^4 + 586*x^3 + 91*x^2 - 496*x - 256,11,x^7 + 2*x^6 - 35*x^5 - 53*x^4 + 264*x^3 + 110*x^2 - 630*x + 337,13,x^7 + 10*x^6 - 287*x^4 - 976*x^3 - 752*x^2 + 489*x + 491[] 257,2,2,x^14 - 2*x^13 - 21*x^12 + 42*x^11 + 163*x^10 - 327*x^9 - 568*x^8 + 1153*x^7 + 830*x^6 - 1755*x^5 - 318*x^4 + 825*x^3 + 10*x^2 - 96*x - 1,3,x^14 - 3*x^13 - 23*x^12 + 74*x^11 + 173*x^10 - 627*x^9 - 500*x^8 + 2254*x^7 + 726*x^6 - 3988*x^5 - 858*x^4 + 3536*x^3 + 960*x^2 - 1280*x - 512,5,x^14 + x^13 - 45*x^12 - 21*x^11 + 740*x^10 - 41*x^9 - 5360*x^8 + 2796*x^7 + 16632*x^6 - 14736*x^5 - 18208*x^4 + 23232*x^3 - 384*x^2 - 5120*x + 512,7,x^14 - 24*x^13 + 227*x^12 - 988*x^11 + 1160*x^10 + 6413*x^9 - 24968*x^8 + 15746*x^7 + 66718*x^6 - 119942*x^5 + 11018*x^4 + 91024*x^3 - 28632*x^2 - 20096*x + 256,11,x^14 - 2*x^13 - 79*x^12 + 131*x^11 + 2172*x^10 - 2382*x^9 - 27190*x^8 + 14565*x^7 + 162892*x^6 - 16416*x^5 - 440000*x^4 - 68608*x^3 + 440448*x^2 + 66560*x - 145408,13,x^14 - 12*x^13 - 4*x^12 + 513*x^11 - 1358*x^10 - 5248*x^9 + 22253*x^8 + 12589*x^7 - 129450*x^6 + 57348*x^5 + 309368*x^4 - 309776*x^3 - 210288*x^2 + 382080*x - 128192[] 258,1,2,x + 1,3,x + 1,5,x - 1,7,x + 5,11,x - 1,13,x + 3[] 258,2,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x,13,x - 2[] 258,3,2,x + 1,3,x - 1,5,x + 3,7,x + 3,11,x + 5,13,x + 3[] 258,4,2,x - 1,3,x + 1,5,x + 2,7,x - 4,11,x - 4,13,x - 6[] 258,5,2,x - 1,3,x + 1,5,x - 3,7,x + 1,11,x + 1,13,x - 1[] 258,6,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x - 5,13,x + 7[] 258,7,2,x - 1,3,x - 1,5,x - 2,7,x + 2,11,x + 4,13,x - 2[] 259,1,2,x - 1,3,x,5,x - 4,7,x - 1,11,x - 4,13,x - 4[] 259,2,2,x^2,3,x^2 - 8,5,x^2 - 6*x + 7,7,x^2 + 2*x + 1,11,x^2 + 6*x + 1,13,x^2 - 2*x - 17[] 259,3,2,x^2 - x - 4,3,x^2,5,x^2 - x - 4,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 - x - 4[] 259,4,2,x^3 - x^2 - 2*x + 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 6*x^2 + 5*x - 13,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + x^2 - 2*x - 1,13,x^3 - x^2 - 16*x - 13[] 259,5,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 9*x^2 + 18*x - 9,13,x^3 + 3*x^2 - 24*x - 53[] 259,6,2,x^4 - 9*x^2 + x + 17,3,x^4 - 2*x^3 - 5*x^2 + 7*x + 4,5,x^4 - 6*x^3 + 7*x^2 + 5*x - 2,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 - 3*x^3 - 22*x^2 + 99*x - 100,13,x^4 - 5*x^3 - 16*x^2 + 47*x + 62[] 259,7,2,x^4 - x^3 - 6*x^2 + 5*x + 4,3,x^4 - 15*x^2 + 3*x + 48,5,x^4 - x^3 - 9*x^2 + 8*x + 13,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 10*x^3 + 15*x^2 + 77*x - 137,13,x^4 + 8*x^3 + 9*x^2 - 7*x + 1[] 260,1,2,x,3,x - 2,5,x + 1,7,x - 2,11,x - 4,13,x + 1[] 260,2,2,x^3,3,x^3 - 2*x^2 - 8*x + 12,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 2*x^2 - 20*x - 24,11,x^3 - 24*x + 36,13,x^3 - 3*x^2 + 3*x - 1[] 261,1,2,x^2 + x - 1,3,x^2,5,x^2 + 4*x + 4,7,x^2 - 5,11,x^2 + 8*x + 11,13,x^2 + 2*x - 19[] 261,2,2,x^2 - x - 1,3,x^2,5,x^2 - 4*x + 4,7,x^2 - 5,11,x^2 - 8*x + 11,13,x^2 + 2*x - 19[] 261,3,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 + 2*x - 1,13,x^2 + 2*x - 7[] 261,4,2,x^2 + x - 1,3,x^2,5,x^2 + 2*x - 4,7,x^2 + 4*x - 1,11,x^2 + 4*x - 1,13,x^2 + 2*x - 19[] 261,5,2,x^3 + 2*x^2 - 4*x - 7,3,x^3,5,x^3 - 16*x - 8,7,x^3 - 4*x^2 - x + 8,11,x^3 - 8*x^2 + 15*x - 4,13,x^3 - 4*x^2 - 7*x + 26[] 262,1,2,x + 1,3,x,5,x,7,x + 5,11,x - 2,13,x + 2[] 262,2,2,x - 1,3,x + 2,5,x + 2,7,x + 3,11,x + 6,13,x - 4[] 262,3,2,x^2 + 2*x + 1,3,x^2 + x - 3,5,x^2 + 5*x + 3,7,x^2 - 3*x - 1,11,x^2 + 7*x + 9,13,x^2 + 5*x + 3[] 262,4,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 - 4*x + 2,7,x^2 - 2*x - 1,11,x^2 - 4*x - 4,13,x^2 - 18[] 262,5,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 4*x + 1,11,x^2 - 12,13,x^2 + 6*x + 6[] 262,6,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 + x - 1,7,x^2 + x - 1,11,x^2 - 5*x + 5,13,x^2 - 3*x - 9[] 263,1,2,x^5 + 2*x^4 - 3*x^3 - 6*x^2 + 1,3,x^5 + 5*x^4 + 5*x^3 - 6*x^2 - 7*x + 1,5,x^5 + 3*x^4 - x^3 - 7*x^2 - 2*x + 1,7,x^5 + 5*x^4 + 4*x^3 - 5*x^2 - 5*x - 1,11,x^5 - 2*x^4 - 22*x^3 - 13*x^2 + 24*x + 17,13,x^5 + 15*x^4 + 79*x^3 + 167*x^2 + 96*x - 53[] 263,2,2,x^17 - x^16 - 26*x^15 + 24*x^14 + 274*x^13 - 225*x^12 - 1505*x^11 + 1041*x^10 + 4613*x^9 - 2467*x^8 - 7815*x^7 + 2761*x^6 + 6709*x^5 - 974*x^4 - 2284*x^3 - 239*x^2 + 135*x + 19,3,x^17 - 7*x^16 - 14*x^15 + 191*x^14 - 93*x^13 - 1956*x^12 + 2598*x^11 + 9587*x^10 - 17149*x^9 - 23845*x^8 + 50477*x^7 + 30119*x^6 - 69326*x^5 - 20491*x^4 + 39160*x^3 + 7677*x^2 - 4259*x - 119,5,x^17 - 3*x^16 - 61*x^15 + 185*x^14 + 1458*x^13 - 4495*x^12 - 17168*x^11 + 54320*x^10 + 102152*x^9 - 337584*x^8 - 280480*x^7 + 1002880*x^6 + 291584*x^5 - 1189120*x^4 - 151040*x^3 + 473088*x^2 + 65536*x - 4096,7,x^17 - 7*x^16 - 56*x^15 + 477*x^14 + 905*x^13 - 12145*x^12 + 584*x^11 + 144260*x^10 - 136136*x^9 - 814096*x^8 + 1150112*x^7 + 1950144*x^6 - 3208448*x^5 - 1505280*x^4 + 2396160*x^3 + 698368*x^2 - 483328*x - 151552,11,x^17 + 2*x^16 - 109*x^15 - 179*x^14 + 4639*x^13 + 5830*x^12 - 98806*x^11 - 85828*x^10 + 1119162*x^9 + 563445*x^8 - 6608205*x^7 - 1222544*x^6 + 18228623*x^5 - 405279*x^4 - 17443186*x^3 - 1627778*x^2 + 3900240*x + 800389,13,x^17 - 27*x^16 + 232*x^15 + 48*x^14 - 12494*x^13 + 65067*x^12 + 39521*x^11 - 1344086*x^10 + 3360234*x^9 + 5503401*x^8 - 36994803*x^7 + 35699891*x^6 + 94564718*x^5 - 233875954*x^4 + 105306969*x^3 + 161866750*x^2 - 192628894*x + 58427707[] 264,1,2,x,3,x + 1,5,x - 2,7,x,11,x - 1,13,x - 2[] 264,2,2,x,3,x - 1,5,x + 2,7,x - 4,11,x + 1,13,x - 6[] 264,3,2,x,3,x - 1,5,x - 4,7,x + 2,11,x + 1,13,x[] 264,4,2,x,3,x - 1,5,x,7,x - 2,11,x - 1,13,x[] Total time: 19.250 seconds, Total memory usage: 6.26MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:02:44 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [264..272] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:02:22 on modular [Seed = 3409723477] ------------------------------------- 264,1,2,$.1,3,$.1 + 1,5,$.1 - 2,7,$.1,11,$.1 - 1,13,$.1 - 2[] 264,2,2,$.1,3,$.1 - 1,5,$.1 + 2,7,$.1 - 4,11,$.1 + 1,13,$.1 - 6[] 264,3,2,$.1,3,$.1 - 1,5,$.1 - 4,7,$.1 + 2,11,$.1 + 1,13,$.1[] 264,4,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 1,13,$.1[] 265,1,2,x + 1,3,x,5,x + 1,7,x - 2,11,x,13,x + 6[] 265,2,2,x^2 + x - 5,3,x^2 + x - 5,5,x^2 + 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + 10*x + 25,13,x^2 - 21[] 265,3,2,x^2 + 2*x - 1,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2 + 4*x - 4,11,x^2 - 4*x + 4,13,x^2 - 2*x - 7[] 265,4,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 + 2*x + 1,7,x^2 - 2*x - 2,11,x^2 - 4*x - 8,13,x^2 - 12[] 265,5,2,x^2 - 3*x + 1,3,x^2 + 3*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x - 1,11,x^2 - 6*x + 9,13,x^2 - 2*x + 1[] 265,6,2,x^2 + x - 3,3,x^2 - x - 3,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 6*x + 9,13,x^2 + 4*x - 9[] 265,7,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 + 10*x + 25,13,x^2 - 2*x - 19[] 265,8,2,x^4 - 4*x^3 + 2*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 4*x + 4,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 4*x^3 - 6*x^2 + 24*x + 8,11,x^4 - 4*x^3 - 20*x^2 + 64*x + 32,13,x^4 + 2*x^3 - 27*x^2 - 92*x - 68[] 266,1,2,x^2 + 2*x + 1,3,x^2 - x - 7,5,x^2 + x - 7,7,x^2 + 2*x + 1,11,x^2 - 3*x - 5,13,x^2 + 2*x - 28[] 266,2,2,x^2 + 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - x - 11,7,x^2 - 2*x + 1,11,x^2 - 7*x + 11,13,x^2 - 6*x + 4[] 266,3,2,x^2 - 2*x + 1,3,x^2 - x - 3,5,x^2 - x - 3,7,x^2 - 2*x + 1,11,x^2 + 5*x + 3,13,x^2 - 6*x - 4[] 266,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + x^2 - 7*x + 4,5,x^3 - 5*x^2 + 3*x + 2,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 3*x^2 - 25*x + 76,13,x^3 + 4*x^2 - 16*x - 8[] 267,1,2,x,3,x + 1,5,x - 4,7,x + 2,11,x - 2,13,x - 6[] 267,2,2,x,3,x - 1,5,x,7,x - 2,11,x - 6,13,x - 2[] 267,3,2,x^3 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 + 6*x^2 + 9*x + 1,11,x^3 - 6*x^2 - 9*x + 71,13,x^3 + 15*x^2 + 72*x + 109[] 267,4,2,x^3 - 2*x^2 - 3*x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 5*x^2 + 4*x + 5,7,x^3 + 4*x^2 + x - 1,11,x^3 + 4*x^2 + x - 1,13,x^3 - 3*x^2 - 10*x - 1[] 267,5,2,x^3 + 4*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 7*x^2 + 14*x + 7,7,x^3 + 4*x^2 - 11*x - 43,11,x^3 + 8*x^2 + 19*x + 13,13,x^3 + 11*x^2 + 38*x + 41[] 267,6,2,x^4 - x^3 - 7*x^2 + 6*x + 7,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 3*x^3 - 6*x^2 + 19*x - 2,7,x^4 - 6*x^3 + x^2 + 19*x - 16,11,x^4 + 6*x^3 - 3*x^2 - 7*x + 4,13,x^4 - 9*x^3 + 10*x^2 + 91*x - 202[] 268,1,2,x,3,x - 2,5,x - 2,7,x - 2,11,x + 4,13,x + 6[] 268,2,2,x^2,3,x^2 - x - 5,5,x^2 + 2*x + 1,7,x^2 - x - 5,11,x^2 - 10*x + 25,13,x^2 - 3*x - 3[] 268,3,2,x^2,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 5*x + 5,11,x^2 + 4*x - 1,13,x^2 + 3*x - 9[] 269,1,2,x,3,x,5,x - 1,7,x + 4,11,x + 3,13,x - 2[] 269,2,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 5*x + 3,3,x^5 + 5*x^4 + 3*x^3 - 15*x^2 - 16*x + 3,5,x^5 + 4*x^4 - x^3 - 16*x^2 - 14*x - 1,7,x^5 + 5*x^4 - 4*x^3 - 25*x^2 - x + 19,11,x^5 + 9*x^4 + 23*x^3 - 59*x - 45,13,x^5 + 5*x^4 - 35*x^3 - 205*x^2 - 192*x + 61[] 269,3,2,x^16 - x^15 - 28*x^14 + 27*x^13 + 314*x^12 - 283*x^11 - 1803*x^10 + 1435*x^9 + 5637*x^8 - 3547*x^7 - 9470*x^6 + 3701*x^5 + 7860*x^4 - 1001*x^3 - 2363*x^2 - 43*x + 172,3,x^16 - 5*x^15 - 22*x^14 + 138*x^13 + 139*x^12 - 1450*x^11 + 41*x^10 + 7440*x^9 - 3354*x^8 - 20186*x^7 + 12462*x^6 + 28989*x^5 - 18771*x^4 - 19974*x^3 + 12032*x^2 + 4633*x - 2654,5,x^16 + x^15 - 46*x^14 - 32*x^13 + 861*x^12 + 316*x^11 - 8506*x^10 - 222*x^9 + 47729*x^8 - 14650*x^7 - 149888*x^6 + 92967*x^5 + 233992*x^4 - 219530*x^3 - 113145*x^2 + 177883*x - 48947,7,x^16 - 11*x^15 - 9*x^14 + 492*x^13 - 1053*x^12 - 7914*x^11 + 30314*x^10 + 46584*x^9 - 336651*x^8 + 83088*x^7 + 1695664*x^6 - 2025023*x^5 - 3085559*x^4 + 6658712*x^3 - 1044425*x^2 - 3548057*x + 1239286,11,x^16 - 16*x^15 + 30*x^14 + 693*x^13 - 3163*x^12 - 8622*x^11 + 61745*x^10 + 35024*x^9 - 506404*x^8 - 53136*x^7 + 1984496*x^6 + 581824*x^5 - 3521152*x^4 - 2514944*x^3 + 1231616*x^2 + 1575936*x + 369664,13,x^16 + x^15 - 118*x^14 + 40*x^13 + 5257*x^12 - 7276*x^11 - 105245*x^10 + 222524*x^9 + 949298*x^8 - 2595172*x^7 - 3434680*x^6 + 13153571*x^5 + 1070523*x^4 - 26094100*x^3 + 13603562*x^2 + 10842305*x - 7490278[] 270,1,2,x + 1,3,x,5,x - 1,7,x - 2,11,x + 3,13,x - 5[] 270,2,2,x + 1,3,x,5,x + 1,7,x - 2,11,x - 3,13,x + 1[] 270,3,2,x - 1,3,x,5,x + 1,7,x - 2,11,x - 3,13,x - 5[] 270,4,2,x - 1,3,x,5,x - 1,7,x - 2,11,x + 3,13,x + 1[] 271,1,2,x^6 + 4*x^5 + x^4 - 9*x^3 - 4*x^2 + 5*x + 1,3,x^6 + x^5 - 5*x^4 - 4*x^3 + 5*x^2 + 2*x - 1,5,x^6 + 8*x^5 + 20*x^4 + 16*x^3 - 2*x^2 - 5*x - 1,7,x^6 + 3*x^5 - 13*x^4 - 20*x^3 + 58*x^2 - 37*x + 7,11,x^6 + 11*x^5 + 34*x^4 + 5*x^3 - 137*x^2 - 214*x - 97,13,x^6 + 2*x^5 - 18*x^4 - 9*x^3 + 44*x^2 + 40*x + 7[] 271,2,2,x^16 - 5*x^15 - 12*x^14 + 91*x^13 + 11*x^12 - 620*x^11 + 381*x^10 + 1953*x^9 - 1863*x^8 - 2853*x^7 + 3137*x^6 + 1830*x^5 - 1758*x^4 - 831*x^3 + 308*x^2 + 204*x + 27,3,x^16 - x^15 - 41*x^14 + 44*x^13 + 663*x^12 - 746*x^11 - 5343*x^10 + 6132*x^9 + 22208*x^8 - 25016*x^7 - 43952*x^6 + 44896*x^5 + 33280*x^4 - 22016*x^3 - 13056*x^2 + 1536*x + 1024,5,x^16 - 10*x^15 + x^14 + 274*x^13 - 606*x^12 - 2545*x^11 + 8910*x^10 + 7903*x^9 - 50940*x^8 + 8944*x^7 + 123487*x^6 - 78423*x^5 - 108147*x^4 + 82115*x^3 + 37001*x^2 - 22695*x - 4725,7,x^16 + 3*x^15 - 58*x^14 - 187*x^13 + 1263*x^12 + 4399*x^11 - 13026*x^10 - 50956*x^9 + 62459*x^8 + 310197*x^7 - 82378*x^6 - 956996*x^5 - 315162*x^4 + 1239685*x^3 + 899123*x^2 - 257399*x - 263719,11,x^16 - 17*x^15 + 49*x^14 + 642*x^13 - 4059*x^12 - 4187*x^11 + 78189*x^10 - 77707*x^9 - 587886*x^8 + 995074*x^7 + 2122184*x^6 - 3966954*x^5 - 4261574*x^4 + 5963025*x^3 + 4848166*x^2 - 1967190*x - 1319031,13,x^16 + 4*x^15 - 122*x^14 - 493*x^13 + 5358*x^12 + 21292*x^11 - 104611*x^10 - 394880*x^9 + 887112*x^8 + 2958088*x^7 - 2769360*x^6 - 6121088*x^5 + 4984960*x^4 + 1402624*x^3 - 961792*x^2 - 98304*x + 44032[] 272,1,2,x,3,x + 2,5,x,7,x,11,x + 2,13,x + 6[] 272,2,2,x,3,x - 2,5,x + 2,7,x - 2,11,x - 6,13,x - 2[] 272,3,2,x,3,x - 2,5,x,7,x - 4,11,x + 6,13,x - 2[] 272,4,2,x,3,x,5,x + 2,7,x + 4,11,x,13,x + 2[] 272,5,2,x^2,3,x^2 - 2*x - 4,5,x^2 - 4*x + 4,7,x^2 + 2*x - 4,11,x^2 + 2*x - 4,13,x^2 - 20[] 272,6,2,x^2,3,x^2 + 2*x - 2,5,x^2 - 12,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2 - 4*x - 8[] Total time: 21.510 seconds, Total memory usage: 6.52MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:11:00 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [272..280] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:10:37 on modular [Seed = 2740202030] ------------------------------------- 272,1,2,$.1,3,$.1 + 2,5,$.1,7,$.1,11,$.1 + 2,13,$.1 + 6[] 272,2,2,$.1,3,$.1 - 2,5,$.1 + 2,7,$.1 - 2,11,$.1 - 6,13,$.1 - 2[] 272,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 4,11,$.1 + 6,13,$.1 - 2[] 272,4,2,$.1,3,$.1,5,$.1 + 2,7,$.1 + 4,11,$.1,13,$.1 + 2[] 272,5,2,$.1^2,3,$.1^2 - 2*$.1 - 4,5,$.1^2 - 4*$.1 + 4,7,$.1^2 + 2*$.1 -
4,11,$.1^2 + 2*$.1 - 4,13,$.1^2 - 20[] 272,6,2,$.1^2,3,$.1^2 + 2*$.1 - 2,5,$.1^2 - 12,7,$.1^2 - 2*$.1 - 2,11,$.1^2 -
6*$.1 + 6,13,$.1^2 - 4*$.1 - 8[] 273,1,2,x + 2,3,x + 1,5,x + 1,7,x - 1,11,x + 2,13,x - 1[] 273,2,2,x - 2,3,x - 1,5,x - 1,7,x + 1,11,x + 2,13,x + 1[] 273,3,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 4*x + 4,13,x^2 + 2*x + 1[] 273,4,2,x^3 + 2*x^2 - 3*x - 2,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 4*x - 8,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 2*x^2 - 28*x + 8,13,x^3 + 3*x^2 + 3*x + 1[] 273,5,2,x^4 - x^3 - 7*x^2 + 5*x + 6,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 3*x^3 - 10*x^2 - 20*x + 24,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 + 2*x^3 - 24*x^2 - 32*x + 96,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 274,1,2,x + 1,3,x,5,x,7,x + 4,11,x + 4,13,x - 4[] 274,2,2,x + 1,3,x,5,x + 3,7,x - 2,11,x + 1,13,x + 2[] 274,3,2,x - 1,3,x + 2,5,x + 3,7,x,11,x + 3,13,x + 6[] 274,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 5*x^2 + 5*x + 1,7,x^3 - 2*x^2 - 8*x - 4,11,x^3 - 5*x^2 - 5*x + 17,13,x^3 + 8*x^2 + 12*x + 4[] 274,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 2*x^4 - 10*x^3 + 20*x^2 - 8,5,x^5 - 5*x^4 - x^3 + 19*x^2 - 16,7,x^5 + 4*x^4 - 8*x^3 - 28*x^2 + 16*x + 32,11,x^5 + x^4 - 21*x^3 - 21*x^2 + 72*x - 16,13,x^5 - 4*x^4 - 20*x^3 + 76*x^2 + 64*x - 256[] 275,1,2,x + 1,3,x,5,x,7,x,11,x + 1,13,x + 2[] 275,2,2,x - 2,3,x - 1,5,x,7,x - 2,11,x - 1,13,x + 4[] 275,3,2,x^2 + x - 3,3,x^2 + x - 3,5,x^2,7,x^2 + 5*x + 3,11,x^2 + 2*x + 1,13,x^2 + 10*x + 25[] 275,4,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2,7,x^2 - x - 11,11,x^2 - 2*x + 1,13,x^2 - 8*x + 11[] 275,5,2,x^2 + 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 - 4*x + 4,11,x^2 - 2*x + 1,13,x^2 - 8*x + 8[] 275,6,2,x^2 - x - 3,3,x^2 - x - 3,5,x^2,7,x^2 - 5*x + 3,11,x^2 + 2*x + 1,13,x^2 - 10*x + 25[] 275,7,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2,7,x^2 + x - 11,11,x^2 - 2*x + 1,13,x^2 + 8*x + 11[] 275,8,2,x^4 - 7*x^2 + 4,3,x^4 - 7*x^2 + 4,5,x^4,7,x^4 - 24*x^2 + 144,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4[] 276,1,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 10,7,x^2 - 4*x - 6,11,x^2,13,x^2 - 8*x + 16[] 276,2,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 4*x + 2,7,x^2 - 2,11,x^2 - 32,13,x^2 - 32[] 277,1,2,x - 1,3,x + 2,5,x - 2,7,x + 4,11,x - 1,13,x + 5[] 277,2,2,x^3 + x^2 - 3*x - 1,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 4*x^2 + 4,7,x^3 - 4*x^2 - 4*x + 20,11,x^3 - 11*x^2 + 37*x - 37,13,x^3 - x^2 - 13*x + 5[] 277,3,2,x^9 + 6*x^8 + 4*x^7 - 37*x^6 - 69*x^5 + 24*x^4 + 119*x^3 + 34*x^2 - 52*x - 25,3,x^9 + 10*x^8 + 31*x^7 + 10*x^6 - 100*x^5 - 105*x^4 + 75*x^3 + 92*x^2 + 4*x - 5,5,x^9 + 12*x^8 + 43*x^7 - 13*x^6 - 390*x^5 - 673*x^4 + 123*x^3 + 1036*x^2 + 635*x + 109,7,x^9 + 2*x^8 - 35*x^7 - 69*x^6 + 420*x^5 + 812*x^4 - 1983*x^3 - 3735*x^2 + 3119*x + 5743,11,x^9 + 14*x^8 + 43*x^7 - 140*x^6 - 653*x^5 + 475*x^4 + 2394*x^3 - 1469*x^2 - 1131*x - 9,13,x^9 + 2*x^8 - 63*x^7 - 164*x^6 + 1169*x^5 + 3371*x^4 - 7559*x^3 - 23687*x^2 + 10754*x + 42085[] 277,4,2,x^9 - 4*x^8 - 6*x^7 + 37*x^6 - 3*x^5 - 100*x^4 + 49*x^3 + 64*x^2 - 20*x - 1,3,x^9 - 6*x^8 - x^7 + 50*x^6 - 20*x^5 - 141*x^4 + 23*x^3 + 120*x^2 + 24*x - 1,5,x^9 - 4*x^8 - 15*x^7 + 69*x^6 + 32*x^5 - 337*x^4 + 237*x^3 + 330*x^2 - 459*x + 145,7,x^9 + 2*x^8 - 23*x^7 - 41*x^6 + 136*x^5 + 228*x^4 - 51*x^3 - 203*x^2 - 77*x - 1,11,x^9 - 2*x^8 - 45*x^7 + 102*x^6 + 519*x^5 - 1187*x^4 - 1370*x^3 + 2773*x^2 + 763*x + 43,13,x^9 + 2*x^8 - 35*x^7 - 40*x^6 + 401*x^5 + 179*x^4 - 1395*x^3 - 547*x^2 + 1010*x + 461[] 278,1,2,x + 1,3,x + 2,5,x - 3,7,x + 1,11,x + 3,13,x - 5[] 278,2,2,x - 1,3,x + 2,5,x + 1,7,x + 5,11,x + 3,13,x - 1[] 278,3,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 + 2*x - 1,7,x^2 + 6*x + 7,11,x^2 - 2*x - 7,13,x^2 + 10*x + 23[] 278,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 + 3,5,x^3 - 12*x - 8,7,x^3 - 9*x^2 + 24*x - 17,11,x^3 - 12*x + 8,13,x^3 - 36*x + 72[] 278,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 10*x^3 + 11*x^2 + 12*x - 2,5,x^5 + 2*x^4 - 9*x^3 - 12*x^2 + 20*x + 8,7,x^5 - 7*x^4 + x^3 + 76*x^2 - 146*x + 61,11,x^5 - 6*x^4 - 19*x^3 + 116*x^2 + 84*x - 376,13,x^5 - 2*x^4 - 33*x^3 + 64*x^2 + 140*x + 56[] 279,1,2,x^2 - 3*x + 1,3,x^2,5,x^2 - 4*x - 1,7,x^2 + 4*x - 1,11,x^2 - 6*x + 4,13,x^2 + 2*x - 4[] 279,2,2,x^2 + x - 1,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 4*x - 1,11,x^2 + 4*x + 4,13,x^2 + 2*x - 4[] 279,3,2,x^3 - 4*x - 1,3,x^3,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 - 4*x^2 - x + 8,11,x^3 - 2*x^2 - 20*x - 16,13,x^3 - 4*x^2 - 16*x + 56[] 279,4,2,x^6 - 12*x^4 + 40*x^2 - 27,3,x^6,5,x^6 - 26*x^4 + 181*x^2 - 192,7,x^6 - 8*x^5 - 2*x^4 + 136*x^3 - 175*x^2 - 576*x + 1024,11,x^6 - 68*x^4 + 1168*x^2 - 768,13,x^6 - 64*x^4 - 80*x^3 + 1024*x^2 + 2560*x + 1600[] 280,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x + 5,13,x - 1[] 280,2,2,x,3,x + 3,5,x - 1,7,x - 1,11,x + 5,13,x + 5[] 280,3,2,x^2,3,x^2 + x - 8,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 7*x + 4,13,x^2 - 3*x - 6[] 280,4,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + x - 4,13,x^2 - x - 38[] Total time: 22.579 seconds, Total memory usage: 6.50MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:18:38 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [280..287] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:18:17 on modular [Seed = 2990880107] ------------------------------------- 280,1,2,$.1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 5,13,$.1 - 1[] 280,2,2,$.1,3,$.1 + 3,5,$.1 - 1,7,$.1 - 1,11,$.1 + 5,13,$.1 + 5[] 280,3,2,$.1^2,3,$.1^2 +$.1 - 8,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 7*$.1 + 4,13,$.1^2 - 3*$.1 - 6[]
280,4,2,$.1^2,3,$.1^2 - $.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 2*$.1 + 1,11,$.1^2
+ $.1 - 4,13,$.1^2 - $.1 - 38[] 281,1,2,x^7 + 2*x^6 - 5*x^5 - 9*x^4 + 7*x^3 + 10*x^2 - 2*x - 1,3,x^7 + 4*x^6 - 2*x^5 - 23*x^4 - 20*x^3 + 6*x^2 + 4*x - 1,5,x^7 + 4*x^6 - 13*x^5 - 58*x^4 - 9*x^3 + 76*x^2 + 51*x + 9,7,x^7 + 12*x^6 + 49*x^5 + 55*x^4 - 147*x^3 - 490*x^2 - 504*x - 177,11,x^7 + 7*x^6 - 22*x^5 - 275*x^4 - 484*x^3 + 1097*x^2 + 4016*x + 3121,13,x^7 + 7*x^6 - 16*x^5 - 167*x^4 - 146*x^3 + 295*x^2 + 376*x + 107[] 281,2,2,x^16 + x^15 - 27*x^14 - 24*x^13 + 294*x^12 + 229*x^11 - 1650*x^10 - 1115*x^9 + 5054*x^8 + 2991*x^7 - 8223*x^6 - 4526*x^5 + 6338*x^4 + 3707*x^3 - 1604*x^2 - 1215*x - 167,3,x^16 - 4*x^15 - 24*x^14 + 105*x^13 + 213*x^12 - 1086*x^11 - 824*x^10 + 5694*x^9 + 911*x^8 - 16142*x^7 + 2792*x^6 + 24266*x^5 - 9130*x^4 - 17154*x^3 + 8640*x^2 + 3847*x - 2158,5,x^16 - 2*x^15 - 51*x^14 + 108*x^13 + 1004*x^12 - 2272*x^11 - 9528*x^10 + 23527*x^9 + 43544*x^8 - 123838*x^7 - 76110*x^6 + 302357*x^5 - 7165*x^4 - 254732*x^3 + 24591*x^2 + 71803*x + 9158,7,x^16 - 16*x^15 + 57*x^14 + 359*x^13 - 2779*x^12 + 222*x^11 + 40216*x^10 - 69329*x^9 - 249828*x^8 + 742632*x^7 + 554336*x^6 - 3298448*x^5 + 664384*x^4 + 6373504*x^3 - 3933952*x^2 - 4035328*x + 2987008,11,x^16 - x^15 - 100*x^14 + 53*x^13 + 3851*x^12 - 544*x^11 - 72826*x^10 - 11166*x^9 + 728551*x^8 + 294344*x^7 - 3800998*x^6 - 2455896*x^5 + 9048488*x^4 + 8109681*x^3 - 5657184*x^2 - 6858135*x - 1476306,13,x^16 - 9*x^15 - 74*x^14 + 859*x^13 + 1328*x^12 - 31309*x^11 + 25786*x^10 + 524405*x^9 - 1198822*x^8 - 3471696*x^7 + 14389568*x^6 - 2926160*x^5 - 51577696*x^4 + 88267136*x^3 - 53487616*x^2 + 6349568*x + 3121664[] 282,1,2,x - 1,3,x + 1,5,x - 2,7,x,11,x,13,x - 2[] 282,2,2,x - 1,3,x + 1,5,x + 4,7,x + 4,11,x,13,x + 2[] 282,3,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 - 12,11,x^2 + 6*x + 6,13,x^2 + 2*x - 26[] 282,4,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 6,7,x^2 - 4*x + 4,11,x^2 - 6,13,x^2 - 4*x - 2[] 282,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 8*x - 4,7,x^3 - 16*x - 16,11,x^3 + 6*x^2 - 16*x - 100,13,x^3 - 28*x - 52[] 283,1,2,x^9 + 6*x^8 + 5*x^7 - 29*x^6 - 50*x^5 + 27*x^4 + 83*x^3 + 19*x^2 - 13*x + 1,3,x^9 + 6*x^8 + 5*x^7 - 27*x^6 - 41*x^5 + 33*x^4 + 64*x^3 - 8*x^2 - 28*x - 4,5,x^9 + 14*x^8 + 70*x^7 + 119*x^6 - 162*x^5 - 897*x^4 - 1200*x^3 - 568*x^2 - 56*x + 4,7,x^9 + 2*x^8 - 35*x^7 - 59*x^6 + 388*x^5 + 485*x^4 - 1723*x^3 - 1021*x^2 + 2753*x - 919,11,x^9 + 5*x^8 - 53*x^7 - 250*x^6 + 908*x^5 + 4006*x^4 - 5573*x^3 - 24230*x^2 + 8533*x + 42269,13,x^9 + 9*x^8 - 24*x^7 - 353*x^6 - 302*x^5 + 2456*x^4 + 2108*x^3 - 5681*x^2 - 3119*x + 3881[] 283,2,2,x^14 - 6*x^13 - 4*x^12 + 83*x^11 - 77*x^10 - 394*x^9 + 617*x^8 + 724*x^7 - 1566*x^6 - 370*x^5 + 1489*x^4 - 153*x^3 - 410*x^2 + 120*x - 8,3,x^14 - 4*x^13 - 21*x^12 + 95*x^11 + 143*x^10 - 815*x^9 - 330*x^8 + 3158*x^7 + 32*x^6 - 5740*x^5 + 524*x^4 + 4204*x^3 - 144*x^2 - 432*x + 32,5,x^14 - 14*x^13 + 52*x^12 + 115*x^11 - 1100*x^10 + 919*x^9 + 7116*x^8 - 13162*x^7 - 17292*x^6 + 49668*x^5 + 8200*x^4 - 66620*x^3 + 10736*x^2 + 21744*x + 2848,7,x^14 - 47*x^12 + 8*x^11 + 729*x^10 - 377*x^9 - 4485*x^8 + 4037*x^7 + 10435*x^6 - 13019*x^5 - 5943*x^4 + 12435*x^3 - 3633*x^2 - 108*x + 31,11,x^14 - 5*x^13 - 67*x^12 + 361*x^11 + 1322*x^10 - 9059*x^9 - 3449*x^8 + 83611*x^7 - 97383*x^6 - 138728*x^5 + 241269*x^4 + 50916*x^3 - 153904*x^2 + 4920*x + 14419,13,x^14 - 9*x^13 - 60*x^12 + 688*x^11 + 1058*x^10 - 20258*x^9 + 202*x^8 + 291882*x^7 - 190576*x^6 - 2108657*x^5 + 1914633*x^4 + 6666922*x^3 - 5938267*x^2 - 4997192*x + 391681[] 284,1,2,x^3,3,x^3 - x^2 - 4*x + 1,5,x^3 - x^2 - 6*x - 3,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 4*x^2 - 12*x + 24,13,x^3 - 4*x^2 - 20*x + 72[] 284,2,2,x^3,3,x^3 + 3*x^2 - 3,5,x^3 + 3*x^2 - 6*x + 1,7,x^3 + 6*x^2 - 24,11,x^3 + 6*x^2 - 24,13,x^3 + 6*x^2 - 24*x - 136[] 285,1,2,x - 1,3,x + 1,5,x + 1,7,x + 2,11,x + 2,13,x + 4[] 285,2,2,x - 1,3,x + 1,5,x - 1,7,x - 4,11,x - 4,13,x - 2[] 285,3,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 6,13,x[] 285,4,2,x^2 - 2*x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x + 2,11,x^2 - 2,13,x^2 - 8*x + 14[] 285,5,2,x^2 - 7,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 2*x - 6,11,x^2 - 6*x + 2,13,x^2 + 6*x + 2[] 285,6,2,x^2 - 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2,11,x^2 - 4*x - 14,13,x^2 + 4*x + 2[] 285,7,2,x^2 - 3,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 2*x - 2,11,x^2 - 6*x + 6,13,x^2 + 2*x - 2[] 286,1,2,x + 1,3,x + 1,5,x + 1,7,x - 1,11,x + 1,13,x + 1[] 286,2,2,x + 1,3,x + 2,5,x - 3,7,x + 1,11,x + 1,13,x - 1[] 286,3,2,x - 1,3,x - 2,5,x + 1,7,x - 1,11,x + 1,13,x + 1[] 286,4,2,x - 1,3,x + 1,5,x + 3,7,x + 5,11,x + 1,13,x - 1[] 286,5,2,x - 1,3,x + 1,5,x - 1,7,x - 3,11,x - 1,13,x - 1[] 286,6,2,x - 1,3,x - 2,5,x - 1,7,x + 3,11,x - 1,13,x - 1[] 286,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 10*x + 8,5,x^3 - 2*x^2 - 9*x + 2,7,x^3 + 4*x^2 - 5*x - 16,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 + 3*x + 1[] 287,1,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 - x - 1,7,x^2 + 2*x + 1,11,x^2 + 2*x + 1,13,x^2 + 8*x + 11[] 287,2,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 + x - 1,7,x^2 - 2*x + 1,11,x^2 - 5,13,x^2 + 6*x + 9[] 287,3,2,x^3 - 4*x^2 + 3*x + 1,3,x^3 - 5*x^2 + 6*x - 1,5,x^3 - 2*x^2 - 8*x + 8,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 - 4*x - 8,13,x^3 - 7*x^2 + 49[] 287,4,2,x^3 - x^2 - 4*x + 3,3,x^3 + x^2 - 8*x - 3,5,x^3 - 6*x^2 + 12*x - 8,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 6*x^2 + 12*x + 8,13,x^3 - 9*x^2 + 22*x - 15[] 287,5,2,x^5 + x^4 - 6*x^3 - 4*x^2 + 6*x + 3,3,x^5 - 4*x^4 + 10*x^2 - 3*x - 1,5,x^5 + 5*x^4 - 11*x^3 - 86*x^2 - 96*x + 24,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - 2*x^4 - 63*x^3 + 140*x^2 + 972*x - 2472,13,x^5 - 5*x^4 - 9*x^3 + 80*x^2 - 120*x + 49[] 287,6,2,x^6 + x^5 - 10*x^4 - 10*x^3 + 23*x^2 + 24*x + 5,3,x^6 + 4*x^5 - 8*x^4 - 46*x^3 - 13*x^2 + 111*x + 100,5,x^6 + x^5 - 29*x^4 - 16*x^3 + 200*x^2 - 16*x - 16,7,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 - 6*x^5 - 29*x^4 + 218*x^3 + 28*x^2 - 1928*x + 2720,13,x^6 - 7*x^5 - 49*x^4 + 330*x^3 + 400*x^2 - 1917*x - 1546[] Total time: 21.100 seconds, Total memory usage: 6.17MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 10:29:27 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [287..294] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 10:29:07 on modular [Seed = 2407009196] ------------------------------------- 287,1,2,$.1^2 + $.1 - 1,3,$.1^2 + $.1 - 1,5,$.1^2 - $.1 - 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 8*$.1 + 11[] 287,2,2,$.1^2 + $.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 + $.1 - 1,7,$.1^2 - 2*$.1 + 1,11,$.1^2 - 5,13,$.1^2 + 6*$.1 + 9[]
287,3,2,$.1^3 - 4*$.1^2 + 3*$.1 + 1,3,$.1^3 - 5*$.1^2 + 6*$.1 - 1,5,$.1^3 - 2*$.1^2 - 8*$.1 + 8,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 - 4*$.1 - 8,13,$.1^3 - 7*$.1^2 + 49[] 287,4,2,$.1^3 - $.1^2 - 4*$.1 + 3,3,$.1^3 +$.1^2 - 8*$.1 - 3,5,$.1^3 - 6*$.1^2 + 12*$.1 - 8,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 + 6*$.1^2 + 12*$.1 +
8,13,$.1^3 - 9*$.1^2 + 22*$.1 - 15[] 287,5,2,$.1^5 + $.1^4 - 6*$.1^3 - 4*$.1^2 + 6*$.1 + 3,3,$.1^5 - 4*$.1^4 +
10*$.1^2 - 3*$.1 - 1,5,$.1^5 + 5*$.1^4 - 11*$.1^3 - 86*$.1^2 - 96*$.1 + 24,7,$.1^5 - 5*$.1^4 + 10*$.1^3 - 10*$.1^2 + 5*$.1 - 1,11,$.1^5 - 2*$.1^4 -
63*$.1^3 + 140*$.1^2 + 972*$.1 - 2472,13,$.1^5 - 5*$.1^4 - 9*$.1^3 + 80*$.1^2 - 120*$.1 + 49[]
287,6,2,$.1^6 +$.1^5 - 10*$.1^4 - 10*$.1^3 + 23*$.1^2 + 24*$.1 + 5,3,$.1^6 + 4*$.1^5 - 8*$.1^4 - 46*$.1^3 - 13*$.1^2 + 111*$.1 + 100,5,$.1^6 +$.1^5 -
29*$.1^4 - 16*$.1^3 + 200*$.1^2 - 16*$.1 - 16,7,$.1^6 + 6*$.1^5 + 15*$.1^4 + 20*$.1^3 + 15*$.1^2 + 6*$.1 + 1,11,$.1^6 - 6*$.1^5 - 29*$.1^4 + 218*$.1^3 +
28*$.1^2 - 1928*$.1 + 2720,13,$.1^6 - 7*$.1^5 - 49*$.1^4 + 330*$.1^3 + 400*$.1^2 - 1917*$.1 - 1546[]
288,1,2,x,3,x,5,x + 4,7,x,11,x,13,x + 6[]
288,2,2,x,3,x,5,x - 2,7,x,11,x,13,x - 6[]
288,3,2,x,3,x,5,x + 2,7,x - 4,11,x - 4,13,x + 2[]
288,4,2,x,3,x,5,x - 4,7,x,11,x,13,x + 6[]
288,5,2,x,3,x,5,x + 2,7,x + 4,11,x + 4,13,x + 2[]
289,1,2,x + 1,3,x,5,x - 2,7,x + 4,11,x,13,x + 2[]
289,2,2,x^2 + x - 3,3,x^2 + x - 3,5,x^2 + x - 3,7,x^2 + 3*x - 1,11,x^2 + 6*x +
9,13,x^2 + 3*x - 1[]
289,3,2,x^2 + x - 3,3,x^2 - x - 3,5,x^2 - x - 3,7,x^2 - 3*x - 1,11,x^2 - 6*x +
9,13,x^2 + 3*x - 1[]
289,4,2,x^3 - 3*x + 1,3,x^3 + 3*x^2 - 3,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 - 3*x +
1,11,x^3 + 6*x^2 - 24,13,x^3 - 6*x^2 - 9*x + 71[]
289,5,2,x^3 - 3*x + 1,3,x^3 - 3*x^2 + 3,5,x^3 - 6*x^2 + 9*x - 1,7,x^3 - 3*x -
1,11,x^3 - 6*x^2 + 24,13,x^3 - 6*x^2 - 9*x + 71[]
289,6,2,x^4 - 4*x^3 + 2*x^2 + 4*x + 1,3,x^4 - 8*x^2 + 8,5,x^4 - 4*x^2 + 2,7,x^4
- 8*x^2 + 8,11,x^4 - 8*x^2 + 8,13,x^4 - 4*x^2 + 4[]
290,1,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 2,13,x + 6[]
290,2,2,x^2 + 2*x + 1,3,x^2 - x - 3,5,x^2 + 2*x + 1,7,x^2 - 5*x + 3,11,x^2 + 2*x
- 12,13,x^2 - 9*x + 17[]
290,3,2,x^2 + 2*x + 1,3,x^2 - x - 3,5,x^2 - 2*x + 1,7,x^2 - 3*x - 1,11,x^2 - 2*x
- 12,13,x^2 + x - 3[]
290,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 3*x + 8,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 3*x^2 - 15*x + 46,11,x^3 - 24*x - 24,13,x^3 - 3*x^2 - 33*x + 118[]
290,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + x^2 - 7*x + 4,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 + x^2 - 5*x - 4,11,x^3 - 2*x^2 - 20*x + 32,13,x^3 - 5*x^2 - 21*x + 98[]
291,1,2,x + 1,3,x + 1,5,x,7,x - 2,11,x + 4,13,x + 2[]
291,2,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x - 4,13,x - 6[]
291,3,2,x - 2,3,x + 1,5,x - 1,7,x - 2,11,x - 4,13,x[]
291,4,2,x + 2,3,x + 1,5,x - 3,7,x + 2,11,x,13,x + 4[]
291,5,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2 - 3*x - 1,11,x^2 + 3*x
- 1,13,x^2 + 3*x - 1[]
291,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - 6*x + 9,7,x^2 + 3*x - 9,11,x^2 +
7*x + 11,13,x^2 - 7*x + 11[]
291,7,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 4*x - 1,7,x^2 + 7*x + 11,11,x^2 - x
- 11,13,x^2 + 9*x + 19[]
291,8,2,x^7 - 11*x^5 + x^4 + 34*x^3 - 5*x^2 - 24*x - 4,3,x^7 - 7*x^6 + 21*x^5 -
35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,5,x^7 - 4*x^6 - 16*x^5 + 52*x^4 + 111*x^3 -
168*x^2 - 336*x - 64,7,x^7 - 9*x^6 + 13*x^5 + 62*x^4 - 124*x^3 - 96*x^2 + 192*x
- 32,11,x^7 + 3*x^6 - 39*x^5 - 88*x^4 + 328*x^3 + 672*x^2 - 384*x - 512,13,x^7 -
11*x^6 + 25*x^5 + 82*x^4 - 276*x^3 - 200*x^2 + 640*x + 448[]
292,1,2,x^2,3,x^2 + x - 1,5,x^2 + 5*x + 5,7,x^2 - 5,11,x^2 + 7*x + 11,13,x^2 + x
- 31[]
292,2,2,x^4,3,x^4 - 3*x^3 - 5*x^2 + 16*x - 8,5,x^4 - 5*x^3 + x^2 + 8*x - 4,7,x^4
- 7*x^2 + 2,11,x^4 - 3*x^3 - 15*x^2 - 10*x + 2,13,x^4 - 5*x^3 + x^2 + 8*x - 4[]
293,1,2,x^8 + 3*x^7 - 4*x^6 - 15*x^5 + 4*x^4 + 21*x^3 - 2*x^2 - 8*x + 1,3,x^8 +
8*x^7 + 17*x^6 - 11*x^5 - 61*x^4 - 12*x^3 + 54*x^2 - 9,5,x^8 + x^7 - 14*x^6 -
12*x^5 + 49*x^4 + 39*x^3 - 43*x^2 - 21*x + 13,7,x^8 + 13*x^7 + 50*x^6 + 4*x^5 -
322*x^4 - 409*x^3 + 356*x^2 + 551*x - 107,11,x^8 + 9*x^7 - 17*x^6 - 299*x^5 -
255*x^4 + 1950*x^3 + 1347*x^2 - 3162*x - 1777,13,x^8 + 8*x^7 - 10*x^6 - 179*x^5
- 66*x^4 + 1301*x^3 + 838*x^2 - 3003*x - 1993[]
293,2,2,x^16 - 3*x^15 - 22*x^14 + 69*x^13 + 184*x^12 - 621*x^11 - 716*x^10 +
2758*x^9 + 1234*x^8 - 6287*x^7 - 554*x^6 + 7023*x^5 - 572*x^4 - 3385*x^3 +
508*x^2 + 526*x - 111,3,x^16 - 10*x^15 + 16*x^14 + 145*x^13 - 539*x^12 -
391*x^11 + 4186*x^10 - 2997*x^9 - 12471*x^8 + 19066*x^7 + 10434*x^6 - 35185*x^5
+ 12204*x^4 + 17688*x^3 - 17052*x^2 + 5482*x - 613,5,x^16 - x^15 - 50*x^14 +
52*x^13 + 967*x^12 - 1133*x^11 - 9107*x^10 + 12731*x^9 + 42279*x^8 - 74396*x^7 -
78548*x^6 + 202208*x^5 - 13072*x^4 - 176512*x^3 + 104320*x^2 - 7424*x -
2304,7,x^16 - 15*x^15 + 47*x^14 + 355*x^13 - 2587*x^12 + 1270*x^11 + 31866*x^10
- 82216*x^9 - 81204*x^8 + 587973*x^7 - 541623*x^6 - 957347*x^5 + 2078389*x^4 -
767685*x^3 - 751840*x^2 + 444163*x + 39801,11,x^16 - 9*x^15 - 66*x^14 + 748*x^13
+ 1441*x^12 - 24992*x^11 - 9096*x^10 + 443284*x^9 - 82288*x^8 - 4603767*x^7 +
1256495*x^6 + 28598848*x^5 - 2437626*x^4 - 100143384*x^3 - 26960213*x^2 +
154057944*x + 107176896,13,x^16 - 10*x^15 - 54*x^14 + 839*x^13 - 450*x^12 -
21927*x^11 + 62138*x^10 + 151969*x^9 - 882035*x^8 + 825676*x^7 + 1529916*x^6 -
3032400*x^5 + 775008*x^4 + 1156352*x^3 - 760128*x^2 + 136192*x - 4096[]
294,1,2,x + 1,3,x + 1,5,x + 3,7,x,11,x - 3,13,x - 4[]
294,2,2,x + 1,3,x + 1,5,x - 4,7,x,11,x + 4,13,x - 4[]
294,3,2,x + 1,3,x - 1,5,x - 3,7,x,11,x - 3,13,x + 4[]
294,4,2,x + 1,3,x - 1,5,x + 4,7,x,11,x + 4,13,x + 4[]
294,5,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 5,13,x[]
294,6,2,x - 1,3,x - 1,5,x + 1,7,x,11,x - 5,13,x[]
294,7,2,x - 1,3,x - 1,5,x - 2,7,x,11,x + 4,13,x + 6[]

Total time: 19.629 seconds, Total memory usage: 6.21MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 10:36:04 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [294..301] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sat Nov 29 2003 10:35:41 on modular  [Seed = 1504631499]
-------------------------------------

294,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 3,7,$.1,11,$.1 - 3,13,$.1 - 4[]
294,2,2,$.1 + 1,3,$.1 + 1,5,$.1 - 4,7,$.1,11,$.1 + 4,13,$.1 - 4[]
294,3,2,$.1 + 1,3,$.1 - 1,5,$.1 - 3,7,$.1,11,$.1 - 3,13,$.1 + 4[]
294,4,2,$.1 + 1,3,$.1 - 1,5,$.1 + 4,7,$.1,11,$.1 + 4,13,$.1 + 4[]
294,5,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 - 5,13,$.1[]
294,6,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 - 5,13,$.1[]
294,7,2,$.1 - 1,3,$.1 - 1,5,$.1 - 2,7,$.1,11,$.1 + 4,13,$.1 + 6[]
295,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3
- 7*x + 7,11,x^3 + 9*x^2 + 20*x + 13,13,x^3 - x^2 - 9*x + 1[]
295,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 6*x^2
+ 3*x - 19,11,x^3 - 3*x^2 - 6*x + 17,13,x^3 + 9*x^2 + 15*x - 17[]
295,3,2,x^6 - 2*x^5 - 6*x^4 + 11*x^3 + 8*x^2 - 11*x - 3,3,x^6 - x^5 - 12*x^4 +
13*x^3 + 28*x^2 - 16*x - 16,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x +
1,7,x^6 - 2*x^5 - 21*x^4 + 57*x^3 + 12*x^2 - 104*x + 48,11,x^6 - 3*x^5 - 12*x^4
+ 33*x^3 + 32*x^2 - 80*x + 32,13,x^6 - 11*x^5 + 23*x^4 + 83*x^3 - 268*x^2 - 64*x
+ 452[]
295,4,2,x^7 - x^6 - 10*x^5 + 7*x^4 + 27*x^3 - 11*x^2 - 10*x - 1,3,x^7 - 3*x^6 -
14*x^5 + 39*x^4 + 52*x^3 - 128*x^2 - 16*x + 32,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 +
35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 4*x^6 - 23*x^5 - 105*x^4 + 40*x^3 + 488*x^2 +
400*x - 32,11,x^7 - 3*x^6 - 66*x^5 + 221*x^4 + 1252*x^3 - 4368*x^2 - 7168*x +
25408,13,x^7 + 9*x^6 - 19*x^5 - 301*x^4 - 6*x^3 + 3276*x^2 + 980*x - 11564[]
296,1,2,x,3,x + 1,5,x + 2,7,x - 1,11,x - 1,13,x + 6[]
296,2,2,x,3,x + 1,5,x,7,x + 3,11,x + 3,13,x[]
296,3,2,x^3,3,x^3 - 2*x^2 - 4*x + 7,5,x^3 + x^2 - 5*x + 2,7,x^3 - 7*x^2 + 10*x +
4,11,x^3 - 36*x + 27,13,x^3 - 3*x^2 - 33*x + 62[]
296,4,2,x^4,3,x^4 - 2*x^3 - 8*x^2 + 15*x + 4,5,x^4 - 5*x^3 - x^2 + 26*x -
16,7,x^4 + x^3 - 18*x^2 - 4*x + 64,11,x^4 - 4*x^3 - 12*x^2 + 63*x - 52,13,x^4 -
5*x^3 - 17*x^2 + 122*x - 160[]
297,1,2,x + 1,3,x,5,x - 2,7,x + 5,11,x + 1,13,x + 2[]
297,2,2,x - 2,3,x,5,x - 2,7,x - 1,11,x + 1,13,x + 5[]
297,3,2,x - 1,3,x,5,x + 2,7,x + 5,11,x - 1,13,x + 2[]
297,4,2,x + 2,3,x,5,x + 2,7,x - 1,11,x - 1,13,x + 5[]
297,5,2,x^2 + 2*x - 2,3,x^2,5,x^2 + 2*x - 2,7,x^2 + 4*x + 1,11,x^2 + 2*x +
1,13,x^2 + 4*x + 1[]
297,6,2,x^2 - 2*x - 2,3,x^2,5,x^2 - 2*x - 2,7,x^2 + 4*x + 1,11,x^2 - 2*x +
1,13,x^2 + 4*x + 1[]
297,7,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 - 2*x^2 - 8*x + 12,7,x^3 - 7*x^2 + 11*x
+ 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 4*x^2 - 4*x + 4[]
297,8,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 + 2*x^2 - 8*x - 12,7,x^3 - 7*x^2 + 11*x
+ 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 4*x^2 - 4*x + 4[]
298,1,2,x + 1,3,x,5,x + 4,7,x - 4,11,x - 2,13,x + 5[]
298,2,2,x - 1,3,x + 2,5,x + 2,7,x + 2,11,x,13,x + 5[]
298,3,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 2*x - 2,11,x^2 -
6*x + 6,13,x^2 + 4*x + 1[]
298,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 5*x^2 + 4*x - 5,5,x^3 - x^2 - 4*x -
1,7,x^3 + 4*x^2 - 12*x - 40,11,x^3 + 5*x^2 - 22*x - 109,13,x^3[]
298,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 10*x^3 + 11*x^2 +
12*x - 2,5,x^5 - 5*x^4 + 2*x^3 + 9*x^2 - 2,7,x^5 - 18*x^3 + 8*x^2 + 40*x +
16,11,x^5 + 3*x^4 - 16*x^3 - 73*x^2 - 84*x - 22,13,x^5 - 6*x^4 - 37*x^3 +
236*x^2 + 32*x - 704[]
299,1,2,x^2 - x - 1,3,x^2 + x - 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 + 3*x +
1,13,x^2 + 2*x + 1[]
299,2,2,x^2 - 5,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 6*x + 4,13,x^2 -
2*x + 1[]
299,3,2,x^2 - x - 4,3,x^2 - x - 4,5,x^2 - x - 4,7,x^2 - 2*x - 16,11,x^2 - 5*x +
2,13,x^2 - 2*x + 1[]
299,4,2,x^2 + x - 5,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 - 2*x + 1,11,x^2 - 3*x -
3,13,x^2 - 2*x + 1[]
299,5,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 + 4*x - 1,11,x^2 - x -
1,13,x^2 - 2*x + 1[]
299,6,2,x^3,3,x^3 + x^2 - 9*x - 5,5,x^3 - x^2 - 7*x - 3,7,x^3 - 2*x^2 - 8*x +
4,11,x^3 - 5*x^2 - 5*x + 27,13,x^3 - 3*x^2 + 3*x - 1[]
299,7,2,x^10 - x^9 - 19*x^8 + 18*x^7 + 127*x^6 - 109*x^5 - 357*x^4 + 252*x^3 +
400*x^2 - 192*x - 128,3,x^10 - 3*x^9 - 19*x^8 + 58*x^7 + 107*x^6 - 343*x^5 -
181*x^4 + 720*x^3 - 56*x^2 - 400*x + 112,5,x^10 - 3*x^9 - 37*x^8 + 112*x^7 +
443*x^6 - 1401*x^5 - 1817*x^4 + 6424*x^3 + 1108*x^2 - 6140*x - 2372,7,x^10 +
2*x^9 - 53*x^8 - 70*x^7 + 1044*x^6 + 640*x^5 - 9072*x^4 + 456*x^3 + 29888*x^2 -
18272*x - 5936,11,x^10 - 3*x^9 - 71*x^8 + 200*x^7 + 1777*x^6 - 4449*x^5 -
19765*x^4 + 39328*x^3 + 100444*x^2 - 119916*x - 190148,13,x^10 + 10*x^9 + 45*x^8
+ 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1[]
300,1,2,x,3,x + 1,5,x,7,x - 1,11,x - 6,13,x + 5[]

Errors: /home/mfd/gomagma: line 2: 24582 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 10:37:09 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [294..299] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 10:36:52 on modular  [Seed = 1369887514]
-------------------------------------

294,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 3,7,$.1,11,$.1 - 3,13,$.1 - 4[]
294,2,2,$.1 + 1,3,$.1 + 1,5,$.1 - 4,7,$.1,11,$.1 + 4,13,$.1 - 4[]
294,3,2,$.1 + 1,3,$.1 - 1,5,$.1 - 3,7,$.1,11,$.1 - 3,13,$.1 + 4[]
294,4,2,$.1 + 1,3,$.1 - 1,5,$.1 + 4,7,$.1,11,$.1 + 4,13,$.1 + 4[]
294,5,2,$.1 - 1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 - 5,13,$.1[]
294,6,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 - 5,13,$.1[]
294,7,2,$.1 - 1,3,$.1 - 1,5,$.1 - 2,7,$.1,11,$.1 + 4,13,$.1 + 6[]
295,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + x^2 - 2*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3
- 7*x + 7,11,x^3 + 9*x^2 + 20*x + 13,13,x^3 - x^2 - 9*x + 1[]
295,2,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 6*x^2
+ 3*x - 19,11,x^3 - 3*x^2 - 6*x + 17,13,x^3 + 9*x^2 + 15*x - 17[]
295,3,2,x^6 - 2*x^5 - 6*x^4 + 11*x^3 + 8*x^2 - 11*x - 3,3,x^6 - x^5 - 12*x^4 +
13*x^3 + 28*x^2 - 16*x - 16,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x +
1,7,x^6 - 2*x^5 - 21*x^4 + 57*x^3 + 12*x^2 - 104*x + 48,11,x^6 - 3*x^5 - 12*x^4
+ 33*x^3 + 32*x^2 - 80*x + 32,13,x^6 - 11*x^5 + 23*x^4 + 83*x^3 - 268*x^2 - 64*x
+ 452[]
295,4,2,x^7 - x^6 - 10*x^5 + 7*x^4 + 27*x^3 - 11*x^2 - 10*x - 1,3,x^7 - 3*x^6 -
14*x^5 + 39*x^4 + 52*x^3 - 128*x^2 - 16*x + 32,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 +
35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 4*x^6 - 23*x^5 - 105*x^4 + 40*x^3 + 488*x^2 +
400*x - 32,11,x^7 - 3*x^6 - 66*x^5 + 221*x^4 + 1252*x^3 - 4368*x^2 - 7168*x +
25408,13,x^7 + 9*x^6 - 19*x^5 - 301*x^4 - 6*x^3 + 3276*x^2 + 980*x - 11564[]
296,1,2,x,3,x + 1,5,x + 2,7,x - 1,11,x - 1,13,x + 6[]
296,2,2,x,3,x + 1,5,x,7,x + 3,11,x + 3,13,x[]
296,3,2,x^3,3,x^3 - 2*x^2 - 4*x + 7,5,x^3 + x^2 - 5*x + 2,7,x^3 - 7*x^2 + 10*x +
4,11,x^3 - 36*x + 27,13,x^3 - 3*x^2 - 33*x + 62[]
296,4,2,x^4,3,x^4 - 2*x^3 - 8*x^2 + 15*x + 4,5,x^4 - 5*x^3 - x^2 + 26*x -
16,7,x^4 + x^3 - 18*x^2 - 4*x + 64,11,x^4 - 4*x^3 - 12*x^2 + 63*x - 52,13,x^4 -
5*x^3 - 17*x^2 + 122*x - 160[]
297,1,2,x + 1,3,x,5,x - 2,7,x + 5,11,x + 1,13,x + 2[]
297,2,2,x - 2,3,x,5,x - 2,7,x - 1,11,x + 1,13,x + 5[]
297,3,2,x - 1,3,x,5,x + 2,7,x + 5,11,x - 1,13,x + 2[]
297,4,2,x + 2,3,x,5,x + 2,7,x - 1,11,x - 1,13,x + 5[]
297,5,2,x^2 + 2*x - 2,3,x^2,5,x^2 + 2*x - 2,7,x^2 + 4*x + 1,11,x^2 + 2*x +
1,13,x^2 + 4*x + 1[]
297,6,2,x^2 - 2*x - 2,3,x^2,5,x^2 - 2*x - 2,7,x^2 + 4*x + 1,11,x^2 - 2*x +
1,13,x^2 + 4*x + 1[]
297,7,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 - 2*x^2 - 8*x + 12,7,x^3 - 7*x^2 + 11*x
+ 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 4*x^2 - 4*x + 4[]
297,8,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 + 2*x^2 - 8*x - 12,7,x^3 - 7*x^2 + 11*x
+ 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 4*x^2 - 4*x + 4[]
298,1,2,x + 1,3,x,5,x + 4,7,x - 4,11,x - 2,13,x + 5[]
298,2,2,x - 1,3,x + 2,5,x + 2,7,x + 2,11,x,13,x + 5[]
298,3,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 2*x - 2,11,x^2 -
6*x + 6,13,x^2 + 4*x + 1[]
298,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 5*x^2 + 4*x - 5,5,x^3 - x^2 - 4*x -
1,7,x^3 + 4*x^2 - 12*x - 40,11,x^3 + 5*x^2 - 22*x - 109,13,x^3[]
298,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 10*x^3 + 11*x^2 +
12*x - 2,5,x^5 - 5*x^4 + 2*x^3 + 9*x^2 - 2,7,x^5 - 18*x^3 + 8*x^2 + 40*x +
16,11,x^5 + 3*x^4 - 16*x^3 - 73*x^2 - 84*x - 22,13,x^5 - 6*x^4 - 37*x^3 +
236*x^2 + 32*x - 704[]
299,1,2,x^2 - x - 1,3,x^2 + x - 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 + 3*x +
1,13,x^2 + 2*x + 1[]
299,2,2,x^2 - 5,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 2*x - 4,11,x^2 + 6*x + 4,13,x^2 -
2*x + 1[]
299,3,2,x^2 - x - 4,3,x^2 - x - 4,5,x^2 - x - 4,7,x^2 - 2*x - 16,11,x^2 - 5*x +
2,13,x^2 - 2*x + 1[]
299,4,2,x^2 + x - 5,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 - 2*x + 1,11,x^2 - 3*x -
3,13,x^2 - 2*x + 1[]
299,5,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 + 4*x - 1,11,x^2 - x -
1,13,x^2 - 2*x + 1[]
299,6,2,x^3,3,x^3 + x^2 - 9*x - 5,5,x^3 - x^2 - 7*x - 3,7,x^3 - 2*x^2 - 8*x +
4,11,x^3 - 5*x^2 - 5*x + 27,13,x^3 - 3*x^2 + 3*x - 1[]
299,7,2,x^10 - x^9 - 19*x^8 + 18*x^7 + 127*x^6 - 109*x^5 - 357*x^4 + 252*x^3 +
400*x^2 - 192*x - 128,3,x^10 - 3*x^9 - 19*x^8 + 58*x^7 + 107*x^6 - 343*x^5 -
181*x^4 + 720*x^3 - 56*x^2 - 400*x + 112,5,x^10 - 3*x^9 - 37*x^8 + 112*x^7 +
443*x^6 - 1401*x^5 - 1817*x^4 + 6424*x^3 + 1108*x^2 - 6140*x - 2372,7,x^10 +
2*x^9 - 53*x^8 - 70*x^7 + 1044*x^6 + 640*x^5 - 9072*x^4 + 456*x^3 + 29888*x^2 -
18272*x - 5936,11,x^10 - 3*x^9 - 71*x^8 + 200*x^7 + 1777*x^6 - 4449*x^5 -
19765*x^4 + 39328*x^3 + 100444*x^2 - 119916*x - 190148,13,x^10 + 10*x^9 + 45*x^8
+ 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1[]

Total time: 16.529 seconds, Total memory usage: 5.44MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 10:43:14 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [299..301] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 10:43:02 on modular  [Seed = 2139684518]
-------------------------------------

299,1,2,$.1^2 -$.1 - 1,3,$.1^2 +$.1 - 1,5,$.1^2 + 3*$.1 + 1,7,$.1^2 + 2*$.1 +
1,11,$.1^2 + 3*$.1 + 1,13,$.1^2 + 2*$.1 + 1[]
299,2,2,$.1^2 - 5,3,$.1^2,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 2*$.1 - 4,11,$.1^2 + 6*$.1 + 4,13,$.1^2 - 2*$.1 + 1[]
299,3,2,$.1^2 -$.1 - 4,3,$.1^2 -$.1 - 4,5,$.1^2 -$.1 - 4,7,$.1^2 - 2*$.1 -
16,11,$.1^2 - 5*$.1 + 2,13,$.1^2 - 2*$.1 + 1[]
299,4,2,$.1^2 +$.1 - 5,3,$.1^2 +$.1 - 5,5,$.1^2 - 3*$.1 - 3,7,$.1^2 - 2*$.1 +
1,11,$.1^2 - 3*$.1 - 3,13,$.1^2 - 2*$.1 + 1[]
299,5,2,$.1^2 +$.1 - 1,3,$.1^2 +$.1 - 1,5,$.1^2 +$.1 - 1,7,$.1^2 + 4*$.1 -
1,11,$.1^2 -$.1 - 1,13,$.1^2 - 2*$.1 + 1[]
299,6,2,$.1^3,3,$.1^3 + $.1^2 - 9*$.1 - 5,5,$.1^3 -$.1^2 - 7*$.1 - 3,7,$.1^3 -
2*$.1^2 - 8*$.1 + 4,11,$.1^3 - 5*$.1^2 - 5*$.1 + 27,13,$.1^3 - 3*$.1^2 + 3*$.1 -
1[]
299,7,2,$.1^10 -$.1^9 - 19*$.1^8 + 18*$.1^7 + 127*$.1^6 - 109*$.1^5 - 357*$.1^4 + 252*$.1^3 + 400*$.1^2 - 192*$.1 - 128,3,$.1^10 - 3*$.1^9 - 19*$.1^8 + 58*$.1^7
+ 107*$.1^6 - 343*$.1^5 - 181*$.1^4 + 720*$.1^3 - 56*$.1^2 - 400*$.1 +
112,5,$.1^10 - 3*$.1^9 - 37*$.1^8 + 112*$.1^7 + 443*$.1^6 - 1401*$.1^5 -
1817*$.1^4 + 6424*$.1^3 + 1108*$.1^2 - 6140*$.1 - 2372,7,$.1^10 + 2*$.1^9 -
53*$.1^8 - 70*$.1^7 + 1044*$.1^6 + 640*$.1^5 - 9072*$.1^4 + 456*$.1^3 +
29888*$.1^2 - 18272*$.1 - 5936,11,$.1^10 - 3*$.1^9 - 71*$.1^8 + 200*$.1^7 +
1777*$.1^6 - 4449*$.1^5 - 19765*$.1^4 + 39328*$.1^3 + 100444*$.1^2 - 119916*$.1
- 190148,13,$.1^10 + 10*$.1^9 + 45*$.1^8 + 120*$.1^7 + 210*$.1^6 + 252*$.1^5 +
210*$.1^4 + 120*$.1^3 + 45*$.1^2 + 10*$.1 + 1[]
300,1,2,x,3,x + 1,5,x,7,x - 1,11,x - 6,13,x + 5[]
300,2,2,x,3,x + 1,5,x,7,x + 4,11,x + 4,13,x[]
300,3,2,x,3,x - 1,5,x,7,x + 1,11,x - 6,13,x - 5[]
300,4,2,x,3,x - 1,5,x,7,x - 4,11,x + 4,13,x[]
301,1,2,x^4 + 4*x^3 + 2*x^2 - 5*x - 3,3,x^4 + 3*x^3 - 2*x^2 - 4*x - 1,5,x^4 +
4*x^3 - 7*x + 3,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 + 15*x^3 + 80*x^2 + 176*x
+ 129,13,x^4 - x^3 - 30*x^2 + 12*x + 217[]
301,2,2,x^5 - 6*x^3 + x^2 + 5*x - 2,3,x^5 + 3*x^4 - 6*x^3 - 18*x^2 + x + 2,5,x^5
+ 6*x^4 - 49*x^2 - 67*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 +
16*x^4 + 83*x^3 + 120*x^2 - 155*x - 283,13,x^5 + 2*x^4 - 35*x^3 - 80*x^2 + 81*x
+ 193[]
301,3,2,x^5 - x^4 - 6*x^3 + 5*x^2 + 6*x - 1,3,x^5 - 5*x^4 + 2*x^3 + 18*x^2 -
15*x - 8,5,x^5 - 4*x^4 - 4*x^3 + 15*x^2 + 17*x + 4,7,x^5 + 5*x^4 + 10*x^3 +
10*x^2 + 5*x + 1,11,x^5 - 13*x^4 + 52*x^3 - 56*x^2 - 23*x + 32,13,x^5 + x^4 -
36*x^3 - 26*x^2 + 147*x - 86[]
301,4,2,x^7 - 4*x^6 - 3*x^5 + 25*x^4 - 13*x^3 - 23*x^2 + 11*x + 2,3,x^7 - x^6 -
14*x^5 + 16*x^4 + 43*x^3 - 54*x^2 - 24*x + 32,5,x^7 - 16*x^5 + 9*x^4 + 57*x^3 -
54*x^2 - 12*x + 16,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x -
1,11,x^7 - 16*x^6 + 83*x^5 - 104*x^4 - 347*x^3 + 881*x^2 - 52*x - 688,13,x^7 +
2*x^6 - 35*x^5 - 102*x^4 + 9*x^3 + 247*x^2 + 220*x + 52[]

Total time: 11.500 seconds, Total memory usage: 4.22MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 10:47:52 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [301..306] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 10:47:35 on modular  [Seed = 267947975]
-------------------------------------

301,1,2,$.1^4 + 4*$.1^3 + 2*$.1^2 - 5*$.1 - 3,3,$.1^4 + 3*$.1^3 - 2*$.1^2 - 4*$.1 - 1,5,$.1^4 + 4*$.1^3 - 7*$.1 + 3,7,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,11,$.1^4 + 15*$.1^3 + 80*$.1^2 + 176*$.1 + 129,13,$.1^4 - $.1^3 - 30*$.1^2 +
12*$.1 + 217[] 301,2,2,$.1^5 - 6*$.1^3 +$.1^2 + 5*$.1 - 2,3,$.1^5 + 3*$.1^4 - 6*$.1^3 -
18*$.1^2 +$.1 + 2,5,$.1^5 + 6*$.1^4 - 49*$.1^2 - 67*$.1 - 4,7,$.1^5 + 5*$.1^4 +
10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,11,$.1^5 + 16*$.1^4 + 83*$.1^3 + 120*$.1^2 - 155*$.1 - 283,13,$.1^5 + 2*$.1^4 - 35*$.1^3 - 80*$.1^2 + 81*$.1 + 193[] 301,3,2,$.1^5 - $.1^4 - 6*$.1^3 + 5*$.1^2 + 6*$.1 - 1,3,$.1^5 - 5*$.1^4 +
2*$.1^3 + 18*$.1^2 - 15*$.1 - 8,5,$.1^5 - 4*$.1^4 - 4*$.1^3 + 15*$.1^2 + 17*$.1
+ 4,7,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,11,$.1^5 - 13*$.1^4 + 52*$.1^3 - 56*$.1^2 - 23*$.1 + 32,13,$.1^5 +$.1^4 - 36*$.1^3 - 26*$.1^2 +
147*$.1 - 86[] 301,4,2,$.1^7 - 4*$.1^6 - 3*$.1^5 + 25*$.1^4 - 13*$.1^3 - 23*$.1^2 + 11*$.1 +
2,3,$.1^7 -$.1^6 - 14*$.1^5 + 16*$.1^4 + 43*$.1^3 - 54*$.1^2 - 24*$.1 + 32,5,$.1^7 - 16*$.1^5 + 9*$.1^4 + 57*$.1^3 - 54*$.1^2 - 12*$.1 + 16,7,$.1^7 -
7*$.1^6 + 21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1,11,$.1^7 - 16*$.1^6 + 83*$.1^5 - 104*$.1^4 - 347*$.1^3 + 881*$.1^2 - 52*$.1 - 688,13,$.1^7
+ 2*$.1^6 - 35*$.1^5 - 102*$.1^4 + 9*$.1^3 + 247*$.1^2 + 220*$.1 + 52[]
302,1,2,x + 1,3,x - 2,5,x - 2,7,x - 4,11,x + 4,13,x[]
302,2,2,x - 1,3,x + 1,5,x + 4,7,x + 2,11,x - 2,13,x + 6[]
302,3,2,x - 1,3,x + 3,5,x,7,x + 2,11,x + 6,13,x + 2[]
302,4,2,x^2 + 2*x + 1,3,x^2 + 2*x - 1,5,x^2,7,x^2 + 4*x - 4,11,x^2 - 4*x -
4,13,x^2 + 8*x + 8[]
302,5,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 10*x^2 - 6*x + 9,5,x^4 + 4*x^3 -
8*x^2 - 44*x - 36,7,x^4 - 2*x^3 - 8*x^2 + 8*x + 4,11,x^4 - 36*x^2 + 4*x +
12,13,x^4 - 14*x^3 + 64*x^2 - 104*x + 36[]
302,6,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 4*x^2 + 8*x - 1,5,x^4 -
8*x^2 - 4*x + 4,7,x^4 - 6*x^3 + 4*x^2 + 24*x - 28,11,x^4 - 20*x^2 - 4*x +
52,13,x^4 - 6*x^3 - 12*x^2 + 64*x - 52[]
303,1,2,x,3,x - 1,5,x + 3,7,x,11,x + 2,13,x + 3[]
303,2,2,x + 2,3,x - 1,5,x + 1,7,x + 2,11,x + 6,13,x - 1[]
303,3,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 1,7,x^2 + 4*x + 2,11,x^2 - 4*x +
4,13,x^2 + 6*x + 1[]
303,4,2,x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 6,3,x^6 - 6*x^5 + 15*x^4 -
20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 6*x^5 + x^4 + 34*x^3 - 16*x^2 - 32*x +
16,7,x^6 - 18*x^4 + 4*x^3 + 80*x^2 - 32*x - 32,11,x^6 - 10*x^5 + 5*x^4 + 144*x^3
- 125*x^2 - 388*x - 164,13,x^6 - 44*x^4 + 14*x^3 + 444*x^2 - 492*x + 53[]
303,5,2,x^7 - 12*x^5 + 40*x^3 + x^2 - 24*x - 4,3,x^7 + 7*x^6 + 21*x^5 + 35*x^4 +
35*x^3 + 21*x^2 + 7*x + 1,5,x^7 - 6*x^6 - 15*x^5 + 132*x^4 - 20*x^3 - 768*x^2 +
688*x + 544,7,x^7 - 6*x^6 - 20*x^5 + 136*x^4 + 112*x^3 - 832*x^2 - 192*x +
1024,11,x^7 + 10*x^6 + x^5 - 312*x^4 - 1293*x^3 - 1600*x^2 + 700*x + 2000,13,x^7
- 10*x^6 + 210*x^4 - 396*x^3 - 104*x^2 + 425*x - 62[]
304,1,2,x,3,x + 1,5,x,7,x + 3,11,x + 2,13,x - 1[]
304,2,2,x,3,x - 2,5,x + 1,7,x - 3,11,x - 3,13,x + 4[]
304,3,2,x,3,x + 1,5,x,7,x - 1,11,x - 6,13,x - 5[]
304,4,2,x,3,x - 2,5,x - 3,7,x - 1,11,x + 3,13,x + 4[]
304,5,2,x,3,x - 1,5,x + 4,7,x + 3,11,x + 2,13,x + 1[]
304,6,2,x,3,x + 2,5,x + 1,7,x - 3,11,x + 5,13,x + 4[]
304,7,2,x^3,3,x^3 + x^2 - 10*x - 8,5,x^3 - x^2 - 10*x + 8,7,x^3 + 4*x^2 - 5*x -
16,11,x^3 - 5*x^2 - 2*x + 8,13,x^3 - 5*x^2 - 2*x + 8[]
305,1,2,x^3 - 3*x + 1,3,x^3 - 3*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 6*x^2 +
3*x - 19,11,x^3 + 6*x^2 + 3*x - 1,13,x^3 + 3*x^2 - 36*x - 127[]
305,2,2,x^4 + 3*x^3 - x^2 - 6*x - 1,3,x^4 + 6*x^3 + 9*x^2 - x - 4,5,x^4 - 4*x^3
+ 6*x^2 - 4*x + 1,7,x^4 + 10*x^3 + 33*x^2 + 41*x + 16,11,x^4 + 2*x^3 - 23*x^2 -
53*x + 32,13,x^4 + x^3 - 8*x^2 + 5*x + 2[]
305,3,2,x^7 + 2*x^6 - 11*x^5 - 19*x^4 + 35*x^3 + 48*x^2 - 25*x - 27,3,x^7 -
15*x^5 + 3*x^4 + 64*x^3 - 8*x^2 - 76*x - 20,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 +
35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 12*x^6 + 33*x^5 + 101*x^4 - 568*x^3 + 472*x^2
+ 464*x + 80,11,x^7 - 2*x^6 - 27*x^5 + 15*x^4 + 220*x^3 + 152*x^2 - 148*x +
12,13,x^7 - 9*x^6 + 12*x^5 + 73*x^4 - 128*x^3 - 200*x^2 + 192*x + 144[]
305,4,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 19*x^3 - 36*x^2 + 5*x + 1,3,x^7 - 6*x^6 +
5*x^5 + 23*x^4 - 28*x^3 - 24*x^2 + 24*x + 8,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1,7,x^7 - 8*x^6 + 7*x^5 + 65*x^4 - 96*x^3 - 120*x^2 +
144*x + 16,11,x^7 + 6*x^6 - 25*x^5 - 153*x^4 + 100*x^3 + 840*x^2 + 216*x +
8,13,x^7 - 5*x^6 - 46*x^5 + 289*x^4 + 176*x^3 - 3560*x^2 + 6432*x - 2864[]
306,1,2,x + 1,3,x,5,x - 2,7,x,11,x - 4,13,x + 2[]
306,2,2,x + 1,3,x,5,x,7,x + 4,11,x + 6,13,x - 2[]
306,3,2,x - 1,3,x,5,x,7,x - 2,11,x,13,x - 2[]
306,4,2,x - 1,3,x,5,x - 4,7,x + 2,11,x,13,x + 6[]
306,5,2,x^2 + 2*x + 1,3,x^2,5,x^2 - 6,7,x^2 - 4*x - 2,11,x^2 - 24,13,x^2 - 4*x -
20[]
306,6,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 6,7,x^2 - 4*x - 2,11,x^2 - 24,13,x^2 - 4*x -
20[]

Total time: 17.329 seconds, Total memory usage: 5.70MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 11:40:11 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [306..312] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 11:39:48 on modular  [Seed = 2472830744]
-------------------------------------

306,1,2,$.1 + 1,3,$.1,5,$.1 - 2,7,$.1,11,$.1 - 4,13,$.1 + 2[]
306,2,2,$.1 + 1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 6,13,$.1 - 2[]
306,3,2,$.1 - 1,3,$.1,5,$.1,7,$.1 - 2,11,$.1,13,$.1 - 2[]
306,4,2,$.1 - 1,3,$.1,5,$.1 - 4,7,$.1 + 2,11,$.1,13,$.1 + 6[]
306,5,2,$.1^2 + 2*$.1 + 1,3,$.1^2,5,$.1^2 - 6,7,$.1^2 - 4*$.1 - 2,11,$.1^2 - 24,13,$.1^2 - 4*$.1 - 20[] 306,6,2,$.1^2 - 2*$.1 + 1,3,$.1^2,5,$.1^2 - 6,7,$.1^2 - 4*$.1 - 2,11,$.1^2 -
24,13,$.1^2 - 4*$.1 - 20[]
307,1,2,x,3,x,5,x - 4,7,x,11,x - 3,13,x - 6[]
307,2,2,x - 1,3,x - 2,5,x,7,x - 3,11,x - 5,13,x[]
307,3,2,x - 2,3,x,5,x - 2,7,x - 3,11,x + 4,13,x[]
307,4,2,x - 2,3,x - 2,5,x,7,x + 3,11,x - 1,13,x - 6[]
307,5,2,x^2 + x - 3,3,x^2 + 3*x - 1,5,x^2 - 6*x + 9,7,x^2 - 5*x + 3,11,x^2 - 7*x
+ 9,13,x^2 + 4*x - 9[]
307,6,2,x^9 - 3*x^8 - 11*x^7 + 30*x^6 + 46*x^5 - 87*x^4 - 91*x^3 + 50*x^2 + 62*x
+ 13,3,x^9 - x^8 - 21*x^7 + 11*x^6 + 162*x^5 - 10*x^4 - 525*x^3 - 169*x^2 +
547*x + 286,5,x^9 - 5*x^8 - 16*x^7 + 83*x^6 + 116*x^5 - 450*x^4 - 482*x^3 +
765*x^2 + 735*x - 100,7,x^9 + 5*x^8 - 17*x^7 - 99*x^6 - 7*x^5 + 432*x^4 +
428*x^3 - 318*x^2 - 558*x - 169,11,x^9 - 47*x^7 - 27*x^6 + 568*x^5 + 650*x^4 -
842*x^3 - 1219*x^2 - 269*x + 5,13,x^9 + 3*x^8 - 49*x^7 - 26*x^6 + 690*x^5 -
968*x^4 - 798*x^3 + 2165*x^2 - 1263*x + 220[]
307,7,2,x^10 + 7*x^9 + 10*x^8 - 28*x^7 - 73*x^6 + 16*x^5 + 128*x^4 + 26*x^3 -
69*x^2 - 18*x - 1,3,x^10 + 4*x^9 - 7*x^8 - 41*x^7 - 8*x^6 + 107*x^5 + 79*x^4 -
50*x^3 - 35*x^2 + 10*x + 1,5,x^10 + 15*x^9 + 83*x^8 + 184*x^7 - 637*x^5 -
732*x^4 + 223*x^3 + 495*x^2 - 45*x + 1,7,x^10 + 3*x^9 - 38*x^8 - 93*x^7 +
522*x^6 + 968*x^5 - 3021*x^4 - 4037*x^3 + 6345*x^2 + 5886*x - 2403,11,x^10 +
10*x^9 - 270*x^7 - 716*x^6 + 1135*x^5 + 7015*x^4 + 9900*x^3 + 4990*x^2 + 171*x -
361,13,x^10 + 11*x^9 - 30*x^8 - 623*x^7 - 559*x^6 + 10436*x^5 + 22728*x^4 -
41589*x^3 - 148643*x^2 - 84705*x + 31181[]
308,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 1,13,x + 4[]
308,2,2,x^2,3,x^2 - 6,5,x^2 - 4*x + 4,7,x^2 + 2*x + 1,11,x^2 + 2*x + 1,13,x^2 -
4*x - 2[]
308,3,2,x^3,3,x^3 + x^2 - 6*x - 2,5,x^3 + x^2 - 16*x - 12,7,x^3 - 3*x^2 + 3*x -
1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 12*x^2 + 34*x + 8[]
309,1,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 2,13,x + 5[]
309,2,2,x^3 - x^2 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - x^2 - 3*x + 1,7,x^3
+ 2*x^2 - 8*x + 4,11,x^3 - 8*x^2 + 16*x - 4,13,x^3 + 3*x^2 - 13*x - 31[]
309,3,2,x^5 + 2*x^4 - 4*x^3 - 6*x^2 + 4*x + 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 +
5*x + 1,5,x^5 + 5*x^4 - 6*x^3 - 56*x^2 - 64*x - 16,7,x^5 + 2*x^4 - 27*x^3 -
42*x^2 + 129*x + 134,11,x^5 + 12*x^4 + 36*x^3 - 16*x^2 - 112*x + 32,13,x^5 - x^4
- 51*x^3 + 25*x^2 + 375*x + 9[]
309,4,2,x^8 + x^7 - 13*x^6 - 11*x^5 + 52*x^4 + 35*x^3 - 59*x^2 - 27*x + 1,3,x^8
- 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,5,x^8 + x^7 -
27*x^6 - 17*x^5 + 196*x^4 - 4*x^3 - 432*x^2 + 304*x - 32,7,x^8 - 6*x^7 - 19*x^6
+ 162*x^5 - 55*x^4 - 1022*x^3 + 1544*x^2 - 220*x - 32,11,x^8 - 6*x^7 - 32*x^6 +
228*x^5 + 88*x^4 - 2144*x^3 + 2880*x^2 - 64*x - 256,13,x^8 - 9*x^7 - 18*x^6 +
354*x^5 - 798*x^4 - 620*x^3 + 2881*x^2 - 1377*x + 106[]
310,1,2,x - 1,3,x - 2,5,x + 1,7,x,11,x - 2,13,x[]
310,2,2,x - 1,3,x + 2,5,x + 1,7,x + 4,11,x,13,x + 4[]
310,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 12,11,x^2 + 2*x -
2,13,x^2 + 6*x + 6[]
310,4,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 4*x -
2,13,x^2 - 4*x - 2[]
310,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 16*x + 16,11,x^3 - 28*x - 52,13,x^3 + 8*x^2 + 16*x + 4[]
311,1,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 2*x^3 - x^2 - 2*x + 1,5,x^4 + x^3 -
3*x^2 - x + 1,7,x^4 + 4*x^3 - 13*x - 11,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4
+ 6*x^3 + 10*x^2 + 3*x - 1[]
311,2,2,x^22 - 2*x^21 - 35*x^20 + 70*x^19 + 517*x^18 - 1033*x^17 - 4195*x^16 +
8357*x^15 + 20417*x^14 - 40403*x^13 - 61287*x^12 + 119701*x^11 + 113017*x^10 -
215615*x^9 - 124399*x^8 + 228609*x^7 + 76453*x^6 - 133295*x^5 - 23503*x^4 +
36742*x^3 + 3587*x^2 - 3200*x - 473,3,x^22 - 2*x^21 - 50*x^20 + 100*x^19 +
1054*x^18 - 2090*x^17 - 12220*x^16 + 23710*x^15 + 85436*x^14 - 158732*x^13 -
372823*x^12 + 638428*x^11 + 1021312*x^10 - 1499190*x^9 - 1731753*x^8 +
1880136*x^7 + 1732827*x^6 - 997894*x^5 - 846784*x^4 + 56220*x^3 + 63398*x^2 +
2766*x - 581,5,x^22 - x^21 - 80*x^20 + 80*x^19 + 2734*x^18 - 2781*x^17 -
52218*x^16 + 54799*x^15 + 611842*x^14 - 669446*x^13 - 4539481*x^12 +
5216024*x^11 + 21207760*x^10 - 25736951*x^9 - 59717725*x^8 + 77226576*x^7 +
90576343*x^6 - 128165703*x^5 - 52348978*x^4 + 91996538*x^3 - 8405884*x^2 -
5816731*x - 405143,7,x^22 - 8*x^21 - 77*x^20 + 751*x^19 + 2057*x^18 - 29039*x^17
- 15212*x^16 + 602096*x^15 - 293191*x^14 - 7369509*x^13 + 7091610*x^12 +
56125407*x^11 - 61368055*x^10 - 277132225*x^9 + 260009583*x^8 + 899877452*x^7 -
487207047*x^6 - 1807798930*x^5 + 21068313*x^4 + 1718049915*x^3 + 879292937*x^2 +
12987869*x - 24640261,11,x^22 - 6*x^21 - 158*x^20 + 1020*x^19 + 10177*x^18 -
72814*x^17 - 340516*x^16 + 2847992*x^15 + 6126512*x^14 - 66931488*x^13 -
50088768*x^12 + 977963776*x^11 - 74690304*x^10 - 8923385856*x^9 + 4847145984*x^8
+ 50054287360*x^7 - 36928937984*x^6 - 166727901184*x^5 + 110340030464*x^4 +
310715056128*x^3 - 85162852352*x^2 - 275443089408*x - 86332669952,13,x^22 -
12*x^21 - 125*x^20 + 1895*x^19 + 5527*x^18 - 128259*x^17 - 57828*x^16 +
4864982*x^15 - 3711305*x^14 - 113354343*x^13 + 167980932*x^12 + 1669526673*x^11
- 3271781053*x^10 - 15371842897*x^9 + 35453664037*x^8 + 83993883166*x^7 -
216607237743*x^6 - 242692713398*x^5 + 680115803253*x^4 + 290042852541*x^3 -
834033148105*x^2 - 92013030575*x + 78103127827[]
312,1,2,x,3,x + 1,5,x,7,x + 4,11,x + 2,13,x + 1[]
312,2,2,x,3,x + 1,5,x + 2,7,x - 4,11,x,13,x - 1[]
312,3,2,x,3,x - 1,5,x,7,x,11,x - 6,13,x + 1[]
312,4,2,x,3,x + 1,5,x - 4,7,x,11,x + 2,13,x + 1[]
312,5,2,x,3,x - 1,5,x + 4,7,x + 4,11,x + 2,13,x + 1[]
312,6,2,x,3,x - 1,5,x - 2,7,x,11,x,13,x - 1[]

Total time: 21.170 seconds, Total memory usage: 6.44MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 11:49:21 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [312..318] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 11:48:59 on modular  [Seed = 3159051800]
-------------------------------------

312,1,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[]
312,2,2,$.1,3,$.1 + 1,5,$.1 + 2,7,$.1 - 4,11,$.1,13,$.1 - 1[]
312,3,2,$.1,3,$.1 - 1,5,$.1,7,$.1,11,$.1 - 6,13,$.1 + 1[]
312,4,2,$.1,3,$.1 + 1,5,$.1 - 4,7,$.1,11,$.1 + 2,13,$.1 + 1[]
312,5,2,$.1,3,$.1 - 1,5,$.1 + 4,7,$.1 + 4,11,$.1 + 2,13,$.1 + 1[]
312,6,2,$.1,3,$.1 - 1,5,$.1 - 2,7,$.1,11,$.1,13,$.1 - 1[]
313,1,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 3*x + 1,7,x^2 - 2*x - 4,11,x^2 -
5,13,x^2 - 7*x + 1[]
313,2,2,x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 - 62*x^6 + 190*x^5 + 196*x^4 -
76*x^3 - 122*x^2 + 2*x + 17,3,x^11 + 8*x^10 + 13*x^9 - 43*x^8 - 138*x^7 - 31*x^6
+ 171*x^5 + 33*x^4 - 90*x^3 + 18*x^2 + 4*x - 1,5,x^11 + 6*x^10 - 13*x^9 -
135*x^8 - 82*x^7 + 822*x^6 + 1216*x^5 - 1314*x^4 - 3151*x^3 - 661*x^2 + 1307*x +
577,7,x^11 + 14*x^10 + 51*x^9 - 111*x^8 - 1036*x^7 - 1273*x^6 + 3469*x^5 +
8394*x^4 + 1303*x^3 - 8825*x^2 - 7006*x - 1532,11,x^11 + 11*x^10 - 9*x^9 -
464*x^8 - 1090*x^7 + 4831*x^6 + 21347*x^5 + 7358*x^4 - 75753*x^3 - 132533*x^2 -
81996*x - 17107,13,x^11 + 7*x^10 - 60*x^9 - 429*x^8 + 1344*x^7 + 9070*x^6 -
15848*x^5 - 78846*x^4 + 106546*x^3 + 225219*x^2 - 305054*x + 84043[]
313,3,2,x^12 - 6*x^11 - 2*x^10 + 69*x^9 - 68*x^8 - 268*x^7 + 399*x^6 + 368*x^5 -
701*x^4 - 57*x^3 + 262*x^2 - 22*x - 19,3,x^12 - x^11 - 23*x^10 + 21*x^9 +
188*x^8 - 152*x^7 - 657*x^6 + 438*x^5 + 945*x^4 - 469*x^3 - 416*x^2 + 112*x +
32,5,x^12 + x^11 - 33*x^10 - 27*x^9 + 346*x^8 + 149*x^7 - 1349*x^6 - 40*x^5 +
1388*x^4 + 101*x^3 - 406*x^2 - 124*x - 8,7,x^12 - 6*x^11 - 19*x^10 + 177*x^9 -
90*x^8 - 1449*x^7 + 2931*x^6 + 1340*x^5 - 9553*x^4 + 10497*x^3 - 4166*x^2 +
250*x + 106,11,x^12 - 9*x^11 - 20*x^10 + 343*x^9 - 218*x^8 - 3962*x^7 + 4665*x^6
+ 19396*x^5 - 21956*x^4 - 43205*x^3 + 29428*x^2 + 40512*x + 928,13,x^12 + 8*x^11
- 35*x^10 - 382*x^9 + 251*x^8 + 6461*x^7 + 1748*x^6 - 49207*x^5 - 19779*x^4 +
172081*x^3 + 17354*x^2 - 230320*x + 79108[]
314,1,2,x + 1,3,x,5,x,7,x + 3,11,x + 2,13,x + 1[]
314,2,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 3*x^5 - 9*x^4 +
26*x^3 + 20*x^2 - 43*x - 25,5,x^6 - x^5 - 23*x^4 + 18*x^3 + 112*x^2 - 123*x -
3,7,x^6 - 3*x^5 - 27*x^4 + 102*x^3 + 98*x^2 - 701*x + 649,11,x^6 - 9*x^5 -
11*x^4 + 282*x^3 - 520*x^2 - 1137*x + 2793,13,x^6 - 4*x^5 - 40*x^4 + 192*x^3 +
64*x^2 - 672*x - 320[]
314,3,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 + x^6 -
17*x^5 - 6*x^4 + 84*x^3 - 19*x^2 - 73*x + 4,5,x^7 - 3*x^6 - 19*x^5 + 58*x^4 +
80*x^3 - 237*x^2 - 115*x + 232,7,x^7 - 4*x^6 - 24*x^5 + 87*x^4 + 136*x^3 -
425*x^2 + 126*x + 5,11,x^7 + x^6 - 61*x^5 + 988*x^3 - 913*x^2 - 989*x +
90,13,x^7 - 7*x^6 - 44*x^5 + 344*x^4 + 464*x^3 - 4928*x^2 + 352*x + 16832[]
315,1,2,x + 1,3,x,5,x + 1,7,x - 1,11,x,13,x + 6[]
315,2,2,x,3,x,5,x - 1,7,x - 1,11,x - 3,13,x - 5[]
315,3,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 + 4*x -
4,13,x^2 + 4*x - 4[]
315,4,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 4*x -
4,13,x^2 + 4*x - 4[]
315,5,2,x^2 - x - 4,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 + x - 4,13,x^2
- 5*x + 2[]
315,6,2,x^2 - 5,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 4*x - 16,13,x^2 -
20[]
316,1,2,x,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 1[]
316,2,2,x,3,x + 3,5,x - 1,7,x - 1,11,x + 6,13,x + 1[]
316,3,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 3*x - 1,7,x^2,11,x^2 - 3*x - 1,13,x^2 - x -
29[]
316,4,2,x^2,3,x^2,5,x^2 + 5*x + 3,7,x^2 + 2*x - 12,11,x^2 + 5*x + 3,13,x^2 + 3*x
- 1[]
317,1,2,x^11 + 3*x^10 - 10*x^9 - 32*x^8 + 31*x^7 + 109*x^6 - 42*x^5 - 147*x^4 +
35*x^3 + 68*x^2 - 19*x - 1,3,x^11 + 11*x^10 + 37*x^9 - x^8 - 239*x^7 - 350*x^6 +
238*x^5 + 755*x^4 + 211*x^3 - 383*x^2 - 252*x - 37,5,x^11 + 4*x^10 - 22*x^9 -
103*x^8 + 78*x^7 + 628*x^6 + 55*x^5 - 1302*x^4 - 253*x^3 + 973*x^2 + 48*x -
144,7,x^11 + 20*x^10 + 147*x^9 + 403*x^8 - 427*x^7 - 4935*x^6 - 9052*x^5 +
1349*x^4 + 21886*x^3 + 24083*x^2 + 8658*x + 324,11,x^11 + 10*x^10 - 19*x^9 -
466*x^8 - 729*x^7 + 6130*x^6 + 16960*x^5 - 24515*x^4 - 94320*x^3 + 27939*x^2 +
142806*x - 55628,13,x^11 + 16*x^10 + 35*x^9 - 700*x^8 - 4497*x^7 - 2129*x^6 +
49343*x^5 + 107373*x^4 - 116494*x^3 - 489295*x^2 - 146956*x + 342164[]
317,2,2,x^15 - x^14 - 22*x^13 + 22*x^12 + 188*x^11 - 184*x^10 - 786*x^9 +
723*x^8 + 1666*x^7 - 1315*x^6 - 1715*x^5 + 910*x^4 + 829*x^3 - 168*x^2 - 129*x +
1,3,x^15 - 11*x^14 + 30*x^13 + 84*x^12 - 549*x^11 + 414*x^10 + 2378*x^9 -
4600*x^8 - 1888*x^7 + 10118*x^6 - 3013*x^5 - 8337*x^4 + 4287*x^3 + 2636*x^2 -
1282*x - 251,5,x^15 - 2*x^14 - 40*x^13 + 81*x^12 + 594*x^11 - 1222*x^10 -
4105*x^9 + 8538*x^8 + 13937*x^7 - 28221*x^6 - 24938*x^5 + 43708*x^4 + 24072*x^3
- 25832*x^2 - 10832*x + 80,7,x^15 - 20*x^14 + 139*x^13 - 213*x^12 - 2063*x^11 +
10345*x^10 - 5644*x^9 - 69675*x^8 + 158086*x^7 + 47475*x^6 - 475434*x^5 +
288528*x^4 + 405976*x^3 - 373400*x^2 - 23248*x + 2704,11,x^15 - 6*x^14 - 67*x^13
+ 382*x^12 + 1823*x^11 - 9214*x^10 - 26096*x^9 + 105977*x^8 + 202604*x^7 -
602465*x^6 - 756834*x^5 + 1659924*x^4 + 1044856*x^3 - 1851192*x^2 - 19776*x +
266288,13,x^15 - 14*x^14 + 11*x^13 + 648*x^12 - 2745*x^11 - 5247*x^10 +
52647*x^9 - 69155*x^8 - 196166*x^7 + 590465*x^6 - 229832*x^5 - 847068*x^4 +
1214792*x^3 - 646464*x^2 + 152304*x - 13232[]
318,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x + 1,13,x + 2[]
318,2,2,x + 1,3,x + 1,5,x - 4,7,x - 1,11,x + 1,13,x + 4[]
318,3,2,x + 1,3,x - 1,5,x,7,x - 5,11,x + 3,13,x + 4[]
318,4,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 5,13,x[]
318,5,2,x - 1,3,x + 1,5,x + 3,7,x + 4,11,x + 5,13,x + 2[]
318,6,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - x - 10,7,x^2,11,x^2 - 3*x -
8,13,x^2 - 12*x + 36[]
318,7,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 + 2*x +
1,13,x^2 + 2*x - 16[]

Total time: 21.840 seconds, Total memory usage: 6.58MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 11:57:21 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [318..324] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 11:56:59 on modular  [Seed = 2773636385]
-------------------------------------

318,1,2,$.1 + 1,3,$.1 + 1,5,$.1 + 1,7,$.1,11,$.1 + 1,13,$.1 + 2[]
318,2,2,$.1 + 1,3,$.1 + 1,5,$.1 - 4,7,$.1 - 1,11,$.1 + 1,13,$.1 + 4[]
318,3,2,$.1 + 1,3,$.1 - 1,5,$.1,7,$.1 - 5,11,$.1 + 3,13,$.1 + 4[]
318,4,2,$.1 - 1,3,$.1 + 1,5,$.1,7,$.1 - 1,11,$.1 - 5,13,$.1[]
318,5,2,$.1 - 1,3,$.1 + 1,5,$.1 + 3,7,$.1 + 4,11,$.1 + 5,13,$.1 + 2[]
318,6,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2*$.1 + 1,5,$.1^2 -$.1 -
10,7,$.1^2,11,$.1^2 - 3*$.1 - 8,13,$.1^2 - 12*$.1 + 36[] 318,7,2,$.1^2 - 2*$.1 + 1,3,$.1^2 - 2*$.1 + 1,5,$.1^2 - $.1 - 4,7,$.1^2 - $.1 - 4,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 2*$.1 - 16[] 319,1,2,x - 2,3,x + 3,5,x - 1,7,x - 4,11,x + 1,13,x - 6[] 319,2,2,x^3 - 3*x - 1,3,x^3 - 3*x + 1,5,x^3 + 6*x^2 + 3*x - 19,7,x^3 + 3*x^2 - 9*x - 19,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 6*x^2 + 3*x - 19[] 319,3,2,x^4 + 2*x^3 - 3*x^2 - 3*x + 2,3,x^4 + 3*x^3 - x^2 - 6*x - 1,5,x^4 + 5*x^3 + 5*x^2 - 2*x - 1,7,x^4 - x^3 - 9*x^2 + 9*x + 8,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 2*x^3 - 29*x^2 + 27*x + 46[] 319,4,2,x^7 - 3*x^6 - 4*x^5 + 15*x^4 + x^3 - 14*x^2 + 1,3,x^7 - 17*x^5 + 3*x^4 + 78*x^3 - 8*x^2 - 96*x + 16,5,x^7 - 4*x^6 - 14*x^5 + 59*x^4 + 36*x^3 - 225*x^2 + 81*x + 81,7,x^7 - x^6 - 25*x^5 + 9*x^4 + 136*x^3 - 56*x^2 - 152*x + 16,11,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,13,x^7 - 51*x^5 + 57*x^4 + 440*x^3 - 768*x^2 - 152*x + 464[] 319,5,2,x^8 - 13*x^6 - x^5 + 50*x^4 + 7*x^3 - 54*x^2 - 5*x + 1,3,x^8 - 4*x^7 - 11*x^6 + 55*x^5 + 10*x^4 - 184*x^3 + 80*x^2 + 112*x - 64,5,x^8 - 10*x^7 + 18*x^6 + 107*x^5 - 406*x^4 + 115*x^3 + 887*x^2 - 641*x - 94,7,x^8 + 7*x^7 - 13*x^6 - 155*x^5 - 128*x^4 + 416*x^3 + 168*x^2 - 432*x + 128,11,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,13,x^8 + 4*x^7 - 43*x^6 - 193*x^5 + 522*x^4 + 3000*x^3 - 520*x^2 - 15168*x - 15520[] 320,1,2,x,3,x,5,x + 1,7,x + 4,11,x + 4,13,x - 2[] 320,2,2,x,3,x - 2,5,x - 1,7,x - 2,11,x,13,x + 2[] 320,3,2,x,3,x - 2,5,x - 1,7,x + 2,11,x - 4,13,x - 6[] 320,4,2,x,3,x + 2,5,x - 1,7,x - 2,11,x + 4,13,x - 6[] 320,5,2,x,3,x,5,x + 1,7,x - 4,11,x - 4,13,x - 2[] 320,6,2,x,3,x + 2,5,x - 1,7,x + 2,11,x,13,x + 2[] 320,7,2,x^2,3,x^2 - 8,5,x^2 + 2*x + 1,7,x^2 - 8,11,x^2 - 32,13,x^2 - 4*x + 4[] 321,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 + 6*x + 4,13,x^2 + 2*x + 1[] 321,2,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 6*x + 9,7,x^2 + 2*x - 4,11,x^2 + 4*x + 4,13,x^2 + 2*x + 1[] 321,3,2,x^6 - 3*x^5 - 5*x^4 + 18*x^3 + x^2 - 19*x + 3,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 6*x^5 + 2*x^4 + 28*x^3 - 10*x^2 - 16*x - 3,7,x^6 - 15*x^4 + 18*x^3 + 13*x^2 - 14*x - 4,11,x^6 - 6*x^5 - 21*x^4 + 138*x^3 - 7*x^2 - 632*x + 636,13,x^6 + 8*x^5 - 4*x^4 - 122*x^3 - 20*x^2 + 500*x - 359[] 321,4,2,x^7 - 14*x^5 - x^4 + 55*x^3 + 8*x^2 - 46*x - 19,3,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,5,x^7 + 8*x^6 + 6*x^5 - 76*x^4 - 102*x^3 + 240*x^2 + 225*x - 250,7,x^7 - 6*x^6 - 15*x^5 + 124*x^4 + 33*x^3 - 788*x^2 + 188*x + 1424,11,x^7 - 4*x^6 - 33*x^5 + 112*x^4 + 277*x^3 - 610*x^2 - 556*x + 976,13,x^7 - 6*x^6 - 20*x^5 + 94*x^4 + 152*x^3 - 276*x^2 - 351*x - 94[] 322,1,2,x + 1,3,x - 2,5,x,7,x - 1,11,x - 4,13,x[] 322,2,2,x + 1,3,x,5,x + 2,7,x - 1,11,x + 4,13,x - 4[] 322,3,2,x - 1,3,x + 2,5,x + 2,7,x + 1,11,x + 2,13,x + 4[] 322,4,2,x - 1,3,x - 2,5,x + 2,7,x - 1,11,x - 6,13,x + 4[] 322,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x - 4,7,x^2 + 2*x + 1,11,x^2,13,x^2 + 4*x - 16[] 322,6,2,x^2 - 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 2*x - 2,7,x^2 - 2*x + 1,11,x^2 - 12,13,x^2 - 4*x - 8[] 322,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 6*x + 8,5,x^3 - 4*x^2 - 2*x + 4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 - 12*x - 16,13,x^3 - 2*x^2 - 16*x + 16[] 323,1,2,x,3,x - 3,5,x + 2,7,x - 4,11,x + 2,13,x - 6[] 323,2,2,x^2 + x - 4,3,x^2 - x - 4,5,x^2 - 4*x + 4,7,x^2 - 2*x - 16,11,x^2 + 4*x + 4,13,x^2 - 4*x + 4[] 323,3,2,x^4 - 6*x^2 - x + 7,3,x^4 + x^3 - 8*x^2 - 10*x - 3,5,x^4 + 7*x^3 + 14*x^2 + 6*x - 1,7,x^4 + 11*x^3 + 41*x^2 + 57*x + 19,11,x^4 + 2*x^3 - 18*x^2 + 7*x + 27,13,x^4 + 10*x^3 + 15*x^2 - 66*x - 71[] 323,4,2,x^5 + 3*x^4 - 2*x^3 - 7*x^2 + 2*x + 1,3,x^5 + 3*x^4 - 4*x^3 - 8*x^2 + 9*x - 2,5,x^5 + 3*x^4 - 6*x^3 - 8*x^2 + x + 2,7,x^5 + 5*x^4 - 3*x^3 - 31*x^2 - 23*x + 8,11,x^5 - 36*x^3 + 31*x^2 + 265*x - 304,13,x^5 + 20*x^4 + 153*x^3 + 558*x^2 + 967*x + 634[] 323,5,2,x^6 - 2*x^5 - 9*x^4 + 15*x^3 + 23*x^2 - 23*x - 21,3,x^6 + 3*x^5 - 6*x^4 - 14*x^3 + 11*x^2 + 6*x - 4,5,x^6 + x^5 - 24*x^4 - 20*x^3 + 149*x^2 + 104*x - 84,7,x^6 - 5*x^5 - x^4 + 27*x^3 - 9*x^2 - 26*x - 4,11,x^6 - 2*x^5 - 40*x^4 + 15*x^3 + 347*x^2 + 146*x + 12,13,x^6 - 14*x^5 + 43*x^4 + 146*x^3 - 743*x^2 - 268*x + 2852[] 323,6,2,x^7 - x^6 - 10*x^5 + 9*x^4 + 26*x^3 - 19*x^2 - 12*x + 8,3,x^7 - 3*x^6 - 9*x^5 + 29*x^4 + 17*x^3 - 68*x^2 + 7*x + 8,5,x^7 - 7*x^6 + 4*x^5 + 54*x^4 - 73*x^3 - 90*x^2 + 124*x - 8,7,x^7 - x^6 - 27*x^5 + 29*x^4 + 227*x^3 - 256*x^2 - 568*x + 608,11,x^7 - 2*x^6 - 46*x^5 + 7*x^4 + 559*x^3 + 592*x^2 - 516*x - 288,13,x^7 - 20*x^6 + 141*x^5 - 342*x^4 - 393*x^3 + 2734*x^2 - 1876*x - 2344[] 324,1,2,x,3,x,5,x - 3,7,x + 1,11,x - 3,13,x + 1[] 324,2,2,x,3,x,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 324,3,2,x,3,x,5,x + 3,7,x - 2,11,x - 6,13,x - 5[] 324,4,2,x,3,x,5,x + 3,7,x + 1,11,x + 3,13,x + 1[] Total time: 21.039 seconds, Total memory usage: 6.57MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:04:28 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [324..330] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sat Nov 29 2003 12:04:05 on modular [Seed = 1921359017] ------------------------------------- 324,1,2,$.1,3,$.1,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 + 1[] 324,2,2,$.1,3,$.1,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[] 324,3,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 2,11,$.1 - 6,13,$.1 - 5[] 324,4,2,$.1,3,$.1,5,$.1 + 3,7,$.1 + 1,11,$.1 + 3,13,$.1 + 1[] 325,1,2,x,3,x + 1,5,x,7,x - 4,11,x + 6,13,x + 1[] 325,2,2,x - 1,3,x - 2,5,x,7,x - 4,11,x - 2,13,x - 1[] 325,3,2,x + 2,3,x + 1,5,x,7,x + 2,11,x - 2,13,x - 1[] 325,4,2,x - 2,3,x - 1,5,x,7,x - 2,11,x - 2,13,x + 1[] 325,5,2,x,3,x - 1,5,x,7,x + 4,11,x + 6,13,x - 1[] 325,6,2,x^2 - 3,3,x^2 + 2*x - 2,5,x^2,7,x^2 + 4*x + 4,11,x^2 + 6*x + 6,13,x^2 + 2*x + 1[] 325,7,2,x^2 - 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 - 2*x - 1,11,x^2 - 10*x + 23,13,x^2 - 2*x + 1[] 325,8,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2,7,x^2 + 4*x - 4,11,x^2 - 4*x + 2,13,x^2 - 2*x + 1[] 325,9,2,x^2 + 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 + 2*x - 1,11,x^2 - 10*x + 23,13,x^2 + 2*x + 1[] 325,10,2,x^3 - 3*x^2 - x + 5,3,x^3 - 4*x^2 + 2*x + 2,5,x^3,7,x^3 - 2*x^2 - 4*x + 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 + 3*x^2 + 3*x + 1[] 325,11,2,x^3 + 3*x^2 - x - 5,3,x^3 + 4*x^2 + 2*x - 2,5,x^3,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 - 3*x^2 + 3*x - 1[] 326,1,2,x + 1,3,x,5,x + 1,7,x + 1,11,x,13,x + 5[] 326,2,2,x + 1,3,x + 2,5,x + 3,7,x + 1,11,x,13,x - 5[] 326,3,2,x - 1,3,x + 2,5,x + 1,7,x + 3,11,x + 4,13,x + 1[] 326,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 3*x^4 - 8*x^3 + 27*x^2 - 5*x - 17,5,x^5 - 9*x^4 + 20*x^3 + 19*x^2 - 77*x + 5,7,x^5 - 4*x^4 - 20*x^3 + 64*x^2 + 64*x - 32,11,x^5 + x^4 - 42*x^3 - 35*x^2 + 383*x + 17,13,x^5 - x^4 - 24*x^3 + 17*x^2 + 121*x - 139[] 326,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 5*x^5 + 29*x^3 - 25*x^2 - 35*x + 36,5,x^6 - 13*x^4 + x^3 + 42*x^2 + 4*x - 31,7,x^6 - 5*x^5 - 20*x^4 + 132*x^3 - 144*x^2 + 32,11,x^6 - x^5 - 38*x^4 + 63*x^3 + 351*x^2 - 837*x + 324,13,x^6 + 4*x^5 - 73*x^4 - 289*x^3 + 1230*x^2 + 4306*x - 1891[] 327,1,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 1,13,x + 4[] 327,2,2,x^3 + 3*x^2 - x - 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + x^2 - 3*x - 1,13,x^3 + 2*x^2 - 4*x - 4[] 327,3,2,x^6 - 4*x^5 - 2*x^4 + 20*x^3 - 8*x^2 - 16*x + 1,3,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,5,x^6 - 5*x^5 - 10*x^4 + 68*x^3 - 40*x^2 - 48*x + 32,7,x^6 + 2*x^5 - 18*x^4 - 44*x^3 + 17*x^2 + 42*x - 16,11,x^6 - 7*x^5 + 52*x^3 - 32*x^2 - 80*x + 64,13,x^6 - 6*x^5 - 20*x^4 + 136*x^3 - 80*x^2 - 160*x + 128[] 327,4,2,x^9 - 3*x^8 - 11*x^7 + 35*x^6 + 34*x^5 - 122*x^4 - 29*x^3 + 127*x^2 + 9*x - 5,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 - x^8 - 33*x^7 + 29*x^6 + 324*x^5 - 248*x^4 - 992*x^3 + 640*x^2 + 64*x - 64,7,x^9 - 6*x^8 - 22*x^7 + 192*x^6 - 151*x^5 - 934*x^4 + 1372*x^3 + 940*x^2 - 1920*x + 512,11,x^9 + 5*x^8 - 51*x^7 - 225*x^6 + 732*x^5 + 2840*x^4 - 2160*x^3 - 7552*x^2 + 1792*x + 5696,13,x^9 - 6*x^8 - 52*x^7 + 284*x^6 + 832*x^5 - 3840*x^4 - 3776*x^3 + 12288*x^2 + 2560*x - 7936[] 328,1,2,x,3,x,5,x + 2,7,x + 2,11,x,13,x + 4[] 328,2,2,x,3,x - 2,5,x - 2,7,x + 2,11,x - 2,13,x - 6[] 328,3,2,x^2,3,x^2 - 2*x - 2,5,x^2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2[] 328,4,2,x^3,3,x^3 + 2*x^2 - 6*x - 10,5,x^3 - 2*x^2 - 8*x + 4,7,x^3 - 4*x^2 - 2*x + 2,11,x^3 + 4*x^2 - 2*x - 2,13,x^3 + 2*x^2 - 28*x + 24[] 328,5,2,x^3,3,x^3 + 4*x^2 + 2*x - 2,5,x^3 + 2*x^2 - 8*x + 4,7,x^3 + 2*x^2 - 14*x + 10,11,x^3 + 10*x^2 + 18*x - 34,13,x^3 + 2*x^2 - 12*x - 8[] 329,1,2,x + 1,3,x + 1,5,x - 3,7,x + 1,11,x - 3,13,x + 6[] 329,2,2,x^2 + 2*x + 1,3,x^2 - x - 4,5,x^2 + 3*x - 2,7,x^2 - 2*x + 1,11,x^2 + 7*x + 8,13,x^2 - 4*x + 4[] 329,3,2,x^3 + x^2 - 2*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 + 3*x - 1,13,x^3 - x^2 - 16*x - 13[] 329,4,2,x^3 - x^2 - 5*x + 1,3,x^3 - x^2 - 9*x + 13,5,x^3 + x^2 - 15*x - 25,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 13*x + 23,13,x^3 + 4*x^2 - 4[] 329,5,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 7*x - 7,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 21*x - 7,13,x^3 + 11*x^2 + 38*x + 41[] 329,6,2,x^5 - x^4 - 11*x^3 + 12*x^2 + 28*x - 33,3,x^5 - 2*x^4 - 9*x^3 + 11*x^2 + 16*x - 16,5,x^5 + 4*x^4 - 5*x^3 - 17*x^2 + 20*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 35*x^3 + 139*x^2 + 188*x - 664,13,x^5 - x^4 - 46*x^3 + 39*x^2 + 112*x + 44[] 329,7,2,x^6 - 12*x^4 + 5*x^3 + 36*x^2 - 29*x + 3,3,x^6 - 3*x^5 - 6*x^4 + 17*x^3 + 12*x^2 - 22*x - 11,5,x^6 - 5*x^5 + 23*x^3 - 4*x^2 - 32*x - 9,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 7*x^5 - 8*x^4 + 111*x^3 - 208*x^2 + 136*x - 27,13,x^6 - 5*x^5 - 28*x^4 + 177*x^3 - 92*x^2 - 528*x + 396[] Errors: /home/mfd/gomagma: line 2: 24876 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:05:06 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [324..329] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:04:49 on modular [Seed = 1805419908] ------------------------------------- 324,1,2,$.1,3,$.1,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 + 1[] 324,2,2,$.1,3,$.1,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[] 324,3,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 2,11,$.1 - 6,13,$.1 - 5[] 324,4,2,$.1,3,$.1,5,$.1 + 3,7,$.1 + 1,11,$.1 + 3,13,$.1 + 1[] 325,1,2,x,3,x + 1,5,x,7,x - 4,11,x + 6,13,x + 1[] 325,2,2,x - 1,3,x - 2,5,x,7,x - 4,11,x - 2,13,x - 1[] 325,3,2,x + 2,3,x + 1,5,x,7,x + 2,11,x - 2,13,x - 1[] 325,4,2,x - 2,3,x - 1,5,x,7,x - 2,11,x - 2,13,x + 1[] 325,5,2,x,3,x - 1,5,x,7,x + 4,11,x + 6,13,x - 1[] 325,6,2,x^2 - 3,3,x^2 + 2*x - 2,5,x^2,7,x^2 + 4*x + 4,11,x^2 + 6*x + 6,13,x^2 + 2*x + 1[] 325,7,2,x^2 - 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 - 2*x - 1,11,x^2 - 10*x + 23,13,x^2 - 2*x + 1[] 325,8,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2,7,x^2 + 4*x - 4,11,x^2 - 4*x + 2,13,x^2 - 2*x + 1[] 325,9,2,x^2 + 2*x - 1,3,x^2 - 8,5,x^2,7,x^2 + 2*x - 1,11,x^2 - 10*x + 23,13,x^2 + 2*x + 1[] 325,10,2,x^3 - 3*x^2 - x + 5,3,x^3 - 4*x^2 + 2*x + 2,5,x^3,7,x^3 - 2*x^2 - 4*x + 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 + 3*x^2 + 3*x + 1[] 325,11,2,x^3 + 3*x^2 - x - 5,3,x^3 + 4*x^2 + 2*x - 2,5,x^3,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + 6*x^2 + 8*x - 2,13,x^3 - 3*x^2 + 3*x - 1[] 326,1,2,x + 1,3,x,5,x + 1,7,x + 1,11,x,13,x + 5[] 326,2,2,x + 1,3,x + 2,5,x + 3,7,x + 1,11,x,13,x - 5[] 326,3,2,x - 1,3,x + 2,5,x + 1,7,x + 3,11,x + 4,13,x + 1[] 326,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 3*x^4 - 8*x^3 + 27*x^2 - 5*x - 17,5,x^5 - 9*x^4 + 20*x^3 + 19*x^2 - 77*x + 5,7,x^5 - 4*x^4 - 20*x^3 + 64*x^2 + 64*x - 32,11,x^5 + x^4 - 42*x^3 - 35*x^2 + 383*x + 17,13,x^5 - x^4 - 24*x^3 + 17*x^2 + 121*x - 139[] 326,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 5*x^5 + 29*x^3 - 25*x^2 - 35*x + 36,5,x^6 - 13*x^4 + x^3 + 42*x^2 + 4*x - 31,7,x^6 - 5*x^5 - 20*x^4 + 132*x^3 - 144*x^2 + 32,11,x^6 - x^5 - 38*x^4 + 63*x^3 + 351*x^2 - 837*x + 324,13,x^6 + 4*x^5 - 73*x^4 - 289*x^3 + 1230*x^2 + 4306*x - 1891[] 327,1,2,x + 1,3,x - 1,5,x + 1,7,x + 2,11,x + 1,13,x + 4[] 327,2,2,x^3 + 3*x^2 - x - 5,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 2*x^2 - 4*x - 4,11,x^3 + x^2 - 3*x - 1,13,x^3 + 2*x^2 - 4*x - 4[] 327,3,2,x^6 - 4*x^5 - 2*x^4 + 20*x^3 - 8*x^2 - 16*x + 1,3,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,5,x^6 - 5*x^5 - 10*x^4 + 68*x^3 - 40*x^2 - 48*x + 32,7,x^6 + 2*x^5 - 18*x^4 - 44*x^3 + 17*x^2 + 42*x - 16,11,x^6 - 7*x^5 + 52*x^3 - 32*x^2 - 80*x + 64,13,x^6 - 6*x^5 - 20*x^4 + 136*x^3 - 80*x^2 - 160*x + 128[] 327,4,2,x^9 - 3*x^8 - 11*x^7 + 35*x^6 + 34*x^5 - 122*x^4 - 29*x^3 + 127*x^2 + 9*x - 5,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 - x^8 - 33*x^7 + 29*x^6 + 324*x^5 - 248*x^4 - 992*x^3 + 640*x^2 + 64*x - 64,7,x^9 - 6*x^8 - 22*x^7 + 192*x^6 - 151*x^5 - 934*x^4 + 1372*x^3 + 940*x^2 - 1920*x + 512,11,x^9 + 5*x^8 - 51*x^7 - 225*x^6 + 732*x^5 + 2840*x^4 - 2160*x^3 - 7552*x^2 + 1792*x + 5696,13,x^9 - 6*x^8 - 52*x^7 + 284*x^6 + 832*x^5 - 3840*x^4 - 3776*x^3 + 12288*x^2 + 2560*x - 7936[] 328,1,2,x,3,x,5,x + 2,7,x + 2,11,x,13,x + 4[] 328,2,2,x,3,x - 2,5,x - 2,7,x + 2,11,x - 2,13,x - 6[] 328,3,2,x^2,3,x^2 - 2*x - 2,5,x^2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2[] 328,4,2,x^3,3,x^3 + 2*x^2 - 6*x - 10,5,x^3 - 2*x^2 - 8*x + 4,7,x^3 - 4*x^2 - 2*x + 2,11,x^3 + 4*x^2 - 2*x - 2,13,x^3 + 2*x^2 - 28*x + 24[] 328,5,2,x^3,3,x^3 + 4*x^2 + 2*x - 2,5,x^3 + 2*x^2 - 8*x + 4,7,x^3 + 2*x^2 - 14*x + 10,11,x^3 + 10*x^2 + 18*x - 34,13,x^3 + 2*x^2 - 12*x - 8[] 329,1,2,x + 1,3,x + 1,5,x - 3,7,x + 1,11,x - 3,13,x + 6[] 329,2,2,x^2 + 2*x + 1,3,x^2 - x - 4,5,x^2 + 3*x - 2,7,x^2 - 2*x + 1,11,x^2 + 7*x + 8,13,x^2 - 4*x + 4[] 329,3,2,x^3 + x^2 - 2*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 4*x^2 + 3*x - 1,13,x^3 - x^2 - 16*x - 13[] 329,4,2,x^3 - x^2 - 5*x + 1,3,x^3 - x^2 - 9*x + 13,5,x^3 + x^2 - 15*x - 25,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 13*x + 23,13,x^3 + 4*x^2 - 4[] 329,5,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 - 7*x - 7,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 21*x - 7,13,x^3 + 11*x^2 + 38*x + 41[] 329,6,2,x^5 - x^4 - 11*x^3 + 12*x^2 + 28*x - 33,3,x^5 - 2*x^4 - 9*x^3 + 11*x^2 + 16*x - 16,5,x^5 + 4*x^4 - 5*x^3 - 17*x^2 + 20*x - 4,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,11,x^5 - 4*x^4 - 35*x^3 + 139*x^2 + 188*x - 664,13,x^5 - x^4 - 46*x^3 + 39*x^2 + 112*x + 44[] 329,7,2,x^6 - 12*x^4 + 5*x^3 + 36*x^2 - 29*x + 3,3,x^6 - 3*x^5 - 6*x^4 + 17*x^3 + 12*x^2 - 22*x - 11,5,x^6 - 5*x^5 + 23*x^3 - 4*x^2 - 32*x - 9,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 7*x^5 - 8*x^4 + 111*x^3 - 208*x^2 + 136*x - 27,13,x^6 - 5*x^5 - 28*x^4 + 177*x^3 - 92*x^2 - 528*x + 396[] Total time: 16.949 seconds, Total memory usage: 5.42MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:10:42 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [329..335] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:10:20 on modular [Seed = 367196343] ------------------------------------- 329,1,2,$.1 + 1,3,$.1 + 1,5,$.1 - 3,7,$.1 + 1,11,$.1 - 3,13,$.1 + 6[] 329,2,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - $.1 - 4,5,$.1^2 + 3*$.1 - 2,7,$.1^2 - 2*$.1 + 1,11,$.1^2 + 7*$.1 + 8,13,$.1^2 - 4*$.1 + 4[] 329,3,2,$.1^3 + $.1^2 - 2*$.1 - 1,3,$.1^3 + 2*$.1^2 - $.1 - 1,5,$.1^3 + 2*$.1^2 -$.1 - 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 + 3*$.1 - 1,13,$.1^3 -$.1^2 - 16*$.1 - 13[] 329,4,2,$.1^3 - $.1^2 - 5*$.1 + 1,3,$.1^3 -$.1^2 - 9*$.1 + 13,5,$.1^3 + $.1^2 - 15*$.1 - 25,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 - $.1^2 - 13*$.1 +
23,13,$.1^3 + 4*$.1^2 - 4[]
329,5,2,$.1^3 +$.1^2 - 2*$.1 - 1,3,$.1^3 + 4*$.1^2 + 3*$.1 - 1,5,$.1^3 - 7*$.1
- 7,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 21*$.1 - 7,13,$.1^3 + 11*$.1^2 + 38*$.1 + 41[]
329,6,2,$.1^5 -$.1^4 - 11*$.1^3 + 12*$.1^2 + 28*$.1 - 33,3,$.1^5 - 2*$.1^4 - 9*$.1^3 + 11*$.1^2 + 16*$.1 - 16,5,$.1^5 + 4*$.1^4 - 5*$.1^3 - 17*$.1^2 + 20*$.1 - 4,7,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,11,$.1^5 - 4*$.1^4 -
35*$.1^3 + 139*$.1^2 + 188*$.1 - 664,13,$.1^5 - $.1^4 - 46*$.1^3 + 39*$.1^2 + 112*$.1 + 44[]
329,7,2,$.1^6 - 12*$.1^4 + 5*$.1^3 + 36*$.1^2 - 29*$.1 + 3,3,$.1^6 - 3*$.1^5 - 6*$.1^4 + 17*$.1^3 + 12*$.1^2 - 22*$.1 - 11,5,$.1^6 - 5*$.1^5 + 23*$.1^3 -
4*$.1^2 - 32*$.1 - 9,7,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1
+ 1,11,$.1^6 - 7*$.1^5 - 8*$.1^4 + 111*$.1^3 - 208*$.1^2 + 136*$.1 - 27,13,$.1^6 - 5*$.1^5 - 28*$.1^4 + 177*$.1^3 - 92*$.1^2 - 528*$.1 + 396[]
330,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x - 1,13,x - 2[]
330,2,2,x + 1,3,x + 1,5,x - 1,7,x + 4,11,x - 1,13,x + 2[]
330,3,2,x - 1,3,x + 1,5,x + 1,7,x - 4,11,x + 1,13,x - 2[]
330,4,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 1,13,x - 6[]
330,5,2,x - 1,3,x - 1,5,x - 1,7,x,11,x + 1,13,x + 2[]
331,1,2,x + 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x + 4[]
331,2,2,x^3 + 2*x^2 - 4*x - 7,3,x^3 + x^2 - 5*x + 2,5,x^3 + 6*x^2 + 8*x +
1,7,x^3 - 3*x^2 - x + 2,11,x^3 + 7*x^2 + 11*x + 4,13,x^3 + 13*x^2 + 41*x - 8[]
331,3,2,x^7 + 2*x^6 - 6*x^5 - 8*x^4 + 11*x^3 + 3*x^2 - 5*x + 1,3,x^7 - 10*x^5 -
3*x^4 + 12*x^3 - 4*x + 1,5,x^7 + 13*x^6 + 58*x^5 + 79*x^4 - 114*x^3 - 335*x^2 -
28*x + 257,7,x^7 + 8*x^6 - 6*x^5 - 184*x^4 - 329*x^3 + 834*x^2 + 2988*x +
2377,11,x^7 + 10*x^6 + 4*x^5 - 206*x^4 - 431*x^3 + 865*x^2 + 2851*x +
1857,13,x^7 - 5*x^6 - 30*x^5 + 189*x^4 - 66*x^3 - 815*x^2 + 906*x - 79[]
331,4,2,x^16 - 3*x^15 - 19*x^14 + 60*x^13 + 136*x^12 - 465*x^11 - 448*x^10 +
1747*x^9 + 657*x^8 - 3241*x^7 - 375*x^6 + 2695*x^5 + 230*x^4 - 855*x^3 - 110*x^2
+ 56*x + 8,3,x^16 + x^15 - 33*x^14 - 25*x^13 + 435*x^12 + 233*x^11 - 2896*x^10 -
999*x^9 + 10181*x^8 + 1965*x^7 - 18302*x^6 - 1340*x^5 + 15636*x^4 - 732*x^3 -
5032*x^2 + 880*x - 32,5,x^16 - 20*x^15 + 151*x^14 - 449*x^13 - 320*x^12 +
5338*x^11 - 9611*x^10 - 11154*x^9 + 52289*x^8 - 26196*x^7 - 82111*x^6 +
92087*x^5 + 30651*x^4 - 65686*x^3 + 3649*x^2 + 10584*x + 157,7,x^16 - x^15 -
61*x^14 + 94*x^13 + 1377*x^12 - 2767*x^11 - 13815*x^10 + 34139*x^9 + 58089*x^8 -
185433*x^7 - 71396*x^6 + 456052*x^5 - 122644*x^4 - 438388*x^3 + 285488*x^2 +
60464*x - 61216,11,x^16 - 9*x^15 - 61*x^14 + 676*x^13 + 1209*x^12 - 19382*x^11 -
8279*x^10 + 274731*x^9 + 13224*x^8 - 2094871*x^7 - 157490*x^6 + 8344536*x^5 +
2432928*x^4 - 14003660*x^3 - 8064856*x^2 + 1680768*x + 888416,13,x^16 - 8*x^15 -
80*x^14 + 838*x^13 + 1115*x^12 - 28708*x^11 + 40887*x^10 + 359296*x^9 -
1099387*x^8 - 989469*x^7 + 7476312*x^6 - 6763164*x^5 - 9092696*x^4 +
18873408*x^3 - 8460480*x^2 - 2000000*x + 1682176[]
332,1,2,x^2,3,x^2 - 7,5,x^2 + 2*x - 6,7,x^2 - 7,11,x^2 - 4*x - 3,13,x^2 + 6*x +
2[]
332,2,2,x^2,3,x^2 + 2*x - 1,5,x^2 - 2,7,x^2 + 6*x + 7,11,x^2 + 6*x + 7,13,x^2 -
2[]
332,3,2,x^3,3,x^3 - 4*x^2 + 3*x + 1,5,x^3 - 2*x^2 - 8*x + 8,7,x^3 - 8*x^2 + 19*x
- 13,11,x^3 + 4*x^2 - 25*x - 71,13,x^3 - 6*x^2 - 16*x + 104[]
333,1,2,x - 1,3,x,5,x + 2,7,x + 4,11,x - 4,13,x + 2[]
333,2,2,x + 1,3,x,5,x - 2,7,x + 4,11,x + 4,13,x + 2[]
333,3,2,x - 2,3,x,5,x - 2,7,x + 1,11,x - 5,13,x + 2[]
333,4,2,x,3,x,5,x,7,x + 1,11,x + 3,13,x + 4[]
333,5,2,x^3 + 3*x^2 - x - 5,3,x^3,5,x^3 + 4*x^2 - 4*x - 20,7,x^3 + 4*x^2 - 8*x -
16,11,x^3 + 4*x^2 - 16*x - 32,13,x^3 + 2*x^2 - 20*x - 8[]
333,6,2,x^4 - 6*x^2 + 3,3,x^4,5,x^4 - 12*x^2 + 12,7,x^4 - 8*x^3 + 24*x^2 - 32*x
+ 16,11,x^4,13,x^4 - 8*x^3 + 24*x^2 - 32*x + 16[]
333,7,2,x^4 - 6*x^2 - 2*x + 5,3,x^4,5,x^4 - 2*x^3 - 8*x^2 + 4,7,x^4 - 4*x^3 -
16*x^2 + 64*x - 16,11,x^4 - 32*x^2 + 32*x + 64,13,x^4 - 4*x^3 - 32*x^2 + 144*x -
80[]
334,1,2,x - 1,3,x,5,x - 3,7,x - 1,11,x,13,x + 2[]
334,2,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2 + 2*x + 1,7,x^2 - 5,11,x^2 + 5*x +
5,13,x^2 - 5[]
334,3,2,x^2 + 2*x + 1,3,x^2 - 8,5,x^2 - 2*x - 1,7,x^2 + 6*x + 9,11,x^2 -
8,13,x^2 - 8*x + 8[]
334,4,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 4*x - 1,7,x^2 + 6*x + 9,11,x^2 +
9*x + 19,13,x^2 - 2*x - 19[]
334,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 5*x - 4,5,x^3 - 13*x + 16,7,x^3 -
13*x + 16,11,x^3 - 11*x^2 + 33*x - 16,13,x^3 + 10*x^2 + 21*x - 4[]
334,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 7*x + 8,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 7*x^2 - 9*x + 88,13,x^3 - 2*x^2 - 9*x + 14[]
335,1,2,x,3,x,5,x - 1,7,x + 2,11,x + 2,13,x + 2[]
335,2,2,x^2 - 2,3,x^2 - 2,5,x^2 + 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 2,13,x^2 +
4*x + 4[]
335,3,2,x^2 - x - 1,3,x^2 - 5,5,x^2 + 2*x + 1,7,x^2 - 5,11,x^2 + 6*x + 4,13,x^2
- 12*x + 36[]
335,4,2,x^7 - 2*x^6 - 12*x^5 + 21*x^4 + 42*x^3 - 52*x^2 - 39*x - 6,3,x^7 - 4*x^6
- 8*x^5 + 46*x^4 - 27*x^3 - 36*x^2 - x + 2,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 +
35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 10*x^6 + 12*x^5 + 176*x^4 - 757*x^3 + 1136*x^2
- 673*x + 134,11,x^7 - 6*x^6 - 32*x^5 + 184*x^4 + 240*x^3 - 1408*x^2 - 576*x +
3072,13,x^7 - 4*x^6 - 45*x^5 + 134*x^4 + 639*x^3 - 1016*x^2 - 2835*x - 778[]
335,5,2,x^11 - 18*x^9 + 2*x^8 + 114*x^7 - 24*x^6 - 306*x^5 + 86*x^4 + 332*x^3 -
109*x^2 - 114*x + 46,3,x^11 - 27*x^9 + 2*x^8 + 263*x^7 - 42*x^6 - 1148*x^5 +
290*x^4 + 2249*x^3 - 858*x^2 - 1622*x + 872,5,x^11 - 11*x^10 + 55*x^9 - 165*x^8
+ 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,7,x^11 -
4*x^10 - 49*x^9 + 184*x^8 + 911*x^7 - 2998*x^6 - 8264*x^5 + 20214*x^4 +
39089*x^3 - 44972*x^2 - 84588*x - 15680,11,x^11 - 6*x^10 - 86*x^9 + 536*x^8 +
2496*x^7 - 15968*x^6 - 32384*x^5 + 195968*x^4 + 219648*x^3 - 888064*x^2 -
844288*x + 542720,13,x^11 - 4*x^10 - 69*x^9 + 330*x^8 + 1207*x^7 - 7760*x^6 -
315*x^5 + 50266*x^4 - 58056*x^3 - 40752*x^2 + 77328*x - 18144[]

Total time: 21.489 seconds, Total memory usage: 6.27MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 12:20:02 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [335..341] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 12:19:39 on modular  [Seed = 66382193]
-------------------------------------

335,1,2,$.1,3,$.1,5,$.1 - 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 2[]
335,2,2,$.1^2 - 2,3,$.1^2 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 4*$.1 + 4,11,$.1^2 - 2,13,$.1^2 + 4*$.1 + 4[] 335,3,2,$.1^2 - $.1 - 1,3,$.1^2 - 5,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 5,11,$.1^2 +
6*$.1 + 4,13,$.1^2 - 12*$.1 + 36[] 335,4,2,$.1^7 - 2*$.1^6 - 12*$.1^5 + 21*$.1^4 + 42*$.1^3 - 52*$.1^2 - 39*$.1 -
6,3,$.1^7 - 4*$.1^6 - 8*$.1^5 + 46*$.1^4 - 27*$.1^3 - 36*$.1^2 - $.1 + 2,5,$.1^7
+ 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,7,$.1^7 - 10*$.1^6 + 12*$.1^5 + 176*$.1^4 - 757*$.1^3 + 1136*$.1^2 - 673*$.1 + 134,11,$.1^7 - 6*$.1^6 - 32*$.1^5 + 184*$.1^4 + 240*$.1^3 - 1408*$.1^2 - 576*$.1
+ 3072,13,$.1^7 - 4*$.1^6 - 45*$.1^5 + 134*$.1^4 + 639*$.1^3 - 1016*$.1^2 -
2835*$.1 - 778[] 335,5,2,$.1^11 - 18*$.1^9 + 2*$.1^8 + 114*$.1^7 - 24*$.1^6 - 306*$.1^5 + 86*$.1^4 + 332*$.1^3 - 109*$.1^2 - 114*$.1 + 46,3,$.1^11 - 27*$.1^9 + 2*$.1^8 +
263*$.1^7 - 42*$.1^6 - 1148*$.1^5 + 290*$.1^4 + 2249*$.1^3 - 858*$.1^2 -
1622*$.1 + 872,5,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 + 330*$.1^7 -
462*$.1^6 + 462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1,7,$.1^11 - 4*$.1^10 - 49*$.1^9 + 184*$.1^8 + 911*$.1^7 - 2998*$.1^6 - 8264*$.1^5 + 20214*$.1^4 + 39089*$.1^3 - 44972*$.1^2 - 84588*$.1 - 15680,11,$.1^11 - 6*$.1^10 - 86*$.1^9 + 536*$.1^8 + 2496*$.1^7 - 15968*$.1^6 - 32384*$.1^5 + 195968*$.1^4 + 219648*$.1^3 - 888064*$.1^2 - 844288*$.1 + 542720,13,$.1^11 - 4*$.1^10 -
69*$.1^9 + 330*$.1^8 + 1207*$.1^7 - 7760*$.1^6 - 315*$.1^5 + 50266*$.1^4 -
58056*$.1^3 - 40752*$.1^2 + 77328*$.1 - 18144[] 336,1,2,x,3,x + 1,5,x - 2,7,x - 1,11,x,13,x + 2[] 336,2,2,x,3,x - 1,5,x - 2,7,x + 1,11,x,13,x - 6[] 336,3,2,x,3,x + 1,5,x,7,x + 1,11,x - 6,13,x - 2[] 336,4,2,x,3,x + 1,5,x + 2,7,x - 1,11,x + 4,13,x + 2[] 336,5,2,x,3,x - 1,5,x + 2,7,x - 1,11,x - 4,13,x - 6[] 336,6,2,x,3,x - 1,5,x - 4,7,x - 1,11,x + 2,13,x + 6[] 337,1,2,x^12 + 6*x^11 + x^10 - 54*x^9 - 76*x^8 + 135*x^7 + 289*x^6 - 97*x^5 - 392*x^4 - 28*x^3 + 201*x^2 + 36*x - 27,3,x^12 + 11*x^11 + 38*x^10 + 6*x^9 - 236*x^8 - 429*x^7 + 35*x^6 + 621*x^5 + 253*x^4 - 297*x^3 - 156*x^2 + 47*x + 25,5,x^12 + 10*x^11 + 17*x^10 - 132*x^9 - 527*x^8 + 35*x^7 + 2998*x^6 + 4271*x^5 - 2229*x^4 - 10525*x^3 - 10100*x^2 - 4125*x - 625,7,x^12 + 13*x^11 + 32*x^10 - 261*x^9 - 1569*x^8 - 1265*x^7 + 9845*x^6 + 26080*x^5 + 10940*x^4 - 30124*x^3 - 31288*x^2 - 4948*x - 9,11,x^12 + 7*x^11 - 46*x^10 - 401*x^9 + 236*x^8 + 6118*x^7 + 6069*x^6 - 24890*x^5 - 28251*x^4 + 44478*x^3 + 28863*x^2 - 36612*x + 6075,13,x^12 + 6*x^11 - 84*x^10 - 532*x^9 + 2177*x^8 + 15792*x^7 - 14373*x^6 - 176312*x^5 - 87376*x^4 + 624217*x^3 + 864963*x^2 + 200995*x - 101313[] 337,2,2,x^15 - 3*x^14 - 18*x^13 + 56*x^12 + 123*x^11 - 402*x^10 - 400*x^9 + 1395*x^8 + 643*x^7 - 2406*x^6 - 496*x^5 + 1843*x^4 + 200*x^3 - 388*x^2 - 69*x + 1,3,x^15 - 9*x^14 + 10*x^13 + 126*x^12 - 356*x^11 - 473*x^10 + 2511*x^9 - 147*x^8 - 7503*x^7 + 3919*x^6 + 10704*x^5 - 6921*x^4 - 7307*x^3 + 3460*x^2 + 2216*x + 64,5,x^15 - 10*x^14 + 11*x^13 + 170*x^12 - 433*x^11 - 1061*x^10 + 3724*x^9 + 2939*x^8 - 14061*x^7 - 3535*x^6 + 24746*x^5 + 2311*x^4 - 17969*x^3 - 3070*x^2 + 3900*x + 1048,7,x^15 - 7*x^14 - 28*x^13 + 263*x^12 + 187*x^11 - 3733*x^10 + 949*x^9 + 25860*x^8 - 16912*x^7 - 91924*x^6 + 79452*x^5 + 153600*x^4 - 164337*x^3 - 77896*x^2 + 127336*x - 33056,11,x^15 - 9*x^14 - 44*x^13 + 659*x^12 - 596*x^11 - 14278*x^10 + 43871*x^9 + 85358*x^8 - 535343*x^7 + 275388*x^6 + 1943157*x^5 - 2657068*x^4 - 1775361*x^3 + 3954164*x^2 + 281822*x - 1662812,13,x^15 + 4*x^14 - 80*x^13 - 228*x^12 + 2533*x^11 + 4102*x^10 - 39373*x^9 - 19254*x^8 + 294312*x^7 - 117851*x^6 - 821659*x^5 + 811293*x^4 + 186277*x^3 - 340210*x^2 + 7376*x + 33040[] 338,1,2,x + 1,3,x,5,x - 1,7,x + 4,11,x + 4,13,x[] 338,2,2,x + 1,3,x + 3,5,x - 1,7,x + 1,11,x - 2,13,x[] 338,3,2,x + 1,3,x + 1,5,x - 3,7,x - 3,11,x,13,x[] 338,4,2,x - 1,3,x,5,x + 1,7,x - 4,11,x - 4,13,x[] 338,5,2,x - 1,3,x - 1,5,x - 3,7,x - 1,11,x + 6,13,x[] 338,6,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x,13,x[] 338,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 4*x + 13,5,x^3 + 2*x^2 - 8*x - 8,7,x^3 - 4*x^2 - 4*x + 8,11,x^3 + 3*x^2 - 4*x - 13,13,x^3[] 338,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 4*x + 13,5,x^3 - 2*x^2 - 8*x + 8,7,x^3 + 4*x^2 - 4*x - 8,11,x^3 - 3*x^2 - 4*x + 13,13,x^3[] 339,1,2,x - 2,3,x + 1,5,x - 2,7,x - 3,11,x + 6,13,x - 5[] 339,2,2,x,3,x - 1,5,x + 1,7,x + 3,11,x + 4,13,x + 2[] 339,3,2,x + 2,3,x - 1,5,x + 3,7,x - 1,11,x + 2,13,x + 2[] 339,4,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 1,7,x^2 + 2*x + 1,11,x^2 - 2,13,x^2 + 8*x + 8[] 339,5,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 7,7,x^2 - 6*x + 9,11,x^2 - 4*x - 4,13,x^2 - 10*x + 25[] 339,6,2,x^2 - 4*x + 4,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 + x - 4,11,x^2 + 2*x - 16,13,x^2 + 6*x + 9[] 339,7,2,x^5 - x^4 - 10*x^3 + 6*x^2 + 22*x + 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 2*x^4 - 20*x^3 - 42*x^2 + 93*x + 202,7,x^5 + 5*x^4 - 5*x^3 - 57*x^2 - 84*x - 32,11,x^5 - 4*x^4 - 20*x^3 + 86*x^2 - 96*x + 32,13,x^5 + 3*x^4 - 24*x^3 - 92*x^2 - 52*x - 8[] 339,8,2,x^5 - 7*x^3 - 4*x^2 + 6*x + 2,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 - 3*x^4 - 6*x^3 + 16*x^2 + x - 1,7,x^5 + 3*x^4 - 18*x^3 - 18*x^2 + 89*x - 41,11,x^5 - 2*x^4 - 30*x^3 + 58*x^2 + 224*x - 424,13,x^5 - 8*x^4 - 11*x^3 + 150*x^2 - 56*x - 92[] 340,1,2,x,3,x,5,x + 1,7,x + 4,11,x - 2,13,x + 6[] 340,2,2,x^3,3,x^3 - 8*x + 4,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 8*x + 4,11,x^3 - 2*x^2 - 16*x - 4,13,x^3 - 2*x^2 - 28*x + 72[] 341,1,2,x^2 - x - 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - x - 11,11,x^2 - 2*x + 1,13,x^2 + 2*x - 19[] 341,2,2,x^4 + 2*x^3 - x^2 - 2*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 6*x + 4,5,x^4 + x^3 - 8*x^2 - 11*x + 1,7,x^4 + 5*x^3 + 4*x^2 - 5*x - 1,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 6*x^3 + 7*x^2 - 6*x - 4[] 341,3,2,x^8 - x^7 - 14*x^6 + 11*x^5 + 60*x^4 - 31*x^3 - 74*x^2 + 5*x + 3,3,x^8 - 4*x^7 - 6*x^6 + 34*x^5 - x^4 - 74*x^3 + 19*x^2 + 42*x + 1,5,x^8 + 5*x^7 - 12*x^6 - 77*x^5 - 11*x^4 + 176*x^3 + 35*x^2 - 77*x + 9,7,x^8 - 7*x^7 - 8*x^6 + 127*x^5 - 137*x^4 - 434*x^3 + 657*x^2 + 393*x - 659,11,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,13,x^8 - 8*x^7 - 10*x^6 + 130*x^5 + 139*x^4 - 600*x^3 - 1171*x^2 - 538*x + 37[] 341,4,2,x^11 - x^10 - 20*x^9 + 20*x^8 + 141*x^7 - 135*x^6 - 421*x^5 + 347*x^4 + 530*x^3 - 288*x^2 - 239*x + 17,3,x^11 - 4*x^10 - 20*x^9 + 88*x^8 + 129*x^7 - 684*x^6 - 233*x^5 + 2146*x^4 - 269*x^3 - 2130*x^2 + 268*x + 304,5,x^11 - 3*x^10 - 35*x^9 + 106*x^8 + 423*x^7 - 1261*x^6 - 2318*x^5 + 6533*x^4 + 5956*x^3 - 14599*x^2 - 6045*x + 10618,7,x^11 - 5*x^10 - 41*x^9 + 234*x^8 + 471*x^7 - 3723*x^6 - 266*x^5 + 23865*x^4 - 21440*x^3 - 48211*x^2 + 83151*x - 32728,11,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,13,x^11 + 2*x^10 - 96*x^9 - 188*x^8 + 3497*x^7 + 6824*x^6 - 58955*x^5 - 115484*x^4 + 433915*x^3 + 842512*x^2 - 913120*x - 1575176[] Total time: 20.420 seconds, Total memory usage: 6.25MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:30:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [341..347] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:30:18 on modular [Seed = 601148375] ------------------------------------- 341,1,2,$.1^2 - $.1 - 1,3,$.1^2 + 2*$.1 + 1,5,$.1^2 + 3*$.1 + 1,7,$.1^2 - $.1 - 11,11,$.1^2 - 2*$.1 + 1,13,$.1^2 + 2*$.1 - 19[] 341,2,2,$.1^4 + 2*$.1^3 -$.1^2 - 2*$.1 + 1,3,$.1^4 + 2*$.1^3 - 5*$.1^2 - 6*$.1 + 4,5,$.1^4 + $.1^3 - 8*$.1^2 - 11*$.1 + 1,7,$.1^4 + 5*$.1^3 + 4*$.1^2 - 5*$.1 - 1,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 6*$.1^3 + 7*$.1^2 - 6*$.1 - 4[] 341,3,2,$.1^8 - $.1^7 - 14*$.1^6 + 11*$.1^5 + 60*$.1^4 - 31*$.1^3 - 74*$.1^2 +
5*$.1 + 3,3,$.1^8 - 4*$.1^7 - 6*$.1^6 + 34*$.1^5 -$.1^4 - 74*$.1^3 + 19*$.1^2 +
42*$.1 + 1,5,$.1^8 + 5*$.1^7 - 12*$.1^6 - 77*$.1^5 - 11*$.1^4 + 176*$.1^3 + 35*$.1^2 - 77*$.1 + 9,7,$.1^8 - 7*$.1^7 - 8*$.1^6 + 127*$.1^5 - 137*$.1^4 -
434*$.1^3 + 657*$.1^2 + 393*$.1 - 659,11,$.1^8 + 8*$.1^7 + 28*$.1^6 + 56*$.1^5 + 70*$.1^4 + 56*$.1^3 + 28*$.1^2 + 8*$.1 + 1,13,$.1^8 - 8*$.1^7 - 10*$.1^6 +
130*$.1^5 + 139*$.1^4 - 600*$.1^3 - 1171*$.1^2 - 538*$.1 + 37[] 341,4,2,$.1^11 - $.1^10 - 20*$.1^9 + 20*$.1^8 + 141*$.1^7 - 135*$.1^6 - 421*$.1^5 + 347*$.1^4 + 530*$.1^3 - 288*$.1^2 - 239*$.1 + 17,3,$.1^11 - 4*$.1^10
- 20*$.1^9 + 88*$.1^8 + 129*$.1^7 - 684*$.1^6 - 233*$.1^5 + 2146*$.1^4 -
269*$.1^3 - 2130*$.1^2 + 268*$.1 + 304,5,$.1^11 - 3*$.1^10 - 35*$.1^9 +
106*$.1^8 + 423*$.1^7 - 1261*$.1^6 - 2318*$.1^5 + 6533*$.1^4 + 5956*$.1^3 -
14599*$.1^2 - 6045*$.1 + 10618,7,$.1^11 - 5*$.1^10 - 41*$.1^9 + 234*$.1^8 +
471*$.1^7 - 3723*$.1^6 - 266*$.1^5 + 23865*$.1^4 - 21440*$.1^3 - 48211*$.1^2 +
83151*$.1 - 32728,11,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 + 330*$.1^7 -
462*$.1^6 + 462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1,13,$.1^11 + 2*$.1^10 - 96*$.1^9 - 188*$.1^8 + 3497*$.1^7 + 6824*$.1^6 - 58955*$.1^5 - 115484*$.1^4 + 433915*$.1^3 + 842512*$.1^2 - 913120*$.1 - 1575176[] 342,1,2,x + 1,3,x,5,x + 2,7,x,11,x + 2,13,x + 4[] 342,2,2,x + 1,3,x,5,x + 2,7,x,11,x - 4,13,x - 2[] 342,3,2,x + 1,3,x,5,x - 4,7,x - 3,11,x + 2,13,x + 1[] 342,4,2,x + 1,3,x,5,x,7,x + 4,11,x,13,x + 4[] 342,5,2,x - 1,3,x,5,x - 2,7,x,11,x - 2,13,x + 4[] 342,6,2,x - 1,3,x,5,x,7,x + 1,11,x - 6,13,x - 5[] 342,7,2,x - 1,3,x,5,x,7,x - 4,11,x + 4,13,x[] 343,1,2,x^3 + 4*x^2 + 3*x - 1,3,x^3,5,x^3,7,x^3,11,x^3 + 9*x^2 + 20*x + 13,13,x^3[] 343,2,2,x^3 - 3*x^2 - 4*x + 13,3,x^3,5,x^3,7,x^3,11,x^3 - 5*x^2 - 36*x + 167,13,x^3[] 343,3,2,x^6 + 2*x^5 - 6*x^4 - 10*x^3 + 10*x^2 + 11*x - 1,3,x^6 + 5*x^5 - x^4 - 34*x^3 - 28*x^2 + 49*x + 49,5,x^6 + 11*x^5 + 38*x^4 + 20*x^3 - 126*x^2 - 196*x - 49,7,x^6,11,x^6 + x^5 - 26*x^4 - 10*x^3 + 159*x^2 + 43*x - 239,13,x^6 + 7*x^5 - 14*x^4 - 154*x^3 - 147*x^2 + 343*x + 343[] 343,4,2,x^6 + 2*x^5 - 6*x^4 - 10*x^3 + 10*x^2 + 11*x - 1,3,x^6 - 5*x^5 - x^4 + 34*x^3 - 28*x^2 - 49*x + 49,5,x^6 - 11*x^5 + 38*x^4 - 20*x^3 - 126*x^2 + 196*x - 49,7,x^6,11,x^6 + x^5 - 26*x^4 - 10*x^3 + 159*x^2 + 43*x - 239,13,x^6 - 7*x^5 - 14*x^4 + 154*x^3 - 147*x^2 - 343*x + 343[] 343,5,2,x^6 - 4*x^5 + 2*x^4 + 6*x^3 - 3*x^2 - 2*x + 1,3,x^6 - 20*x^4 + 124*x^2 - 232,5,x^6 - 24*x^4 + 164*x^2 - 232,7,x^6,11,x^6 - 2*x^5 - 3*x^4 + 6*x^3 + 2*x^2 - 4*x + 1,13,x^6 - 70*x^4 + 1568*x^2 - 11368[] 344,1,2,x,3,x,5,x + 2,7,x + 2,11,x - 1,13,x + 1[] 344,2,2,x^2,3,x^2 + 2*x - 2,5,x^2 + 2*x - 2,7,x^2 + 2*x - 2,11,x^2 + 6*x + 9,13,x^2 + 6*x + 9[] 344,3,2,x^3,3,x^3 - 3*x^2 - x + 4,5,x^3 - x^2 - 5*x - 2,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - x^2 - 32*x + 64,13,x^3 - 3*x^2 - 40*x + 148[] 344,4,2,x^5,3,x^5 + x^4 - 13*x^3 - 8*x^2 + 42*x + 8,5,x^5 - x^4 - 21*x^3 + 26*x^2 + 110*x - 164,7,x^5 - 2*x^4 - 22*x^3 + 24*x^2 + 104*x - 64,11,x^5 - 2*x^4 - 31*x^3 + 48*x^2 + 192*x - 320,13,x^5 - 8*x^4 - 7*x^3 + 106*x^2 + 28*x - 8[] 345,1,2,x,3,x + 1,5,x + 1,7,x - 1,11,x - 4,13,x[] 345,2,2,x - 2,3,x + 1,5,x - 1,7,x - 3,11,x - 2,13,x + 2[] 345,3,2,x - 1,3,x - 1,5,x + 1,7,x - 4,11,x - 4,13,x - 6[] 345,4,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x + 4,13,x + 2[] 345,5,2,x,3,x - 1,5,x + 1,7,x + 3,11,x + 4,13,x[] 345,6,2,x + 2,3,x - 1,5,x - 1,7,x + 5,11,x + 2,13,x + 6[] 345,7,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x - 7,11,x^2 + 8*x + 14,13,x^2 - 4*x + 2[] 345,8,2,x^2 + 2*x - 2,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + 2*x - 2,13,x^2 - 2*x - 26[] 345,9,2,x^2 - 6,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 6,13,x^2 - 4*x - 2[] 345,10,2,x^3 + x^2 - 4*x - 2,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 6*x^2 + 5*x + 8,11,x^3 + 2*x^2 - 6*x - 8,13,x^3 - 4*x^2 - 2*x + 4[] 346,1,2,x - 1,3,x - 1,5,x + 1,7,x - 4,11,x - 4,13,x + 6[] 346,2,2,x - 1,3,x + 1,5,x + 3,7,x + 2,11,x + 4,13,x[] 346,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 6*x + 4,5,x^3 - 4*x - 1,7,x^3 + 3*x^2 - x - 4,11,x^3 - 12*x^2 + 48*x - 64,13,x^3 - 16*x - 8[] 346,4,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 5*x - 1,5,x^4 + 5*x^3 - 20*x - 8,7,x^4 + x^3 - 22*x^2 - x + 82,11,x^4 + 13*x^3 + 46*x^2 - 3*x - 164,13,x^4 - 3*x^3 - 18*x^2 + 37*x - 16[] 346,5,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 + 3*x^4 - 8*x^3 - 21*x^2 + 18*x + 28,5,x^5 - 5*x^4 - 7*x^3 + 60*x^2 - 44*x - 56,7,x^5 + 2*x^4 - 12*x^3 - 20*x^2 + 33*x + 43,11,x^5 - 5*x^4 - 14*x^3 + 55*x^2 + 52*x - 48,13,x^5 - 9*x^4 + 16*x^3 + 49*x^2 - 158*x + 108[] 347,1,2,x + 2,3,x - 1,5,x,7,x + 2,11,x + 3,13,x + 2[] 347,2,2,x^2 - 2*x + 1,3,x^2 + x - 1,5,x^2 + 2*x - 4,7,x^2 + 4*x + 4,11,x^2 - 3*x + 1,13,x^2 + 7*x + 11[] 347,3,2,x^7 + 2*x^6 - 7*x^5 - 15*x^4 + 6*x^3 + 22*x^2 + 9*x + 1,3,x^7 + 7*x^6 + 9*x^5 - 33*x^4 - 88*x^3 - 29*x^2 + 74*x + 52,5,x^7 + 8*x^6 + 17*x^5 - 5*x^4 - 34*x^3 + 4*x^2 + 20*x - 7,7,x^7 + 5*x^6 - 16*x^5 - 101*x^4 + 2*x^3 + 391*x^2 + 131*x - 241,11,x^7 - 2*x^6 - 49*x^5 + 42*x^4 + 708*x^3 - 178*x^2 - 3012*x - 241,13,x^7 + 22*x^6 + 171*x^5 + 483*x^4 - 188*x^3 - 2572*x^2 - 1463*x + 439[] 347,4,2,x^19 - 30*x^17 + x^16 + 374*x^15 - 21*x^14 - 2509*x^13 + 166*x^12 + 9794*x^11 - 586*x^10 - 22435*x^9 + 749*x^8 + 28885*x^7 + 329*x^6 - 18752*x^5 - 878*x^4 + 4788*x^3 - 64*x^2 - 352*x + 32,3,x^19 - 7*x^18 - 15*x^17 + 200*x^16 - 82*x^15 - 2248*x^14 + 3021*x^13 + 12520*x^12 - 24550*x^11 - 35088*x^10 + 93955*x^9 + 40425*x^8 - 182034*x^7 + 6073*x^6 + 166727*x^5 - 35466*x^4 - 62207*x^3 + 9197*x^2 + 8954*x + 332,5,x^19 - 10*x^18 - 13*x^17 + 407*x^16 - 538*x^15 - 6534*x^14 + 15728*x^13 + 51265*x^12 - 171692*x^11 - 187966*x^10 + 951140*x^9 + 150336*x^8 - 2755080*x^7 + 848464*x^6 + 3887232*x^5 - 1878368*x^4 - 2406336*x^3 + 916352*x^2 + 595200*x + 24064,7,x^19 - 9*x^18 - 42*x^17 + 573*x^16 + 128*x^15 - 13897*x^14 + 17867*x^13 + 161413*x^12 - 344862*x^11 - 910492*x^10 + 2632844*x^9 + 2154744*x^8 - 9084272*x^7 - 1049520*x^6 + 13525472*x^5 - 1666496*x^4 - 6550400*x^3 - 194304*x^2 + 728064*x + 74752,11,x^19 - 113*x^17 + 71*x^16 + 5073*x^15 - 6646*x^14 - 115317*x^13 + 234224*x^12 + 1356714*x^11 - 3949803*x^10 - 6819222*x^9 + 32420953*x^8 - 4265833*x^7 - 107914763*x^6 + 130828209*x^5 + 30172714*x^4 - 139580357*x^3 + 81655891*x^2 - 16016817*x + 661909,13,x^19 - 39*x^18 + 622*x^17 - 4840*x^16 + 12521*x^15 + 92504*x^14 - 951637*x^13 + 3328320*x^12 - 1975275*x^11 - 22577295*x^10 + 69174531*x^9 - 27939688*x^8 - 216015592*x^7 + 379040948*x^6 + 16430721*x^5 - 577483356*x^4 + 441702328*x^3 + 48794013*x^2 - 132517280*x + 23914336[] Total time: 18.969 seconds, Total memory usage: 6.05MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:40:40 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [347..353] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:40:20 on modular [Seed = 3325109148] ------------------------------------- 347,1,2,$.1 + 2,3,$.1 - 1,5,$.1,7,$.1 + 2,11,$.1 + 3,13,$.1 + 2[] 347,2,2,$.1^2 - 2*$.1 + 1,3,$.1^2 + $.1 - 1,5,$.1^2 + 2*$.1 - 4,7,$.1^2 + 4*$.1 + 4,11,$.1^2 - 3*$.1 + 1,13,$.1^2 + 7*$.1 + 11[] 347,3,2,$.1^7 + 2*$.1^6 - 7*$.1^5 - 15*$.1^4 + 6*$.1^3 + 22*$.1^2 + 9*$.1 +
1,3,$.1^7 + 7*$.1^6 + 9*$.1^5 - 33*$.1^4 - 88*$.1^3 - 29*$.1^2 + 74*$.1 + 52,5,$.1^7 + 8*$.1^6 + 17*$.1^5 - 5*$.1^4 - 34*$.1^3 + 4*$.1^2 + 20*$.1 -
7,7,$.1^7 + 5*$.1^6 - 16*$.1^5 - 101*$.1^4 + 2*$.1^3 + 391*$.1^2 + 131*$.1 - 241,11,$.1^7 - 2*$.1^6 - 49*$.1^5 + 42*$.1^4 + 708*$.1^3 - 178*$.1^2 - 3012*$.1
- 241,13,$.1^7 + 22*$.1^6 + 171*$.1^5 + 483*$.1^4 - 188*$.1^3 - 2572*$.1^2 -
1463*$.1 + 439[] 347,4,2,$.1^19 - 30*$.1^17 +$.1^16 + 374*$.1^15 - 21*$.1^14 - 2509*$.1^13 + 166*$.1^12 + 9794*$.1^11 - 586*$.1^10 - 22435*$.1^9 + 749*$.1^8 + 28885*$.1^7 + 329*$.1^6 - 18752*$.1^5 - 878*$.1^4 + 4788*$.1^3 - 64*$.1^2 - 352*$.1 + 32,3,$.1^19 - 7*$.1^18 - 15*$.1^17 + 200*$.1^16 - 82*$.1^15 - 2248*$.1^14 + 3021*$.1^13 + 12520*$.1^12 - 24550*$.1^11 - 35088*$.1^10 + 93955*$.1^9 +
40425*$.1^8 - 182034*$.1^7 + 6073*$.1^6 + 166727*$.1^5 - 35466*$.1^4 - 62207*$.1^3 + 9197*$.1^2 + 8954*$.1 + 332,5,$.1^19 - 10*$.1^18 - 13*$.1^17 + 407*$.1^16 - 538*$.1^15 - 6534*$.1^14 + 15728*$.1^13 + 51265*$.1^12 -
171692*$.1^11 - 187966*$.1^10 + 951140*$.1^9 + 150336*$.1^8 - 2755080*$.1^7 + 848464*$.1^6 + 3887232*$.1^5 - 1878368*$.1^4 - 2406336*$.1^3 + 916352*$.1^2 +
595200*$.1 + 24064,7,$.1^19 - 9*$.1^18 - 42*$.1^17 + 573*$.1^16 + 128*$.1^15 -
13897*$.1^14 + 17867*$.1^13 + 161413*$.1^12 - 344862*$.1^11 - 910492*$.1^10 + 2632844*$.1^9 + 2154744*$.1^8 - 9084272*$.1^7 - 1049520*$.1^6 + 13525472*$.1^5 -
1666496*$.1^4 - 6550400*$.1^3 - 194304*$.1^2 + 728064*$.1 + 74752,11,$.1^19 - 113*$.1^17 + 71*$.1^16 + 5073*$.1^15 - 6646*$.1^14 - 115317*$.1^13 +
234224*$.1^12 + 1356714*$.1^11 - 3949803*$.1^10 - 6819222*$.1^9 + 32420953*$.1^8 - 4265833*$.1^7 - 107914763*$.1^6 + 130828209*$.1^5 + 30172714*$.1^4 - 139580357*$.1^3 + 81655891*$.1^2 - 16016817*$.1 + 661909,13,$.1^19 - 39*$.1^18 +
622*$.1^17 - 4840*$.1^16 + 12521*$.1^15 + 92504*$.1^14 - 951637*$.1^13 + 3328320*$.1^12 - 1975275*$.1^11 - 22577295*$.1^10 + 69174531*$.1^9 - 27939688*$.1^8 - 216015592*$.1^7 + 379040948*$.1^6 + 16430721*$.1^5 - 577483356*$.1^4 + 441702328*$.1^3 + 48794013*$.1^2 - 132517280*$.1 + 23914336[] 348,1,2,x,3,x + 1,5,x + 2,7,x - 1,11,x - 3,13,x - 5[] 348,2,2,x,3,x + 1,5,x,7,x + 3,11,x + 3,13,x + 3[] 348,3,2,x,3,x - 1,5,x + 4,7,x + 3,11,x + 1,13,x + 3[] 348,4,2,x,3,x - 1,5,x - 2,7,x - 1,11,x - 1,13,x + 3[] 349,1,2,x^11 + 5*x^10 - x^9 - 35*x^8 - 24*x^7 + 80*x^6 + 66*x^5 - 77*x^4 - 56*x^3 + 31*x^2 + 15*x - 4,3,x^11 + 6*x^10 - 55*x^8 - 64*x^7 + 135*x^6 + 218*x^5 - 47*x^4 - 98*x^3 + 25*x^2 + 4*x - 1,5,x^11 + 9*x^10 + 8*x^9 - 129*x^8 - 295*x^7 + 570*x^6 + 1931*x^5 - 533*x^4 - 4548*x^3 - 1490*x^2 + 3401*x + 2066,7,x^11 + 3*x^10 - 41*x^9 - 137*x^8 + 487*x^7 + 1943*x^6 - 1428*x^5 - 9862*x^4 - 3862*x^3 + 11740*x^2 + 4981*x - 4808,11,x^11 + 31*x^10 + 410*x^9 + 3003*x^8 + 13177*x^7 + 34629*x^6 + 49499*x^5 + 22418*x^4 - 30350*x^3 - 38416*x^2 - 8307*x + 1366,13,x^11 + 4*x^10 - 73*x^9 - 315*x^8 + 1748*x^7 + 8617*x^6 - 12681*x^5 - 90736*x^4 - 38072*x^3 + 237723*x^2 + 314825*x + 110828[] 349,2,2,x^17 - 5*x^16 - 14*x^15 + 102*x^14 + 26*x^13 - 792*x^12 + 474*x^11 + 2887*x^10 - 3021*x^9 - 4835*x^8 + 6673*x^7 + 2880*x^6 - 5373*x^5 - 164*x^4 + 1075*x^3 + 75*x^2 - 41*x - 4,3,x^17 - 6*x^16 - 20*x^15 + 177*x^14 + 48*x^13 - 1985*x^12 + 1406*x^11 + 10845*x^10 - 12658*x^9 - 31199*x^8 + 44236*x^7 + 48099*x^6 - 74028*x^5 - 39044*x^4 + 57120*x^3 + 17296*x^2 - 15296*x - 5056,5,x^17 - 5*x^16 - 37*x^15 + 214*x^14 + 419*x^13 - 3319*x^12 - 857*x^11 + 23008*x^10 - 10989*x^9 - 73502*x^8 + 63382*x^7 + 97594*x^6 - 116692*x^5 - 24693*x^4 + 66466*x^3 - 24778*x^2 + 2789*x + 2,7,x^17 - x^16 - 62*x^15 + 108*x^14 + 1446*x^13 - 3592*x^12 - 14668*x^11 + 50964*x^10 + 46043*x^9 - 311849*x^8 + 167240*x^7 + 607051*x^6 - 885383*x^5 + 307370*x^4 + 57048*x^3 - 28554*x^2 - 2663*x + 142,11,x^17 - 39*x^16 + 637*x^15 - 5462*x^14 + 23655*x^13 - 18200*x^12 - 307653*x^11 + 1355416*x^10 - 1191873*x^9 - 6344921*x^8 + 18465668*x^7 - 7646257*x^6 - 33914554*x^5 + 47577880*x^4 - 10495234*x^3 - 12511566*x^2 + 6304189*x - 778568,13,x^17 + 6*x^16 - 87*x^15 - 529*x^14 + 2510*x^13 + 16439*x^12 - 28043*x^11 - 226068*x^10 + 81674*x^9 + 1436433*x^8 + 514933*x^7 - 3879170*x^6 - 3100324*x^5 + 3028472*x^4 + 3960064*x^3 + 1329408*x^2 + 137408*x - 896[] 350,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x - 3,13,x + 2[] 350,2,2,x + 1,3,x,5,x,7,x - 1,11,x - 4,13,x - 6[] 350,3,2,x + 1,3,x - 3,5,x,7,x - 1,11,x + 5,13,x - 6[] 350,4,2,x - 1,3,x - 2,5,x,7,x + 1,11,x,13,x - 4[] 350,5,2,x - 1,3,x + 3,5,x,7,x + 1,11,x + 5,13,x + 6[] 350,6,2,x - 1,3,x - 1,5,x,7,x - 1,11,x - 3,13,x - 2[] 350,7,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 24,13,x^2 - 4*x - 2[] 350,8,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2,7,x^2 - 2*x + 1,11,x^2 - 24,13,x^2 + 4*x - 2[] 351,1,2,x^2 + x - 1,3,x^2,5,x^2 + 3*x + 1,7,x^2 - 5,11,x^2 + 5*x - 5,13,x^2 + 2*x + 1[] 351,2,2,x^2 - x - 3,3,x^2,5,x^2 - 5*x + 3,7,x^2 + 2*x + 1,11,x^2 - x - 3,13,x^2 - 2*x + 1[] 351,3,2,x^2 - x - 1,3,x^2,5,x^2 - 3*x + 1,7,x^2 - 5,11,x^2 - 5*x - 5,13,x^2 + 2*x + 1[] 351,4,2,x^2 + x - 3,3,x^2,5,x^2 + 5*x + 3,7,x^2 + 2*x + 1,11,x^2 + x - 3,13,x^2 - 2*x + 1[] 351,5,2,x^4 - 7*x^2 + 3,3,x^4,5,x^4 - 16*x^2 + 27,7,x^4 - 8*x^3 + 24*x^2 - 32*x + 16,11,x^4 - 28*x^2 + 48,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 351,6,2,x^4 - 9*x^2 + 19,3,x^4,5,x^4 - 16*x^2 + 19,7,x^4 - 40*x^2 + 400,11,x^4 - 44*x^2 + 304,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 352,1,2,x,3,x + 1,5,x - 1,7,x + 4,11,x + 1,13,x + 2[] 352,2,2,x,3,x + 1,5,x + 3,7,x - 4,11,x + 1,13,x + 2[] 352,3,2,x,3,x - 1,5,x - 1,7,x - 4,11,x - 1,13,x + 2[] 352,4,2,x,3,x - 3,5,x - 1,7,x,11,x + 1,13,x + 6[] 352,5,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x + 2[] 352,6,2,x,3,x + 3,5,x - 1,7,x,11,x - 1,13,x + 6[] 352,7,2,x^2,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2,11,x^2 - 2*x + 1,13,x^2 - 4*x + 4[] 352,8,2,x^2,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2,11,x^2 + 2*x + 1,13,x^2 - 4*x + 4[] 353,1,2,x + 1,3,x - 2,5,x - 2,7,x + 2,11,x - 4,13,x - 2[] 353,2,2,x^3 - x^2 - 6*x + 4,3,x^3 - 3*x^2 - x + 2,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 - 2*x^2 - 5*x + 2,11,x^3 - 3*x^2 - x + 4,13,x^3 - 11*x^2 + 35*x - 26[] 353,3,2,x^11 + 5*x^10 - x^9 - 36*x^8 - 28*x^7 + 82*x^6 + 87*x^5 - 65*x^4 - 71*x^3 + 21*x^2 + 14*x - 4,3,x^11 + 5*x^10 - 7*x^9 - 64*x^8 - 36*x^7 + 175*x^6 + 126*x^5 - 186*x^4 - 104*x^3 + 72*x^2 + 18*x + 1,5,x^11 + 4*x^10 - 18*x^9 - 81*x^8 + 53*x^7 + 384*x^6 + 56*x^5 - 495*x^4 - 148*x^3 + 153*x^2 + 26*x + 1,7,x^11 + 25*x^10 + 259*x^9 + 1407*x^8 + 4053*x^7 + 4609*x^6 - 4827*x^5 - 17025*x^4 - 6326*x^3 + 14629*x^2 + 6466*x - 5575,11,x^11 + 4*x^10 - 64*x^9 - 310*x^8 + 1013*x^7 + 7581*x^6 + 4661*x^5 - 50668*x^4 - 142459*x^3 - 159283*x^2 - 80334*x - 14697,13,x^11 + 13*x^10 + 17*x^9 - 425*x^8 - 1863*x^7 + 1016*x^6 + 18114*x^5 + 21395*x^4 - 38907*x^3 - 81473*x^2 - 11214*x + 32157[] 353,4,2,x^14 - 4*x^13 - 14*x^12 + 71*x^11 + 47*x^10 - 452*x^9 + 101*x^8 + 1251*x^7 - 740*x^6 - 1488*x^5 + 1096*x^4 + 600*x^3 - 410*x^2 - 42*x - 1,3,x^14 + 2*x^13 - 26*x^12 - 48*x^11 + 262*x^10 + 447*x^9 - 1279*x^8 - 2024*x^7 + 3081*x^6 + 4547*x^5 - 3326*x^4 - 4522*x^3 + 1322*x^2 + 1308*x - 322,5,x^14 + 4*x^13 - 39*x^12 - 151*x^11 + 592*x^10 + 2235*x^9 - 4272*x^8 - 16368*x^7 + 13846*x^6 + 60545*x^5 - 10522*x^4 - 98304*x^3 - 25184*x^2 + 36240*x + 10400,7,x^14 - 29*x^13 + 352*x^12 - 2260*x^11 + 7591*x^10 - 6997*x^9 - 45654*x^8 + 210050*x^7 - 425708*x^6 + 476445*x^5 - 279130*x^4 + 48708*x^3 + 31114*x^2 - 16770*x + 2290,11,x^14 + 7*x^13 - 70*x^12 - 473*x^11 + 1808*x^10 + 10840*x^9 - 21587*x^8 - 101229*x^7 + 105583*x^6 + 399873*x^5 - 195880*x^4 - 578384*x^3 + 168704*x^2 + 229888*x - 57856,13,x^14 - 2*x^13 - 92*x^12 + 219*x^11 + 3314*x^10 - 8885*x^9 - 59691*x^8 + 176589*x^7 + 560201*x^6 - 1845067*x^5 - 2466086*x^4 + 9702888*x^3 + 2569392*x^2 - 20177168*x + 8277472[] Total time: 19.059 seconds, Total memory usage: 6.15MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:48:56 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [353..359] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:48:36 on modular [Seed = 4127265372] ------------------------------------- 353,1,2,$.1 + 1,3,$.1 - 2,5,$.1 - 2,7,$.1 + 2,11,$.1 - 4,13,$.1 - 2[] 353,2,2,$.1^3 - $.1^2 - 6*$.1 + 4,3,$.1^3 - 3*$.1^2 - $.1 + 2,5,$.1^3 - 2*$.1^2 - 5*$.1 + 2,7,$.1^3 - 2*$.1^2 - 5*$.1 + 2,11,$.1^3 - 3*$.1^2 -$.1 + 4,13,$.1^3 - 11*$.1^2 + 35*$.1 - 26[] 353,3,2,$.1^11 + 5*$.1^10 -$.1^9 - 36*$.1^8 - 28*$.1^7 + 82*$.1^6 + 87*$.1^5 -
65*$.1^4 - 71*$.1^3 + 21*$.1^2 + 14*$.1 - 4,3,$.1^11 + 5*$.1^10 - 7*$.1^9 - 64*$.1^8 - 36*$.1^7 + 175*$.1^6 + 126*$.1^5 - 186*$.1^4 - 104*$.1^3 + 72*$.1^2 +
18*$.1 + 1,5,$.1^11 + 4*$.1^10 - 18*$.1^9 - 81*$.1^8 + 53*$.1^7 + 384*$.1^6 + 56*$.1^5 - 495*$.1^4 - 148*$.1^3 + 153*$.1^2 + 26*$.1 + 1,7,$.1^11 + 25*$.1^10 +
259*$.1^9 + 1407*$.1^8 + 4053*$.1^7 + 4609*$.1^6 - 4827*$.1^5 - 17025*$.1^4 -
6326*$.1^3 + 14629*$.1^2 + 6466*$.1 - 5575,11,$.1^11 + 4*$.1^10 - 64*$.1^9 -
310*$.1^8 + 1013*$.1^7 + 7581*$.1^6 + 4661*$.1^5 - 50668*$.1^4 - 142459*$.1^3 -
159283*$.1^2 - 80334*$.1 - 14697,13,$.1^11 + 13*$.1^10 + 17*$.1^9 - 425*$.1^8 -
1863*$.1^7 + 1016*$.1^6 + 18114*$.1^5 + 21395*$.1^4 - 38907*$.1^3 - 81473*$.1^2
- 11214*$.1 + 32157[] 353,4,2,$.1^14 - 4*$.1^13 - 14*$.1^12 + 71*$.1^11 + 47*$.1^10 - 452*$.1^9 + 101*$.1^8 + 1251*$.1^7 - 740*$.1^6 - 1488*$.1^5 + 1096*$.1^4 + 600*$.1^3 - 410*$.1^2 - 42*$.1 - 1,3,$.1^14 + 2*$.1^13 - 26*$.1^12 - 48*$.1^11 + 262*$.1^10
+ 447*$.1^9 - 1279*$.1^8 - 2024*$.1^7 + 3081*$.1^6 + 4547*$.1^5 - 3326*$.1^4 -
4522*$.1^3 + 1322*$.1^2 + 1308*$.1 - 322,5,$.1^14 + 4*$.1^13 - 39*$.1^12 -
151*$.1^11 + 592*$.1^10 + 2235*$.1^9 - 4272*$.1^8 - 16368*$.1^7 + 13846*$.1^6 +
60545*$.1^5 - 10522*$.1^4 - 98304*$.1^3 - 25184*$.1^2 + 36240*$.1 + 10400,7,$.1^14 - 29*$.1^13 + 352*$.1^12 - 2260*$.1^11 + 7591*$.1^10 - 6997*$.1^9 - 45654*$.1^8 + 210050*$.1^7 - 425708*$.1^6 + 476445*$.1^5 - 279130*$.1^4 +
48708*$.1^3 + 31114*$.1^2 - 16770*$.1 + 2290,11,$.1^14 + 7*$.1^13 - 70*$.1^12 -
473*$.1^11 + 1808*$.1^10 + 10840*$.1^9 - 21587*$.1^8 - 101229*$.1^7 + 105583*$.1^6 + 399873*$.1^5 - 195880*$.1^4 - 578384*$.1^3 + 168704*$.1^2 +
229888*$.1 - 57856,13,$.1^14 - 2*$.1^13 - 92*$.1^12 + 219*$.1^11 + 3314*$.1^10 -
8885*$.1^9 - 59691*$.1^8 + 176589*$.1^7 + 560201*$.1^6 - 1845067*$.1^5 - 2466086*$.1^4 + 9702888*$.1^3 + 2569392*$.1^2 - 20177168*$.1 + 8277472[] 354,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x + 5,13,x - 1[] 354,2,2,x + 1,3,x + 1,5,x - 2,7,x,11,x - 4,13,x + 6[] 354,3,2,x + 1,3,x - 1,5,x,7,x + 1,11,x - 3,13,x - 5[] 354,4,2,x - 1,3,x + 1,5,x,7,x,11,x - 4,13,x - 4[] 354,5,2,x - 1,3,x + 1,5,x - 4,7,x,11,x + 4,13,x[] 354,6,2,x - 1,3,x + 1,5,x + 4,7,x + 1,11,x + 3,13,x + 1[] 354,7,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x - 10,7,x^2 - 8*x + 16,11,x^2 + 4*x + 4,13,x^2 + 2*x - 10[] 354,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 6*x + 8,7,x^3 + x^2 - 16*x + 16,11,x^3 - x^2 - 32*x + 76,13,x^3 - x^2 - 4*x + 2[] 355,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x,13,x - 5[] 355,2,2,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,3,x^4 + x^3 - 3*x^2 - x + 1,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - x^3 - 10*x^2 - 8*x - 1,11,x^4 + 9*x^3 + 22*x^2 + 16*x + 1,13,x^4 + 2*x^3 - 20*x^2 + 29*x - 11[] 355,3,2,x^4 + 4*x^3 + 2*x^2 - 5*x - 3,3,x^4 + 3*x^3 - x^2 - 5*x + 1,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 5*x^3 - 6*x^2 - 36*x - 27,11,x^4 + x^3 - 24*x^2 - 12*x + 43,13,x^4 + 14*x^3 + 54*x^2 + 9*x - 161[] 355,4,2,x^6 - 3*x^5 - 6*x^4 + 21*x^3 + 4*x^2 - 35*x + 16,3,x^6 - 3*x^5 - 7*x^4 + 25*x^3 - 5*x^2 - 18*x + 8,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 6*x^5 + 3*x^4 + 24*x^3 - 15*x^2 - 13*x + 8,11,x^6 - 3*x^5 - 22*x^4 + 4*x^3 + 73*x^2 + 4*x - 64,13,x^6 - 5*x^5 - 30*x^4 + 129*x^3 + 80*x^2 - x - 2[] 355,5,2,x^8 - 4*x^7 - 5*x^6 + 31*x^5 - 3*x^4 - 57*x^3 + 5*x^2 + 32*x + 8,3,x^8 + x^7 - 19*x^6 - 13*x^5 + 113*x^4 + 48*x^3 - 204*x^2 - 64*x + 64,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 5*x^7 - 25*x^6 - 97*x^5 + 291*x^4 + 472*x^3 - 1421*x^2 + 188*x + 668,11,x^8 - 7*x^7 - 40*x^6 + 336*x^5 + 259*x^4 - 4496*x^3 + 3144*x^2 + 11008*x - 4096,13,x^8 + 4*x^7 - 49*x^6 - 99*x^5 + 877*x^4 + 223*x^3 - 4755*x^2 + 1312*x + 6352[] 356,1,2,x,3,x + 1,5,x + 1,7,x,11,x,13,x + 4[] 356,2,2,x^7,3,x^7 - x^6 - 18*x^5 + 18*x^4 + 93*x^3 - 95*x^2 - 126*x + 134,5,x^7 - 3*x^6 - 22*x^5 + 54*x^4 + 117*x^3 - 215*x^2 + 96*x - 12,7,x^7 - 36*x^5 + 8*x^4 + 360*x^3 - 244*x^2 - 952*x + 872,11,x^7 - 8*x^6 - 28*x^5 + 304*x^4 + 16*x^3 - 2800*x^2 + 1152*x + 6912,13,x^7 - 10*x^6 - 32*x^5 + 576*x^4 - 848*x^3 - 7344*x^2 + 27072*x - 26048[] 357,1,2,x,3,x + 1,5,x - 1,7,x + 1,11,x - 3,13,x - 3[] 357,2,2,x,3,x + 1,5,x - 1,7,x - 1,11,x + 5,13,x + 5[] 357,3,2,x - 2,3,x - 1,5,x - 1,7,x + 1,11,x - 1,13,x - 1[] 357,4,2,x + 2,3,x - 1,5,x + 3,7,x - 1,11,x + 3,13,x - 1[] 357,5,2,x^2 - 2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 1,7,x^2 + 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + 6*x + 7[] 357,6,2,x^2 + 2*x - 2,3,x^2 - 2*x + 1,5,x^2 + 4*x + 1,7,x^2 + 2*x + 1,11,x^2 + 10*x + 25,13,x^2 + 4*x - 23[] 357,7,2,x^3 - x^2 - 4*x + 2,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 3*x + 2,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 5*x + 4,13,x^3 + 2*x^2 - 23*x - 62[] 357,8,2,x^4 - 2*x^3 - 5*x^2 + 8*x + 2,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 2*x^3 - 13*x^2 - 20*x - 4,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 2*x^3 - 23*x^2 + 80*x - 64,13,x^4 - 2*x^3 - 13*x^2 + 20*x - 4[] 358,1,2,x + 1,3,x - 2,5,x,7,x + 2,11,x - 5,13,x - 6[] 358,2,2,x - 1,3,x + 2,5,x,7,x - 2,11,x - 3,13,x - 2[] 358,3,2,x^2 + 2*x + 1,3,x^2 - x - 5,5,x^2 - 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 2*x + 1,13,x^2 + 3*x - 3[] 358,4,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - x - 11,7,x^2 - 4*x + 4,11,x^2 + 2*x - 4,13,x^2 + 11*x + 29[] 358,5,2,x^2 - 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 - 4*x - 1,13,x^2 - 3*x + 1[] 358,6,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 4*x - 1,7,x^2 + 6*x + 9,11,x^2 - 5,13,x^2 + 3*x - 9[] 358,7,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 7*x^2 - 8*x - 1,5,x^4 + 7*x^3 + 12*x^2 - 3*x - 13,7,x^4 - 17*x^2 + 68,11,x^4 + 4*x^3 - 11*x^2 - 30*x + 52,13,x^4 + 8*x^3 + 7*x^2 - 70*x - 137[] 359,1,2,x - 1,3,x + 2,5,x - 1,7,x - 1,11,x + 2,13,x + 6[] 359,2,2,x + 1,3,x,5,x - 1,7,x + 1,11,x + 2,13,x[] 359,3,2,x^4 + 2*x^3 - 3*x^2 - 5*x + 1,3,x^4 + x^3 - 4*x^2 - x + 2,5,x^4 + 6*x^3 + 9*x^2 + x - 1,7,x^4 + 3*x^3 - x^2 - 6*x - 1,11,x^4 - x^3 - 4*x^2 + x + 2,13,x^4 + 5*x^3 - 5*x - 2[] 359,4,2,x^24 - x^23 - 39*x^22 + 38*x^21 + 658*x^20 - 619*x^19 - 6300*x^18 + 5654*x^17 + 37740*x^16 - 31780*x^15 - 147096*x^14 + 113400*x^13 + 376092*x^12 - 255412*x^11 - 621508*x^10 + 349080*x^9 + 638532*x^8 - 266744*x^7 - 378124*x^6 + 98609*x^5 + 110695*x^4 - 14509*x^3 - 11972*x^2 + 780*x + 381,3,x^24 - 5*x^23 - 43*x^22 + 244*x^21 + 730*x^20 - 5047*x^19 - 5907*x^18 + 57923*x^17 + 17687*x^16 - 406074*x^15 + 67031*x^14 + 1808670*x^13 - 762586*x^12 - 5180837*x^11 + 2757430*x^10 + 9527658*x^9 - 4960839*x^8 - 11153867*x^7 + 4462237*x^6 + 8084680*x^5 - 1630622*x^4 - 3295895*x^3 - 52340*x^2 + 569928*x + 116220,5,x^24 - 6*x^23 - 69*x^22 + 467*x^21 + 1858*x^20 - 15164*x^19 - 23636*x^18 + 267639*x^17 + 117204*x^16 - 2810581*x^15 + 361049*x^14 + 18183228*x^13 - 6736119*x^12 - 73400500*x^11 + 27673727*x^10 + 184563711*x^9 - 40548680*x^8 - 273285446*x^7 - 1013221*x^6 + 201596727*x^5 + 30252732*x^4 - 60035364*x^3 - 9319637*x^2 + 6343389*x + 470595,7,x^24 - 5*x^23 - 114*x^22 + 641*x^21 + 5174*x^20 - 34398*x^19 - 112225*x^18 + 995574*x^17 + 887868*x^16 - 16586560*x^15 + 9274640*x^14 + 154492864*x^13 - 258142784*x^12 - 667474304*x^11 + 2055038208*x^10 + 84195328*x^9 - 5784735744*x^8 + 6531266560*x^7 - 286748672*x^6 - 3293741056*x^5 + 1408040960*x^4 + 294420480*x^3 - 233504768*x^2 + 6422528*x + 7602176,11,x^24 - x^23 - 169*x^22 + 126*x^21 + 12398*x^20 - 6197*x^19 - 519473*x^18 + 142367*x^17 + 13756217*x^16 - 1107152*x^15 - 240666717*x^14 - 16619292*x^13 + 2827831610*x^12 + 467702785*x^11 - 22280707192*x^10 - 4576511138*x^9 + 115550031501*x^8 + 22525582681*x^7 - 376953626781*x^6 - 55187488438*x^5 + 699077626886*x^4 + 52803563063*x^3 - 563144202202*x^2 + 519529404*x + 10936677960,13,x^24 - 19*x^23 - 40*x^22 + 2811*x^21 - 8740*x^20 - 166732*x^19 + 940532*x^18 + 4929984*x^17 - 42016912*x^16 - 66630272*x^15 + 1059257920*x^14 - 100152576*x^13 - 16382637568*x^12 + 17675379712*x^11 + 158158316544*x^10 - 281003210752*x^9 - 924055621632*x^8 + 2228757315584*x^7 + 2924503531520*x^6 - 9682178965504*x^5 - 3197478961152*x^4 + 21392562978816*x^3 - 4807181991936*x^2 - 17987890839552*x + 9644547244032[] Total time: 19.760 seconds, Total memory usage: 6.20MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sat Nov 29 12:58:17 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [359..361] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sat Nov 29 2003 12:58:04 on modular [Seed = 2657714156] ------------------------------------- 359,1,2,$.1 - 1,3,$.1 + 2,5,$.1 - 1,7,$.1 - 1,11,$.1 + 2,13,$.1 + 6[] 359,2,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1 + 2,13,$.1[] 359,3,2,$.1^4 + 2*$.1^3 - 3*$.1^2 - 5*$.1 + 1,3,$.1^4 + $.1^3 - 4*$.1^2 - $.1 + 2,5,$.1^4 + 6*$.1^3 + 9*$.1^2 + $.1 - 1,7,$.1^4 + 3*$.1^3 -$.1^2 - 6*$.1 - 1,11,$.1^4 - $.1^3 - 4*$.1^2 + $.1 + 2,13,$.1^4 + 5*$.1^3 - 5*$.1 - 2[]
359,4,2,$.1^24 -$.1^23 - 39*$.1^22 + 38*$.1^21 + 658*$.1^20 - 619*$.1^19 -
6300*$.1^18 + 5654*$.1^17 + 37740*$.1^16 - 31780*$.1^15 - 147096*$.1^14 + 113400*$.1^13 + 376092*$.1^12 - 255412*$.1^11 - 621508*$.1^10 + 349080*$.1^9 +
638532*$.1^8 - 266744*$.1^7 - 378124*$.1^6 + 98609*$.1^5 + 110695*$.1^4 - 14509*$.1^3 - 11972*$.1^2 + 780*$.1 + 381,3,$.1^24 - 5*$.1^23 - 43*$.1^22 + 244*$.1^21 + 730*$.1^20 - 5047*$.1^19 - 5907*$.1^18 + 57923*$.1^17 +
17687*$.1^16 - 406074*$.1^15 + 67031*$.1^14 + 1808670*$.1^13 - 762586*$.1^12 - 5180837*$.1^11 + 2757430*$.1^10 + 9527658*$.1^9 - 4960839*$.1^8 - 11153867*$.1^7
+ 4462237*$.1^6 + 8084680*$.1^5 - 1630622*$.1^4 - 3295895*$.1^3 - 52340*$.1^2 + 569928*$.1 + 116220,5,$.1^24 - 6*$.1^23 - 69*$.1^22 + 467*$.1^21 + 1858*$.1^20 - 15164*$.1^19 - 23636*$.1^18 + 267639*$.1^17 + 117204*$.1^16 - 2810581*$.1^15 +
361049*$.1^14 + 18183228*$.1^13 - 6736119*$.1^12 - 73400500*$.1^11 +
27673727*$.1^10 + 184563711*$.1^9 - 40548680*$.1^8 - 273285446*$.1^7 -
1013221*$.1^6 + 201596727*$.1^5 + 30252732*$.1^4 - 60035364*$.1^3 -
9319637*$.1^2 + 6343389*$.1 + 470595,7,$.1^24 - 5*$.1^23 - 114*$.1^22 + 641*$.1^21 + 5174*$.1^20 - 34398*$.1^19 - 112225*$.1^18 + 995574*$.1^17 +
887868*$.1^16 - 16586560*$.1^15 + 9274640*$.1^14 + 154492864*$.1^13 -
258142784*$.1^12 - 667474304*$.1^11 + 2055038208*$.1^10 + 84195328*$.1^9 -
5784735744*$.1^8 + 6531266560*$.1^7 - 286748672*$.1^6 - 3293741056*$.1^5 +
1408040960*$.1^4 + 294420480*$.1^3 - 233504768*$.1^2 + 6422528*$.1 +
7602176,11,$.1^24 -$.1^23 - 169*$.1^22 + 126*$.1^21 + 12398*$.1^20 - 6197*$.1^19 - 519473*$.1^18 + 142367*$.1^17 + 13756217*$.1^16 - 1107152*$.1^15 -
240666717*$.1^14 - 16619292*$.1^13 + 2827831610*$.1^12 + 467702785*$.1^11 -
22280707192*$.1^10 - 4576511138*$.1^9 + 115550031501*$.1^8 + 22525582681*$.1^7 -
376953626781*$.1^6 - 55187488438*$.1^5 + 699077626886*$.1^4 + 52803563063*$.1^3
- 563144202202*$.1^2 + 519529404*$.1 + 10936677960,13,$.1^24 - 19*$.1^23 -
40*$.1^22 + 2811*$.1^21 - 8740*$.1^20 - 166732*$.1^19 + 940532*$.1^18 + 4929984*$.1^17 - 42016912*$.1^16 - 66630272*$.1^15 + 1059257920*$.1^14 - 100152576*$.1^13 - 16382637568*$.1^12 + 17675379712*$.1^11 + 158158316544*$.1^10 - 281003210752*$.1^9 - 924055621632*$.1^8 + 2228757315584*$.1^7 +
2924503531520*$.1^6 - 9682178965504*$.1^5 - 3197478961152*$.1^4 + 21392562978816*$.1^3 - 4807181991936*$.1^2 - 17987890839552*$.1 +
9644547244032[]
360,1,2,x,3,x,5,x - 1,7,x - 2,11,x + 2,13,x - 4[]
360,2,2,x,3,x,5,x + 1,7,x,11,x - 4,13,x - 6[]
360,3,2,x,3,x,5,x + 1,7,x - 2,11,x - 2,13,x - 4[]
360,4,2,x,3,x,5,x + 1,7,x + 4,11,x + 4,13,x + 2[]
360,5,2,x,3,x,5,x - 1,7,x - 4,11,x,13,x + 6[]
361,1,2,x,3,x,5,x + 1,7,x - 3,11,x + 5,13,x[]
361,2,2,x,3,x - 2,5,x - 3,7,x + 1,11,x - 3,13,x - 4[]
361,3,2,x^2 - 5,3,x^2 - 4*x + 4,5,x^2 - x - 1,7,x^2 + 2*x - 4,11,x^2 - 6*x +
4,13,x^2 - 3*x - 9[]
361,4,2,x^2 - 5,3,x^2 + 4*x + 4,5,x^2 - x - 1,7,x^2 + 2*x - 4,11,x^2 - 6*x +
4,13,x^2 + 3*x - 9[]
361,5,2,x^2 - x - 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 6*x + 9,11,x^2 + x -
1,13,x^2 + 2*x + 1[]
361,6,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 6*x + 9,11,x^2 + x -
1,13,x^2 - 2*x + 1[]
361,7,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 - 3,7,x^3 - 3*x +
1,11,x^3 - 9*x - 9,13,x^3 - 21*x + 37[]
361,8,2,x^3 - 3*x^2 + 3,3,x^3 - 3*x^2 + 1,5,x^3 + 3*x^2 - 3,7,x^3 - 3*x +
1,11,x^3 - 9*x - 9,13,x^3 - 21*x - 37[]
361,9,2,x^4 - 5*x^2 + 5,3,x^4 - 5*x^2 + 5,5,x^4 + 4*x^3 - 4*x^2 - 16*x +
16,7,x^4 + 8*x^3 + 14*x^2 - 8*x + 1,11,x^4 + 10*x^3 + 35*x^2 + 50*x + 25,13,x^4
- 10*x^2 + 5[]

Total time: 13.529 seconds, Total memory usage: 4.75MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:01:27 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [367..373] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 13:01:07 on modular  [Seed = 3175767040]
-------------------------------------

367,1,2,$.1^11 + 8*$.1^10 + 16*$.1^9 - 26*$.1^8 - 121*$.1^7 - 61*$.1^6 +
197*$.1^5 + 212*$.1^4 - 66*$.1^3 - 132*$.1^2 - 12*$.1 + 13,3,$.1^11 + 6*$.1^10 + 3*$.1^9 - 41*$.1^8 - 64*$.1^7 + 64*$.1^6 + 158*$.1^5 - 9*$.1^4 - 118*$.1^3 -
14*$.1^2 + 24*$.1 - 1,5,$.1^11 + 8*$.1^10 + 7*$.1^9 - 85*$.1^8 - 191*$.1^7 + 190*$.1^6 + 791*$.1^5 + 247*$.1^4 - 815*$.1^3 - 687*$.1^2 - 128*$.1 + 5,7,$.1^11
+ 7*$.1^10 - 13*$.1^9 - 186*$.1^8 - 277*$.1^7 + 859*$.1^6 + 2780*$.1^5 +
1778*$.1^4 - 1871*$.1^3 - 2671*$.1^2 - 799*$.1 + 25,11,$.1^11 + 10*$.1^10 -
12*$.1^9 - 313*$.1^8 - 120*$.1^7 + 3196*$.1^6 + 661*$.1^5 - 11246*$.1^4 +
2768*$.1^3 + 5371*$.1^2 - 892*$.1 - 743,13,$.1^11 + 5*$.1^10 - 48*$.1^9 -
277*$.1^8 + 569*$.1^7 + 4656*$.1^6 + 745*$.1^5 - 22685*$.1^4 - 14329*$.1^3 +
25989*$.1^2 - 1682*$.1 - 2621[]
367,2,2,$.1^19 - 9*$.1^18 + 11*$.1^17 + 123*$.1^16 - 372*$.1^15 - 469*$.1^14 +
2884*$.1^13 - 550*$.1^12 - 10042*$.1^11 + 8029*$.1^10 + 17059*$.1^9 - 20350*$.1^8 - 12836*$.1^7 + 20779*$.1^6 + 2682*$.1^5 - 7739*$.1^4 + 63*$.1^3 + 899*$.1^2 - 27*$.1 - 29,3,$.1^19 - 4*$.1^18 - 35*$.1^17 + 149*$.1^16 + 486*$.1^15 - 2260*$.1^14 - 3442*$.1^13 + 18203*$.1^12 + 13108*$.1^11 -
84580*$.1^10 - 25304*$.1^9 + 229397*$.1^8 + 19212*$.1^7 - 348172*$.1^6 - 3000*$.1^5 + 262144*$.1^4 + 15968*$.1^3 - 68672*$.1^2 - 21504*$.1 -
1792,5,$.1^19 - 6*$.1^18 - 43*$.1^17 + 309*$.1^16 + 595*$.1^15 - 6046*$.1^14 -
2461*$.1^13 + 58707*$.1^12 - 5347*$.1^11 - 322649*$.1^10 + 48332*$.1^9 + 1052323*$.1^8 + 41520*$.1^7 - 1950148*$.1^6 - 697328*$.1^5 + 1640832*$.1^4 +
1181408*$.1^3 - 153984*$.1^2 - 315520*$.1 - 68864,7,$.1^19 - $.1^18 - 68*$.1^17
+ 93*$.1^16 + 1821*$.1^15 - 3162*$.1^14 - 24162*$.1^13 + 51825*$.1^12 + 161877*$.1^11 - 438685*$.1^10 - 465321*$.1^9 + 1870316*$.1^8 + 63387*$.1^7 -
3600393*$.1^6 + 1757269*$.1^5 + 2308835*$.1^4 - 1465397*$.1^3 - 561533*$.1^2 + 257949*$.1 + 75177,11,$.1^19 - 4*$.1^18 - 120*$.1^17 + 545*$.1^16 + 5632*$.1^15 - 29392*$.1^14 - 128435*$.1^13 + 812306*$.1^12 + 1363286*$.1^11 - 12382021*$.1^10 - 2606314*$.1^9 + 102742747*$.1^8 - 71962574*$.1^7 - 413796744*$.1^6 + 565237368*$.1^5 + 539820496*$.1^4 - 1225061216*$.1^3 + 173670080*$.1^2 + 608625792*$.1 - 263379712,13,$.1^19 - 5*$.1^18 - 99*$.1^17 +
398*$.1^16 + 4006*$.1^15 - 11816*$.1^14 - 82529*$.1^13 + 167855*$.1^12 + 890309*$.1^11 - 1326823*$.1^10 - 4991303*$.1^9 + 6366113*$.1^8 + 13486540*$.1^7
- 17861951*$.1^6 - 12151477*$.1^5 + 22331038*$.1^4 - 6313452*$.1^3 -
683605*$.1^2 + 175252*$.1 - 2548[]
368,1,2,x,3,x,5,x,7,x + 4,11,x + 6,13,x + 2[]
368,2,2,x,3,x - 1,5,x + 4,7,x + 2,11,x - 4,13,x + 5[]
368,3,2,x,3,x + 3,5,x,7,x - 2,11,x,13,x + 5[]
368,4,2,x,3,x - 1,5,x + 2,7,x - 4,11,x - 2,13,x - 7[]
368,5,2,x,3,x,5,x - 4,7,x - 4,11,x + 2,13,x + 2[]
368,6,2,x,3,x - 3,5,x + 2,7,x - 4,11,x + 2,13,x + 5[]
368,7,2,x,3,x + 1,5,x,7,x + 2,11,x,13,x + 1[]
368,8,2,x^2,3,x^2 - x - 4,5,x^2 - 4*x + 4,7,x^2,11,x^2 + 2*x - 16,13,x^2 - 5*x +
2[]
368,9,2,x^2,3,x^2 - 5,5,x^2 + 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 6*x + 4,13,x^2 -
6*x + 9[]
369,1,2,x - 2,3,x,5,x - 4,7,x + 2,11,x - 3,13,x + 6[]
369,2,2,x,3,x,5,x - 2,7,x + 4,11,x + 5,13,x + 4[]
369,3,2,x^2 - 2,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 + 2*x - 1,13,x^2 -
4*x - 14[]
369,4,2,x^3 + 2*x^2 - 2*x - 2,3,x^3,5,x^3 + 4*x^2 + 2*x - 2,7,x^3 - 4*x -
2,11,x^3 + 11*x^2 + 37*x + 37,13,x^3 + 2*x^2 - 12*x + 10[]
369,5,2,x^3 - 2*x^2 - 2*x + 2,3,x^3,5,x^3 - 4*x^2 + 2*x + 2,7,x^3 - 4*x -
2,11,x^3 - 11*x^2 + 37*x - 37,13,x^3 + 2*x^2 - 12*x + 10[]
369,6,2,x^3 - x^2 - 5*x + 1,3,x^3,5,x^3 - 2*x^2 - 4*x + 4,7,x^3 - 6*x^2 + 8*x -
2,11,x^3 + 2*x^2 - 20*x - 50,13,x^3 + 2*x^2 - 12*x - 8[]
369,7,2,x^3 + x^2 - 4*x - 2,3,x^3,5,x^3 + 4*x^2 - 2*x - 4,7,x^3 - 2*x^2 - 14*x +
32,11,x^3 - 4*x^2 + x + 4,13,x^3 - 8*x^2 + 14*x + 4[]
370,1,2,x + 1,3,x,5,x + 1,7,x,11,x + 4,13,x - 2[]
370,2,2,x + 1,3,x + 2,5,x + 1,7,x + 1,11,x - 3,13,x + 4[]
370,3,2,x + 1,3,x - 2,5,x - 1,7,x - 1,11,x - 3,13,x[]
370,4,2,x - 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x - 2[]
370,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 +
4*x - 8,13,x^2 + 4*x - 8[]
370,6,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 + 3*x - 6,11,x^2 + x
- 8,13,x^2 - 2*x - 32[]
370,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 10*x + 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 +
x^2 - 8*x - 10,11,x^3 - 11*x^2 + 28*x + 8,13,x^3 - 40*x - 32[]
371,1,2,x - 1,3,x + 1,5,x,7,x + 1,11,x,13,x - 1[]
371,2,2,x - 2,3,x,5,x - 3,7,x - 1,11,x - 3,13,x + 6[]
371,3,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 + 3*x + 1,7,x^2 - 2*x + 1,11,x^2 -
5,13,x^2 + 3*x + 1[]
371,4,2,x^3 - 4*x - 1,3,x^3 - 4*x + 1,5,x^3 + 5*x^2 + 3*x - 8,7,x^3 + 3*x^2 +
3*x + 1,11,x^3 + 4*x^2 - x - 8,13,x^3 + 12*x^2 + 44*x + 47[]
371,5,2,x^9 - 15*x^7 + x^6 + 74*x^5 - 9*x^4 - 132*x^3 + 24*x^2 + 64*x - 16,3,x^9
- 3*x^8 - 15*x^7 + 42*x^6 + 76*x^5 - 172*x^4 - 172*x^3 + 192*x^2 + 176*x +
32,5,x^9 - 9*x^8 + 9*x^7 + 130*x^6 - 395*x^5 - 83*x^4 + 1495*x^3 - 1218*x^2 -
960*x + 1112,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 +
36*x^2 + 9*x + 1,11,x^9 - 59*x^7 + 56*x^6 + 1139*x^5 - 1836*x^4 - 7209*x^3 +
12916*x^2 + 14240*x - 23872,13,x^9 - 13*x^8 + 3*x^7 + 590*x^6 - 2604*x^5 +
1880*x^4 + 7728*x^3 - 13600*x^2 + 6720*x - 896[]
371,6,2,x^11 + x^10 - 20*x^9 - 19*x^8 + 140*x^7 + 125*x^6 - 396*x^5 - 333*x^4 +
359*x^3 + 298*x^2 - 4*x - 24,3,x^11 + x^10 - 26*x^9 - 17*x^8 + 251*x^7 + 86*x^6
- 1088*x^5 - 144*x^4 + 2012*x^3 + 248*x^2 - 1296*x - 400,5,x^11 - 2*x^10 -
37*x^9 + 49*x^8 + 514*x^7 - 359*x^6 - 3152*x^5 + 632*x^4 + 7624*x^3 + 916*x^2 -
3680*x + 768,7,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 -
330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,11,x^11 - 5*x^10 - 58*x^9 + 238*x^8 +
1089*x^7 - 2465*x^6 - 9480*x^5 + 1576*x^4 + 19376*x^3 + 7984*x^2 - 6272*x -
3072,13,x^11 - 13*x^10 + 2*x^9 + 537*x^8 - 1277*x^7 - 7054*x^6 + 21444*x^5 +
35208*x^4 - 113840*x^3 - 47264*x^2 + 181184*x - 73600[]
372,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x,13,x + 6[]
372,2,2,x,3,x - 1,5,x + 3,7,x + 5,11,x - 2,13,x + 4[]
372,3,2,x,3,x - 1,5,x + 2,7,x - 4,11,x,13,x - 2[]
372,4,2,x,3,x - 1,5,x - 3,7,x + 1,11,x,13,x - 2[]
372,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2 + x - 4,11,x^2 - 2*x -
16,13,x^2 - 6*x - 8[]
373,1,2,x + 2,3,x - 1,5,x - 2,7,x + 4,11,x + 6,13,x + 1[]
373,2,2,x^12 + 4*x^11 - 8*x^10 - 43*x^9 + 14*x^8 + 161*x^7 + 17*x^6 - 260*x^5 -
53*x^4 + 177*x^3 + 18*x^2 - 42*x + 7,3,x^12 + 15*x^11 + 88*x^10 + 237*x^9 +
183*x^8 - 518*x^7 - 1320*x^6 - 819*x^5 + 588*x^4 + 1026*x^3 + 491*x^2 + 98*x +
7,5,x^12 + 11*x^11 + 26*x^10 - 118*x^9 - 605*x^8 - 182*x^7 + 3140*x^6 + 4749*x^5
- 2919*x^4 - 10800*x^3 - 6876*x^2 - 689*x + 331,7,x^12 + x^11 - 47*x^10 - 41*x^9
+ 841*x^8 + 585*x^7 - 7225*x^6 - 3446*x^5 + 30765*x^4 + 7470*x^3 - 59872*x^2 -
3760*x + 40397,11,x^12 + 8*x^11 - 35*x^10 - 352*x^9 + 261*x^8 + 4248*x^7 -
2641*x^6 - 19126*x^5 + 22857*x^4 + 10925*x^3 - 20993*x^2 + 1383*x + 3397,13,x^12
+ 10*x^11 - 36*x^10 - 625*x^9 - 608*x^8 + 11245*x^7 + 29822*x^6 - 48645*x^5 -
246092*x^4 - 198302*x^3 + 119773*x^2 + 149389*x + 33169[]
373,3,2,x^17 - 4*x^16 - 18*x^15 + 85*x^14 + 111*x^13 - 713*x^12 - 211*x^11 +
3017*x^10 - 469*x^9 - 6832*x^8 + 2513*x^7 + 8146*x^6 - 3634*x^5 - 4743*x^4 +
2092*x^3 + 1142*x^2 - 417*x - 62,3,x^17 - 14*x^16 + 61*x^15 + 17*x^14 - 866*x^13
+ 1843*x^12 + 2698*x^11 - 13639*x^10 + 5907*x^9 + 34646*x^8 - 42911*x^7 -
24721*x^6 + 64125*x^5 - 14879*x^4 - 21272*x^3 + 6996*x^2 + 2464*x - 464,5,x^17 -
9*x^16 - 8*x^15 + 282*x^14 - 461*x^13 - 2974*x^12 + 8406*x^11 + 12105*x^10 -
55679*x^9 - 6974*x^8 + 171042*x^7 - 73089*x^6 - 246837*x^5 + 168692*x^4 +
161652*x^3 - 131216*x^2 - 38512*x + 33856,7,x^17 - 3*x^16 - 59*x^15 + 203*x^14 +
1181*x^13 - 4735*x^12 - 9117*x^11 + 47250*x^10 + 20329*x^9 - 220646*x^8 +
65432*x^7 + 456300*x^6 - 320455*x^5 - 299884*x^4 + 290500*x^3 - 8688*x^2 -
27600*x + 2944,11,x^17 - 16*x^16 + 36*x^15 + 706*x^14 - 4217*x^13 - 5808*x^12 +
101605*x^11 - 143010*x^10 - 915761*x^9 + 2938069*x^8 + 1586119*x^7 -
17823126*x^6 + 18908999*x^5 + 25080886*x^4 - 70775476*x^3 + 60414065*x^2 -
22749671*x + 3214412,13,x^17 + x^16 - 93*x^15 - 138*x^14 + 3054*x^13 + 5139*x^12
- 44918*x^11 - 72993*x^10 + 331571*x^9 + 471762*x^8 - 1261603*x^7 - 1397971*x^6
+ 2332782*x^5 + 1584167*x^4 - 1689197*x^3 - 199911*x^2 + 270108*x - 36259[]

Total time: 20.369 seconds, Total memory usage: 6.51MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:11:00 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [373..379] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 13:10:40 on modular  [Seed = 2723511516]
-------------------------------------

373,1,2,$.1 + 2,3,$.1 - 1,5,$.1 - 2,7,$.1 + 4,11,$.1 + 6,13,$.1 + 1[]
373,2,2,$.1^12 + 4*$.1^11 - 8*$.1^10 - 43*$.1^9 + 14*$.1^8 + 161*$.1^7 +
17*$.1^6 - 260*$.1^5 - 53*$.1^4 + 177*$.1^3 + 18*$.1^2 - 42*$.1 + 7,3,$.1^12 + 15*$.1^11 + 88*$.1^10 + 237*$.1^9 + 183*$.1^8 - 518*$.1^7 - 1320*$.1^6 - 819*$.1^5 + 588*$.1^4 + 1026*$.1^3 + 491*$.1^2 + 98*$.1 + 7,5,$.1^12 + 11*$.1^11
+ 26*$.1^10 - 118*$.1^9 - 605*$.1^8 - 182*$.1^7 + 3140*$.1^6 + 4749*$.1^5 -
2919*$.1^4 - 10800*$.1^3 - 6876*$.1^2 - 689*$.1 + 331,7,$.1^12 +$.1^11 -
47*$.1^10 - 41*$.1^9 + 841*$.1^8 + 585*$.1^7 - 7225*$.1^6 - 3446*$.1^5 +
30765*$.1^4 + 7470*$.1^3 - 59872*$.1^2 - 3760*$.1 + 40397,11,$.1^12 + 8*$.1^11 -
35*$.1^10 - 352*$.1^9 + 261*$.1^8 + 4248*$.1^7 - 2641*$.1^6 - 19126*$.1^5 +
22857*$.1^4 + 10925*$.1^3 - 20993*$.1^2 + 1383*$.1 + 3397,13,$.1^12 + 10*$.1^11
- 36*$.1^10 - 625*$.1^9 - 608*$.1^8 + 11245*$.1^7 + 29822*$.1^6 - 48645*$.1^5 -
246092*$.1^4 - 198302*$.1^3 + 119773*$.1^2 + 149389*$.1 + 33169[]
373,3,2,$.1^17 - 4*$.1^16 - 18*$.1^15 + 85*$.1^14 + 111*$.1^13 - 713*$.1^12 -
211*$.1^11 + 3017*$.1^10 - 469*$.1^9 - 6832*$.1^8 + 2513*$.1^7 + 8146*$.1^6 -
3634*$.1^5 - 4743*$.1^4 + 2092*$.1^3 + 1142*$.1^2 - 417*$.1 - 62,3,$.1^17 -
14*$.1^16 + 61*$.1^15 + 17*$.1^14 - 866*$.1^13 + 1843*$.1^12 + 2698*$.1^11 -
13639*$.1^10 + 5907*$.1^9 + 34646*$.1^8 - 42911*$.1^7 - 24721*$.1^6 + 64125*$.1^5 - 14879*$.1^4 - 21272*$.1^3 + 6996*$.1^2 + 2464*$.1 - 464,5,$.1^17 - 9*$.1^16 - 8*$.1^15 + 282*$.1^14 - 461*$.1^13 - 2974*$.1^12 + 8406*$.1^11 + 12105*$.1^10 - 55679*$.1^9 - 6974*$.1^8 + 171042*$.1^7 - 73089*$.1^6 -
246837*$.1^5 + 168692*$.1^4 + 161652*$.1^3 - 131216*$.1^2 - 38512*$.1 + 33856,7,$.1^17 - 3*$.1^16 - 59*$.1^15 + 203*$.1^14 + 1181*$.1^13 - 4735*$.1^12 - 9117*$.1^11 + 47250*$.1^10 + 20329*$.1^9 - 220646*$.1^8 + 65432*$.1^7 +
456300*$.1^6 - 320455*$.1^5 - 299884*$.1^4 + 290500*$.1^3 - 8688*$.1^2 - 27600*$.1 + 2944,11,$.1^17 - 16*$.1^16 + 36*$.1^15 + 706*$.1^14 - 4217*$.1^13 - 5808*$.1^12 + 101605*$.1^11 - 143010*$.1^10 - 915761*$.1^9 + 2938069*$.1^8 +
1586119*$.1^7 - 17823126*$.1^6 + 18908999*$.1^5 + 25080886*$.1^4 -
70775476*$.1^3 + 60414065*$.1^2 - 22749671*$.1 + 3214412,13,$.1^17 + $.1^16 - 93*$.1^15 - 138*$.1^14 + 3054*$.1^13 + 5139*$.1^12 - 44918*$.1^11 - 72993*$.1^10 + 331571*$.1^9 + 471762*$.1^8 - 1261603*$.1^7 - 1397971*$.1^6 + 2332782*$.1^5 +
1584167*$.1^4 - 1689197*$.1^3 - 199911*$.1^2 + 270108*$.1 - 36259[]
374,1,2,x + 1,3,x,5,x,7,x + 2,11,x + 1,13,x + 2[]
374,2,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 6*x - 5,5,x^3 + x^2 - 10*x -
15,7,x^3 - x^2 - 16*x + 25,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 11*x^2 + 34*x -
29[]
374,3,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 2*x + 7,5,x^3 + x^2 - 10*x +
9,7,x^3 - 7*x^2 + 12*x - 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 - 2*x - 7[]
374,4,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - x^3 - 10*x^2 + 9*x + 16,5,x^4 -
5*x^3 - 6*x^2 + 47*x - 36,7,x^4 - x^3 - 22*x^2 + 3*x + 98,11,x^4 - 4*x^3 + 6*x^2
- 4*x + 1,13,x^4 + 3*x^3 - 44*x^2 - 65*x + 350[]
374,5,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 13*x - 4,5,x^4 +
x^3 - 12*x^2 - 13*x - 2,7,x^4 - x^3 - 16*x^2 + 37*x - 16,11,x^4 - 4*x^3 + 6*x^2
- 4*x + 1,13,x^4 + x^3 - 44*x^2 - 67*x + 2[]
375,1,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 + x - 1,11,x^2 - 4*x - 1,13,x^2
+ 8*x + 11[]
375,2,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 5*x + 5,11,x^2 + 8*x +
11,13,x^2 - 6*x + 9[]
375,3,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 - x - 1,11,x^2 - 4*x - 1,13,x^2
- 8*x + 11[]
375,4,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 5*x + 5,11,x^2 + 8*x +
11,13,x^2 + 6*x + 9[]
375,5,2,x^4 + 3*x^3 - 3*x^2 - 11*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x +
1,5,x^4,7,x^4 - 4*x^3 - 16*x^2 + 40*x + 80,11,x^4 - 6*x^3 - 12*x^2 + 88*x -
16,13,x^4 - 8*x^3 - 8*x^2 + 136*x - 176[]
375,6,2,x^4 - 3*x^3 - 3*x^2 + 11*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x +
1,5,x^4,7,x^4 + 4*x^3 - 16*x^2 - 40*x + 80,11,x^4 - 6*x^3 - 12*x^2 + 88*x -
16,13,x^4 + 8*x^3 - 8*x^2 - 136*x - 176[]
376,1,2,x^2,3,x^2 + x - 1,5,x^2 + 2*x - 4,7,x^2 + 3*x + 1,11,x^2 + 6*x +
4,13,x^2 - 2*x - 4[]
376,2,2,x^2,3,x^2 + x - 1,5,x^2 + 4*x + 4,7,x^2 - x - 11,11,x^2 + 4*x + 4,13,x^2
+ 6*x + 4[]
376,3,2,x^4,3,x^4 - 3*x^3 - 5*x^2 + 16*x - 8,5,x^4 - 14*x^2 + 8,7,x^4 - 5*x^3 +
x^2 + 8*x - 4,11,x^4 - 8*x^3 - 2*x^2 + 72*x + 40,13,x^4 + 10*x^3 + 10*x^2 -
116*x - 200[]
376,4,2,x^4,3,x^4 + x^3 - 9*x^2 - 4*x + 16,5,x^4 - 4*x^3 - 4*x^2 + 16*x +
16,7,x^4 + 3*x^3 - 11*x^2 - 8*x + 16,11,x^4 - 4*x^3 - 4*x^2 + 16*x + 16,13,x^4 -
12*x^3 + 44*x^2 - 48*x + 16[]
377,1,2,x - 1,3,x,5,x + 2,7,x,11,x + 4,13,x - 1[]
377,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 - 4*x +
4,13,x^2 + 2*x + 1[]
377,3,2,x^5 + x^4 - 5*x^3 - 3*x^2 + 6*x + 1,3,x^5 + 4*x^4 + x^3 - 6*x^2 +
1,5,x^5 + 2*x^4 - 10*x^3 - 11*x^2 + 10*x + 9,7,x^5 + 11*x^4 + 41*x^3 + 64*x^2 +
41*x + 9,11,x^5 - 3*x^4 - 24*x^3 + 73*x^2 + 61*x - 179,13,x^5 + 5*x^4 + 10*x^3 +
10*x^2 + 5*x + 1[]
377,4,2,x^5 + 3*x^4 - 3*x^3 - 13*x^2 - 8*x - 1,3,x^5 + 4*x^4 - 5*x^3 - 30*x^2 -
16*x + 7,5,x^5 - 2*x^4 - 12*x^3 + 27*x^2 + 2*x - 3,7,x^5 + 15*x^4 + 79*x^3 +
166*x^2 + 109*x + 21,11,x^5 + 7*x^4 - 67*x^2 - 71*x + 27,13,x^5 - 5*x^4 + 10*x^3
- 10*x^2 + 5*x - 1[]
377,5,2,x^7 - 3*x^6 - 8*x^5 + 26*x^4 + 9*x^3 - 36*x^2 - 14*x + 3,3,x^7 - 2*x^6 -
11*x^5 + 16*x^4 + 30*x^3 - 33*x^2 - 6*x + 2,5,x^7 + 2*x^6 - 18*x^5 - 7*x^4 +
106*x^3 - 111*x^2 - 8*x + 36,7,x^7 - 7*x^6 + 5*x^5 + 52*x^4 - 117*x^3 + 51*x^2 +
40*x - 18,11,x^7 + 3*x^6 - 66*x^5 - 159*x^4 + 1199*x^3 + 1051*x^2 - 8080*x +
6508,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[]
377,6,2,x^9 - x^8 - 13*x^7 + 13*x^6 + 51*x^5 - 50*x^4 - 59*x^3 + 45*x^2 + 20*x -
3,3,x^9 - 19*x^7 + 6*x^6 + 120*x^5 - 59*x^4 - 304*x^3 + 184*x^2 + 264*x -
184,5,x^9 - 2*x^8 - 24*x^7 + 39*x^6 + 178*x^5 - 247*x^4 - 400*x^3 + 536*x^2 +
32*x - 48,7,x^9 - 17*x^8 + 99*x^7 - 150*x^6 - 655*x^5 + 2625*x^4 - 1932*x^3 -
2672*x^2 + 2032*x + 1352,11,x^9 - 3*x^8 - 38*x^7 + 145*x^6 + 151*x^5 - 747*x^4 -
272*x^3 + 984*x^2 + 464*x - 48,13,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 -
126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1[]
378,1,2,x + 1,3,x,5,x + 1,7,x + 1,11,x + 5,13,x[]
378,2,2,x + 1,3,x,5,x,7,x - 1,11,x,13,x - 5[]
378,3,2,x + 1,3,x,5,x + 4,7,x + 1,11,x - 4,13,x - 3[]
378,4,2,x + 1,3,x,5,x + 3,7,x - 1,11,x - 3,13,x + 4[]
378,5,2,x - 1,3,x,5,x - 1,7,x + 1,11,x - 5,13,x[]
378,6,2,x - 1,3,x,5,x - 4,7,x + 1,11,x + 4,13,x - 3[]
378,7,2,x - 1,3,x,5,x,7,x - 1,11,x,13,x - 5[]
378,8,2,x - 1,3,x,5,x - 3,7,x - 1,11,x + 3,13,x + 4[]
379,1,2,x^13 + 5*x^12 - 5*x^11 - 56*x^10 - 27*x^9 + 210*x^8 + 184*x^7 - 347*x^6
- 346*x^5 + 252*x^4 + 246*x^3 - 60*x^2 - 48*x - 1,3,x^13 + 5*x^12 - 9*x^11 -
76*x^10 - 29*x^9 + 318*x^8 + 271*x^7 - 507*x^6 - 493*x^5 + 280*x^4 + 291*x^3 -
22*x^2 - 37*x - 2,5,x^13 + 20*x^12 + 156*x^11 + 555*x^10 + 551*x^9 - 2138*x^8 -
6937*x^7 - 5820*x^6 + 2699*x^5 + 6331*x^4 + 3300*x^3 + 684*x^2 + 45*x - 1,7,x^13
+ 3*x^12 - 51*x^11 - 165*x^10 + 927*x^9 + 3231*x^8 - 7121*x^7 - 26856*x^6 +
22770*x^5 + 88955*x^4 - 44958*x^3 - 103932*x^2 + 61419*x - 6962,11,x^13 +
20*x^12 + 118*x^11 - 159*x^10 - 4297*x^9 - 13356*x^8 + 15642*x^7 + 163400*x^6 +
305266*x^5 + 144171*x^4 - 90510*x^3 - 63404*x^2 + 4863*x + 982,13,x^13 + 11*x^12
- 19*x^11 - 598*x^10 - 1283*x^9 + 8493*x^8 + 33160*x^7 - 21888*x^6 - 215862*x^5
- 127992*x^4 + 378558*x^3 + 364127*x^2 - 41109*x - 77076[]
379,2,2,x^18 - 3*x^17 - 22*x^16 + 69*x^15 + 190*x^14 - 638*x^13 - 807*x^12 +
3041*x^11 + 1680*x^10 - 7967*x^9 - 1220*x^8 + 11334*x^7 - 1006*x^6 - 8079*x^5 +
1938*x^4 + 2287*x^3 - 752*x^2 - 68*x + 24,3,x^18 - x^17 - 37*x^16 + 36*x^15 +
559*x^14 - 528*x^13 - 4439*x^12 + 4029*x^11 + 19833*x^10 - 16844*x^9 - 49523*x^8
+ 37022*x^7 + 65433*x^6 - 37568*x^5 - 43264*x^4 + 15784*x^3 + 12768*x^2 - 1952*x
- 1216,5,x^18 - 22*x^17 + 186*x^16 - 638*x^15 - 432*x^14 + 10139*x^13 -
24686*x^12 - 19276*x^11 + 178471*x^10 - 200705*x^9 - 313477*x^8 + 829502*x^7 -
236421*x^6 - 754823*x^5 + 554475*x^4 + 137385*x^3 - 165124*x^2 - 5558*x +
13539,7,x^18 - x^17 - 71*x^16 + 103*x^15 + 1973*x^14 - 3563*x^13 - 27635*x^12 +
57544*x^11 + 212620*x^10 - 495675*x^9 - 908364*x^8 + 2385308*x^7 + 2003077*x^6 -
6316692*x^5 - 1626708*x^4 + 8415004*x^3 - 938464*x^2 - 4314960*x +
1667936,11,x^18 - 10*x^17 - 56*x^16 + 835*x^15 + 139*x^14 - 25232*x^13 +
44874*x^12 + 320464*x^11 - 991608*x^10 - 1295023*x^9 + 7267954*x^8 - 2597706*x^7
- 15131019*x^6 + 10747474*x^5 + 12487788*x^4 - 8891044*x^3 - 4374984*x^2 +
1890416*x + 722208,13,x^18 - 9*x^17 - 73*x^16 + 808*x^15 + 1737*x^14 -
29343*x^13 - 4988*x^12 + 551478*x^11 - 460270*x^10 - 5643760*x^9 + 8372598*x^8 +
29575499*x^7 - 60491577*x^6 - 59028994*x^5 + 179211796*x^4 - 27182716*x^3 -
123218944*x^2 + 59018432*x + 568064[]

Total time: 19.579 seconds, Total memory usage: 6.48MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:21:31 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [379..385] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 13:21:08 on modular  [Seed = 1270650754]
-------------------------------------

379,1,2,$.1^13 + 5*$.1^12 - 5*$.1^11 - 56*$.1^10 - 27*$.1^9 + 210*$.1^8 +
184*$.1^7 - 347*$.1^6 - 346*$.1^5 + 252*$.1^4 + 246*$.1^3 - 60*$.1^2 - 48*$.1 - 1,3,$.1^13 + 5*$.1^12 - 9*$.1^11 - 76*$.1^10 - 29*$.1^9 + 318*$.1^8 + 271*$.1^7
- 507*$.1^6 - 493*$.1^5 + 280*$.1^4 + 291*$.1^3 - 22*$.1^2 - 37*$.1 - 2,5,$.1^13 + 20*$.1^12 + 156*$.1^11 + 555*$.1^10 + 551*$.1^9 - 2138*$.1^8 - 6937*$.1^7 - 5820*$.1^6 + 2699*$.1^5 + 6331*$.1^4 + 3300*$.1^3 + 684*$.1^2 + 45*$.1 - 1,7,$.1^13 + 3*$.1^12 - 51*$.1^11 - 165*$.1^10 + 927*$.1^9 + 3231*$.1^8 - 7121*$.1^7 - 26856*$.1^6 + 22770*$.1^5 + 88955*$.1^4 - 44958*$.1^3 -
103932*$.1^2 + 61419*$.1 - 6962,11,$.1^13 + 20*$.1^12 + 118*$.1^11 - 159*$.1^10
- 4297*$.1^9 - 13356*$.1^8 + 15642*$.1^7 + 163400*$.1^6 + 305266*$.1^5 + 144171*$.1^4 - 90510*$.1^3 - 63404*$.1^2 + 4863*$.1 + 982,13,$.1^13 + 11*$.1^12 - 19*$.1^11 - 598*$.1^10 - 1283*$.1^9 + 8493*$.1^8 + 33160*$.1^7 - 21888*$.1^6 - 215862*$.1^5 - 127992*$.1^4 + 378558*$.1^3 + 364127*$.1^2 - 41109*$.1 - 77076[]
379,2,2,$.1^18 - 3*$.1^17 - 22*$.1^16 + 69*$.1^15 + 190*$.1^14 - 638*$.1^13 -
807*$.1^12 + 3041*$.1^11 + 1680*$.1^10 - 7967*$.1^9 - 1220*$.1^8 + 11334*$.1^7 -
1006*$.1^6 - 8079*$.1^5 + 1938*$.1^4 + 2287*$.1^3 - 752*$.1^2 - 68*$.1 +
24,3,$.1^18 -$.1^17 - 37*$.1^16 + 36*$.1^15 + 559*$.1^14 - 528*$.1^13 -
4439*$.1^12 + 4029*$.1^11 + 19833*$.1^10 - 16844*$.1^9 - 49523*$.1^8 + 37022*$.1^7 + 65433*$.1^6 - 37568*$.1^5 - 43264*$.1^4 + 15784*$.1^3 +
12768*$.1^2 - 1952*$.1 - 1216,5,$.1^18 - 22*$.1^17 + 186*$.1^16 - 638*$.1^15 -
432*$.1^14 + 10139*$.1^13 - 24686*$.1^12 - 19276*$.1^11 + 178471*$.1^10 - 200705*$.1^9 - 313477*$.1^8 + 829502*$.1^7 - 236421*$.1^6 - 754823*$.1^5 +
554475*$.1^4 + 137385*$.1^3 - 165124*$.1^2 - 5558*$.1 + 13539,7,$.1^18 -$.1^17
- 71*$.1^16 + 103*$.1^15 + 1973*$.1^14 - 3563*$.1^13 - 27635*$.1^12 + 57544*$.1^11 + 212620*$.1^10 - 495675*$.1^9 - 908364*$.1^8 + 2385308*$.1^7 +
2003077*$.1^6 - 6316692*$.1^5 - 1626708*$.1^4 + 8415004*$.1^3 - 938464*$.1^2 - 4314960*$.1 + 1667936,11,$.1^18 - 10*$.1^17 - 56*$.1^16 + 835*$.1^15 +
139*$.1^14 - 25232*$.1^13 + 44874*$.1^12 + 320464*$.1^11 - 991608*$.1^10 - 1295023*$.1^9 + 7267954*$.1^8 - 2597706*$.1^7 - 15131019*$.1^6 + 10747474*$.1^5
+ 12487788*$.1^4 - 8891044*$.1^3 - 4374984*$.1^2 + 1890416*$.1 +
722208,13,$.1^18 - 9*$.1^17 - 73*$.1^16 + 808*$.1^15 + 1737*$.1^14 - 29343*$.1^13 - 4988*$.1^12 + 551478*$.1^11 - 460270*$.1^10 - 5643760*$.1^9 +
8372598*$.1^8 + 29575499*$.1^7 - 60491577*$.1^6 - 59028994*$.1^5 +
179211796*$.1^4 - 27182716*$.1^3 - 123218944*$.1^2 + 59018432*$.1 + 568064[]
380,1,2,x,3,x - 2,5,x + 1,7,x - 2,11,x,13,x - 6[]
380,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 4,13,x + 4[]
380,3,2,x^2,3,x^2 + 4*x + 2,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 + 4*x +
4,13,x^2 + 4*x - 14[]
380,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 - 4*x + 4,11,x^2 - 12,13,x^2 +
2*x - 2[]
381,1,2,x - 2,3,x - 1,5,x - 3,7,x + 4,11,x - 6,13,x + 7[]
381,2,2,x,3,x - 1,5,x + 1,7,x + 2,11,x + 4,13,x + 3[]
381,3,2,x^5 + x^4 - 5*x^3 - 3*x^2 + 5*x + 2,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 +
5*x + 1,5,x^5 + 5*x^4 - 2*x^3 - 24*x^2 + 16,7,x^5 - 24*x^3 + 8*x^2 + 80*x -
64,11,x^5 + 16*x^4 + 91*x^3 + 220*x^2 + 193*x + 2,13,x^5 - 3*x^4 - 11*x^3 +
47*x^2 - 41*x - 1[]
381,4,2,x^5 - 2*x^4 - 6*x^3 + 10*x^2 + 5*x - 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 +
5*x + 1,5,x^5 - x^4 - 9*x^3 + 11*x^2 + 7*x - 1,7,x^5 - 13*x^3 - 4*x^2 + 33*x +
2,11,x^5 - 14*x^4 + 63*x^3 - 96*x^2 + 33*x + 8,13,x^5 + 5*x^4 - 3*x^3 - 33*x^2 -
9*x + 19[]
381,5,2,x^9 + 2*x^8 - 14*x^7 - 26*x^6 + 59*x^5 + 99*x^4 - 66*x^3 - 102*x^2 -
24*x - 1,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 +
9*x - 1,5,x^9 + 4*x^8 - 25*x^7 - 94*x^6 + 185*x^5 + 524*x^4 - 612*x^3 - 384*x^2
+ 592*x - 160,7,x^9 - 10*x^8 + 7*x^7 + 222*x^6 - 707*x^5 - 532*x^4 + 5304*x^3 -
7544*x^2 + 2352*x + 1152,11,x^9 - 8*x^8 - 18*x^7 + 238*x^6 - 29*x^5 - 2258*x^4 +
1474*x^3 + 7234*x^2 - 3671*x - 5644,13,x^9 - 14*x^8 + 30*x^7 + 344*x^6 -
1521*x^5 - 894*x^4 + 10198*x^3 - 5728*x^2 - 4575*x + 418[]
382,1,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 4*x + 1,5,x^3 + 4*x^2 + x - 1,7,x^3
+ x^2 - 4*x + 1,11,x^3 + 3*x^2 - 10*x - 25,13,x^3 + 3*x^2 + 3*x + 1[]
382,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 5*x^2 + 6*x + 1,5,x^3 + 6*x^2 + 5*x -
13,7,x^3 + 5*x^2 - 8*x - 41,11,x^3 + 3*x^2 - 18*x - 27,13,x^3 + 11*x^2 + 31*x +
13[]
382,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 3*x^3 - 2*x^2 + 9*x - 4,5,x^4 -
4*x^3 + x^2 + 5*x - 2,7,x^4 - x^3 - 6*x^2 + 3*x + 8,11,x^4 - 3*x^3 - 10*x^2 +
33*x - 20,13,x^4 + x^3 - 11*x^2 - x + 2[]
382,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 3*x^4 - 8*x^3 + 25*x^2 +
8*x - 32,5,x^5 - 8*x^4 + 13*x^3 + 23*x^2 - 36*x - 36,7,x^5 - x^4 - 18*x^3 -
23*x^2 + 8*x + 16,11,x^5 - 5*x^4 - 22*x^3 + 113*x^2 + 62*x - 446,13,x^5 - x^4 -
33*x^3 + 73*x^2 + 44*x + 4[]
383,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - x - 1,7,x^2 + 4*x - 1,11,x^2 - 5*x +
5,13,x^2[]
383,2,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 - x^2 + 8*x + 3,3,x^6 - x^5 - 6*x^4 + 5*x^3
+ 5*x^2 - 2*x - 1,5,x^6 + 4*x^5 - 15*x^3 - 14*x^2 + 2*x + 3,7,x^6 + 7*x^5 +
12*x^4 - 14*x^3 - 55*x^2 - 39*x - 1,11,x^6 + 7*x^5 + 8*x^4 - 32*x^3 - 66*x^2 +
2*x + 43,13,x^6 + 18*x^5 + 122*x^4 + 376*x^3 + 482*x^2 + 139*x + 11[]
383,3,2,x^24 - 5*x^23 - 26*x^22 + 160*x^21 + 244*x^20 - 2173*x^19 - 711*x^18 +
16368*x^17 - 4007*x^16 - 75111*x^15 + 42025*x^14 + 217575*x^13 - 160547*x^12 -
399209*x^11 + 331301*x^10 + 452295*x^9 - 388291*x^8 - 296126*x^7 + 247918*x^6 +
96139*x^5 - 75925*x^4 - 9553*x^3 + 8302*x^2 - 342*x - 49,3,x^24 - 2*x^23 -
51*x^22 + 104*x^21 + 1109*x^20 - 2290*x^19 - 13450*x^18 + 27911*x^17 +
100018*x^16 - 206849*x^15 - 472337*x^14 + 965359*x^13 + 1415309*x^12 -
2843156*x^11 - 2583424*x^10 + 5141445*x^9 + 2555730*x^8 - 5332948*x^7 -
929626*x^6 + 2720600*x^5 - 153532*x^4 - 425022*x^3 + 17806*x^2 + 19571*x +
743,5,x^24 - 3*x^23 - 89*x^22 + 259*x^21 + 3375*x^20 - 9557*x^19 - 70951*x^18 +
196783*x^17 + 899813*x^16 - 2474270*x^15 - 6999964*x^14 + 19514728*x^13 +
32247680*x^12 - 95294656*x^11 - 78085888*x^10 + 273042688*x^9 + 61524736*x^8 -
408682496*x^7 + 74373120*x^6 + 247068672*x^5 - 100229120*x^4 - 38567936*x^3 +
23134208*x^2 - 2490368*x - 65536,7,x^24 - 17*x^23 + 36*x^22 + 942*x^21 -
5769*x^20 - 11929*x^19 + 182178*x^18 - 205659*x^17 - 2403957*x^16 + 6825011*x^15
+ 13078328*x^14 - 71066450*x^13 - 1315722*x^12 + 361882707*x^11 - 292414708*x^10
- 990516687*x^9 + 1345964622*x^8 + 1461617571*x^7 - 2834498399*x^6 -
1056451767*x^5 + 3147665499*x^4 + 245611927*x^3 - 1779168466*x^2 + 40526951*x +
405907721,11,x^24 - 170*x^22 + 3*x^21 + 12126*x^20 - 670*x^19 - 473243*x^18 +
52527*x^17 + 11062807*x^16 - 1980462*x^15 - 159713668*x^14 + 39812152*x^13 +
1420991840*x^12 - 438268128*x^11 - 7585055872*x^10 + 2621443712*x^9 +
23139197184*x^8 - 8438759936*x^7 - 37824342016*x^6 + 15647381504*x^5 +
29517463552*x^4 - 15904178176*x^3 - 7621558272*x^2 + 6398541824*x -
1074200576,13,x^24 - 28*x^23 + 178*x^22 + 2020*x^21 - 29764*x^20 + 23887*x^19 +
1415095*x^18 - 6150628*x^17 - 25591408*x^16 + 225928952*x^15 - 9428192*x^14 -
3724661216*x^13 + 6876164864*x^12 + 29302047872*x^11 - 100363459584*x^10 -
79709571072*x^9 + 627035143168*x^8 - 242064082944*x^7 - 1764248862720*x^6 +
1677457481728*x^5 + 1825612185600*x^4 - 2161780850688*x^3 - 781524729856*x^2 +
821170274304*x + 147586023424[]
384,1,2,x,3,x + 1,5,x,7,x + 2,11,x + 4,13,x + 6[]
384,2,2,x,3,x - 1,5,x,7,x - 2,11,x - 4,13,x + 6[]
384,3,2,x,3,x - 1,5,x,7,x + 2,11,x - 4,13,x - 6[]
384,4,2,x,3,x - 1,5,x - 4,7,x - 2,11,x + 4,13,x + 2[]
384,5,2,x,3,x + 1,5,x,7,x - 2,11,x + 4,13,x - 6[]
384,6,2,x,3,x + 1,5,x - 4,7,x + 2,11,x - 4,13,x + 2[]
384,7,2,x,3,x + 1,5,x + 4,7,x - 2,11,x - 4,13,x - 2[]
384,8,2,x,3,x - 1,5,x + 4,7,x + 2,11,x + 4,13,x - 2[]
385,1,2,x + 1,3,x,5,x - 1,7,x + 1,11,x - 1,13,x + 6[]
385,2,2,x + 1,3,x + 2,5,x - 1,7,x - 1,11,x + 1,13,x - 4[]
385,3,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 - 2*x +
1,13,x^2 - 4*x + 2[]
385,4,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 + 2*x +
1,13,x^2 + 2*x - 2[]
385,5,2,x^3 + 3*x^2 - x - 5,3,x^3 + 2*x^2 - 2*x - 2,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 2*x^2 - 22*x - 2[]
385,6,2,x^3 + 3*x^2 - x - 5,3,x^3 + 4*x^2 + 2*x - 2,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 8*x^2 + 18*x + 10[]
385,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 4*x + 2,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 -
3*x^2 + 3*x - 1,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 4*x + 2[]
385,8,2,x^4 - 2*x^3 - 6*x^2 + 8*x + 7,3,x^4 - 2*x^3 - 8*x^2 + 10*x + 16,5,x^4 -
4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 + 4*x^3 + 6*x^2 +
4*x + 1,13,x^4 + 8*x^3 - 8*x^2 - 162*x - 236[]

Total time: 22.049 seconds, Total memory usage: 6.61MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:31:39 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [385..391] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sat Nov 29 2003 13:31:16 on modular  [Seed = 1921362139]
-------------------------------------

385,1,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 1,13,$.1 + 6[]
385,2,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 - 1,11,$.1 + 1,13,$.1 - 4[]
385,3,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 + 2[] 385,4,2,$.1^2 - 3,3,$.1^2 - 2*$.1 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 2*$.1 +
1,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 2*$.1 - 2[]
385,5,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 2*$.1^2 - 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 3*$.1^2 + 3*$.1 + 1,13,$.1^3 - 2*$.1^2 - 22*$.1 - 2[]
385,6,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 4*$.1^2 + 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 + 8*$.1^2 + 18*$.1 + 10[]
385,7,2,$.1^3 -$.1^2 - 3*$.1 + 1,3,$.1^3 - 4*$.1 + 2,5,$.1^3 - 3*$.1^2 + 3*$.1
- 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 - 4*$.1 + 2[]
385,8,2,$.1^4 - 2*$.1^3 - 6*$.1^2 + 8*$.1 + 7,3,$.1^4 - 2*$.1^3 - 8*$.1^2 + 10*$.1 + 16,5,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 8*$.1^3 -
8*$.1^2 - 162*$.1 - 236[]
386,1,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2 - x - 1,7,x^2 + 4*x + 4,11,x^2 + 4*x +
4,13,x^2 + 3*x - 9[]
386,2,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 5*x + 5,7,x^2 + 2*x - 4,11,x^2 +
2*x - 4,13,x^2 + 7*x + 1[]
386,3,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - x^5 - 12*x^4 +
7*x^3 + 40*x^2 - 13*x - 37,5,x^6 + 5*x^5 - 8*x^4 - 49*x^3 + 22*x^2 + 103*x -
63,7,x^6 - 8*x^5 + 136*x^3 - 320*x^2 + 80*x + 176,11,x^6 + 2*x^5 - 36*x^4 -
56*x^3 + 344*x^2 + 352*x - 336,13,x^6 - 9*x^5 - 8*x^4 + 227*x^3 - 448*x^2 -
221*x + 773[]
386,4,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - 3*x^6
- 10*x^5 + 33*x^4 + 14*x^3 - 91*x^2 + 45*x + 16,5,x^7 - 5*x^6 - 8*x^5 + 59*x^4 +
14*x^3 - 227*x^2 + 3*x + 284,7,x^7 - 2*x^6 - 24*x^5 + 40*x^4 + 152*x^3 - 112*x^2
- 336*x - 128,11,x^7 - 2*x^6 - 36*x^5 + 16*x^4 + 256*x^3 - 96*x^2 - 496*x +
352,13,x^7 - 5*x^6 - 56*x^5 + 249*x^4 + 788*x^3 - 2689*x^2 - 2317*x + 3076[]
387,1,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 3,13,x + 5[]
387,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 3,13,x + 5[]
387,3,2,x,3,x,5,x - 2,7,x + 2,11,x - 5,13,x - 3[]
387,4,2,x + 1,3,x,5,x + 2,7,x,11,x,13,x + 2[]
387,5,2,x - 2,3,x,5,x - 4,7,x,11,x + 3,13,x + 5[]
387,6,2,x^2,3,x^2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 - 27,13,x^2 - 10*x + 25[]
387,7,2,x^2 - 2,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 2*x - 7,13,x^2 -
2*x - 7[]
387,8,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 2*x - 1,7,x^2 - 2*x - 7,11,x^2 + 6*x +
7,13,x^2 + 10*x + 25[]
387,9,2,x^3 - 2*x^2 - 5*x + 8,3,x^3,5,x^3 - 4*x^2 - x + 2,7,x^3 - 4*x^2 - 3*x +
10,11,x^3 + x^2 - 19*x + 25,13,x^3 - 9*x^2 + 27*x - 27[]
387,10,2,x^4 - 10*x^2 + 25,3,x^4,5,x^4 - 9*x^2 + 4,7,x^4 + 2*x^3 - 31*x^2 - 32*x
+ 256,11,x^4 - 9*x^2 + 4,13,x^4 - 10*x^3 + 5*x^2 + 100*x + 100[]
388,1,2,x^3,3,x^3 + 2*x^2 - x - 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3 - x^2 - 16*x -
13,11,x^3 + 7*x^2 - 49,13,x^3 + 4*x^2 + 3*x - 1[]
388,2,2,x^5,3,x^5 - 2*x^4 - 9*x^3 + 15*x^2 + 20*x - 24,5,x^5 - 5*x^4 - 4*x^3 +
41*x^2 - 8*x - 76,7,x^5 - x^4 - 12*x^3 + x^2 + 10*x + 2,11,x^5 - 5*x^4 - 4*x^3 +
23*x^2 + 28*x + 8,13,x^5 - 6*x^4 - 21*x^3 + 115*x^2 + 100*x - 500[]
389,1,2,x + 2,3,x + 2,5,x + 3,7,x + 5,11,x + 4,13,x + 3[]
389,2,2,x^2 - 2,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 + 2*x - 7,11,x^2 + 4*x +
4,13,x^2 - 2*x - 7[]
389,3,2,x^3 - 4*x - 2,3,x^3 - 4*x + 2,5,x^3 + 5*x^2 + 3*x - 5,7,x^3 + 3*x^2 +
3*x + 1,11,x^3 + 4*x^2 - 4,13,x^3 + 9*x^2 + 27*x + 27[]
389,4,2,x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1,3,x^6 + 5*x^5 + 4*x^4 -
13*x^3 - 21*x^2 - 6*x + 1,5,x^6 - 3*x^5 - 11*x^4 + 30*x^3 + 38*x^2 - 67*x -
59,7,x^6 + 4*x^5 - 18*x^4 - 110*x^3 - 136*x^2 + 61*x + 139,11,x^6 + 2*x^5 -
39*x^4 - 136*x^3 + 89*x^2 + 655*x + 409,13,x^6 + 5*x^5 - 33*x^4 - 238*x^3 -
409*x^2 - 148*x + 1[]
389,5,2,x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 - 2023*x^14 +
7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 + 6954*x^8 -
74752*x^7 + 1407*x^6 + 46330*x^5 - 1087*x^4 - 12558*x^3 - 942*x^2 + 960*x +
148,3,x^20 - 11*x^19 + 19*x^18 + 204*x^17 - 845*x^16 - 781*x^15 + 8883*x^14 -
6177*x^13 - 40916*x^12 + 63058*x^11 + 85034*x^10 - 215618*x^9 - 46920*x^8 +
342529*x^7 - 84612*x^6 - 241030*x^5 + 112365*x^4 + 51018*x^3 - 28526*x^2 +
3560*x - 100,5,x^20 - x^19 - 58*x^18 + 69*x^17 + 1338*x^16 - 1962*x^15 -
15578*x^14 + 28633*x^13 + 93460*x^12 - 224324*x^11 - 236982*x^10 + 902782*x^9 -
92649*x^8 - 1549758*x^7 + 1240027*x^6 + 457997*x^5 - 897661*x^4 + 293181*x^3 +
17361*x^2 - 16713*x + 757,7,x^20 - 12*x^19 - 8*x^18 + 602*x^17 - 1355*x^16 -
11751*x^15 + 44797*x^14 + 105012*x^13 - 632038*x^12 - 274991*x^11 + 4756743*x^10
- 2413492*x^9 - 19377380*x^8 + 21737168*x^7 + 37613472*x^6 - 64826048*x^5 -
17117376*x^4 + 68169472*x^3 - 23637760*x^2 - 4162560*x + 1715200,11,x^20 -
10*x^19 - 71*x^18 + 1000*x^17 + 825*x^16 - 38773*x^15 + 56185*x^14 + 714296*x^13
- 2098532*x^12 - 5826144*x^11 + 28736608*x^10 + 7095232*x^9 - 174873152*x^8 +
152530432*x^7 + 436532992*x^6 - 742544384*x^5 - 208098304*x^4 + 1038184448*x^3 -
471076864*x^2 - 156303360*x + 92979200,13,x^20 - 17*x^19 + 12*x^18 + 1261*x^17 -
5711*x^16 - 29277*x^15 + 237009*x^14 + 79260*x^13 - 3979139*x^12 + 6049839*x^11
+ 28107002*x^10 - 83032878*x^9 - 46796396*x^8 + 371031699*x^7 - 191435207*x^6 -
567769995*x^5 + 474808960*x^4 + 358305542*x^3 - 255218964*x^2 - 124967058*x -
4360151[]

Errors: /home/mfd/gomagma: line 2: 25135 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:32:35 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [385..389] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 13:32:20 on modular  [Seed = 1788719875]
-------------------------------------

385,1,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 1,13,$.1 + 6[]
385,2,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1 - 1,11,$.1 + 1,13,$.1 - 4[]
385,3,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 + 2[] 385,4,2,$.1^2 - 3,3,$.1^2 - 2*$.1 - 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 2*$.1 +
1,11,$.1^2 + 2*$.1 + 1,13,$.1^2 + 2*$.1 - 2[]
385,5,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 2*$.1^2 - 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 3*$.1^2 + 3*$.1 + 1,13,$.1^3 - 2*$.1^2 - 22*$.1 - 2[]
385,6,2,$.1^3 + 3*$.1^2 - $.1 - 5,3,$.1^3 + 4*$.1^2 + 2*$.1 - 2,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 + 8*$.1^2 + 18*$.1 + 10[]
385,7,2,$.1^3 -$.1^2 - 3*$.1 + 1,3,$.1^3 - 4*$.1 + 2,5,$.1^3 - 3*$.1^2 + 3*$.1
- 1,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 - 3*$.1^2 + 3*$.1 - 1,13,$.1^3 - 4*$.1 + 2[]
385,8,2,$.1^4 - 2*$.1^3 - 6*$.1^2 + 8*$.1 + 7,3,$.1^4 - 2*$.1^3 - 8*$.1^2 + 10*$.1 + 16,5,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,11,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 8*$.1^3 -
8*$.1^2 - 162*$.1 - 236[]
386,1,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2 - x - 1,7,x^2 + 4*x + 4,11,x^2 + 4*x +
4,13,x^2 + 3*x - 9[]
386,2,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 5*x + 5,7,x^2 + 2*x - 4,11,x^2 +
2*x - 4,13,x^2 + 7*x + 1[]
386,3,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - x^5 - 12*x^4 +
7*x^3 + 40*x^2 - 13*x - 37,5,x^6 + 5*x^5 - 8*x^4 - 49*x^3 + 22*x^2 + 103*x -
63,7,x^6 - 8*x^5 + 136*x^3 - 320*x^2 + 80*x + 176,11,x^6 + 2*x^5 - 36*x^4 -
56*x^3 + 344*x^2 + 352*x - 336,13,x^6 - 9*x^5 - 8*x^4 + 227*x^3 - 448*x^2 -
221*x + 773[]
386,4,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - 3*x^6
- 10*x^5 + 33*x^4 + 14*x^3 - 91*x^2 + 45*x + 16,5,x^7 - 5*x^6 - 8*x^5 + 59*x^4 +
14*x^3 - 227*x^2 + 3*x + 284,7,x^7 - 2*x^6 - 24*x^5 + 40*x^4 + 152*x^3 - 112*x^2
- 336*x - 128,11,x^7 - 2*x^6 - 36*x^5 + 16*x^4 + 256*x^3 - 96*x^2 - 496*x +
352,13,x^7 - 5*x^6 - 56*x^5 + 249*x^4 + 788*x^3 - 2689*x^2 - 2317*x + 3076[]
387,1,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 3,13,x + 5[]
387,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 3,13,x + 5[]
387,3,2,x,3,x,5,x - 2,7,x + 2,11,x - 5,13,x - 3[]
387,4,2,x + 1,3,x,5,x + 2,7,x,11,x,13,x + 2[]
387,5,2,x - 2,3,x,5,x - 4,7,x,11,x + 3,13,x + 5[]
387,6,2,x^2,3,x^2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 - 27,13,x^2 - 10*x + 25[]
387,7,2,x^2 - 2,3,x^2,5,x^2 + 4*x + 2,7,x^2 + 4*x + 2,11,x^2 - 2*x - 7,13,x^2 -
2*x - 7[]
387,8,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 2*x - 1,7,x^2 - 2*x - 7,11,x^2 + 6*x +
7,13,x^2 + 10*x + 25[]
387,9,2,x^3 - 2*x^2 - 5*x + 8,3,x^3,5,x^3 - 4*x^2 - x + 2,7,x^3 - 4*x^2 - 3*x +
10,11,x^3 + x^2 - 19*x + 25,13,x^3 - 9*x^2 + 27*x - 27[]
387,10,2,x^4 - 10*x^2 + 25,3,x^4,5,x^4 - 9*x^2 + 4,7,x^4 + 2*x^3 - 31*x^2 - 32*x
+ 256,11,x^4 - 9*x^2 + 4,13,x^4 - 10*x^3 + 5*x^2 + 100*x + 100[]
388,1,2,x^3,3,x^3 + 2*x^2 - x - 1,5,x^3 + 5*x^2 + 6*x + 1,7,x^3 - x^2 - 16*x -
13,11,x^3 + 7*x^2 - 49,13,x^3 + 4*x^2 + 3*x - 1[]
388,2,2,x^5,3,x^5 - 2*x^4 - 9*x^3 + 15*x^2 + 20*x - 24,5,x^5 - 5*x^4 - 4*x^3 +
41*x^2 - 8*x - 76,7,x^5 - x^4 - 12*x^3 + x^2 + 10*x + 2,11,x^5 - 5*x^4 - 4*x^3 +
23*x^2 + 28*x + 8,13,x^5 - 6*x^4 - 21*x^3 + 115*x^2 + 100*x - 500[]
389,1,2,x + 2,3,x + 2,5,x + 3,7,x + 5,11,x + 4,13,x + 3[]
389,2,2,x^2 - 2,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 + 2*x - 7,11,x^2 + 4*x +
4,13,x^2 - 2*x - 7[]
389,3,2,x^3 - 4*x - 2,3,x^3 - 4*x + 2,5,x^3 + 5*x^2 + 3*x - 5,7,x^3 + 3*x^2 +
3*x + 1,11,x^3 + 4*x^2 - 4,13,x^3 + 9*x^2 + 27*x + 27[]
389,4,2,x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1,3,x^6 + 5*x^5 + 4*x^4 -
13*x^3 - 21*x^2 - 6*x + 1,5,x^6 - 3*x^5 - 11*x^4 + 30*x^3 + 38*x^2 - 67*x -
59,7,x^6 + 4*x^5 - 18*x^4 - 110*x^3 - 136*x^2 + 61*x + 139,11,x^6 + 2*x^5 -
39*x^4 - 136*x^3 + 89*x^2 + 655*x + 409,13,x^6 + 5*x^5 - 33*x^4 - 238*x^3 -
409*x^2 - 148*x + 1[]
389,5,2,x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 - 2023*x^14 +
7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 + 6954*x^8 -
74752*x^7 + 1407*x^6 + 46330*x^5 - 1087*x^4 - 12558*x^3 - 942*x^2 + 960*x +
148,3,x^20 - 11*x^19 + 19*x^18 + 204*x^17 - 845*x^16 - 781*x^15 + 8883*x^14 -
6177*x^13 - 40916*x^12 + 63058*x^11 + 85034*x^10 - 215618*x^9 - 46920*x^8 +
342529*x^7 - 84612*x^6 - 241030*x^5 + 112365*x^4 + 51018*x^3 - 28526*x^2 +
3560*x - 100,5,x^20 - x^19 - 58*x^18 + 69*x^17 + 1338*x^16 - 1962*x^15 -
15578*x^14 + 28633*x^13 + 93460*x^12 - 224324*x^11 - 236982*x^10 + 902782*x^9 -
92649*x^8 - 1549758*x^7 + 1240027*x^6 + 457997*x^5 - 897661*x^4 + 293181*x^3 +
17361*x^2 - 16713*x + 757,7,x^20 - 12*x^19 - 8*x^18 + 602*x^17 - 1355*x^16 -
11751*x^15 + 44797*x^14 + 105012*x^13 - 632038*x^12 - 274991*x^11 + 4756743*x^10
- 2413492*x^9 - 19377380*x^8 + 21737168*x^7 + 37613472*x^6 - 64826048*x^5 -
17117376*x^4 + 68169472*x^3 - 23637760*x^2 - 4162560*x + 1715200,11,x^20 -
10*x^19 - 71*x^18 + 1000*x^17 + 825*x^16 - 38773*x^15 + 56185*x^14 + 714296*x^13
- 2098532*x^12 - 5826144*x^11 + 28736608*x^10 + 7095232*x^9 - 174873152*x^8 +
152530432*x^7 + 436532992*x^6 - 742544384*x^5 - 208098304*x^4 + 1038184448*x^3 -
471076864*x^2 - 156303360*x + 92979200,13,x^20 - 17*x^19 + 12*x^18 + 1261*x^17 -
5711*x^16 - 29277*x^15 + 237009*x^14 + 79260*x^13 - 3979139*x^12 + 6049839*x^11
+ 28107002*x^10 - 83032878*x^9 - 46796396*x^8 + 371031699*x^7 - 191435207*x^6 -
567769995*x^5 + 474808960*x^4 + 358305542*x^3 - 255218964*x^2 - 124967058*x -
4360151[]

Total time: 15.179 seconds, Total memory usage: 5.35MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:40:17 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [389..395] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sat Nov 29 2003 13:39:54 on modular  [Seed = 367185330]
-------------------------------------

389,1,2,$.1 + 2,3,$.1 + 2,5,$.1 + 3,7,$.1 + 5,11,$.1 + 4,13,$.1 + 3[]
389,2,2,$.1^2 - 2,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 - 7,11,$.1^2 + 4*$.1 + 4,13,$.1^2 - 2*$.1 - 7[] 389,3,2,$.1^3 - 4*$.1 - 2,3,$.1^3 - 4*$.1 + 2,5,$.1^3 + 5*$.1^2 + 3*$.1 -
5,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 - 4,13,$.1^3 + 9*$.1^2 + 27*$.1 + 27[]
389,4,2,$.1^6 + 3*$.1^5 - 2*$.1^4 - 8*$.1^3 + 2*$.1^2 + 4*$.1 - 1,3,$.1^6 + 5*$.1^5 + 4*$.1^4 - 13*$.1^3 - 21*$.1^2 - 6*$.1 + 1,5,$.1^6 - 3*$.1^5 - 11*$.1^4 + 30*$.1^3 + 38*$.1^2 - 67*$.1 - 59,7,$.1^6 + 4*$.1^5 - 18*$.1^4 - 110*$.1^3 -
136*$.1^2 + 61*$.1 + 139,11,$.1^6 + 2*$.1^5 - 39*$.1^4 - 136*$.1^3 + 89*$.1^2 + 655*$.1 + 409,13,$.1^6 + 5*$.1^5 - 33*$.1^4 - 238*$.1^3 - 409*$.1^2 - 148*$.1 +
1[]
389,5,2,$.1^20 - 3*$.1^19 - 29*$.1^18 + 91*$.1^17 + 338*$.1^16 - 1130*$.1^15 -
2023*$.1^14 + 7432*$.1^13 + 6558*$.1^12 - 28021*$.1^11 - 10909*$.1^10 + 61267*$.1^9 + 6954*$.1^8 - 74752*$.1^7 + 1407*$.1^6 + 46330*$.1^5 - 1087*$.1^4 - 12558*$.1^3 - 942*$.1^2 + 960*$.1 + 148,3,$.1^20 - 11*$.1^19 + 19*$.1^18 + 204*$.1^17 - 845*$.1^16 - 781*$.1^15 + 8883*$.1^14 - 6177*$.1^13 - 40916*$.1^12 + 63058*$.1^11 + 85034*$.1^10 - 215618*$.1^9 - 46920*$.1^8 + 342529*$.1^7 -
84612*$.1^6 - 241030*$.1^5 + 112365*$.1^4 + 51018*$.1^3 - 28526*$.1^2 + 3560*$.1
- 100,5,$.1^20 -$.1^19 - 58*$.1^18 + 69*$.1^17 + 1338*$.1^16 - 1962*$.1^15 -
15578*$.1^14 + 28633*$.1^13 + 93460*$.1^12 - 224324*$.1^11 - 236982*$.1^10 + 902782*$.1^9 - 92649*$.1^8 - 1549758*$.1^7 + 1240027*$.1^6 + 457997*$.1^5 -
897661*$.1^4 + 293181*$.1^3 + 17361*$.1^2 - 16713*$.1 + 757,7,$.1^20 - 12*$.1^19
- 8*$.1^18 + 602*$.1^17 - 1355*$.1^16 - 11751*$.1^15 + 44797*$.1^14 + 105012*$.1^13 - 632038*$.1^12 - 274991*$.1^11 + 4756743*$.1^10 - 2413492*$.1^9 -
19377380*$.1^8 + 21737168*$.1^7 + 37613472*$.1^6 - 64826048*$.1^5 -
17117376*$.1^4 + 68169472*$.1^3 - 23637760*$.1^2 - 4162560*$.1 +
1715200,11,$.1^20 - 10*$.1^19 - 71*$.1^18 + 1000*$.1^17 + 825*$.1^16 - 38773*$.1^15 + 56185*$.1^14 + 714296*$.1^13 - 2098532*$.1^12 - 5826144*$.1^11 +
28736608*$.1^10 + 7095232*$.1^9 - 174873152*$.1^8 + 152530432*$.1^7 +
436532992*$.1^6 - 742544384*$.1^5 - 208098304*$.1^4 + 1038184448*$.1^3 -
471076864*$.1^2 - 156303360*$.1 + 92979200,13,$.1^20 - 17*$.1^19 + 12*$.1^18 + 1261*$.1^17 - 5711*$.1^16 - 29277*$.1^15 + 237009*$.1^14 + 79260*$.1^13 -
3979139*$.1^12 + 6049839*$.1^11 + 28107002*$.1^10 - 83032878*$.1^9 -
46796396*$.1^8 + 371031699*$.1^7 - 191435207*$.1^6 - 567769995*$.1^5 +
474808960*$.1^4 + 358305542*$.1^3 - 255218964*$.1^2 - 124967058*$.1 - 4360151[]
390,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x,13,x + 1[]
390,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 4,13,x + 1[]
390,3,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x,13,x + 1[]
390,4,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 1[]
390,5,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 4,13,x + 1[]
390,6,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x - 1[]
390,7,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x - 1[]
390,8,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 -
32,13,x^2 + 2*x + 1[]
391,1,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 + 2*x - 4,11,x^2 + 8*x
+ 16,13,x^2 + 2*x + 1[]
391,2,2,x^3 + x^2 - 4*x - 3,3,x^3 + 6*x^2 + 12*x + 8,5,x^3 + 3*x^2 - 2*x -
7,7,x^3 - x^2 - 4*x + 3,11,x^3 - x^2 - 8*x + 3,13,x^3 - x^2 - 26*x - 15[]
391,3,2,x^3 + x^2 - 4*x + 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 5*x^2 + 4*x -
5,11,x^3 + 3*x^2 - 10*x - 25,13,x^3 + 3*x^2 - 10*x + 1[]
391,4,2,x^9 - 2*x^8 - 12*x^7 + 23*x^6 + 43*x^5 - 79*x^4 - 43*x^3 + 78*x^2 + 11*x
- 21,3,x^9 - 2*x^8 - 20*x^7 + 36*x^6 + 124*x^5 - 192*x^4 - 248*x^3 + 256*x^2 +
160*x - 64,5,x^9 - 7*x^8 + x^7 + 92*x^6 - 216*x^5 + 15*x^4 + 421*x^3 - 391*x^2 +
64*x + 3,7,x^9 - 3*x^8 - 27*x^7 + 94*x^6 + 194*x^5 - 863*x^4 - 215*x^3 +
2593*x^2 - 918*x - 1493,11,x^9 - 11*x^8 + 11*x^7 + 246*x^6 - 834*x^5 - 213*x^4 +
3633*x^3 - 2305*x^2 - 4100*x + 3723,13,x^9 + 9*x^8 - 35*x^7 - 454*x^6 - 132*x^5
+ 5675*x^4 + 8067*x^3 - 10191*x^2 - 13434*x + 5161[]
391,5,2,x^12 - 4*x^11 - 12*x^10 + 62*x^9 + 27*x^8 - 321*x^7 + 108*x^6 + 625*x^5
- 362*x^4 - 372*x^3 + 116*x^2 + 97*x + 13,3,x^12 - 2*x^11 - 31*x^10 + 60*x^9 +
348*x^8 - 652*x^7 - 1708*x^6 + 3064*x^5 + 3608*x^4 - 5728*x^3 - 3424*x^2 +
3264*x + 1792,5,x^12 - 5*x^11 - 33*x^10 + 178*x^9 + 338*x^8 - 2109*x^7 -
1131*x^6 + 9799*x^5 + 574*x^4 - 15637*x^3 - 3040*x^2 + 7912*x + 3080,7,x^12 +
9*x^11 - 13*x^10 - 286*x^9 - 174*x^8 + 3313*x^7 + 2875*x^6 - 18363*x^5 -
8640*x^4 + 46363*x^3 - 10702*x^2 - 19252*x + 7264,11,x^12 - 11*x^11 - 27*x^10 +
610*x^9 - 492*x^8 - 11697*x^7 + 21625*x^6 + 87835*x^5 - 213962*x^4 - 184849*x^3
+ 691228*x^2 - 260608*x - 179200,13,x^12 - 7*x^11 - 58*x^10 + 525*x^9 + 327*x^8
- 10629*x^7 + 16951*x^6 + 54704*x^5 - 178361*x^4 + 133768*x^3 + 14316*x^2 -
18959*x + 50[]
392,1,2,x,3,x + 1,5,x + 1,7,x,11,x - 3,13,x + 6[]
392,2,2,x,3,x - 1,5,x - 1,7,x,11,x - 3,13,x - 6[]
392,3,2,x,3,x + 2,5,x - 4,7,x,11,x,13,x[]
392,4,2,x,3,x - 3,5,x + 1,7,x,11,x + 1,13,x - 2[]
392,5,2,x,3,x,5,x + 2,7,x,11,x + 4,13,x + 2[]
392,6,2,x,3,x + 3,5,x - 1,7,x,11,x + 1,13,x + 2[]
392,7,2,x^2,3,x^2 - 8,5,x^2 - 8,7,x^2,11,x^2 + 8*x + 16,13,x^2 - 8[]
392,8,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2,11,x^2 - 12*x + 36,13,x^2 - 32[]
393,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2*x +
1,13,x^2 - 10*x + 25[]
393,2,2,x^4 + x^3 - 4*x^2 - 2*x + 3,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 -
6*x^2 + x + 7,7,x^4 + 8*x^3 + 17*x^2 - 19,11,x^4 - 2*x^3 - 26*x^2 - 13*x +
3,13,x^4 + 9*x^3 + 12*x^2 - 44*x - 21[]
393,3,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 8*x^3 +
18*x^2 + 3*x - 19,7,x^4 + 8*x^3 + 13*x^2 - 12*x + 1,11,x^4 + 4*x^3 - 30*x^2 -
103*x + 109,13,x^4 + 5*x^3 - 24*x^2 - 80*x + 139[]
393,4,2,x^5 - 2*x^4 - 7*x^3 + 12*x^2 + 9*x - 9,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 +
5*x + 1,5,x^5 + 2*x^4 - 14*x^3 - 23*x^2 + 17*x - 2,7,x^5 - 4*x^4 - 7*x^3 +
48*x^2 - 63*x + 24,11,x^5 + 6*x^4 - 38*x^3 - 229*x^2 + 183*x + 1388,13,x^5 +
3*x^4 - 38*x^3 - 76*x^2 + 303*x + 158[]
393,5,2,x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 5,3,x^6 - 6*x^5 + 15*x^4 -
20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 8*x^5 + 18*x^4 - x^3 - 27*x^2 + 8*x + 8,7,x^6
- 4*x^5 - 11*x^4 + 28*x^3 + 45*x^2 - 48*x - 64,11,x^6 - 6*x^5 - x^4 + 45*x^3 -
19*x^2 - 69*x + 5,13,x^6 + 3*x^5 - 29*x^4 - 75*x^3 - 29*x^2 + 18*x - 1[]

Errors: /home/mfd/gomagma: line 2: 25160 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:41:09 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [389..393] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 13:40:49 on modular  [Seed = 184409446]
-------------------------------------

389,1,2,$.1 + 2,3,$.1 + 2,5,$.1 + 3,7,$.1 + 5,11,$.1 + 4,13,$.1 + 3[]
389,2,2,$.1^2 - 2,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 + 1,7,$.1^2 + 2*$.1 - 7,11,$.1^2 + 4*$.1 + 4,13,$.1^2 - 2*$.1 - 7[] 389,3,2,$.1^3 - 4*$.1 - 2,3,$.1^3 - 4*$.1 + 2,5,$.1^3 + 5*$.1^2 + 3*$.1 -
5,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 4*$.1^2 - 4,13,$.1^3 + 9*$.1^2 + 27*$.1 + 27[]
389,4,2,$.1^6 + 3*$.1^5 - 2*$.1^4 - 8*$.1^3 + 2*$.1^2 + 4*$.1 - 1,3,$.1^6 + 5*$.1^5 + 4*$.1^4 - 13*$.1^3 - 21*$.1^2 - 6*$.1 + 1,5,$.1^6 - 3*$.1^5 - 11*$.1^4 + 30*$.1^3 + 38*$.1^2 - 67*$.1 - 59,7,$.1^6 + 4*$.1^5 - 18*$.1^4 - 110*$.1^3 -
136*$.1^2 + 61*$.1 + 139,11,$.1^6 + 2*$.1^5 - 39*$.1^4 - 136*$.1^3 + 89*$.1^2 + 655*$.1 + 409,13,$.1^6 + 5*$.1^5 - 33*$.1^4 - 238*$.1^3 - 409*$.1^2 - 148*$.1 +
1[]
389,5,2,$.1^20 - 3*$.1^19 - 29*$.1^18 + 91*$.1^17 + 338*$.1^16 - 1130*$.1^15 -
2023*$.1^14 + 7432*$.1^13 + 6558*$.1^12 - 28021*$.1^11 - 10909*$.1^10 + 61267*$.1^9 + 6954*$.1^8 - 74752*$.1^7 + 1407*$.1^6 + 46330*$.1^5 - 1087*$.1^4 - 12558*$.1^3 - 942*$.1^2 + 960*$.1 + 148,3,$.1^20 - 11*$.1^19 + 19*$.1^18 + 204*$.1^17 - 845*$.1^16 - 781*$.1^15 + 8883*$.1^14 - 6177*$.1^13 - 40916*$.1^12 + 63058*$.1^11 + 85034*$.1^10 - 215618*$.1^9 - 46920*$.1^8 + 342529*$.1^7 -
84612*$.1^6 - 241030*$.1^5 + 112365*$.1^4 + 51018*$.1^3 - 28526*$.1^2 + 3560*$.1
- 100,5,$.1^20 -$.1^19 - 58*$.1^18 + 69*$.1^17 + 1338*$.1^16 - 1962*$.1^15 -
15578*$.1^14 + 28633*$.1^13 + 93460*$.1^12 - 224324*$.1^11 - 236982*$.1^10 + 902782*$.1^9 - 92649*$.1^8 - 1549758*$.1^7 + 1240027*$.1^6 + 457997*$.1^5 -
897661*$.1^4 + 293181*$.1^3 + 17361*$.1^2 - 16713*$.1 + 757,7,$.1^20 - 12*$.1^19
- 8*$.1^18 + 602*$.1^17 - 1355*$.1^16 - 11751*$.1^15 + 44797*$.1^14 + 105012*$.1^13 - 632038*$.1^12 - 274991*$.1^11 + 4756743*$.1^10 - 2413492*$.1^9 -
19377380*$.1^8 + 21737168*$.1^7 + 37613472*$.1^6 - 64826048*$.1^5 -
17117376*$.1^4 + 68169472*$.1^3 - 23637760*$.1^2 - 4162560*$.1 +
1715200,11,$.1^20 - 10*$.1^19 - 71*$.1^18 + 1000*$.1^17 + 825*$.1^16 - 38773*$.1^15 + 56185*$.1^14 + 714296*$.1^13 - 2098532*$.1^12 - 5826144*$.1^11 +
28736608*$.1^10 + 7095232*$.1^9 - 174873152*$.1^8 + 152530432*$.1^7 +
436532992*$.1^6 - 742544384*$.1^5 - 208098304*$.1^4 + 1038184448*$.1^3 -
471076864*$.1^2 - 156303360*$.1 + 92979200,13,$.1^20 - 17*$.1^19 + 12*$.1^18 + 1261*$.1^17 - 5711*$.1^16 - 29277*$.1^15 + 237009*$.1^14 + 79260*$.1^13 -
3979139*$.1^12 + 6049839*$.1^11 + 28107002*$.1^10 - 83032878*$.1^9 -
46796396*$.1^8 + 371031699*$.1^7 - 191435207*$.1^6 - 567769995*$.1^5 +
474808960*$.1^4 + 358305542*$.1^3 - 255218964*$.1^2 - 124967058*$.1 - 4360151[]
390,1,2,x + 1,3,x + 1,5,x + 1,7,x,11,x,13,x + 1[]
390,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 4,13,x + 1[]
390,3,2,x + 1,3,x - 1,5,x + 1,7,x - 4,11,x,13,x + 1[]
390,4,2,x + 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x - 1[]
390,5,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 4,13,x + 1[]
390,6,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x - 1[]
390,7,2,x - 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x - 1[]
390,8,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 8,11,x^2 -
32,13,x^2 + 2*x + 1[]
391,1,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x - 4,7,x^2 + 2*x - 4,11,x^2 + 8*x
+ 16,13,x^2 + 2*x + 1[]
391,2,2,x^3 + x^2 - 4*x - 3,3,x^3 + 6*x^2 + 12*x + 8,5,x^3 + 3*x^2 - 2*x -
7,7,x^3 - x^2 - 4*x + 3,11,x^3 - x^2 - 8*x + 3,13,x^3 - x^2 - 26*x - 15[]
391,3,2,x^3 + x^2 - 4*x + 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 5*x^2 + 4*x -
5,11,x^3 + 3*x^2 - 10*x - 25,13,x^3 + 3*x^2 - 10*x + 1[]
391,4,2,x^9 - 2*x^8 - 12*x^7 + 23*x^6 + 43*x^5 - 79*x^4 - 43*x^3 + 78*x^2 + 11*x
- 21,3,x^9 - 2*x^8 - 20*x^7 + 36*x^6 + 124*x^5 - 192*x^4 - 248*x^3 + 256*x^2 +
160*x - 64,5,x^9 - 7*x^8 + x^7 + 92*x^6 - 216*x^5 + 15*x^4 + 421*x^3 - 391*x^2 +
64*x + 3,7,x^9 - 3*x^8 - 27*x^7 + 94*x^6 + 194*x^5 - 863*x^4 - 215*x^3 +
2593*x^2 - 918*x - 1493,11,x^9 - 11*x^8 + 11*x^7 + 246*x^6 - 834*x^5 - 213*x^4 +
3633*x^3 - 2305*x^2 - 4100*x + 3723,13,x^9 + 9*x^8 - 35*x^7 - 454*x^6 - 132*x^5
+ 5675*x^4 + 8067*x^3 - 10191*x^2 - 13434*x + 5161[]
391,5,2,x^12 - 4*x^11 - 12*x^10 + 62*x^9 + 27*x^8 - 321*x^7 + 108*x^6 + 625*x^5
- 362*x^4 - 372*x^3 + 116*x^2 + 97*x + 13,3,x^12 - 2*x^11 - 31*x^10 + 60*x^9 +
348*x^8 - 652*x^7 - 1708*x^6 + 3064*x^5 + 3608*x^4 - 5728*x^3 - 3424*x^2 +
3264*x + 1792,5,x^12 - 5*x^11 - 33*x^10 + 178*x^9 + 338*x^8 - 2109*x^7 -
1131*x^6 + 9799*x^5 + 574*x^4 - 15637*x^3 - 3040*x^2 + 7912*x + 3080,7,x^12 +
9*x^11 - 13*x^10 - 286*x^9 - 174*x^8 + 3313*x^7 + 2875*x^6 - 18363*x^5 -
8640*x^4 + 46363*x^3 - 10702*x^2 - 19252*x + 7264,11,x^12 - 11*x^11 - 27*x^10 +
610*x^9 - 492*x^8 - 11697*x^7 + 21625*x^6 + 87835*x^5 - 213962*x^4 - 184849*x^3
+ 691228*x^2 - 260608*x - 179200,13,x^12 - 7*x^11 - 58*x^10 + 525*x^9 + 327*x^8
- 10629*x^7 + 16951*x^6 + 54704*x^5 - 178361*x^4 + 133768*x^3 + 14316*x^2 -
18959*x + 50[]
392,1,2,x,3,x + 1,5,x + 1,7,x,11,x - 3,13,x + 6[]
392,2,2,x,3,x - 1,5,x - 1,7,x,11,x - 3,13,x - 6[]
392,3,2,x,3,x + 2,5,x - 4,7,x,11,x,13,x[]
392,4,2,x,3,x - 3,5,x + 1,7,x,11,x + 1,13,x - 2[]
392,5,2,x,3,x,5,x + 2,7,x,11,x + 4,13,x + 2[]
392,6,2,x,3,x + 3,5,x - 1,7,x,11,x + 1,13,x + 2[]
392,7,2,x^2,3,x^2 - 8,5,x^2 - 8,7,x^2,11,x^2 + 8*x + 16,13,x^2 - 8[]
392,8,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2,11,x^2 - 12*x + 36,13,x^2 - 32[]
393,1,2,x^2 + 2*x - 1,3,x^2 + 2*x + 1,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2*x +
1,13,x^2 - 10*x + 25[]
393,2,2,x^4 + x^3 - 4*x^2 - 2*x + 3,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 -
6*x^2 + x + 7,7,x^4 + 8*x^3 + 17*x^2 - 19,11,x^4 - 2*x^3 - 26*x^2 - 13*x +
3,13,x^4 + 9*x^3 + 12*x^2 - 44*x - 21[]
393,3,2,x^4 + 3*x^3 - 4*x - 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 + 8*x^3 +
18*x^2 + 3*x - 19,7,x^4 + 8*x^3 + 13*x^2 - 12*x + 1,11,x^4 + 4*x^3 - 30*x^2 -
103*x + 109,13,x^4 + 5*x^3 - 24*x^2 - 80*x + 139[]
393,4,2,x^5 - 2*x^4 - 7*x^3 + 12*x^2 + 9*x - 9,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 +
5*x + 1,5,x^5 + 2*x^4 - 14*x^3 - 23*x^2 + 17*x - 2,7,x^5 - 4*x^4 - 7*x^3 +
48*x^2 - 63*x + 24,11,x^5 + 6*x^4 - 38*x^3 - 229*x^2 + 183*x + 1388,13,x^5 +
3*x^4 - 38*x^3 - 76*x^2 + 303*x + 158[]
393,5,2,x^6 - x^5 - 7*x^4 + 5*x^3 + 13*x^2 - 4*x - 5,3,x^6 - 6*x^5 + 15*x^4 -
20*x^3 + 15*x^2 - 6*x + 1,5,x^6 - 8*x^5 + 18*x^4 - x^3 - 27*x^2 + 8*x + 8,7,x^6
- 4*x^5 - 11*x^4 + 28*x^3 + 45*x^2 - 48*x - 64,11,x^6 - 6*x^5 - x^4 + 45*x^3 -
19*x^2 - 69*x + 5,13,x^6 + 3*x^5 - 29*x^4 - 75*x^3 - 29*x^2 + 18*x - 1[]

Total time: 19.360 seconds, Total memory usage: 6.24MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:46:53 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [393..397] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 13:46:34 on modular  [Seed = 1003285996]
-------------------------------------

393,1,2,$.1^2 + 2*$.1 - 1,3,$.1^2 + 2*$.1 + 1,5,$.1^2 - 8,7,$.1^2 - 8*$.1 + 16,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 10*$.1 + 25[] 393,2,2,$.1^4 + $.1^3 - 4*$.1^2 - 2*$.1 + 3,3,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,5,$.1^4 - 6*$.1^2 +$.1 + 7,7,$.1^4 + 8*$.1^3 + 17*$.1^2 - 19,11,$.1^4 -
2*$.1^3 - 26*$.1^2 - 13*$.1 + 3,13,$.1^4 + 9*$.1^3 + 12*$.1^2 - 44*$.1 - 21[] 393,3,2,$.1^4 + 3*$.1^3 - 4*$.1 - 1,3,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 +
1,5,$.1^4 + 8*$.1^3 + 18*$.1^2 + 3*$.1 - 19,7,$.1^4 + 8*$.1^3 + 13*$.1^2 - 12*$.1 + 1,11,$.1^4 + 4*$.1^3 - 30*$.1^2 - 103*$.1 + 109,13,$.1^4 + 5*$.1^3 -
24*$.1^2 - 80*$.1 + 139[]
393,4,2,$.1^5 - 2*$.1^4 - 7*$.1^3 + 12*$.1^2 + 9*$.1 - 9,3,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,5,$.1^5 + 2*$.1^4 - 14*$.1^3 - 23*$.1^2 + 17*$.1 - 2,7,$.1^5 - 4*$.1^4 - 7*$.1^3 + 48*$.1^2 - 63*$.1 + 24,11,$.1^5 + 6*$.1^4 -
38*$.1^3 - 229*$.1^2 + 183*$.1 + 1388,13,$.1^5 + 3*$.1^4 - 38*$.1^3 - 76*$.1^2 + 303*$.1 + 158[]
393,5,2,$.1^6 -$.1^5 - 7*$.1^4 + 5*$.1^3 + 13*$.1^2 - 4*$.1 - 5,3,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1,5,$.1^6 - 8*$.1^5 +
18*$.1^4 -$.1^3 - 27*$.1^2 + 8*$.1 + 8,7,$.1^6 - 4*$.1^5 - 11*$.1^4 + 28*$.1^3
+ 45*$.1^2 - 48*$.1 - 64,11,$.1^6 - 6*$.1^5 - $.1^4 + 45*$.1^3 - 19*$.1^2 - 69*$.1 + 5,13,$.1^6 + 3*$.1^5 - 29*$.1^4 - 75*$.1^3 - 29*$.1^2 + 18*$.1 - 1[]
394,1,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 3*x - 5,7,x^2 - 4*x + 4,11,x^2 - 2*x -
28,13,x^2 - 3*x - 5[]
394,2,2,x^2 - 2*x + 1,3,x^2 - 5,5,x^2 - 5*x + 5,7,x^2 + 6*x + 9,11,x^2 - 3*x -
9,13,x^2 - 6*x + 9[]
394,3,2,x^2 - 2*x + 1,3,x^2 + x - 5,5,x^2,7,x^2 - 4*x + 4,11,x^2 + 3*x -
3,13,x^2 + 2*x - 20[]
394,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 +
5*x + 5,13,x^2 + 2*x - 19[]
394,5,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 3*x^3 - 2*x^2 - 7*x + 1,5,x^4 +
5*x^3 + x^2 - 20*x - 16,7,x^4 - 2*x^3 - 15*x^2 - 4*x + 4,11,x^4 + 8*x^3 + 15*x^2
+ 6*x - 1,13,x^4 - 4*x^3 - 15*x^2 - 2*x + 4[]
394,6,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 2*x^3 - 7*x^2 + 8*x + 16,5,x^4 -
2*x^3 - 7*x^2 + 8*x - 1,7,x^4 - 17*x^2 + 68,11,x^4 - 11*x^3 + 39*x^2 - 46*x +
4,13,x^4 + 5*x^3 - 14*x^2 - 91*x - 89[]
395,1,2,x + 1,3,x,5,x - 1,7,x + 4,11,x - 4,13,x - 6[]
395,2,2,x + 1,3,x - 2,5,x - 1,7,x - 2,11,x - 4,13,x + 6[]
395,3,2,x + 2,3,x + 1,5,x - 1,7,x - 3,11,x + 3,13,x - 4[]
395,4,2,x^3 - 3*x + 1,3,x^3 - 3*x + 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 3*x^2 -
6*x + 1,11,x^3 + 6*x^2 + 3*x - 19,13,x^3 + 6*x^2 + 9*x + 3[]
395,5,2,x^3 - 6*x^2 + 12*x - 8,3,x^3 - x^2 - 5*x + 3,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 3*x^2 - 15*x + 43,11,x^3 - 3*x^2 - 21*x - 13,13,x^3[]
395,6,2,x^3 + 2*x^2 - x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3
+ 3*x^2 - 4*x - 13,11,x^3 - 2*x^2 - x + 1,13,x^3 + 10*x^2 + 31*x + 29[]
395,7,2,x^4 - x^3 - 7*x^2 + 6*x - 1,3,x^4 - 2*x^3 - 9*x^2 + 17*x + 6,5,x^4 -
4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 3*x^3 - 4*x^2 + 7*x - 2,11,x^4 + 6*x^3 + 3*x^2 -
11*x + 4,13,x^4 - 8*x^3 - 9*x^2 + 167*x - 234[]
395,8,2,x^11 - 21*x^9 + x^8 + 159*x^7 - 18*x^6 - 511*x^5 + 105*x^4 + 604*x^3 -
208*x^2 - 128*x + 48,3,x^11 + 2*x^10 - 25*x^9 - 45*x^8 + 223*x^7 + 334*x^6 -
901*x^5 - 1011*x^4 + 1640*x^3 + 1180*x^2 - 1060*x - 284,5,x^11 + 11*x^10 +
55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 +
11*x + 1,7,x^11 - 7*x^10 - 32*x^9 + 303*x^8 + 79*x^7 - 4099*x^6 + 5048*x^5 +
15889*x^4 - 36724*x^3 + 20024*x^2 - 3584*x + 196,11,x^11 - 6*x^10 - 59*x^9 +
421*x^8 + 827*x^7 - 9196*x^6 + 2851*x^5 + 68405*x^4 - 81792*x^3 - 90008*x^2 +
86480*x - 11952,13,x^11 - 14*x^10 - 3*x^9 + 735*x^8 - 1604*x^7 - 13832*x^6 +
40784*x^5 + 105456*x^4 - 368960*x^3 - 182272*x^2 + 1167360*x - 763904[]
396,1,2,x,3,x,5,x + 2,7,x + 2,11,x + 1,13,x + 2[]
396,2,2,x,3,x,5,x + 2,7,x - 2,11,x - 1,13,x - 6[]
396,3,2,x,3,x,5,x - 3,7,x - 2,11,x - 1,13,x + 4[]
397,1,2,x^2 + 2*x - 1,3,x^2,5,x^2 + 4*x + 4,7,x^2 - 6*x + 7,11,x^2 - 8,13,x^2 +
8*x + 8[]
397,2,2,x^2 - 2*x - 1,3,x^2 - 4*x + 2,5,x^2 - 2,7,x^2 + 2*x - 7,11,x^2 - 4*x +
2,13,x^2 - 4*x - 14[]
397,3,2,x^5 - 6*x^3 + x^2 + 7*x - 1,3,x^5 - 5*x^4 + 4*x^3 + 9*x^2 - 8*x -
2,5,x^5 + 2*x^4 - 9*x^3 - x^2 + 6*x + 2,7,x^5 - x^4 - 11*x^3 + 16*x^2 + 16*x -
25,11,x^5 - 6*x^4 - 6*x^3 + 84*x^2 - 112*x - 16,13,x^5 - 2*x^4 - 19*x^3 - 29*x^2
- 14*x - 2[]
397,4,2,x^10 - 7*x^9 + 8*x^8 + 43*x^7 - 105*x^6 - 26*x^5 + 234*x^4 - 119*x^3 -
82*x^2 + 47*x + 3,3,x^10 - 19*x^8 + 3*x^7 + 132*x^6 - 36*x^5 - 397*x^4 + 120*x^3
+ 468*x^2 - 71*x - 177,5,x^10 - 7*x^9 - 9*x^8 + 145*x^7 - 124*x^6 - 766*x^5 +
891*x^4 + 1276*x^3 - 841*x^2 - 648*x + 81,7,x^10 - 10*x^9 + 17*x^8 + 97*x^7 -
277*x^6 - 250*x^5 + 1035*x^4 + 112*x^3 - 1154*x^2 - 7*x + 239,11,x^10 - 15*x^9 +
55*x^8 + 188*x^7 - 1775*x^6 + 4272*x^5 - 3580*x^4 - 367*x^3 + 1360*x^2 + 39*x -
81,13,x^10 + 7*x^9 - 14*x^8 - 161*x^7 + 15*x^6 + 1275*x^5 + 254*x^4 - 4036*x^3 +
247*x^2 + 4260*x - 1777[]
397,5,2,x^13 + 7*x^12 + 5*x^11 - 63*x^10 - 124*x^9 + 157*x^8 + 526*x^7 + 2*x^6 -
794*x^5 - 328*x^4 + 408*x^3 + 203*x^2 - 66*x - 23,3,x^13 + 11*x^12 + 31*x^11 -
67*x^10 - 461*x^9 - 347*x^8 + 1652*x^7 + 2845*x^6 - 1038*x^5 - 4630*x^4 -
2122*x^3 + 459*x^2 + 185*x - 31,5,x^13 + 5*x^12 - 30*x^11 - 165*x^10 + 298*x^9 +
1906*x^8 - 1254*x^7 - 9724*x^6 + 2486*x^5 + 21499*x^4 - 2856*x^3 - 15007*x^2 +
915*x + 25,7,x^13 + 17*x^12 + 91*x^11 - 15*x^10 - 1968*x^9 - 7460*x^8 - 8546*x^7
+ 8484*x^6 + 23360*x^5 + 936*x^4 - 19934*x^3 - 2011*x^2 + 6421*x - 593,11,x^13 +
31*x^12 + 381*x^11 + 2186*x^10 + 3741*x^9 - 21606*x^8 - 122592*x^7 - 153927*x^6
+ 381830*x^5 + 1323595*x^4 + 1292273*x^3 + 383314*x^2 - 48624*x - 21272,13,x^13
- x^12 - 83*x^11 + 135*x^10 + 2434*x^9 - 4874*x^8 - 31822*x^7 + 72166*x^6 +
183608*x^5 - 469892*x^4 - 317478*x^3 + 1110975*x^2 - 429135*x + 37507[]

Total time: 18.250 seconds, Total memory usage: 6.06MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sat Nov 29 13:53:50 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [397..400] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sat Nov 29 2003 13:53:36 on modular  [Seed = 634581320]
-------------------------------------

397,1,2,$.1^2 + 2*$.1 - 1,3,$.1^2,5,$.1^2 + 4*$.1 + 4,7,$.1^2 - 6*$.1 + 7,11,$.1^2 - 8,13,$.1^2 + 8*$.1 + 8[]
397,2,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2 - 2,7,$.1^2 + 2*$.1 - 7,11,$.1^2 - 4*$.1 + 2,13,$.1^2 - 4*$.1 - 14[] 397,3,2,$.1^5 - 6*$.1^3 +$.1^2 + 7*$.1 - 1,3,$.1^5 - 5*$.1^4 + 4*$.1^3 +
9*$.1^2 - 8*$.1 - 2,5,$.1^5 + 2*$.1^4 - 9*$.1^3 -$.1^2 + 6*$.1 + 2,7,$.1^5 -
$.1^4 - 11*$.1^3 + 16*$.1^2 + 16*$.1 - 25,11,$.1^5 - 6*$.1^4 - 6*$.1^3 + 84*$.1^2 - 112*$.1 - 16,13,$.1^5 - 2*$.1^4 - 19*$.1^3 - 29*$.1^2 - 14*$.1 - 2[]
397,4,2,$.1^10 - 7*$.1^9 + 8*$.1^8 + 43*$.1^7 - 105*$.1^6 - 26*$.1^5 + 234*$.1^4 - 119*$.1^3 - 82*$.1^2 + 47*$.1 + 3,3,$.1^10 - 19*$.1^8 + 3*$.1^7 + 132*$.1^6 -
36*$.1^5 - 397*$.1^4 + 120*$.1^3 + 468*$.1^2 - 71*$.1 - 177,5,$.1^10 - 7*$.1^9 - 9*$.1^8 + 145*$.1^7 - 124*$.1^6 - 766*$.1^5 + 891*$.1^4 + 1276*$.1^3 - 841*$.1^2
- 648*$.1 + 81,7,$.1^10 - 10*$.1^9 + 17*$.1^8 + 97*$.1^7 - 277*$.1^6 - 250*$.1^5 + 1035*$.1^4 + 112*$.1^3 - 1154*$.1^2 - 7*$.1 + 239,11,$.1^10 - 15*$.1^9 + 55*$.1^8 + 188*$.1^7 - 1775*$.1^6 + 4272*$.1^5 - 3580*$.1^4 - 367*$.1^3 + 1360*$.1^2 + 39*$.1 - 81,13,$.1^10 + 7*$.1^9 - 14*$.1^8 - 161*$.1^7 + 15*$.1^6 +
1275*$.1^5 + 254*$.1^4 - 4036*$.1^3 + 247*$.1^2 + 4260*$.1 - 1777[] 397,5,2,$.1^13 + 7*$.1^12 + 5*$.1^11 - 63*$.1^10 - 124*$.1^9 + 157*$.1^8 + 526*$.1^7 + 2*$.1^6 - 794*$.1^5 - 328*$.1^4 + 408*$.1^3 + 203*$.1^2 - 66*$.1 -
23,3,$.1^13 + 11*$.1^12 + 31*$.1^11 - 67*$.1^10 - 461*$.1^9 - 347*$.1^8 +
1652*$.1^7 + 2845*$.1^6 - 1038*$.1^5 - 4630*$.1^4 - 2122*$.1^3 + 459*$.1^2 +
185*$.1 - 31,5,$.1^13 + 5*$.1^12 - 30*$.1^11 - 165*$.1^10 + 298*$.1^9 +
1906*$.1^8 - 1254*$.1^7 - 9724*$.1^6 + 2486*$.1^5 + 21499*$.1^4 - 2856*$.1^3 -
15007*$.1^2 + 915*$.1 + 25,7,$.1^13 + 17*$.1^12 + 91*$.1^11 - 15*$.1^10 -
1968*$.1^9 - 7460*$.1^8 - 8546*$.1^7 + 8484*$.1^6 + 23360*$.1^5 + 936*$.1^4 -
19934*$.1^3 - 2011*$.1^2 + 6421*$.1 - 593,11,$.1^13 + 31*$.1^12 + 381*$.1^11 +
2186*$.1^10 + 3741*$.1^9 - 21606*$.1^8 - 122592*$.1^7 - 153927*$.1^6 + 381830*$.1^5 + 1323595*$.1^4 + 1292273*$.1^3 + 383314*$.1^2 - 48624*$.1 -
21272,13,$.1^13 -$.1^12 - 83*$.1^11 + 135*$.1^10 + 2434*$.1^9 - 4874*$.1^8 -
31822*$.1^7 + 72166*$.1^6 + 183608*$.1^5 - 469892*$.1^4 - 317478*$.1^3 + 1110975*$.1^2 - 429135*$.1 + 37507[] 398,1,2,x + 1,3,x - 2,5,x + 2,7,x,11,x - 2,13,x - 6[] 398,2,2,x^2 + 2*x + 1,3,x^2 + x - 1,5,x^2,7,x^2 + 3*x + 1,11,x^2 - x - 11,13,x^2 + 6*x + 4[] 398,3,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 2*x - 4,7,x^2 + 7*x + 11,11,x^2 + 7*x + 11,13,x^2 + 4*x + 4[] 398,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - x^5 - 14*x^4 + 5*x^3 + 54*x^2 + 9*x - 27,5,x^6 - 4*x^5 - 20*x^4 + 84*x^3 + 32*x^2 - 224*x + 48,7,x^6 - 11*x^5 + 22*x^4 + 117*x^3 - 414*x^2 - 3*x + 737,11,x^6 + 7*x^5 - 26*x^4 - 159*x^3 + 314*x^2 + 533*x - 933,13,x^6 + 2*x^5 - 44*x^4 - 92*x^3 + 416*x^2 + 1104*x + 656[] 398,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 3*x^5 - 6*x^4 + 21*x^3 + 2*x^2 - 21*x - 5,5,x^6 - 2*x^5 - 16*x^4 + 28*x^3 + 32*x^2 - 64*x + 16,7,x^6 - 7*x^5 + 8*x^4 + 37*x^3 - 96*x^2 + 69*x - 13,11,x^6 - 5*x^5 - 18*x^4 + 67*x^3 + 130*x^2 - 71*x + 5,13,x^6 - 52*x^4 + 60*x^3 + 712*x^2 - 1520*x - 16[] 399,1,2,x - 1,3,x + 1,5,x,7,x + 1,11,x + 2,13,x + 4[] 399,2,2,x + 1,3,x + 1,5,x,7,x - 1,11,x + 2,13,x[] 399,3,2,x + 1,3,x - 1,5,x - 4,7,x + 1,11,x + 2,13,x - 4[] 399,4,2,x^3 - x^2 - 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 + 4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 16*x - 16,13,x^3 - 6*x^2 - 4*x + 8[] 399,5,2,x^3 - x^2 - 7*x + 9,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 8*x - 4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 4*x^2 - 16*x + 48,13,x^3 - 2*x^2 - 20*x - 8[] 399,6,2,x^5 - 3*x^4 - 4*x^3 + 14*x^2 - 3*x - 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 - 4*x^4 - 12*x^3 + 48*x^2 + 4*x - 8,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 - 8*x^4 - 32*x^3 + 304*x^2 + 224*x - 2816,13,x^5 + 6*x^4 - 40*x^3 - 224*x^2 + 384*x + 1984[] 399,7,2,x^5 - x^4 - 8*x^3 + 6*x^2 + 13*x - 3,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 + 2*x^4 - 16*x^3 - 8*x^2 + 68*x - 48,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,11,x^5 + 2*x^4 - 32*x^3 - 16*x^2 + 256*x - 192,13,x^5 - 8*x^4 - 8*x^3 + 112*x^2 + 32*x - 256[] 400,1,2,x,3,x,5,x,7,x + 4,11,x + 4,13,x - 2[] 400,2,2,x,3,x + 3,5,x,7,x - 2,11,x + 1,13,x + 4[] 400,3,2,x,3,x - 2,5,x,7,x - 2,11,x - 4,13,x + 4[] 400,4,2,x,3,x + 2,5,x,7,x + 2,11,x - 4,13,x - 4[] 400,5,2,x,3,x - 3,5,x,7,x + 2,11,x + 1,13,x - 4[] 400,6,2,x,3,x - 1,5,x,7,x - 2,11,x - 3,13,x - 4[] 400,7,2,x,3,x + 2,5,x,7,x - 2,11,x,13,x + 2[] 400,8,2,x,3,x + 1,5,x,7,x + 2,11,x - 3,13,x + 4[] Total time: 14.039 seconds, Total memory usage: 5.43MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:46:06 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [400..406] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 02:45:39 on modular [Seed = 4161693582] ------------------------------------- 400,1,2,$.1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 4,13,$.1 - 2[] 400,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 + 1,13,$.1 + 4[] 400,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 4[] 400,4,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 - 4,13,$.1 - 4[] 400,5,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 + 1,13,$.1 - 4[] 400,6,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 3,13,$.1 - 4[] 400,7,2,$.1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1,13,$.1 + 2[] 400,8,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 2,11,$.1 - 3,13,$.1 + 4[] 401,1,2,x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4,3,x^12 + 5*x^11 - 7*x^10 - 66*x^9 - 33*x^8 + 249*x^7 + 270*x^6 - 258*x^5 - 363*x^4 + 54*x^3 + 136*x^2 - 16,5,x^12 + 7*x^11 - 9*x^10 - 142*x^9 - 93*x^8 + 880*x^7 + 869*x^6 - 2355*x^5 - 1980*x^4 + 3042*x^3 + 1412*x^2 - 1552*x - 79,7,x^12 + 20*x^11 + 155*x^10 + 516*x^9 + 46*x^8 - 5172*x^7 - 15538*x^6 - 11740*x^5 + 30845*x^4 + 83664*x^3 + 81306*x^2 + 32396*x + 2657,11,x^12 + 11*x^11 - 9*x^10 - 451*x^9 - 829*x^8 + 5973*x^7 + 17916*x^6 - 24578*x^5 - 119209*x^4 - 29312*x^3 + 224591*x^2 + 217928*x + 41849,13,x^12 + 11*x^11 - 17*x^10 - 534*x^9 - 1050*x^8 + 5361*x^7 + 13008*x^6 - 23718*x^5 - 42795*x^4 + 49694*x^3 + 21668*x^2 - 9160*x - 272[] 401,2,2,x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44,3,x^21 - 3*x^20 - 37*x^19 + 112*x^18 + 572*x^17 - 1750*x^16 - 4821*x^15 + 14940*x^14 + 24209*x^13 - 76294*x^12 - 74001*x^11 + 239594*x^10 + 133106*x^9 - 457051*x^8 - 121988*x^7 + 501440*x^6 + 21445*x^5 - 278838*x^4 + 44972*x^3 + 55992*x^2 - 21840*x + 2176,5,x^21 - 3*x^20 - 61*x^19 + 194*x^18 + 1512*x^17 - 5215*x^16 - 19300*x^15 + 75661*x^14 + 128652*x^13 - 640637*x^12 - 336982*x^11 + 3173409*x^10 - 785768*x^9 - 8594568*x^8 + 7111131*x^7 + 10298067*x^6 - 15120487*x^5 - 1215456*x^4 + 10541238*x^3 - 4468704*x^2 - 686527*x + 543818,7,x^21 - 24*x^20 + 195*x^19 - 236*x^18 - 5466*x^17 + 28324*x^16 + 9918*x^15 - 432740*x^14 + 844081*x^13 + 2219324*x^12 - 9342038*x^11 + 830912*x^10 + 38273997*x^9 - 42544268*x^8 - 54586056*x^7 + 119960784*x^6 - 13453488*x^5 - 96133952*x^4 + 56121600*x^3 + 6590464*x^2 - 9138432*x + 667648,11,x^21 - x^20 - 133*x^19 + 169*x^18 + 7471*x^17 - 11763*x^16 - 229832*x^15 + 438954*x^14 + 4175027*x^13 - 9581728*x^12 - 44526253*x^11 + 124643620*x^10 + 251896037*x^9 - 934300300*x^8 - 464605776*x^7 + 3623452320*x^6 - 1606573440*x^5 - 5297593344*x^4 + 6110001408*x^3 - 1368589312*x^2 - 367203328*x + 18550784,13,x^21 - 9*x^20 - 109*x^19 + 1118*x^18 + 4634*x^17 - 58263*x^16 - 90876*x^15 + 1658206*x^14 + 519427*x^13 - 28086092*x^12 + 11520128*x^11 + 288867488*x^10 - 257320016*x^9 - 1759190240*x^8 + 2219776000*x^7 + 5836035584*x^6 - 9500805376*x^5 - 8335835648*x^4 + 18968096768*x^3 + 139124736*x^2 - 12677169152*x + 5112193024[] 402,1,2,x + 1,3,x + 1,5,x - 1,7,x + 3,11,x,13,x + 4[] 402,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 402,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 4[] 402,4,2,x - 1,3,x + 1,5,x - 2,7,x - 2,11,x + 4,13,x[] 402,5,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 + 4*x + 4,13,x^2 + 2*x - 2[] 402,6,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 10,7,x^2 + x - 10,11,x^2 - 8*x + 16,13,x^2 - 8*x + 16[] 402,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - x^2 - 4*x + 2,11,x^3 - 28*x + 16,13,x^3 + 6*x^2 - 22*x - 136[] 403,1,2,x^2 - 3*x + 1,3,x^2 + 4*x + 4,5,x^2 - 5,7,x^2 - 2*x + 1,11,x^2 - 20,13,x^2 - 2*x + 1[] 403,2,2,x^6 + 2*x^5 - 7*x^4 - 13*x^3 + 6*x^2 + 7*x - 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 11*x^2 + x + 1,5,x^6 + 9*x^5 + 20*x^4 - 19*x^3 - 75*x^2 + 14*x + 39,7,x^6 - 29*x^4 - 6*x^3 + 175*x^2 + 121*x - 113,11,x^6 + 5*x^5 - 18*x^4 - 49*x^3 + 147*x^2 - 76*x + 9,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 403,3,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 20*x^3 - 37*x^2 + x + 4,3,x^7 - 5*x^6 + 28*x^4 - 25*x^3 - 21*x^2 + 15*x + 8,5,x^7 - 11*x^6 + 38*x^5 - 27*x^4 - 75*x^3 + 80*x^2 + 39*x - 4,7,x^7 - 4*x^6 - 7*x^5 + 24*x^4 + 7*x^3 - 23*x^2 - 7*x + 2,11,x^7 - 8*x^6 - 3*x^5 + 99*x^4 + 10*x^3 - 307*x^2 - 17*x + 283,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 403,4,2,x^8 + 5*x^7 - 30*x^5 - 24*x^4 + 54*x^3 + 54*x^2 - 28*x - 29,3,x^8 + 3*x^7 - 12*x^6 - 36*x^5 + 31*x^4 + 97*x^3 - 29*x^2 - 72*x + 12,5,x^8 + 15*x^7 + 83*x^6 + 192*x^5 + 99*x^4 - 225*x^3 - 158*x^2 + 90*x + 3,7,x^8 + 4*x^7 - 20*x^6 - 88*x^5 + 46*x^4 + 335*x^3 + 50*x^2 - 181*x + 29,11,x^8 + 5*x^7 - 56*x^6 - 309*x^5 + 705*x^4 + 4994*x^3 + 769*x^2 - 17712*x - 14580,13,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[] 403,5,2,x^8 + x^7 - 11*x^6 - 10*x^5 + 37*x^4 + 33*x^3 - 36*x^2 - 33*x - 4,3,x^8 - 7*x^7 + 8*x^6 + 42*x^5 - 107*x^4 + 15*x^3 + 141*x^2 - 104*x + 16,5,x^8 - 11*x^7 + 32*x^6 + 35*x^5 - 263*x^4 + 126*x^3 + 537*x^2 - 346*x - 232,7,x^8 + 2*x^7 - 39*x^6 - 42*x^5 + 527*x^4 + 185*x^3 - 2717*x^2 + 250*x + 3824,11,x^8 + 2*x^7 - 31*x^6 - 51*x^5 + 238*x^4 + 267*x^3 - 631*x^2 - 319*x + 484,13,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1[] 404,1,2,x,3,x + 2,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 404,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 2,13,x + 3[] 404,3,2,x^7,3,x^7 - 2*x^6 - 17*x^5 + 36*x^4 + 64*x^3 - 148*x^2 + 11*x + 58,5,x^7 - 31*x^5 + 8*x^4 + 262*x^3 - 160*x^2 - 503*x + 250,7,x^7 - 2*x^6 - 39*x^5 + 62*x^4 + 438*x^3 - 474*x^2 - 1365*x + 698,11,x^7 - 4*x^6 - 43*x^5 + 122*x^4 + 548*x^3 - 1178*x^2 - 2085*x + 3482,13,x^7 - 4*x^6 - 55*x^5 + 244*x^4 + 534*x^3 - 2528*x^2 + 25*x + 58[] 405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[] 405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[] 405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[] Errors: /home/mfd/gomagma: line 2: 27309 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:46:57 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [400..405] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 02:46:33 on modular [Seed = 3759570924] ------------------------------------- 400,1,2,$.1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 4,13,$.1 - 2[] 400,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 + 1,13,$.1 + 4[] 400,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 4[] 400,4,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 - 4,13,$.1 - 4[] 400,5,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 + 1,13,$.1 - 4[] 400,6,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 3,13,$.1 - 4[] 400,7,2,$.1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1,13,$.1 + 2[] 400,8,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 2,11,$.1 - 3,13,$.1 + 4[] 401,1,2,x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4,3,x^12 + 5*x^11 - 7*x^10 - 66*x^9 - 33*x^8 + 249*x^7 + 270*x^6 - 258*x^5 - 363*x^4 + 54*x^3 + 136*x^2 - 16,5,x^12 + 7*x^11 - 9*x^10 - 142*x^9 - 93*x^8 + 880*x^7 + 869*x^6 - 2355*x^5 - 1980*x^4 + 3042*x^3 + 1412*x^2 - 1552*x - 79,7,x^12 + 20*x^11 + 155*x^10 + 516*x^9 + 46*x^8 - 5172*x^7 - 15538*x^6 - 11740*x^5 + 30845*x^4 + 83664*x^3 + 81306*x^2 + 32396*x + 2657,11,x^12 + 11*x^11 - 9*x^10 - 451*x^9 - 829*x^8 + 5973*x^7 + 17916*x^6 - 24578*x^5 - 119209*x^4 - 29312*x^3 + 224591*x^2 + 217928*x + 41849,13,x^12 + 11*x^11 - 17*x^10 - 534*x^9 - 1050*x^8 + 5361*x^7 + 13008*x^6 - 23718*x^5 - 42795*x^4 + 49694*x^3 + 21668*x^2 - 9160*x - 272[] 401,2,2,x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44,3,x^21 - 3*x^20 - 37*x^19 + 112*x^18 + 572*x^17 - 1750*x^16 - 4821*x^15 + 14940*x^14 + 24209*x^13 - 76294*x^12 - 74001*x^11 + 239594*x^10 + 133106*x^9 - 457051*x^8 - 121988*x^7 + 501440*x^6 + 21445*x^5 - 278838*x^4 + 44972*x^3 + 55992*x^2 - 21840*x + 2176,5,x^21 - 3*x^20 - 61*x^19 + 194*x^18 + 1512*x^17 - 5215*x^16 - 19300*x^15 + 75661*x^14 + 128652*x^13 - 640637*x^12 - 336982*x^11 + 3173409*x^10 - 785768*x^9 - 8594568*x^8 + 7111131*x^7 + 10298067*x^6 - 15120487*x^5 - 1215456*x^4 + 10541238*x^3 - 4468704*x^2 - 686527*x + 543818,7,x^21 - 24*x^20 + 195*x^19 - 236*x^18 - 5466*x^17 + 28324*x^16 + 9918*x^15 - 432740*x^14 + 844081*x^13 + 2219324*x^12 - 9342038*x^11 + 830912*x^10 + 38273997*x^9 - 42544268*x^8 - 54586056*x^7 + 119960784*x^6 - 13453488*x^5 - 96133952*x^4 + 56121600*x^3 + 6590464*x^2 - 9138432*x + 667648,11,x^21 - x^20 - 133*x^19 + 169*x^18 + 7471*x^17 - 11763*x^16 - 229832*x^15 + 438954*x^14 + 4175027*x^13 - 9581728*x^12 - 44526253*x^11 + 124643620*x^10 + 251896037*x^9 - 934300300*x^8 - 464605776*x^7 + 3623452320*x^6 - 1606573440*x^5 - 5297593344*x^4 + 6110001408*x^3 - 1368589312*x^2 - 367203328*x + 18550784,13,x^21 - 9*x^20 - 109*x^19 + 1118*x^18 + 4634*x^17 - 58263*x^16 - 90876*x^15 + 1658206*x^14 + 519427*x^13 - 28086092*x^12 + 11520128*x^11 + 288867488*x^10 - 257320016*x^9 - 1759190240*x^8 + 2219776000*x^7 + 5836035584*x^6 - 9500805376*x^5 - 8335835648*x^4 + 18968096768*x^3 + 139124736*x^2 - 12677169152*x + 5112193024[] 402,1,2,x + 1,3,x + 1,5,x - 1,7,x + 3,11,x,13,x + 4[] 402,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 402,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 4[] 402,4,2,x - 1,3,x + 1,5,x - 2,7,x - 2,11,x + 4,13,x[] 402,5,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 + 4*x + 4,13,x^2 + 2*x - 2[] 402,6,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 10,7,x^2 + x - 10,11,x^2 - 8*x + 16,13,x^2 - 8*x + 16[] 402,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - x^2 - 4*x + 2,11,x^3 - 28*x + 16,13,x^3 + 6*x^2 - 22*x - 136[] 403,1,2,x^2 - 3*x + 1,3,x^2 + 4*x + 4,5,x^2 - 5,7,x^2 - 2*x + 1,11,x^2 - 20,13,x^2 - 2*x + 1[] 403,2,2,x^6 + 2*x^5 - 7*x^4 - 13*x^3 + 6*x^2 + 7*x - 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 11*x^2 + x + 1,5,x^6 + 9*x^5 + 20*x^4 - 19*x^3 - 75*x^2 + 14*x + 39,7,x^6 - 29*x^4 - 6*x^3 + 175*x^2 + 121*x - 113,11,x^6 + 5*x^5 - 18*x^4 - 49*x^3 + 147*x^2 - 76*x + 9,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 403,3,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 20*x^3 - 37*x^2 + x + 4,3,x^7 - 5*x^6 + 28*x^4 - 25*x^3 - 21*x^2 + 15*x + 8,5,x^7 - 11*x^6 + 38*x^5 - 27*x^4 - 75*x^3 + 80*x^2 + 39*x - 4,7,x^7 - 4*x^6 - 7*x^5 + 24*x^4 + 7*x^3 - 23*x^2 - 7*x + 2,11,x^7 - 8*x^6 - 3*x^5 + 99*x^4 + 10*x^3 - 307*x^2 - 17*x + 283,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 403,4,2,x^8 + 5*x^7 - 30*x^5 - 24*x^4 + 54*x^3 + 54*x^2 - 28*x - 29,3,x^8 + 3*x^7 - 12*x^6 - 36*x^5 + 31*x^4 + 97*x^3 - 29*x^2 - 72*x + 12,5,x^8 + 15*x^7 + 83*x^6 + 192*x^5 + 99*x^4 - 225*x^3 - 158*x^2 + 90*x + 3,7,x^8 + 4*x^7 - 20*x^6 - 88*x^5 + 46*x^4 + 335*x^3 + 50*x^2 - 181*x + 29,11,x^8 + 5*x^7 - 56*x^6 - 309*x^5 + 705*x^4 + 4994*x^3 + 769*x^2 - 17712*x - 14580,13,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[] 403,5,2,x^8 + x^7 - 11*x^6 - 10*x^5 + 37*x^4 + 33*x^3 - 36*x^2 - 33*x - 4,3,x^8 - 7*x^7 + 8*x^6 + 42*x^5 - 107*x^4 + 15*x^3 + 141*x^2 - 104*x + 16,5,x^8 - 11*x^7 + 32*x^6 + 35*x^5 - 263*x^4 + 126*x^3 + 537*x^2 - 346*x - 232,7,x^8 + 2*x^7 - 39*x^6 - 42*x^5 + 527*x^4 + 185*x^3 - 2717*x^2 + 250*x + 3824,11,x^8 + 2*x^7 - 31*x^6 - 51*x^5 + 238*x^4 + 267*x^3 - 631*x^2 - 319*x + 484,13,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1[] 404,1,2,x,3,x + 2,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 404,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 2,13,x + 3[] 404,3,2,x^7,3,x^7 - 2*x^6 - 17*x^5 + 36*x^4 + 64*x^3 - 148*x^2 + 11*x + 58,5,x^7 - 31*x^5 + 8*x^4 + 262*x^3 - 160*x^2 - 503*x + 250,7,x^7 - 2*x^6 - 39*x^5 + 62*x^4 + 438*x^3 - 474*x^2 - 1365*x + 698,11,x^7 - 4*x^6 - 43*x^5 + 122*x^4 + 548*x^3 - 1178*x^2 - 2085*x + 3482,13,x^7 - 4*x^6 - 55*x^5 + 244*x^4 + 534*x^3 - 2528*x^2 + 25*x + 58[] 405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[] 405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[] 405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[] 405,4,2,x,3,x,5,x - 1,7,x - 2,11,x - 3,13,x + 4[] 405,5,2,x - 2,3,x,5,x - 1,7,x,11,x - 5,13,x - 4[] 405,6,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 2[] 405,7,2,x^2 - 2*x - 2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 8*x + 13,13,x^2 + 4*x - 8[] 405,8,2,x^2 + 2*x - 2,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 + 8*x + 13,13,x^2 + 4*x - 8[] 405,9,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 + 2*x^2 - 8*x - 12,13,x^3 - 4*x^2 - 4*x + 4[] 405,10,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 - 2*x^2 - 8*x + 12,13,x^3 - 4*x^2 - 4*x + 4[] Errors: /home/mfd/gomagma: line 2: 27317 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:47:37 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [400..404] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 02:47:16 on modular [Seed = 3894310713] ------------------------------------- 400,1,2,$.1,3,$.1,5,$.1,7,$.1 + 4,11,$.1 + 4,13,$.1 - 2[] 400,2,2,$.1,3,$.1 + 3,5,$.1,7,$.1 - 2,11,$.1 + 1,13,$.1 + 4[] 400,3,2,$.1,3,$.1 - 2,5,$.1,7,$.1 - 2,11,$.1 - 4,13,$.1 + 4[] 400,4,2,$.1,3,$.1 + 2,5,$.1,7,$.1 + 2,11,$.1 - 4,13,$.1 - 4[] 400,5,2,$.1,3,$.1 - 3,5,$.1,7,$.1 + 2,11,$.1 + 1,13,$.1 - 4[] 400,6,2,$.1,3,$.1 - 1,5,$.1,7,$.1 - 2,11,$.1 - 3,13,$.1 - 4[] 400,7,2,$.1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1,13,$.1 + 2[] 400,8,2,$.1,3,$.1 + 1,5,$.1,7,$.1 + 2,11,$.1 - 3,13,$.1 + 4[] 401,1,2,x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4,3,x^12 + 5*x^11 - 7*x^10 - 66*x^9 - 33*x^8 + 249*x^7 + 270*x^6 - 258*x^5 - 363*x^4 + 54*x^3 + 136*x^2 - 16,5,x^12 + 7*x^11 - 9*x^10 - 142*x^9 - 93*x^8 + 880*x^7 + 869*x^6 - 2355*x^5 - 1980*x^4 + 3042*x^3 + 1412*x^2 - 1552*x - 79,7,x^12 + 20*x^11 + 155*x^10 + 516*x^9 + 46*x^8 - 5172*x^7 - 15538*x^6 - 11740*x^5 + 30845*x^4 + 83664*x^3 + 81306*x^2 + 32396*x + 2657,11,x^12 + 11*x^11 - 9*x^10 - 451*x^9 - 829*x^8 + 5973*x^7 + 17916*x^6 - 24578*x^5 - 119209*x^4 - 29312*x^3 + 224591*x^2 + 217928*x + 41849,13,x^12 + 11*x^11 - 17*x^10 - 534*x^9 - 1050*x^8 + 5361*x^7 + 13008*x^6 - 23718*x^5 - 42795*x^4 + 49694*x^3 + 21668*x^2 - 9160*x - 272[] 401,2,2,x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44,3,x^21 - 3*x^20 - 37*x^19 + 112*x^18 + 572*x^17 - 1750*x^16 - 4821*x^15 + 14940*x^14 + 24209*x^13 - 76294*x^12 - 74001*x^11 + 239594*x^10 + 133106*x^9 - 457051*x^8 - 121988*x^7 + 501440*x^6 + 21445*x^5 - 278838*x^4 + 44972*x^3 + 55992*x^2 - 21840*x + 2176,5,x^21 - 3*x^20 - 61*x^19 + 194*x^18 + 1512*x^17 - 5215*x^16 - 19300*x^15 + 75661*x^14 + 128652*x^13 - 640637*x^12 - 336982*x^11 + 3173409*x^10 - 785768*x^9 - 8594568*x^8 + 7111131*x^7 + 10298067*x^6 - 15120487*x^5 - 1215456*x^4 + 10541238*x^3 - 4468704*x^2 - 686527*x + 543818,7,x^21 - 24*x^20 + 195*x^19 - 236*x^18 - 5466*x^17 + 28324*x^16 + 9918*x^15 - 432740*x^14 + 844081*x^13 + 2219324*x^12 - 9342038*x^11 + 830912*x^10 + 38273997*x^9 - 42544268*x^8 - 54586056*x^7 + 119960784*x^6 - 13453488*x^5 - 96133952*x^4 + 56121600*x^3 + 6590464*x^2 - 9138432*x + 667648,11,x^21 - x^20 - 133*x^19 + 169*x^18 + 7471*x^17 - 11763*x^16 - 229832*x^15 + 438954*x^14 + 4175027*x^13 - 9581728*x^12 - 44526253*x^11 + 124643620*x^10 + 251896037*x^9 - 934300300*x^8 - 464605776*x^7 + 3623452320*x^6 - 1606573440*x^5 - 5297593344*x^4 + 6110001408*x^3 - 1368589312*x^2 - 367203328*x + 18550784,13,x^21 - 9*x^20 - 109*x^19 + 1118*x^18 + 4634*x^17 - 58263*x^16 - 90876*x^15 + 1658206*x^14 + 519427*x^13 - 28086092*x^12 + 11520128*x^11 + 288867488*x^10 - 257320016*x^9 - 1759190240*x^8 + 2219776000*x^7 + 5836035584*x^6 - 9500805376*x^5 - 8335835648*x^4 + 18968096768*x^3 + 139124736*x^2 - 12677169152*x + 5112193024[] 402,1,2,x + 1,3,x + 1,5,x - 1,7,x + 3,11,x,13,x + 4[] 402,2,2,x + 1,3,x - 1,5,x - 2,7,x,11,x - 4,13,x + 2[] 402,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 4[] 402,4,2,x - 1,3,x + 1,5,x - 2,7,x - 2,11,x + 4,13,x[] 402,5,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 6*x + 6,11,x^2 + 4*x + 4,13,x^2 + 2*x - 2[] 402,6,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 10,7,x^2 + x - 10,11,x^2 - 8*x + 16,13,x^2 - 8*x + 16[] 402,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - x^2 - 4*x + 2,11,x^3 - 28*x + 16,13,x^3 + 6*x^2 - 22*x - 136[] 403,1,2,x^2 - 3*x + 1,3,x^2 + 4*x + 4,5,x^2 - 5,7,x^2 - 2*x + 1,11,x^2 - 20,13,x^2 - 2*x + 1[] 403,2,2,x^6 + 2*x^5 - 7*x^4 - 13*x^3 + 6*x^2 + 7*x - 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 - 11*x^2 + x + 1,5,x^6 + 9*x^5 + 20*x^4 - 19*x^3 - 75*x^2 + 14*x + 39,7,x^6 - 29*x^4 - 6*x^3 + 175*x^2 + 121*x - 113,11,x^6 + 5*x^5 - 18*x^4 - 49*x^3 + 147*x^2 - 76*x + 9,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 403,3,2,x^7 - 2*x^6 - 9*x^5 + 17*x^4 + 20*x^3 - 37*x^2 + x + 4,3,x^7 - 5*x^6 + 28*x^4 - 25*x^3 - 21*x^2 + 15*x + 8,5,x^7 - 11*x^6 + 38*x^5 - 27*x^4 - 75*x^3 + 80*x^2 + 39*x - 4,7,x^7 - 4*x^6 - 7*x^5 + 24*x^4 + 7*x^3 - 23*x^2 - 7*x + 2,11,x^7 - 8*x^6 - 3*x^5 + 99*x^4 + 10*x^3 - 307*x^2 - 17*x + 283,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] 403,4,2,x^8 + 5*x^7 - 30*x^5 - 24*x^4 + 54*x^3 + 54*x^2 - 28*x - 29,3,x^8 + 3*x^7 - 12*x^6 - 36*x^5 + 31*x^4 + 97*x^3 - 29*x^2 - 72*x + 12,5,x^8 + 15*x^7 + 83*x^6 + 192*x^5 + 99*x^4 - 225*x^3 - 158*x^2 + 90*x + 3,7,x^8 + 4*x^7 - 20*x^6 - 88*x^5 + 46*x^4 + 335*x^3 + 50*x^2 - 181*x + 29,11,x^8 + 5*x^7 - 56*x^6 - 309*x^5 + 705*x^4 + 4994*x^3 + 769*x^2 - 17712*x - 14580,13,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[] 403,5,2,x^8 + x^7 - 11*x^6 - 10*x^5 + 37*x^4 + 33*x^3 - 36*x^2 - 33*x - 4,3,x^8 - 7*x^7 + 8*x^6 + 42*x^5 - 107*x^4 + 15*x^3 + 141*x^2 - 104*x + 16,5,x^8 - 11*x^7 + 32*x^6 + 35*x^5 - 263*x^4 + 126*x^3 + 537*x^2 - 346*x - 232,7,x^8 + 2*x^7 - 39*x^6 - 42*x^5 + 527*x^4 + 185*x^3 - 2717*x^2 + 250*x + 3824,11,x^8 + 2*x^7 - 31*x^6 - 51*x^5 + 238*x^4 + 267*x^3 - 631*x^2 - 319*x + 484,13,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1[] 404,1,2,x,3,x + 2,5,x - 3,7,x - 2,11,x + 6,13,x - 5[] 404,2,2,x,3,x,5,x + 1,7,x + 2,11,x + 2,13,x + 3[] 404,3,2,x^7,3,x^7 - 2*x^6 - 17*x^5 + 36*x^4 + 64*x^3 - 148*x^2 + 11*x + 58,5,x^7 - 31*x^5 + 8*x^4 + 262*x^3 - 160*x^2 - 503*x + 250,7,x^7 - 2*x^6 - 39*x^5 + 62*x^4 + 438*x^3 - 474*x^2 - 1365*x + 698,11,x^7 - 4*x^6 - 43*x^5 + 122*x^4 + 548*x^3 - 1178*x^2 - 2085*x + 3482,13,x^7 - 4*x^6 - 55*x^5 + 244*x^4 + 534*x^3 - 2528*x^2 + 25*x + 58[] Total time: 18.969 seconds, Total memory usage: 6.32MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 02:58:13 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [404..408] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 02:57:49 on modular [Seed = 2205490731] ------------------------------------- 404,1,2,$.1,3,$.1 + 2,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[] 404,2,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 3[] 404,3,2,$.1^7,3,$.1^7 - 2*$.1^6 - 17*$.1^5 + 36*$.1^4 + 64*$.1^3 - 148*$.1^2 +
11*$.1 + 58,5,$.1^7 - 31*$.1^5 + 8*$.1^4 + 262*$.1^3 - 160*$.1^2 - 503*$.1 + 250,7,$.1^7 - 2*$.1^6 - 39*$.1^5 + 62*$.1^4 + 438*$.1^3 - 474*$.1^2 - 1365*$.1 +
698,11,$.1^7 - 4*$.1^6 - 43*$.1^5 + 122*$.1^4 + 548*$.1^3 - 1178*$.1^2 -
2085*$.1 + 3482,13,$.1^7 - 4*$.1^6 - 55*$.1^5 + 244*$.1^4 + 534*$.1^3 -
2528*$.1^2 + 25*$.1 + 58[]
405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[]
405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[]
405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[]
405,4,2,x,3,x,5,x - 1,7,x - 2,11,x - 3,13,x + 4[]
405,5,2,x - 2,3,x,5,x - 1,7,x,11,x - 5,13,x - 4[]
405,6,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 2[]
405,7,2,x^2 - 2*x - 2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 8*x +
13,13,x^2 + 4*x - 8[]
405,8,2,x^2 + 2*x - 2,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 + 8*x +
13,13,x^2 + 4*x - 8[]
405,9,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 3*x +
3,11,x^3 + 2*x^2 - 8*x - 12,13,x^3 - 4*x^2 - 4*x + 4[]
405,10,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 5*x^2 + 3*x +
3,11,x^3 - 2*x^2 - 8*x + 12,13,x^3 - 4*x^2 - 4*x + 4[]
406,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 4,13,x[]
406,2,2,x + 1,3,x - 2,5,x - 2,7,x - 1,11,x - 4,13,x + 2[]
406,3,2,x + 1,3,x - 1,5,x + 3,7,x - 1,11,x + 3,13,x + 1[]
406,4,2,x - 1,3,x + 1,5,x + 3,7,x + 1,11,x + 1,13,x + 1[]
406,5,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x - 2,7,x^2 + 2*x + 1,11,x^2 -
12,13,x^2 + 2*x - 2[]
406,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 4,5,x^3 - 5*x^2 + 2*x +
10,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 24*x - 20,13,x^3 - 7*x^2 + 10*x - 2[]
406,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 4*x + 8,5,x^4 + x^3
- 14*x^2 - 24*x + 4,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 7*x^3 + 8*x^2 +
16*x - 16,13,x^4 + 7*x^3 - 26*x^2 - 176*x + 28[]
407,1,2,x^4 + x^3 - 4*x^2 + 1,3,x^4 - 4*x^2 - x + 1,5,x^4 - x^3 - 4*x^2 + 2*x +
3,7,x^4 + 7*x^3 + 8*x^2 - 30*x - 53,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 +
10*x^3 + 24*x^2 + 11*x - 3[]
407,2,2,x^4 - x^3 - 4*x^2 + 2*x + 3,3,x^4 + 4*x^3 - 9*x + 1,5,x^4 + 5*x^3 +
4*x^2 - 8*x - 9,7,x^4 + x^3 - 4*x^2 + 1,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4
+ 12*x^3 + 48*x^2 + 71*x + 31[]
407,3,2,x^11 - 2*x^10 - 16*x^9 + 32*x^8 + 89*x^7 - 179*x^6 - 201*x^5 + 407*x^4 +
168*x^3 - 333*x^2 - 51*x + 75,3,x^11 - 24*x^9 + 3*x^8 + 209*x^7 - 48*x^6 -
824*x^5 + 260*x^4 + 1448*x^3 - 560*x^2 - 880*x + 400,5,x^11 - x^10 - 46*x^9 +
48*x^8 + 767*x^7 - 786*x^6 - 5700*x^5 + 5224*x^4 + 19152*x^3 - 13536*x^2 -
24000*x + 9600,7,x^11 - 9*x^10 - 8*x^9 + 250*x^8 - 297*x^7 - 2188*x^6 + 3800*x^5
+ 6880*x^4 - 12736*x^3 - 5632*x^2 + 10240*x + 1024,11,x^11 + 11*x^10 + 55*x^9 +
165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x +
1,13,x^11 - 22*x^10 + 156*x^9 - 153*x^8 - 2747*x^7 + 9382*x^6 + 6848*x^5 -
61630*x^4 + 35796*x^3 + 77376*x^2 - 42204*x - 10228[]
407,4,2,x^12 - x^11 - 18*x^10 + 18*x^9 + 111*x^8 - 104*x^7 - 274*x^6 + 212*x^5 +
255*x^4 - 129*x^3 - 78*x^2 + 4*x + 1,3,x^12 - 8*x^11 + 4*x^10 + 115*x^9 -
251*x^8 - 396*x^7 + 1528*x^6 - 220*x^5 - 2592*x^4 + 1440*x^3 + 1328*x^2 - 752*x
- 208,5,x^12 - 5*x^11 - 32*x^10 + 182*x^9 + 275*x^8 - 2228*x^7 + 120*x^6 +
10912*x^5 - 10016*x^4 - 15424*x^3 + 29312*x^2 - 15872*x + 2816,7,x^12 - 7*x^11 -
44*x^10 + 416*x^9 + 229*x^8 - 8052*x^7 + 11288*x^6 + 50304*x^5 - 133760*x^4 +
8320*x^3 + 173056*x^2 - 45056*x - 38912,11,x^12 - 12*x^11 + 66*x^10 - 220*x^9 +
495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x +
1,13,x^12 - 14*x^11 + 735*x^9 - 1983*x^8 - 13336*x^7 + 54856*x^6 + 81234*x^5 -
560040*x^4 + 178164*x^3 + 1945404*x^2 - 2543220*x + 604836[]

Errors: /home/mfd/gomagma: line 2: 27350 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 02:59:03 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [404..407] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 02:58:46 on modular  [Seed = 2340231144]
-------------------------------------

404,1,2,$.1,3,$.1 + 2,5,$.1 - 3,7,$.1 - 2,11,$.1 + 6,13,$.1 - 5[]
404,2,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 + 2,13,$.1 + 3[]
404,3,2,$.1^7,3,$.1^7 - 2*$.1^6 - 17*$.1^5 + 36*$.1^4 + 64*$.1^3 - 148*$.1^2 + 11*$.1 + 58,5,$.1^7 - 31*$.1^5 + 8*$.1^4 + 262*$.1^3 - 160*$.1^2 - 503*$.1 +
250,7,$.1^7 - 2*$.1^6 - 39*$.1^5 + 62*$.1^4 + 438*$.1^3 - 474*$.1^2 - 1365*$.1 + 698,11,$.1^7 - 4*$.1^6 - 43*$.1^5 + 122*$.1^4 + 548*$.1^3 - 1178*$.1^2 - 2085*$.1 + 3482,13,$.1^7 - 4*$.1^6 - 55*$.1^5 + 244*$.1^4 + 534*$.1^3 - 2528*$.1^2 + 25*$.1 + 58[] 405,1,2,x,3,x,5,x + 1,7,x - 2,11,x + 3,13,x + 4[] 405,2,2,x - 1,3,x,5,x + 1,7,x + 3,11,x + 2,13,x + 2[] 405,3,2,x + 2,3,x,5,x + 1,7,x,11,x + 5,13,x - 4[] 405,4,2,x,3,x,5,x - 1,7,x - 2,11,x - 3,13,x + 4[] 405,5,2,x - 2,3,x,5,x - 1,7,x,11,x - 5,13,x - 4[] 405,6,2,x + 1,3,x,5,x - 1,7,x + 3,11,x - 2,13,x + 2[] 405,7,2,x^2 - 2*x - 2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 8*x + 13,13,x^2 + 4*x - 8[] 405,8,2,x^2 + 2*x - 2,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 6*x + 6,11,x^2 + 8*x + 13,13,x^2 + 4*x - 8[] 405,9,2,x^3 - x^2 - 5*x + 3,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 + 2*x^2 - 8*x - 12,13,x^3 - 4*x^2 - 4*x + 4[] 405,10,2,x^3 + x^2 - 5*x - 3,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 5*x^2 + 3*x + 3,11,x^3 - 2*x^2 - 8*x + 12,13,x^3 - 4*x^2 - 4*x + 4[] 406,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 4,13,x[] 406,2,2,x + 1,3,x - 2,5,x - 2,7,x - 1,11,x - 4,13,x + 2[] 406,3,2,x + 1,3,x - 1,5,x + 3,7,x - 1,11,x + 3,13,x + 1[] 406,4,2,x - 1,3,x + 1,5,x + 3,7,x + 1,11,x + 1,13,x + 1[] 406,5,2,x^2 - 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x - 2,7,x^2 + 2*x + 1,11,x^2 - 12,13,x^2 + 2*x - 2[] 406,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 8*x + 4,5,x^3 - 5*x^2 + 2*x + 10,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - x^2 - 24*x - 20,13,x^3 - 7*x^2 + 10*x - 2[] 406,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 4*x + 8,5,x^4 + x^3 - 14*x^2 - 24*x + 4,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 - 7*x^3 + 8*x^2 + 16*x - 16,13,x^4 + 7*x^3 - 26*x^2 - 176*x + 28[] 407,1,2,x^4 + x^3 - 4*x^2 + 1,3,x^4 - 4*x^2 - x + 1,5,x^4 - x^3 - 4*x^2 + 2*x + 3,7,x^4 + 7*x^3 + 8*x^2 - 30*x - 53,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 + 10*x^3 + 24*x^2 + 11*x - 3[] 407,2,2,x^4 - x^3 - 4*x^2 + 2*x + 3,3,x^4 + 4*x^3 - 9*x + 1,5,x^4 + 5*x^3 + 4*x^2 - 8*x - 9,7,x^4 + x^3 - 4*x^2 + 1,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 + 12*x^3 + 48*x^2 + 71*x + 31[] 407,3,2,x^11 - 2*x^10 - 16*x^9 + 32*x^8 + 89*x^7 - 179*x^6 - 201*x^5 + 407*x^4 + 168*x^3 - 333*x^2 - 51*x + 75,3,x^11 - 24*x^9 + 3*x^8 + 209*x^7 - 48*x^6 - 824*x^5 + 260*x^4 + 1448*x^3 - 560*x^2 - 880*x + 400,5,x^11 - x^10 - 46*x^9 + 48*x^8 + 767*x^7 - 786*x^6 - 5700*x^5 + 5224*x^4 + 19152*x^3 - 13536*x^2 - 24000*x + 9600,7,x^11 - 9*x^10 - 8*x^9 + 250*x^8 - 297*x^7 - 2188*x^6 + 3800*x^5 + 6880*x^4 - 12736*x^3 - 5632*x^2 + 10240*x + 1024,11,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,13,x^11 - 22*x^10 + 156*x^9 - 153*x^8 - 2747*x^7 + 9382*x^6 + 6848*x^5 - 61630*x^4 + 35796*x^3 + 77376*x^2 - 42204*x - 10228[] 407,4,2,x^12 - x^11 - 18*x^10 + 18*x^9 + 111*x^8 - 104*x^7 - 274*x^6 + 212*x^5 + 255*x^4 - 129*x^3 - 78*x^2 + 4*x + 1,3,x^12 - 8*x^11 + 4*x^10 + 115*x^9 - 251*x^8 - 396*x^7 + 1528*x^6 - 220*x^5 - 2592*x^4 + 1440*x^3 + 1328*x^2 - 752*x - 208,5,x^12 - 5*x^11 - 32*x^10 + 182*x^9 + 275*x^8 - 2228*x^7 + 120*x^6 + 10912*x^5 - 10016*x^4 - 15424*x^3 + 29312*x^2 - 15872*x + 2816,7,x^12 - 7*x^11 - 44*x^10 + 416*x^9 + 229*x^8 - 8052*x^7 + 11288*x^6 + 50304*x^5 - 133760*x^4 + 8320*x^3 + 173056*x^2 - 45056*x - 38912,11,x^12 - 12*x^11 + 66*x^10 - 220*x^9 + 495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x + 1,13,x^12 - 14*x^11 + 735*x^9 - 1983*x^8 - 13336*x^7 + 54856*x^6 + 81234*x^5 - 560040*x^4 + 178164*x^3 + 1945404*x^2 - 2543220*x + 604836[] Total time: 16.229 seconds, Total memory usage: 5.41MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:04:39 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [407..413] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. ** Magma V2.10-6 Sun Nov 30 2003 03:04:15 on modular [Seed = 1453378946] ------------------------------------- 407,1,2,$.1^4 + $.1^3 - 4*$.1^2 + 1,3,$.1^4 - 4*$.1^2 - $.1 + 1,5,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,7,$.1^4 + 7*$.1^3 + 8*$.1^2 - 30*$.1 - 53,11,$.1^4 +
4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 10*$.1^3 + 24*$.1^2 + 11*$.1 - 3[] 407,2,2,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,3,$.1^4 + 4*$.1^3 - 9*$.1 +
1,5,$.1^4 + 5*$.1^3 + 4*$.1^2 - 8*$.1 - 9,7,$.1^4 +$.1^3 - 4*$.1^2 + 1,11,$.1^4
- 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,13,$.1^4 + 12*$.1^3 + 48*$.1^2 + 71*$.1 + 31[] 407,3,2,$.1^11 - 2*$.1^10 - 16*$.1^9 + 32*$.1^8 + 89*$.1^7 - 179*$.1^6 - 201*$.1^5 + 407*$.1^4 + 168*$.1^3 - 333*$.1^2 - 51*$.1 + 75,3,$.1^11 - 24*$.1^9
+ 3*$.1^8 + 209*$.1^7 - 48*$.1^6 - 824*$.1^5 + 260*$.1^4 + 1448*$.1^3 -
560*$.1^2 - 880*$.1 + 400,5,$.1^11 -$.1^10 - 46*$.1^9 + 48*$.1^8 + 767*$.1^7 - 786*$.1^6 - 5700*$.1^5 + 5224*$.1^4 + 19152*$.1^3 - 13536*$.1^2 - 24000*$.1 + 9600,7,$.1^11 - 9*$.1^10 - 8*$.1^9 + 250*$.1^8 - 297*$.1^7 - 2188*$.1^6 + 3800*$.1^5 + 6880*$.1^4 - 12736*$.1^3 - 5632*$.1^2 + 10240*$.1 + 1024,11,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3 + 55*$.1^2 + 11*$.1 + 1,13,$.1^11 - 22*$.1^10 + 156*$.1^9
- 153*$.1^8 - 2747*$.1^7 + 9382*$.1^6 + 6848*$.1^5 - 61630*$.1^4 + 35796*$.1^3 +
77376*$.1^2 - 42204*$.1 - 10228[]
407,4,2,$.1^12 -$.1^11 - 18*$.1^10 + 18*$.1^9 + 111*$.1^8 - 104*$.1^7 -
274*$.1^6 + 212*$.1^5 + 255*$.1^4 - 129*$.1^3 - 78*$.1^2 + 4*$.1 + 1,3,$.1^12 - 8*$.1^11 + 4*$.1^10 + 115*$.1^9 - 251*$.1^8 - 396*$.1^7 + 1528*$.1^6 - 220*$.1^5
- 2592*$.1^4 + 1440*$.1^3 + 1328*$.1^2 - 752*$.1 - 208,5,$.1^12 - 5*$.1^11 -
32*$.1^10 + 182*$.1^9 + 275*$.1^8 - 2228*$.1^7 + 120*$.1^6 + 10912*$.1^5 -
10016*$.1^4 - 15424*$.1^3 + 29312*$.1^2 - 15872*$.1 + 2816,7,$.1^12 - 7*$.1^11 -
44*$.1^10 + 416*$.1^9 + 229*$.1^8 - 8052*$.1^7 + 11288*$.1^6 + 50304*$.1^5 -
133760*$.1^4 + 8320*$.1^3 + 173056*$.1^2 - 45056*$.1 - 38912,11,$.1^12 - 12*$.1^11 + 66*$.1^10 - 220*$.1^9 + 495*$.1^8 - 792*$.1^7 + 924*$.1^6 - 792*$.1^5 + 495*$.1^4 - 220*$.1^3 + 66*$.1^2 - 12*$.1 + 1,13,$.1^12 - 14*$.1^11
+ 735*$.1^9 - 1983*$.1^8 - 13336*$.1^7 + 54856*$.1^6 + 81234*$.1^5 - 560040*$.1^4 + 178164*$.1^3 + 1945404*$.1^2 - 2543220*$.1 + 604836[] 408,1,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 408,2,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x + 5[] 408,3,2,x,3,x + 1,5,x - 3,7,x,11,x + 1,13,x - 3[] 408,4,2,x,3,x - 1,5,x - 2,7,x + 4,11,x - 4,13,x - 6[] 408,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 4,7,x^2 + 2*x - 16,11,x^2 + 9*x + 16,13,x^2 + 3*x - 2[] 408,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 + x - 14,7,x^2 - 8*x + 16,11,x^2 + 3*x - 12,13,x^2 - x - 14[] 409,1,2,x^13 + 6*x^12 + 2*x^11 - 47*x^10 - 64*x^9 + 117*x^8 + 226*x^7 - 94*x^6 - 278*x^5 + 9*x^4 + 134*x^3 + 15*x^2 - 22*x - 4,3,x^13 + 3*x^12 - 15*x^11 - 49*x^10 + 62*x^9 + 246*x^8 - 55*x^7 - 408*x^6 + 38*x^5 + 272*x^4 - 51*x^3 - 64*x^2 + 22*x - 1,5,x^13 + 10*x^12 + 15*x^11 - 147*x^10 - 503*x^9 + 467*x^8 + 3660*x^7 + 1621*x^6 - 9806*x^5 - 9811*x^4 + 7795*x^3 + 11811*x^2 + 2790*x - 171,7,x^13 + 9*x^12 - 8*x^11 - 272*x^10 - 526*x^9 + 1605*x^8 + 4612*x^7 - 2986*x^6 - 12805*x^5 - 85*x^4 + 11495*x^3 + 4353*x^2 - 893*x - 361,11,x^13 + 26*x^12 + 258*x^11 + 1081*x^10 + 210*x^9 - 14427*x^8 - 44686*x^7 - 9053*x^6 + 177762*x^5 + 263786*x^4 - 79735*x^3 - 414834*x^2 - 243630*x - 14347,13,x^13 + 3*x^12 - 69*x^11 - 218*x^10 + 1639*x^9 + 5759*x^8 - 14252*x^7 - 65061*x^6 + 5742*x^5 + 252815*x^4 + 321799*x^3 + 128485*x^2 + 8065*x - 1831[] 409,2,2,x^20 - 5*x^19 - 19*x^18 + 126*x^17 + 100*x^16 - 1283*x^15 + 247*x^14 + 6767*x^13 - 4554*x^12 - 19689*x^11 + 18771*x^10 + 31011*x^9 - 35515*x^8 - 23548*x^7 + 31466*x^6 + 5354*x^5 - 10552*x^4 + 1129*x^3 + 523*x^2 - 54*x - 4,3,x^20 - x^19 - 43*x^18 + 43*x^17 + 770*x^16 - 742*x^15 - 7523*x^14 + 6640*x^13 + 44254*x^12 - 33176*x^11 - 163247*x^10 + 91556*x^9 + 379858*x^8 - 121845*x^7 - 538772*x^6 + 24992*x^5 + 417136*x^4 + 98080*x^3 - 123840*x^2 - 64128*x - 7936,5,x^20 - 8*x^19 - 25*x^18 + 339*x^17 - 73*x^16 - 5519*x^15 + 7786*x^14 + 43033*x^13 - 93848*x^12 - 160799*x^11 + 500285*x^10 + 218665*x^9 - 1333960*x^8 + 220157*x^7 + 1717578*x^6 - 875008*x^5 - 838232*x^4 + 649944*x^3 - 13040*x^2 - 35916*x - 2412,7,x^20 - 5*x^19 - 60*x^18 + 340*x^17 + 1276*x^16 - 8885*x^15 - 11420*x^14 + 119286*x^13 + 20939*x^12 - 909731*x^11 + 382277*x^10 + 4046437*x^9 - 3102111*x^8 - 10182997*x^7 + 9750164*x^6 + 13080780*x^5 - 12859068*x^4 - 7114292*x^3 + 4115996*x^2 + 2565948*x + 334126,11,x^20 - 30*x^19 + 340*x^18 - 1391*x^17 - 5028*x^16 + 75155*x^15 - 248768*x^14 - 310789*x^13 + 4354008*x^12 - 9372430*x^11 - 10656087*x^10 + 76307340*x^9 - 82153612*x^8 - 142849065*x^7 + 383618660*x^6 - 114166400*x^5 - 435600764*x^4 + 422353454*x^3 + 18207646*x^2 - 154653238*x + 45344434,13,x^20 + 7*x^19 - 107*x^18 - 824*x^17 + 4419*x^16 + 39503*x^15 - 86484*x^14 - 1001445*x^13 + 721924*x^12 + 14609397*x^11 + 640203*x^10 - 125194851*x^9 - 53698305*x^8 + 614885465*x^7 + 339715190*x^6 - 1594500300*x^5 - 703861704*x^4 + 1761581616*x^3 + 174121440*x^2 - 226273216*x - 38869888[] 410,1,2,x + 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x + 4[] 410,2,2,x + 1,3,x,5,x - 1,7,x + 2,11,x + 6,13,x + 2[] 410,3,2,x - 1,3,x + 2,5,x + 1,7,x + 2,11,x - 2,13,x + 6[] 410,4,2,x - 1,3,x,5,x - 1,7,x - 4,11,x,13,x + 2[] 410,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 - 2*x - 4,13,x^2 + 8*x + 16[] 410,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 4*x - 8[] 410,7,2,x^2 + 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 - 2*x - 16,13,x^2 - 8*x + 16[] 410,8,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 24,13,x^2 - 8*x + 16[] 410,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 8*x + 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 + 4*x^2 - 16*x - 48,13,x^3 - 8*x^2 - 8*x + 112[] 411,1,2,x^3 - x^2 - 2*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 - 4*x + 1,11,x^3 + 3*x^2 - 4*x - 13,13,x^3 + 11*x^2 + 38*x + 41[] 411,2,2,x^3 - 6*x^2 + 12*x - 8,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 3*x + 5,7,x^3 - 13*x + 13,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 2*x^2 - 16*x - 8[] 411,3,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 + 3*x^2 - 3,11,x^3 + 9*x^2 + 24*x + 19,13,x^3 + 3*x^2 - 6*x - 17[] 411,4,2,x^5 + x^4 - 7*x^3 - 10*x^2 + 1,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 - 6*x^4 + 2*x^3 + 29*x^2 - 13*x - 41,7,x^5 + x^4 - 9*x^3 - 8*x^2 + 18*x + 13,11,x^5 - x^4 - 22*x^3 + 31*x^2 + 120*x - 208,13,x^5 + x^4 - 54*x^3 + 33*x^2 + 784*x - 1516[] 411,5,2,x^9 - 16*x^7 + x^6 + 82*x^5 - 9*x^4 - 141*x^3 + 18*x^2 + 52*x + 8,3,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,5,x^9 - 6*x^8 - 15*x^7 + 130*x^6 + x^5 - 816*x^4 + 464*x^3 + 1608*x^2 - 925*x - 482,7,x^9 - 7*x^8 - 18*x^7 + 212*x^6 - 196*x^5 - 1292*x^4 + 2254*x^3 + 1409*x^2 - 3651*x + 584,11,x^9 - 7*x^8 - 50*x^7 + 395*x^6 + 520*x^5 - 6292*x^4 + 3112*x^3 + 22496*x^2 - 23040*x - 2048,13,x^9 - 7*x^8 - 38*x^7 + 275*x^6 + 244*x^5 - 2072*x^4 - 856*x^3 + 2976*x^2 - 160*x - 320[] Errors: /home/mfd/gomagma: line 2: 27394 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:05:26 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [407..411] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 03:05:04 on modular [Seed = 1538113727] ------------------------------------- 407,1,2,$.1^4 + $.1^3 - 4*$.1^2 + 1,3,$.1^4 - 4*$.1^2 - $.1 + 1,5,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,7,$.1^4 + 7*$.1^3 + 8*$.1^2 - 30*$.1 - 53,11,$.1^4 +
4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,13,$.1^4 + 10*$.1^3 + 24*$.1^2 + 11*$.1 - 3[] 407,2,2,$.1^4 - $.1^3 - 4*$.1^2 + 2*$.1 + 3,3,$.1^4 + 4*$.1^3 - 9*$.1 +
1,5,$.1^4 + 5*$.1^3 + 4*$.1^2 - 8*$.1 - 9,7,$.1^4 +$.1^3 - 4*$.1^2 + 1,11,$.1^4
- 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,13,$.1^4 + 12*$.1^3 + 48*$.1^2 + 71*$.1 + 31[] 407,3,2,$.1^11 - 2*$.1^10 - 16*$.1^9 + 32*$.1^8 + 89*$.1^7 - 179*$.1^6 - 201*$.1^5 + 407*$.1^4 + 168*$.1^3 - 333*$.1^2 - 51*$.1 + 75,3,$.1^11 - 24*$.1^9
+ 3*$.1^8 + 209*$.1^7 - 48*$.1^6 - 824*$.1^5 + 260*$.1^4 + 1448*$.1^3 -
560*$.1^2 - 880*$.1 + 400,5,$.1^11 -$.1^10 - 46*$.1^9 + 48*$.1^8 + 767*$.1^7 - 786*$.1^6 - 5700*$.1^5 + 5224*$.1^4 + 19152*$.1^3 - 13536*$.1^2 - 24000*$.1 + 9600,7,$.1^11 - 9*$.1^10 - 8*$.1^9 + 250*$.1^8 - 297*$.1^7 - 2188*$.1^6 + 3800*$.1^5 + 6880*$.1^4 - 12736*$.1^3 - 5632*$.1^2 + 10240*$.1 + 1024,11,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3 + 55*$.1^2 + 11*$.1 + 1,13,$.1^11 - 22*$.1^10 + 156*$.1^9
- 153*$.1^8 - 2747*$.1^7 + 9382*$.1^6 + 6848*$.1^5 - 61630*$.1^4 + 35796*$.1^3 +
77376*$.1^2 - 42204*$.1 - 10228[]
407,4,2,$.1^12 -$.1^11 - 18*$.1^10 + 18*$.1^9 + 111*$.1^8 - 104*$.1^7 -
274*$.1^6 + 212*$.1^5 + 255*$.1^4 - 129*$.1^3 - 78*$.1^2 + 4*$.1 + 1,3,$.1^12 - 8*$.1^11 + 4*$.1^10 + 115*$.1^9 - 251*$.1^8 - 396*$.1^7 + 1528*$.1^6 - 220*$.1^5
- 2592*$.1^4 + 1440*$.1^3 + 1328*$.1^2 - 752*$.1 - 208,5,$.1^12 - 5*$.1^11 -
32*$.1^10 + 182*$.1^9 + 275*$.1^8 - 2228*$.1^7 + 120*$.1^6 + 10912*$.1^5 -
10016*$.1^4 - 15424*$.1^3 + 29312*$.1^2 - 15872*$.1 + 2816,7,$.1^12 - 7*$.1^11 -
44*$.1^10 + 416*$.1^9 + 229*$.1^8 - 8052*$.1^7 + 11288*$.1^6 + 50304*$.1^5 -
133760*$.1^4 + 8320*$.1^3 + 173056*$.1^2 - 45056*$.1 - 38912,11,$.1^12 - 12*$.1^11 + 66*$.1^10 - 220*$.1^9 + 495*$.1^8 - 792*$.1^7 + 924*$.1^6 - 792*$.1^5 + 495*$.1^4 - 220*$.1^3 + 66*$.1^2 - 12*$.1 + 1,13,$.1^12 - 14*$.1^11
+ 735*$.1^9 - 1983*$.1^8 - 13336*$.1^7 + 54856*$.1^6 + 81234*$.1^5 - 560040*$.1^4 + 178164*$.1^3 + 1945404*$.1^2 - 2543220*$.1 + 604836[] 408,1,2,x,3,x - 1,5,x,7,x - 2,11,x,13,x - 2[] 408,2,2,x,3,x - 1,5,x + 3,7,x + 4,11,x - 1,13,x + 5[] 408,3,2,x,3,x + 1,5,x - 3,7,x,11,x + 1,13,x - 3[] 408,4,2,x,3,x - 1,5,x - 2,7,x + 4,11,x - 4,13,x - 6[] 408,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 4,7,x^2 + 2*x - 16,11,x^2 + 9*x + 16,13,x^2 + 3*x - 2[] 408,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 + x - 14,7,x^2 - 8*x + 16,11,x^2 + 3*x - 12,13,x^2 - x - 14[] 409,1,2,x^13 + 6*x^12 + 2*x^11 - 47*x^10 - 64*x^9 + 117*x^8 + 226*x^7 - 94*x^6 - 278*x^5 + 9*x^4 + 134*x^3 + 15*x^2 - 22*x - 4,3,x^13 + 3*x^12 - 15*x^11 - 49*x^10 + 62*x^9 + 246*x^8 - 55*x^7 - 408*x^6 + 38*x^5 + 272*x^4 - 51*x^3 - 64*x^2 + 22*x - 1,5,x^13 + 10*x^12 + 15*x^11 - 147*x^10 - 503*x^9 + 467*x^8 + 3660*x^7 + 1621*x^6 - 9806*x^5 - 9811*x^4 + 7795*x^3 + 11811*x^2 + 2790*x - 171,7,x^13 + 9*x^12 - 8*x^11 - 272*x^10 - 526*x^9 + 1605*x^8 + 4612*x^7 - 2986*x^6 - 12805*x^5 - 85*x^4 + 11495*x^3 + 4353*x^2 - 893*x - 361,11,x^13 + 26*x^12 + 258*x^11 + 1081*x^10 + 210*x^9 - 14427*x^8 - 44686*x^7 - 9053*x^6 + 177762*x^5 + 263786*x^4 - 79735*x^3 - 414834*x^2 - 243630*x - 14347,13,x^13 + 3*x^12 - 69*x^11 - 218*x^10 + 1639*x^9 + 5759*x^8 - 14252*x^7 - 65061*x^6 + 5742*x^5 + 252815*x^4 + 321799*x^3 + 128485*x^2 + 8065*x - 1831[] 409,2,2,x^20 - 5*x^19 - 19*x^18 + 126*x^17 + 100*x^16 - 1283*x^15 + 247*x^14 + 6767*x^13 - 4554*x^12 - 19689*x^11 + 18771*x^10 + 31011*x^9 - 35515*x^8 - 23548*x^7 + 31466*x^6 + 5354*x^5 - 10552*x^4 + 1129*x^3 + 523*x^2 - 54*x - 4,3,x^20 - x^19 - 43*x^18 + 43*x^17 + 770*x^16 - 742*x^15 - 7523*x^14 + 6640*x^13 + 44254*x^12 - 33176*x^11 - 163247*x^10 + 91556*x^9 + 379858*x^8 - 121845*x^7 - 538772*x^6 + 24992*x^5 + 417136*x^4 + 98080*x^3 - 123840*x^2 - 64128*x - 7936,5,x^20 - 8*x^19 - 25*x^18 + 339*x^17 - 73*x^16 - 5519*x^15 + 7786*x^14 + 43033*x^13 - 93848*x^12 - 160799*x^11 + 500285*x^10 + 218665*x^9 - 1333960*x^8 + 220157*x^7 + 1717578*x^6 - 875008*x^5 - 838232*x^4 + 649944*x^3 - 13040*x^2 - 35916*x - 2412,7,x^20 - 5*x^19 - 60*x^18 + 340*x^17 + 1276*x^16 - 8885*x^15 - 11420*x^14 + 119286*x^13 + 20939*x^12 - 909731*x^11 + 382277*x^10 + 4046437*x^9 - 3102111*x^8 - 10182997*x^7 + 9750164*x^6 + 13080780*x^5 - 12859068*x^4 - 7114292*x^3 + 4115996*x^2 + 2565948*x + 334126,11,x^20 - 30*x^19 + 340*x^18 - 1391*x^17 - 5028*x^16 + 75155*x^15 - 248768*x^14 - 310789*x^13 + 4354008*x^12 - 9372430*x^11 - 10656087*x^10 + 76307340*x^9 - 82153612*x^8 - 142849065*x^7 + 383618660*x^6 - 114166400*x^5 - 435600764*x^4 + 422353454*x^3 + 18207646*x^2 - 154653238*x + 45344434,13,x^20 + 7*x^19 - 107*x^18 - 824*x^17 + 4419*x^16 + 39503*x^15 - 86484*x^14 - 1001445*x^13 + 721924*x^12 + 14609397*x^11 + 640203*x^10 - 125194851*x^9 - 53698305*x^8 + 614885465*x^7 + 339715190*x^6 - 1594500300*x^5 - 703861704*x^4 + 1761581616*x^3 + 174121440*x^2 - 226273216*x - 38869888[] 410,1,2,x + 1,3,x + 2,5,x - 1,7,x - 2,11,x,13,x + 4[] 410,2,2,x + 1,3,x,5,x - 1,7,x + 2,11,x + 6,13,x + 2[] 410,3,2,x - 1,3,x + 2,5,x + 1,7,x + 2,11,x - 2,13,x + 6[] 410,4,2,x - 1,3,x,5,x - 1,7,x - 4,11,x,13,x + 2[] 410,5,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 - 2*x - 4,13,x^2 + 8*x + 16[] 410,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 4*x - 8[] 410,7,2,x^2 + 2*x + 1,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 - 2*x - 16,13,x^2 - 8*x + 16[] 410,8,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 24,13,x^2 - 8*x + 16[] 410,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 8*x + 4,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 + 4*x^2 - 16*x - 48,13,x^3 - 8*x^2 - 8*x + 112[] 411,1,2,x^3 - x^2 - 2*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - x - 1,7,x^3 + 3*x^2 - 4*x + 1,11,x^3 + 3*x^2 - 4*x - 13,13,x^3 + 11*x^2 + 38*x + 41[] 411,2,2,x^3 - 6*x^2 + 12*x - 8,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 2*x^2 - 3*x + 5,7,x^3 - 13*x + 13,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 2*x^2 - 16*x - 8[] 411,3,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 9*x + 1,7,x^3 + 3*x^2 - 3,11,x^3 + 9*x^2 + 24*x + 19,13,x^3 + 3*x^2 - 6*x - 17[] 411,4,2,x^5 + x^4 - 7*x^3 - 10*x^2 + 1,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,5,x^5 - 6*x^4 + 2*x^3 + 29*x^2 - 13*x - 41,7,x^5 + x^4 - 9*x^3 - 8*x^2 + 18*x + 13,11,x^5 - x^4 - 22*x^3 + 31*x^2 + 120*x - 208,13,x^5 + x^4 - 54*x^3 + 33*x^2 + 784*x - 1516[] 411,5,2,x^9 - 16*x^7 + x^6 + 82*x^5 - 9*x^4 - 141*x^3 + 18*x^2 + 52*x + 8,3,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1,5,x^9 - 6*x^8 - 15*x^7 + 130*x^6 + x^5 - 816*x^4 + 464*x^3 + 1608*x^2 - 925*x - 482,7,x^9 - 7*x^8 - 18*x^7 + 212*x^6 - 196*x^5 - 1292*x^4 + 2254*x^3 + 1409*x^2 - 3651*x + 584,11,x^9 - 7*x^8 - 50*x^7 + 395*x^6 + 520*x^5 - 6292*x^4 + 3112*x^3 + 22496*x^2 - 23040*x - 2048,13,x^9 - 7*x^8 - 38*x^7 + 275*x^6 + 244*x^5 - 2072*x^4 - 856*x^3 + 2976*x^2 - 160*x - 320[] Total time: 21.010 seconds, Total memory usage: 6.07MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 03:13:36 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [411..415] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 03:13:15 on modular [Seed = 1988161465] ------------------------------------- 411,1,2,$.1^3 - $.1^2 - 2*$.1 + 1,3,$.1^3 + 3*$.1^2 + 3*$.1 + 1,5,$.1^3 +
2*$.1^2 -$.1 - 1,7,$.1^3 + 3*$.1^2 - 4*$.1 + 1,11,$.1^3 + 3*$.1^2 - 4*$.1 -
13,13,$.1^3 + 11*$.1^2 + 38*$.1 + 41[] 411,2,2,$.1^3 - 6*$.1^2 + 12*$.1 - 8,3,$.1^3 - 3*$.1^2 + 3*$.1 - 1,5,$.1^3 -
2*$.1^2 - 3*$.1 + 5,7,$.1^3 - 13*$.1 + 13,11,$.1^3 - 4*$.1^2 - 12*$.1 + 40,13,$.1^3 - 2*$.1^2 - 16*$.1 - 8[]
411,3,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 - 3*$.1^2 + 3*$.1 - 1,5,$.1^3 + 6*$.1^2 + 9*$.1 + 1,7,$.1^3 + 3*$.1^2 - 3,11,$.1^3 + 9*$.1^2 + 24*$.1 + 19,13,$.1^3 +
3*$.1^2 - 6*$.1 - 17[]
411,4,2,$.1^5 +$.1^4 - 7*$.1^3 - 10*$.1^2 + 1,3,$.1^5 - 5*$.1^4 + 10*$.1^3 - 10*$.1^2 + 5*$.1 - 1,5,$.1^5 - 6*$.1^4 + 2*$.1^3 + 29*$.1^2 - 13*$.1 -
41,7,$.1^5 +$.1^4 - 9*$.1^3 - 8*$.1^2 + 18*$.1 + 13,11,$.1^5 - $.1^4 - 22*$.1^3
+ 31*$.1^2 + 120*$.1 - 208,13,$.1^5 +$.1^4 - 54*$.1^3 + 33*$.1^2 + 784*$.1 - 1516[] 411,5,2,$.1^9 - 16*$.1^7 +$.1^6 + 82*$.1^5 - 9*$.1^4 - 141*$.1^3 + 18*$.1^2 +
52*$.1 + 8,3,$.1^9 + 9*$.1^8 + 36*$.1^7 + 84*$.1^6 + 126*$.1^5 + 126*$.1^4 + 84*$.1^3 + 36*$.1^2 + 9*$.1 + 1,5,$.1^9 - 6*$.1^8 - 15*$.1^7 + 130*$.1^6 + $.1^5 - 816*$.1^4 + 464*$.1^3 + 1608*$.1^2 - 925*$.1 - 482,7,$.1^9 - 7*$.1^8 - 18*$.1^7 + 212*$.1^6 - 196*$.1^5 - 1292*$.1^4 + 2254*$.1^3 + 1409*$.1^2 - 3651*$.1 + 584,11,$.1^9 - 7*$.1^8 - 50*$.1^7 + 395*$.1^6 + 520*$.1^5 - 6292*$.1^4 + 3112*$.1^3 + 22496*$.1^2 - 23040*$.1 - 2048,13,$.1^9 - 7*$.1^8 - 38*$.1^7 + 275*$.1^6 + 244*$.1^5 - 2072*$.1^4 - 856*$.1^3 + 2976*$.1^2 - 160*$.1
- 320[]
412,1,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 5,7,x^2 - 21,11,x^2 + 3*x - 3,13,x^2 +
7*x + 7[]
412,2,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 2*x - 4,7,x^2 + 3*x + 1,11,x^2 + 4*x +
4,13,x^2 + x - 1[]
412,3,2,x^4,3,x^4 - 2*x^3 - 5*x^2 + 6*x + 4,5,x^4 - 3*x^3 - 7*x^2 + 12*x -
4,7,x^4 - 5*x^3 + 4*x^2 + 5*x - 1,11,x^4 - 7*x^3 + 3*x^2 + 48*x - 64,13,x^4 -
19*x^2 + 89[]
413,1,2,x^2 - 5,3,x^2 + x - 1,5,x^2 - 2*x - 4,7,x^2 + 2*x + 1,11,x^2 + 5*x +
5,13,x^2 - x - 11[]
413,2,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - x + 4,5,x^3 - 16*x + 8,7,x^3 +
3*x^2 + 3*x + 1,11,x^3 - 3*x^2 - x + 4,13,x^3 + 3*x^2 - 43*x - 98[]
413,3,2,x^5 + 2*x^4 - 3*x^3 - 5*x^2 + x + 1,3,x^5 + 5*x^4 + 4*x^3 - 7*x^2 - 7*x
+ 1,5,x^5 - x^4 - 5*x^3 + 3*x^2 + 2*x - 1,7,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x
+ 1,11,x^5 + 7*x^4 + 6*x^3 - 31*x^2 - 35*x + 25,13,x^5 + 3*x^4 - 21*x^3 - 23*x^2
+ 112*x - 47[]
413,4,2,x^5 - 4*x^4 - 3*x^3 + 29*x^2 - 35*x + 11,3,x^5 - 7*x^4 + 8*x^3 + 33*x^2
- 67*x + 13,5,x^5 + 3*x^4 - 5*x^3 - 5*x^2 + 6*x - 1,7,x^5 + 5*x^4 + 10*x^3 +
10*x^2 + 5*x + 1,11,x^5 - 9*x^4 + 129*x^2 - 73*x - 481,13,x^5 + x^4 - 13*x^3 -
15*x^2 + 42*x + 55[]
413,5,2,x^5 - 5*x^3 - x^2 + 5*x + 1,3,x^5 + 7*x^4 + 14*x^3 + 3*x^2 - 9*x +
1,5,x^5 + 5*x^4 - x^3 - 27*x^2 - 24*x - 1,7,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x
- 1,11,x^5 - x^4 - 36*x^3 - 15*x^2 + 199*x + 157,13,x^5 + 17*x^4 + 95*x^3 +
165*x^2 - 78*x - 139[]
413,6,2,x^9 - 13*x^7 + x^6 + 54*x^5 - 7*x^4 - 75*x^3 + 9*x^2 + 17*x - 3,3,x^9 -
7*x^8 + 7*x^7 + 46*x^6 - 94*x^5 - 69*x^4 + 243*x^3 - 32*x^2 - 171*x + 73,5,x^9 -
3*x^8 - 25*x^7 + 77*x^6 + 188*x^5 - 589*x^4 - 460*x^3 + 1340*x^2 + 448*x -
432,7,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x
- 1,11,x^9 - 3*x^8 - 47*x^7 + 164*x^6 + 492*x^5 - 2085*x^4 + 417*x^3 + 2270*x^2
- 113*x - 423,13,x^9 - 13*x^8 + 22*x^7 + 416*x^6 - 2398*x^5 + 2337*x^4 +
16559*x^3 - 59020*x^2 + 75478*x - 34703[]
414,1,2,x + 1,3,x,5,x + 2,7,x,11,x,13,x + 2[]
414,2,2,x - 1,3,x,5,x + 4,7,x + 4,11,x + 2,13,x + 2[]
414,3,2,x - 1,3,x,5,x,7,x - 2,11,x,13,x - 2[]
414,4,2,x - 1,3,x,5,x - 2,7,x + 2,11,x - 6,13,x + 2[]
414,5,2,x^2 + 2*x + 1,3,x^2,5,x^2 + 2*x - 6,7,x^2 - 4*x + 4,11,x^2 - 2*x -
6,13,x^2 - 28[]
414,6,2,x^2 + 2*x + 1,3,x^2,5,x^2 - 2*x - 4,7,x^2 - 20,11,x^2 - 6*x + 4,13,x^2 -
20[]
414,7,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 2*x - 6,7,x^2 - 4*x + 4,11,x^2 + 2*x -
6,13,x^2 - 28[]
415,1,2,x - 1,3,x - 3,5,x - 1,7,x - 1,11,x - 3,13,x + 6[]
415,2,2,x^2 + x - 1,3,x^2 + x - 1,5,x^2 - 2*x + 1,7,x^2 - 5,11,x^2 + 4*x +
4,13,x^2 + 3*x + 1[]
415,3,2,x^6 - 2*x^5 - 5*x^4 + 9*x^3 + 5*x^2 - 6*x - 1,3,x^6 - 3*x^5 - 9*x^4 +
26*x^3 + 16*x^2 - 48*x + 16,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x +
1,7,x^6 - 15*x^4 - 2*x^3 + 52*x^2 + 8*x - 16,11,x^6 - 4*x^5 - 27*x^4 + 108*x^3 +
9*x^2 - 256*x + 92,13,x^6 - 7*x^5 - 4*x^4 + 29*x^3 - 4*x^2 - 7*x - 1[]
415,4,2,x^7 + 3*x^6 - 6*x^5 - 19*x^4 + 9*x^3 + 28*x^2 - 4*x - 8,3,x^7 + 5*x^6 +
x^5 - 21*x^4 - 10*x^3 + 23*x^2 - 2*x - 1,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 +
35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 6*x^6 + x^5 - 41*x^4 - 51*x^3 + 10*x^2 + 9*x +
1,11,x^7 + 2*x^6 - 48*x^5 - 83*x^4 + 617*x^3 + 907*x^2 - 1276*x - 508,13,x^7 +
5*x^6 - 39*x^5 - 156*x^4 + 308*x^3 + 656*x^2 - 832*x - 256[]
415,5,2,x^11 - 20*x^9 - x^8 + 146*x^7 + 15*x^6 - 464*x^5 - 76*x^4 + 567*x^3 +
136*x^2 - 100*x - 8,3,x^11 - 27*x^9 + 4*x^8 + 258*x^7 - 71*x^6 - 1041*x^5 +
362*x^4 + 1712*x^3 - 448*x^2 - 1008*x + 64,5,x^11 - 11*x^10 + 55*x^9 - 165*x^8 +
330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,7,x^11 +
3*x^10 - 50*x^9 - 97*x^8 + 968*x^7 + 664*x^6 - 8499*x^5 + 3974*x^4 + 25460*x^3 -
34872*x^2 + 10640*x + 1024,11,x^11 + x^10 - 76*x^9 - 49*x^8 + 1991*x^7 + 67*x^6
- 21282*x^5 + 19366*x^4 + 75983*x^3 - 162888*x^2 + 113756*x - 26896,13,x^11 -
x^10 - 88*x^9 + 43*x^8 + 2724*x^7 + 615*x^6 - 36217*x^5 - 34976*x^4 + 170244*x^3
+ 283536*x^2 + 56960*x - 23296[]

Total time: 19.989 seconds, Total memory usage: 6.11MB

************** MAGMA *****************
Time: Sun Nov 30 03:18:04 2003

Input: 123*3456

Output: Magma V2.10-6     Sun Nov 30 2003 03:18:00 on modular  [Seed = 1704197513]
-------------------------------------

425088

Total time: 3.309 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 03:20:15 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [415..419] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 03:19:56 on modular  [Seed = 283543400]
-------------------------------------

415,1,2,$.1 - 1,3,$.1 - 3,5,$.1 - 1,7,$.1 - 1,11,$.1 - 3,13,$.1 + 6[]
415,2,2,$.1^2 +$.1 - 1,3,$.1^2 +$.1 - 1,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 5,11,$.1^2 + 4*$.1 + 4,13,$.1^2 + 3*$.1 + 1[] 415,3,2,$.1^6 - 2*$.1^5 - 5*$.1^4 + 9*$.1^3 + 5*$.1^2 - 6*$.1 - 1,3,$.1^6 -
3*$.1^5 - 9*$.1^4 + 26*$.1^3 + 16*$.1^2 - 48*$.1 + 16,5,$.1^6 + 6*$.1^5 + 15*$.1^4 + 20*$.1^3 + 15*$.1^2 + 6*$.1 + 1,7,$.1^6 - 15*$.1^4 - 2*$.1^3 +
52*$.1^2 + 8*$.1 - 16,11,$.1^6 - 4*$.1^5 - 27*$.1^4 + 108*$.1^3 + 9*$.1^2 - 256*$.1 + 92,13,$.1^6 - 7*$.1^5 - 4*$.1^4 + 29*$.1^3 - 4*$.1^2 - 7*$.1 - 1[]
415,4,2,$.1^7 + 3*$.1^6 - 6*$.1^5 - 19*$.1^4 + 9*$.1^3 + 28*$.1^2 - 4*$.1 - 8,3,$.1^7 + 5*$.1^6 +$.1^5 - 21*$.1^4 - 10*$.1^3 + 23*$.1^2 - 2*$.1 - 1,5,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,7,$.1^7 +
6*$.1^6 +$.1^5 - 41*$.1^4 - 51*$.1^3 + 10*$.1^2 + 9*$.1 + 1,11,$.1^7 + 2*$.1^6
- 48*$.1^5 - 83*$.1^4 + 617*$.1^3 + 907*$.1^2 - 1276*$.1 - 508,13,$.1^7 +
5*$.1^6 - 39*$.1^5 - 156*$.1^4 + 308*$.1^3 + 656*$.1^2 - 832*$.1 - 256[]
415,5,2,$.1^11 - 20*$.1^9 - $.1^8 + 146*$.1^7 + 15*$.1^6 - 464*$.1^5 - 76*$.1^4 + 567*$.1^3 + 136*$.1^2 - 100*$.1 - 8,3,$.1^11 - 27*$.1^9 + 4*$.1^8 + 258*$.1^7
- 71*$.1^6 - 1041*$.1^5 + 362*$.1^4 + 1712*$.1^3 - 448*$.1^2 - 1008*$.1 +
64,5,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 + 330*$.1^7 - 462*$.1^6 +
462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1,7,$.1^11 + 3*$.1^10 - 50*$.1^9 - 97*$.1^8 + 968*$.1^7 + 664*$.1^6 - 8499*$.1^5 + 3974*$.1^4 + 25460*$.1^3 - 34872*$.1^2 + 10640*$.1 + 1024,11,$.1^11 +$.1^10 - 76*$.1^9 - 49*$.1^8 + 1991*$.1^7 + 67*$.1^6 - 21282*$.1^5 + 19366*$.1^4 + 75983*$.1^3 - 162888*$.1^2 + 113756*$.1 - 26896,13,$.1^11 - $.1^10 - 88*$.1^9 + 43*$.1^8 + 2724*$.1^7 + 615*$.1^6 - 36217*$.1^5 - 34976*$.1^4 + 170244*$.1^3 + 283536*$.1^2 + 56960*$.1 - 23296[]
416,1,2,x,3,x - 1,5,x - 1,7,x - 3,11,x - 2,13,x - 1[]
416,2,2,x,3,x + 1,5,x - 1,7,x + 3,11,x + 2,13,x - 1[]
416,3,2,x^2,3,x^2 + x - 4,5,x^2 + 3*x - 2,7,x^2 + 3*x - 2,11,x^2 + 4*x +
4,13,x^2 + 2*x + 1[]
416,4,2,x^2,3,x^2 - 5,5,x^2 - 6*x + 9,7,x^2 - 5,11,x^2 - 20,13,x^2 + 2*x + 1[]
416,5,2,x^2,3,x^2 - x - 4,5,x^2 + 3*x - 2,7,x^2 - 3*x - 2,11,x^2 - 4*x +
4,13,x^2 + 2*x + 1[]
416,6,2,x^4,3,x^4 - 13*x^2 + 32,5,x^4 + 2*x^3 - 19*x^2 - 20*x + 100,7,x^4 -
29*x^2 + 200,11,x^4 - 28*x^2 + 32,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[]
417,1,2,x - 1,3,x + 1,5,x - 2,7,x,11,x - 5,13,x - 5[]
417,2,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 7*x + 11,11,x^2 -
5,13,x^2 + 6*x + 4[]
417,3,2,x^3 - 4*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 -
5*x^2 + 3*x + 8,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 5*x^2 + 2*x - 4[]
417,4,2,x^3 - 4*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 - 7*x + 26,7,x^3 -
5*x^2 + 3*x + 8,11,x^3 - 4*x^2 - x + 8,13,x^3 - 4*x^2 - 16*x + 56[]
417,5,2,x^7 + 3*x^6 - 6*x^5 - 19*x^4 + 9*x^3 + 30*x^2 - 8,3,x^7 + 7*x^6 + 21*x^5
+ 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,5,x^7 + 4*x^6 - 13*x^5 - 55*x^4 + 45*x^3 +
208*x^2 - 9*x - 149,7,x^7 + 9*x^6 + 9*x^5 - 109*x^4 - 276*x^3 + 5*x^2 + 300*x +
125,11,x^7 + 4*x^6 - 45*x^5 - 207*x^4 + 347*x^3 + 2494*x^2 + 2881*x + 829,13,x^7
+ 4*x^6 - 62*x^5 - 251*x^4 + 905*x^3 + 3849*x^2 + 350*x - 3868[]
417,6,2,x^7 - 14*x^5 + 2*x^4 + 57*x^3 - 14*x^2 - 56*x + 8,3,x^7 - 7*x^6 + 21*x^5
- 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,5,x^7 + 4*x^6 - 8*x^5 - 31*x^4 + 5*x^3 +
41*x^2 + 24*x + 4,7,x^7 - 6*x^6 - 24*x^5 + 165*x^4 + 121*x^3 - 1193*x^2 + 280*x
+ 784,11,x^7 + 4*x^6 - 41*x^5 - 135*x^4 + 555*x^3 + 1390*x^2 - 2275*x -
4907,13,x^7 - 4*x^6 - 41*x^5 + 147*x^4 + 219*x^3 - 466*x^2 - 475*x + 107[]
418,1,2,x - 1,3,x + 1,5,x + 2,7,x + 3,11,x + 1,13,x - 1[]
418,2,2,x - 1,3,x,5,x - 2,7,x - 2,11,x - 1,13,x + 2[]
418,3,2,x - 1,3,x - 3,5,x + 2,7,x - 1,11,x - 1,13,x + 7[]
418,4,2,x^2 + 2*x + 1,3,x^2 - x - 4,5,x^2 - 4*x + 4,7,x^2 - 3*x - 2,11,x^2 - 2*x
+ 1,13,x^2 + 3*x - 2[]
418,5,2,x^2 + 2*x + 1,3,x^2 + 3*x - 1,5,x^2 + x - 3,7,x^2 + x - 3,11,x^2 - 2*x +
1,13,x^2 + 3*x - 1[]
418,6,2,x^2 - 2*x + 1,3,x^2 + x - 5,5,x^2 - 3*x - 3,7,x^2 + 5*x + 1,11,x^2 - 2*x
+ 1,13,x^2 - 7*x + 7[]
418,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 6*x - 3,5,x^3 + 3*x^2 - 9*x - 18,7,x^3 +
6*x^2 - 6*x - 57,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 18*x - 29[]
418,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 5*x + 4,5,x^3 - 5*x^2 + 3*x +
2,7,x^3 - x^2 - 7*x - 4,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 5*x^2 + x + 14[]
419,1,2,x^9 + 2*x^8 - 7*x^7 - 13*x^6 + 15*x^5 + 25*x^4 - 9*x^3 - 15*x^2 - x +
1,3,x^9 + 4*x^8 - 4*x^7 - 28*x^6 - 9*x^5 + 47*x^4 + 29*x^3 - 15*x^2 - 9*x +
1,5,x^9 + 5*x^8 - 4*x^7 - 35*x^6 + 2*x^5 + 54*x^4 - 8*x^3 - 17*x^2 + 1,7,x^9 +
7*x^8 - 101*x^6 - 215*x^5 + 118*x^4 + 666*x^3 + 271*x^2 - 483*x - 307,11,x^9 +
6*x^8 - 3*x^7 - 60*x^6 - 50*x^5 + 144*x^4 + 200*x^3 + 28*x^2 - 8*x - 1,13,x^9 +
19*x^8 + 135*x^7 + 408*x^6 + 214*x^5 - 1651*x^4 - 3652*x^3 - 1917*x^2 + 1271*x +
1093[]
419,2,2,x^26 - 2*x^25 - 43*x^24 + 85*x^23 + 807*x^22 - 1571*x^21 - 8689*x^20 +
16575*x^19 + 59362*x^18 - 110217*x^17 - 268789*x^16 + 481513*x^15 + 817911*x^14
- 1398615*x^13 - 1658267*x^12 + 2674771*x^11 + 2166607*x^10 - 3262315*x^9 -
1701132*x^8 + 2384864*x^7 + 697992*x^6 - 932912*x^5 - 104448*x^4 + 158080*x^3 -
4736*x^2 - 6656*x + 512,3,x^26 - 2*x^25 - 56*x^24 + 112*x^23 + 1360*x^22 -
2697*x^21 - 18861*x^20 + 36655*x^19 + 165783*x^18 - 310509*x^17 - 970565*x^16 +
1709870*x^15 + 3873246*x^14 - 6194080*x^13 - 10579146*x^12 + 14580799*x^11 +
19436188*x^10 - 21403195*x^9 - 22833853*x^8 + 17959682*x^7 + 15322485*x^6 -
7282611*x^5 - 4620027*x^4 + 1147264*x^3 + 536568*x^2 - 50646*x - 19573,5,x^26 -
5*x^25 - 76*x^24 + 408*x^23 + 2350*x^22 - 14020*x^21 - 37353*x^20 + 263933*x^19
+ 308436*x^18 - 2970100*x^17 - 978578*x^16 + 20527286*x^15 - 3301588*x^14 -
86879933*x^13 + 37204504*x^12 + 221113241*x^11 - 119074256*x^10 - 327914224*x^9
+ 180330624*x^8 + 261570439*x^7 - 138751056*x^6 - 93983582*x^5 + 50686447*x^4 +
7883301*x^3 - 6367075*x^2 + 703704*x + 3636,7,x^26 - 7*x^25 - 94*x^24 + 755*x^23
+ 3376*x^22 - 34335*x^21 - 50704*x^20 + 855286*x^19 - 38855*x^18 - 12649727*x^17
+ 12756501*x^16 + 111894539*x^15 - 196143244*x^14 - 557701291*x^13 +
1414715108*x^12 + 1277746296*x^11 - 5200868214*x^10 - 218735889*x^9 +
9073283331*x^8 - 2545605634*x^7 - 7481074932*x^6 + 2325109394*x^5 +
2658406017*x^4 - 250096947*x^3 - 240212414*x^2 + 7413162*x + 6287437,11,x^26 -
4*x^25 - 177*x^24 + 656*x^23 + 13862*x^22 - 46540*x^21 - 636334*x^20 +
1880028*x^19 + 19069370*x^18 - 47726569*x^17 - 392271834*x^16 + 789666148*x^15 +
5655617024*x^14 - 8493715936*x^13 - 57153539904*x^12 + 56629921664*x^11 +
396922638976*x^10 - 200663798272*x^9 - 1812408616960*x^8 + 132693870592*x^7 +
5016124092416*x^6 + 1392906018816*x^5 - 7264942759936*x^4 - 3756369494016*x^3 +
4146471239680*x^2 + 2654302830592*x - 147968098304,13,x^26 - 27*x^25 + 163*x^24
+ 1928*x^23 - 27449*x^22 + 23700*x^21 + 1267187*x^20 - 5766791*x^19 -
21347328*x^18 + 211203676*x^17 - 82055796*x^16 - 3557303755*x^15 +
8511540838*x^14 + 27889892344*x^13 - 134521938974*x^12 - 27055321906*x^11 +
981401106854*x^10 - 1155399404446*x^9 - 3089614789233*x^8 + 7805633569236*x^7 +
101494956628*x^6 - 16093016897986*x^5 + 15461823929882*x^4 - 1041139154045*x^3 -
3230579452834*x^2 + 384994835418*x + 100306912571[]

Total time: 16.789 seconds, Total memory usage: 5.52MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 03:29:33 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [419..425] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 03:29:10 on modular  [Seed = 167746571]
-------------------------------------

419,1,2,$.1^9 + 2*$.1^8 - 7*$.1^7 - 13*$.1^6 + 15*$.1^5 + 25*$.1^4 - 9*$.1^3 - 15*$.1^2 - $.1 + 1,3,$.1^9 + 4*$.1^8 - 4*$.1^7 - 28*$.1^6 - 9*$.1^5 + 47*$.1^4 + 29*$.1^3 - 15*$.1^2 - 9*$.1 + 1,5,$.1^9 + 5*$.1^8 - 4*$.1^7 - 35*$.1^6 + 2*$.1^5 + 54*$.1^4 - 8*$.1^3 - 17*$.1^2 + 1,7,$.1^9 + 7*$.1^8 - 101*$.1^6 - 215*$.1^5 +
118*$.1^4 + 666*$.1^3 + 271*$.1^2 - 483*$.1 - 307,11,$.1^9 + 6*$.1^8 - 3*$.1^7 - 60*$.1^6 - 50*$.1^5 + 144*$.1^4 + 200*$.1^3 + 28*$.1^2 - 8*$.1 - 1,13,$.1^9 +
19*$.1^8 + 135*$.1^7 + 408*$.1^6 + 214*$.1^5 - 1651*$.1^4 - 3652*$.1^3 -
1917*$.1^2 + 1271*$.1 + 1093[]
419,2,2,$.1^26 - 2*$.1^25 - 43*$.1^24 + 85*$.1^23 + 807*$.1^22 - 1571*$.1^21 -
8689*$.1^20 + 16575*$.1^19 + 59362*$.1^18 - 110217*$.1^17 - 268789*$.1^16 + 481513*$.1^15 + 817911*$.1^14 - 1398615*$.1^13 - 1658267*$.1^12 + 2674771*$.1^11
+ 2166607*$.1^10 - 3262315*$.1^9 - 1701132*$.1^8 + 2384864*$.1^7 + 697992*$.1^6 - 932912*$.1^5 - 104448*$.1^4 + 158080*$.1^3 - 4736*$.1^2 - 6656*$.1 +
512,3,$.1^26 - 2*$.1^25 - 56*$.1^24 + 112*$.1^23 + 1360*$.1^22 - 2697*$.1^21 -
18861*$.1^20 + 36655*$.1^19 + 165783*$.1^18 - 310509*$.1^17 - 970565*$.1^16 + 1709870*$.1^15 + 3873246*$.1^14 - 6194080*$.1^13 - 10579146*$.1^12 + 14580799*$.1^11 + 19436188*$.1^10 - 21403195*$.1^9 - 22833853*$.1^8 + 17959682*$.1^7 + 15322485*$.1^6 - 7282611*$.1^5 - 4620027*$.1^4 + 1147264*$.1^3
+ 536568*$.1^2 - 50646*$.1 - 19573,5,$.1^26 - 5*$.1^25 - 76*$.1^24 + 408*$.1^23
+ 2350*$.1^22 - 14020*$.1^21 - 37353*$.1^20 + 263933*$.1^19 + 308436*$.1^18 - 2970100*$.1^17 - 978578*$.1^16 + 20527286*$.1^15 - 3301588*$.1^14 - 86879933*$.1^13 + 37204504*$.1^12 + 221113241*$.1^11 - 119074256*$.1^10 - 327914224*$.1^9 + 180330624*$.1^8 + 261570439*$.1^7 - 138751056*$.1^6 - 93983582*$.1^5 + 50686447*$.1^4 + 7883301*$.1^3 - 6367075*$.1^2 + 703704*$.1 +
3636,7,$.1^26 - 7*$.1^25 - 94*$.1^24 + 755*$.1^23 + 3376*$.1^22 - 34335*$.1^21 -
50704*$.1^20 + 855286*$.1^19 - 38855*$.1^18 - 12649727*$.1^17 + 12756501*$.1^16 + 111894539*$.1^15 - 196143244*$.1^14 - 557701291*$.1^13 + 1414715108*$.1^12 + 1277746296*$.1^11 - 5200868214*$.1^10 - 218735889*$.1^9 + 9073283331*$.1^8 - 2545605634*$.1^7 - 7481074932*$.1^6 + 2325109394*$.1^5 + 2658406017*$.1^4 - 250096947*$.1^3 - 240212414*$.1^2 + 7413162*$.1 + 6287437,11,$.1^26 - 4*$.1^25 -
177*$.1^24 + 656*$.1^23 + 13862*$.1^22 - 46540*$.1^21 - 636334*$.1^20 + 1880028*$.1^19 + 19069370*$.1^18 - 47726569*$.1^17 - 392271834*$.1^16 + 789666148*$.1^15 + 5655617024*$.1^14 - 8493715936*$.1^13 - 57153539904*$.1^12 + 56629921664*$.1^11 + 396922638976*$.1^10 - 200663798272*$.1^9 -
1812408616960*$.1^8 + 132693870592*$.1^7 + 5016124092416*$.1^6 + 1392906018816*$.1^5 - 7264942759936*$.1^4 - 3756369494016*$.1^3 +
4146471239680*$.1^2 + 2654302830592*$.1 - 147968098304,13,$.1^26 - 27*$.1^25 +
163*$.1^24 + 1928*$.1^23 - 27449*$.1^22 + 23700*$.1^21 + 1267187*$.1^20 - 5766791*$.1^19 - 21347328*$.1^18 + 211203676*$.1^17 - 82055796*$.1^16 - 3557303755*$.1^15 + 8511540838*$.1^14 + 27889892344*$.1^13 - 134521938974*$.1^12 - 27055321906*$.1^11 + 981401106854*$.1^10 - 1155399404446*$.1^9 -
3089614789233*$.1^8 + 7805633569236*$.1^7 + 101494956628*$.1^6 - 16093016897986*$.1^5 + 15461823929882*$.1^4 - 1041139154045*$.1^3 -
3230579452834*$.1^2 + 384994835418*$.1 + 100306912571[]
420,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 2,13,x - 4[]
420,2,2,x,3,x + 1,5,x - 1,7,x - 1,11,x + 2,13,x - 4[]
420,3,2,x,3,x - 1,5,x + 1,7,x - 1,11,x - 6,13,x + 4[]
420,4,2,x,3,x - 1,5,x - 1,7,x + 1,11,x - 2,13,x - 4[]
421,1,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 74*x^11 + 296*x^10 + 488*x^9 -
494*x^8 - 1157*x^7 + 205*x^6 + 1137*x^5 + 203*x^4 - 374*x^3 - 127*x^2 + 3*x +
3,3,x^15 + 9*x^14 + 14*x^13 - 91*x^12 - 305*x^11 + 132*x^10 + 1479*x^9 + 921*x^8
- 2331*x^7 - 2352*x^6 + 977*x^5 + 898*x^4 - 420*x^3 + 17*x^2 + 11*x - 1,5,x^15 +
11*x^14 + 16*x^13 - 230*x^12 - 930*x^11 + 436*x^10 + 7576*x^9 + 7865*x^8 -
19233*x^7 - 37504*x^6 + 6032*x^5 + 47371*x^4 + 18885*x^3 - 11778*x^2 - 5830*x +
349,7,x^15 + 5*x^14 - 50*x^13 - 242*x^12 + 936*x^11 + 4262*x^10 - 8233*x^9 -
33810*x^8 + 36283*x^7 + 126356*x^6 - 89105*x^5 - 218711*x^4 + 124893*x^3 +
148397*x^2 - 75624*x - 13779,11,x^15 + 33*x^14 + 439*x^13 + 2752*x^12 +
4484*x^11 - 47895*x^10 - 329709*x^9 - 710805*x^8 + 700910*x^7 + 6176673*x^6 +
8607514*x^5 - 6970844*x^4 - 27108950*x^3 - 13911998*x^2 + 13470597*x +
10339781,13,x^15 + 8*x^14 - 74*x^13 - 663*x^12 + 1843*x^11 + 19456*x^10 -
24399*x^9 - 279096*x^8 + 231495*x^7 + 2108724*x^6 - 1675809*x^5 - 7940159*x^4 +
7233336*x^3 + 11299279*x^2 - 12659976*x + 1817397[]
421,2,2,x^19 - 4*x^18 - 20*x^17 + 93*x^16 + 145*x^15 - 874*x^14 - 402*x^13 +
4263*x^12 - 159*x^11 - 11551*x^10 + 3133*x^9 + 17375*x^8 - 5935*x^7 - 14018*x^6
+ 4016*x^5 + 5896*x^4 - 1088*x^3 - 1185*x^2 + 101*x + 89,3,x^19 - 7*x^18 -
14*x^17 + 193*x^16 - 93*x^15 - 2088*x^14 + 2959*x^13 + 11085*x^12 - 23111*x^11 -
28776*x^10 + 86085*x^9 + 26346*x^8 - 164972*x^7 + 24505*x^6 + 152723*x^5 -
58753*x^4 - 51424*x^3 + 25848*x^2 - 1440*x - 64,5,x^19 - 7*x^18 - 27*x^17 +
273*x^16 + 101*x^15 - 4023*x^14 + 3046*x^13 + 28479*x^12 - 37573*x^11 -
101239*x^10 + 172591*x^9 + 170130*x^8 - 365278*x^7 - 99967*x^6 + 341999*x^5 -
20468*x^4 - 116495*x^3 + 26317*x^2 + 6952*x - 1367,7,x^19 - 3*x^18 - 66*x^17 +
238*x^16 + 1480*x^15 - 6706*x^14 - 10957*x^13 + 79510*x^12 - 24177*x^11 -
352324*x^10 + 430239*x^9 + 415669*x^8 - 872771*x^7 - 38067*x^6 + 613432*x^5 -
128311*x^4 - 154668*x^3 + 42700*x^2 + 12144*x - 3632,11,x^19 - 31*x^18 +
367*x^17 - 1800*x^16 - 484*x^15 + 43833*x^14 - 166849*x^13 + 49087*x^12 +
1209170*x^11 - 3296987*x^10 + 2907210*x^9 + 1405296*x^8 - 4451506*x^7 +
2474298*x^6 + 577657*x^5 - 1121663*x^4 + 425536*x^3 - 53776*x^2 - 976*x +
368,13,x^19 + 2*x^18 - 116*x^17 - 333*x^16 + 4635*x^15 + 18244*x^14 - 69879*x^13
- 402476*x^12 + 153875*x^11 + 3524646*x^10 + 3806553*x^9 - 10139483*x^8 -
20373936*x^7 + 6415283*x^6 + 34491570*x^5 + 8830049*x^4 - 21836432*x^3 -
9430500*x^2 + 3945040*x + 1163344[]

Errors: /home/mfd/gomagma: line 2: 27485 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 03:30:32 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [419..421] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 03:30:11 on modular  [Seed = 986492925]
-------------------------------------

419,1,2,$.1^9 + 2*$.1^8 - 7*$.1^7 - 13*$.1^6 + 15*$.1^5 + 25*$.1^4 - 9*$.1^3 - 15*$.1^2 - $.1 + 1,3,$.1^9 + 4*$.1^8 - 4*$.1^7 - 28*$.1^6 - 9*$.1^5 + 47*$.1^4 + 29*$.1^3 - 15*$.1^2 - 9*$.1 + 1,5,$.1^9 + 5*$.1^8 - 4*$.1^7 - 35*$.1^6 + 2*$.1^5 + 54*$.1^4 - 8*$.1^3 - 17*$.1^2 + 1,7,$.1^9 + 7*$.1^8 - 101*$.1^6 - 215*$.1^5 +
118*$.1^4 + 666*$.1^3 + 271*$.1^2 - 483*$.1 - 307,11,$.1^9 + 6*$.1^8 - 3*$.1^7 - 60*$.1^6 - 50*$.1^5 + 144*$.1^4 + 200*$.1^3 + 28*$.1^2 - 8*$.1 - 1,13,$.1^9 +
19*$.1^8 + 135*$.1^7 + 408*$.1^6 + 214*$.1^5 - 1651*$.1^4 - 3652*$.1^3 -
1917*$.1^2 + 1271*$.1 + 1093[]
419,2,2,$.1^26 - 2*$.1^25 - 43*$.1^24 + 85*$.1^23 + 807*$.1^22 - 1571*$.1^21 -
8689*$.1^20 + 16575*$.1^19 + 59362*$.1^18 - 110217*$.1^17 - 268789*$.1^16 + 481513*$.1^15 + 817911*$.1^14 - 1398615*$.1^13 - 1658267*$.1^12 + 2674771*$.1^11
+ 2166607*$.1^10 - 3262315*$.1^9 - 1701132*$.1^8 + 2384864*$.1^7 + 697992*$.1^6 - 932912*$.1^5 - 104448*$.1^4 + 158080*$.1^3 - 4736*$.1^2 - 6656*$.1 +
512,3,$.1^26 - 2*$.1^25 - 56*$.1^24 + 112*$.1^23 + 1360*$.1^22 - 2697*$.1^21 -
18861*$.1^20 + 36655*$.1^19 + 165783*$.1^18 - 310509*$.1^17 - 970565*$.1^16 + 1709870*$.1^15 + 3873246*$.1^14 - 6194080*$.1^13 - 10579146*$.1^12 + 14580799*$.1^11 + 19436188*$.1^10 - 21403195*$.1^9 - 22833853*$.1^8 + 17959682*$.1^7 + 15322485*$.1^6 - 7282611*$.1^5 - 4620027*$.1^4 + 1147264*$.1^3
+ 536568*$.1^2 - 50646*$.1 - 19573,5,$.1^26 - 5*$.1^25 - 76*$.1^24 + 408*$.1^23
+ 2350*$.1^22 - 14020*$.1^21 - 37353*$.1^20 + 263933*$.1^19 + 308436*$.1^18 - 2970100*$.1^17 - 978578*$.1^16 + 20527286*$.1^15 - 3301588*$.1^14 - 86879933*$.1^13 + 37204504*$.1^12 + 221113241*$.1^11 - 119074256*$.1^10 - 327914224*$.1^9 + 180330624*$.1^8 + 261570439*$.1^7 - 138751056*$.1^6 - 93983582*$.1^5 + 50686447*$.1^4 + 7883301*$.1^3 - 6367075*$.1^2 + 703704*$.1 +
3636,7,$.1^26 - 7*$.1^25 - 94*$.1^24 + 755*$.1^23 + 3376*$.1^22 - 34335*$.1^21 -
50704*$.1^20 + 855286*$.1^19 - 38855*$.1^18 - 12649727*$.1^17 + 12756501*$.1^16 + 111894539*$.1^15 - 196143244*$.1^14 - 557701291*$.1^13 + 1414715108*$.1^12 + 1277746296*$.1^11 - 5200868214*$.1^10 - 218735889*$.1^9 + 9073283331*$.1^8 - 2545605634*$.1^7 - 7481074932*$.1^6 + 2325109394*$.1^5 + 2658406017*$.1^4 - 250096947*$.1^3 - 240212414*$.1^2 + 7413162*$.1 + 6287437,11,$.1^26 - 4*$.1^25 -
177*$.1^24 + 656*$.1^23 + 13862*$.1^22 - 46540*$.1^21 - 636334*$.1^20 + 1880028*$.1^19 + 19069370*$.1^18 - 47726569*$.1^17 - 392271834*$.1^16 + 789666148*$.1^15 + 5655617024*$.1^14 - 8493715936*$.1^13 - 57153539904*$.1^12 + 56629921664*$.1^11 + 396922638976*$.1^10 - 200663798272*$.1^9 -
1812408616960*$.1^8 + 132693870592*$.1^7 + 5016124092416*$.1^6 + 1392906018816*$.1^5 - 7264942759936*$.1^4 - 3756369494016*$.1^3 +
4146471239680*$.1^2 + 2654302830592*$.1 - 147968098304,13,$.1^26 - 27*$.1^25 +
163*$.1^24 + 1928*$.1^23 - 27449*$.1^22 + 23700*$.1^21 + 1267187*$.1^20 - 5766791*$.1^19 - 21347328*$.1^18 + 211203676*$.1^17 - 82055796*$.1^16 - 3557303755*$.1^15 + 8511540838*$.1^14 + 27889892344*$.1^13 - 134521938974*$.1^12 - 27055321906*$.1^11 + 981401106854*$.1^10 - 1155399404446*$.1^9 -
3089614789233*$.1^8 + 7805633569236*$.1^7 + 101494956628*$.1^6 - 16093016897986*$.1^5 + 15461823929882*$.1^4 - 1041139154045*$.1^3 -
3230579452834*$.1^2 + 384994835418*$.1 + 100306912571[]
420,1,2,x,3,x + 1,5,x + 1,7,x + 1,11,x - 2,13,x - 4[]
420,2,2,x,3,x + 1,5,x - 1,7,x - 1,11,x + 2,13,x - 4[]
420,3,2,x,3,x - 1,5,x + 1,7,x - 1,11,x - 6,13,x + 4[]
420,4,2,x,3,x - 1,5,x - 1,7,x + 1,11,x - 2,13,x - 4[]
421,1,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 74*x^11 + 296*x^10 + 488*x^9 -
494*x^8 - 1157*x^7 + 205*x^6 + 1137*x^5 + 203*x^4 - 374*x^3 - 127*x^2 + 3*x +
3,3,x^15 + 9*x^14 + 14*x^13 - 91*x^12 - 305*x^11 + 132*x^10 + 1479*x^9 + 921*x^8
- 2331*x^7 - 2352*x^6 + 977*x^5 + 898*x^4 - 420*x^3 + 17*x^2 + 11*x - 1,5,x^15 +
11*x^14 + 16*x^13 - 230*x^12 - 930*x^11 + 436*x^10 + 7576*x^9 + 7865*x^8 -
19233*x^7 - 37504*x^6 + 6032*x^5 + 47371*x^4 + 18885*x^3 - 11778*x^2 - 5830*x +
349,7,x^15 + 5*x^14 - 50*x^13 - 242*x^12 + 936*x^11 + 4262*x^10 - 8233*x^9 -
33810*x^8 + 36283*x^7 + 126356*x^6 - 89105*x^5 - 218711*x^4 + 124893*x^3 +
148397*x^2 - 75624*x - 13779,11,x^15 + 33*x^14 + 439*x^13 + 2752*x^12 +
4484*x^11 - 47895*x^10 - 329709*x^9 - 710805*x^8 + 700910*x^7 + 6176673*x^6 +
8607514*x^5 - 6970844*x^4 - 27108950*x^3 - 13911998*x^2 + 13470597*x +
10339781,13,x^15 + 8*x^14 - 74*x^13 - 663*x^12 + 1843*x^11 + 19456*x^10 -
24399*x^9 - 279096*x^8 + 231495*x^7 + 2108724*x^6 - 1675809*x^5 - 7940159*x^4 +
7233336*x^3 + 11299279*x^2 - 12659976*x + 1817397[]
421,2,2,x^19 - 4*x^18 - 20*x^17 + 93*x^16 + 145*x^15 - 874*x^14 - 402*x^13 +
4263*x^12 - 159*x^11 - 11551*x^10 + 3133*x^9 + 17375*x^8 - 5935*x^7 - 14018*x^6
+ 4016*x^5 + 5896*x^4 - 1088*x^3 - 1185*x^2 + 101*x + 89,3,x^19 - 7*x^18 -
14*x^17 + 193*x^16 - 93*x^15 - 2088*x^14 + 2959*x^13 + 11085*x^12 - 23111*x^11 -
28776*x^10 + 86085*x^9 + 26346*x^8 - 164972*x^7 + 24505*x^6 + 152723*x^5 -
58753*x^4 - 51424*x^3 + 25848*x^2 - 1440*x - 64,5,x^19 - 7*x^18 - 27*x^17 +
273*x^16 + 101*x^15 - 4023*x^14 + 3046*x^13 + 28479*x^12 - 37573*x^11 -
101239*x^10 + 172591*x^9 + 170130*x^8 - 365278*x^7 - 99967*x^6 + 341999*x^5 -
20468*x^4 - 116495*x^3 + 26317*x^2 + 6952*x - 1367,7,x^19 - 3*x^18 - 66*x^17 +
238*x^16 + 1480*x^15 - 6706*x^14 - 10957*x^13 + 79510*x^12 - 24177*x^11 -
352324*x^10 + 430239*x^9 + 415669*x^8 - 872771*x^7 - 38067*x^6 + 613432*x^5 -
128311*x^4 - 154668*x^3 + 42700*x^2 + 12144*x - 3632,11,x^19 - 31*x^18 +
367*x^17 - 1800*x^16 - 484*x^15 + 43833*x^14 - 166849*x^13 + 49087*x^12 +
1209170*x^11 - 3296987*x^10 + 2907210*x^9 + 1405296*x^8 - 4451506*x^7 +
2474298*x^6 + 577657*x^5 - 1121663*x^4 + 425536*x^3 - 53776*x^2 - 976*x +
368,13,x^19 + 2*x^18 - 116*x^17 - 333*x^16 + 4635*x^15 + 18244*x^14 - 69879*x^13
- 402476*x^12 + 153875*x^11 + 3524646*x^10 + 3806553*x^9 - 10139483*x^8 -
20373936*x^7 + 6415283*x^6 + 34491570*x^5 + 8830049*x^4 - 21836432*x^3 -
9430500*x^2 + 3945040*x + 1163344[]

Total time: 19.100 seconds, Total memory usage: 6.25MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 03:36:08 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [421..425] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 03:35:49 on modular  [Seed = 702528920]
-------------------------------------

421,1,2,$.1^15 + 6*$.1^14 - 2*$.1^13 - 71*$.1^12 - 74*$.1^11 + 296*$.1^10 +
488*$.1^9 - 494*$.1^8 - 1157*$.1^7 + 205*$.1^6 + 1137*$.1^5 + 203*$.1^4 -
374*$.1^3 - 127*$.1^2 + 3*$.1 + 3,3,$.1^15 + 9*$.1^14 + 14*$.1^13 - 91*$.1^12 - 305*$.1^11 + 132*$.1^10 + 1479*$.1^9 + 921*$.1^8 - 2331*$.1^7 - 2352*$.1^6 + 977*$.1^5 + 898*$.1^4 - 420*$.1^3 + 17*$.1^2 + 11*$.1 - 1,5,$.1^15 + 11*$.1^14 +
16*$.1^13 - 230*$.1^12 - 930*$.1^11 + 436*$.1^10 + 7576*$.1^9 + 7865*$.1^8 -
19233*$.1^7 - 37504*$.1^6 + 6032*$.1^5 + 47371*$.1^4 + 18885*$.1^3 - 11778*$.1^2
- 5830*$.1 + 349,7,$.1^15 + 5*$.1^14 - 50*$.1^13 - 242*$.1^12 + 936*$.1^11 +
4262*$.1^10 - 8233*$.1^9 - 33810*$.1^8 + 36283*$.1^7 + 126356*$.1^6 - 89105*$.1^5 - 218711*$.1^4 + 124893*$.1^3 + 148397*$.1^2 - 75624*$.1 -
13779,11,$.1^15 + 33*$.1^14 + 439*$.1^13 + 2752*$.1^12 + 4484*$.1^11 - 47895*$.1^10 - 329709*$.1^9 - 710805*$.1^8 + 700910*$.1^7 + 6176673*$.1^6 +
8607514*$.1^5 - 6970844*$.1^4 - 27108950*$.1^3 - 13911998*$.1^2 + 13470597*$.1 + 10339781,13,$.1^15 + 8*$.1^14 - 74*$.1^13 - 663*$.1^12 + 1843*$.1^11 +
19456*$.1^10 - 24399*$.1^9 - 279096*$.1^8 + 231495*$.1^7 + 2108724*$.1^6 - 1675809*$.1^5 - 7940159*$.1^4 + 7233336*$.1^3 + 11299279*$.1^2 - 12659976*$.1 +
1817397[]
421,2,2,$.1^19 - 4*$.1^18 - 20*$.1^17 + 93*$.1^16 + 145*$.1^15 - 874*$.1^14 -
402*$.1^13 + 4263*$.1^12 - 159*$.1^11 - 11551*$.1^10 + 3133*$.1^9 + 17375*$.1^8
- 5935*$.1^7 - 14018*$.1^6 + 4016*$.1^5 + 5896*$.1^4 - 1088*$.1^3 - 1185*$.1^2 +
101*$.1 + 89,3,$.1^19 - 7*$.1^18 - 14*$.1^17 + 193*$.1^16 - 93*$.1^15 -
2088*$.1^14 + 2959*$.1^13 + 11085*$.1^12 - 23111*$.1^11 - 28776*$.1^10 + 86085*$.1^9 + 26346*$.1^8 - 164972*$.1^7 + 24505*$.1^6 + 152723*$.1^5 -
58753*$.1^4 - 51424*$.1^3 + 25848*$.1^2 - 1440*$.1 - 64,5,$.1^19 - 7*$.1^18 -
27*$.1^17 + 273*$.1^16 + 101*$.1^15 - 4023*$.1^14 + 3046*$.1^13 + 28479*$.1^12 -
37573*$.1^11 - 101239*$.1^10 + 172591*$.1^9 + 170130*$.1^8 - 365278*$.1^7 - 99967*$.1^6 + 341999*$.1^5 - 20468*$.1^4 - 116495*$.1^3 + 26317*$.1^2 + 6952*$.1 - 1367,7,$.1^19 - 3*$.1^18 - 66*$.1^17 + 238*$.1^16 + 1480*$.1^15 - 6706*$.1^14 - 10957*$.1^13 + 79510*$.1^12 - 24177*$.1^11 - 352324*$.1^10 + 430239*$.1^9 +
415669*$.1^8 - 872771*$.1^7 - 38067*$.1^6 + 613432*$.1^5 - 128311*$.1^4 - 154668*$.1^3 + 42700*$.1^2 + 12144*$.1 - 3632,11,$.1^19 - 31*$.1^18 + 367*$.1^17 - 1800*$.1^16 - 484*$.1^15 + 43833*$.1^14 - 166849*$.1^13 + 49087*$.1^12 +
1209170*$.1^11 - 3296987*$.1^10 + 2907210*$.1^9 + 1405296*$.1^8 - 4451506*$.1^7 + 2474298*$.1^6 + 577657*$.1^5 - 1121663*$.1^4 + 425536*$.1^3 - 53776*$.1^2 -
976*$.1 + 368,13,$.1^19 + 2*$.1^18 - 116*$.1^17 - 333*$.1^16 + 4635*$.1^15 +
18244*$.1^14 - 69879*$.1^13 - 402476*$.1^12 + 153875*$.1^11 + 3524646*$.1^10 + 3806553*$.1^9 - 10139483*$.1^8 - 20373936*$.1^7 + 6415283*$.1^6 + 34491570*$.1^5
+ 8830049*$.1^4 - 21836432*$.1^3 - 9430500*$.1^2 + 3945040*$.1 + 1163344[]
422,1,2,x + 1,3,x,5,x - 1,7,x + 2,11,x + 3,13,x + 7[]
422,2,2,x^2 + 2*x + 1,3,x^2 - 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - 8*x + 16,11,x^2 -
2*x - 4,13,x^2[]
422,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 8*x - 3,5,x^3 + 5*x^2 + 4*x -
1,7,x^3 + 5*x^2 - 9,11,x^3 - 9*x^2 + 22*x - 15,13,x^3 + 11*x^2 + 30*x - 1[]
422,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 6*x - 5,5,x^3 - x^2 - 10*x +
15,7,x^3 - x^2 - 6*x + 5,11,x^3 + 5*x^2 - 8*x - 3,13,x^3 - 11*x^2 + 34*x - 29[]
422,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 5*x^2 + 6*x + 1,5,x^3 + 3*x^2 - 4*x -
13,7,x^3 + 9*x^2 + 20*x - 1,11,x^3 + 5*x^2 - 8*x - 41,13,x^3 + 7*x^2 - 49[]
422,6,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 4*x^5 - 4*x^4 +
28*x^3 - 15*x^2 - 33*x + 28,5,x^6 + 2*x^5 - 11*x^4 - 9*x^3 + 35*x^2 + 6*x -
28,7,x^6 - 7*x^5 + 4*x^4 + 45*x^3 - 30*x^2 - 88*x - 32,11,x^6 - 4*x^5 - 25*x^4 +
103*x^3 + 11*x^2 - 182*x - 68,13,x^6 - 8*x^5 - 17*x^4 + 127*x^3 + 293*x^2 + 56*x
- 64[]
423,1,2,x + 2,3,x,5,x + 3,7,x - 1,11,x - 3,13,x[]
423,2,2,x - 2,3,x,5,x - 3,7,x - 1,11,x + 3,13,x[]
423,3,2,x - 1,3,x,5,x,7,x - 4,11,x,13,x - 6[]
423,4,2,x - 2,3,x,5,x - 3,7,x + 3,11,x - 5,13,x - 2[]
423,5,2,x,3,x,5,x - 1,7,x + 3,11,x - 3,13,x + 4[]
423,6,2,x - 1,3,x,5,x + 2,7,x,11,x + 4,13,x + 2[]
423,7,2,x + 2,3,x,5,x - 1,7,x + 3,11,x + 1,13,x + 2[]
423,8,2,x^2 - x - 4,3,x^2,5,x^2 + x - 4,7,x^2 - x - 4,11,x^2 + 7*x + 8,13,x^2 +
6*x - 8[]
423,9,2,x^3 + 2*x^2 - 3*x - 2,3,x^3,5,x^3 + x^2 - 4*x - 2,7,x^3 + 3*x^2 - 4*x -
8,11,x^3 + 9*x^2 + 20*x + 8,13,x^3 + 4*x^2 - 12*x - 16[]
423,10,2,x^3 - 2*x^2 - 3*x + 2,3,x^3,5,x^3 - x^2 - 4*x + 2,7,x^3 + 3*x^2 - 4*x -
8,11,x^3 - 9*x^2 + 20*x - 8,13,x^3 + 4*x^2 - 12*x - 16[]
423,11,2,x^4 + x^3 - 5*x^2 - 5*x - 1,3,x^4,5,x^4 - 2*x^3 - 16*x^2 + 16*x +
48,7,x^4 - 4*x^3 - 7*x^2 + 44*x - 43,11,x^4 - 6*x^3 - 4*x^2 + 56*x - 48,13,x^4 -
8*x^3 + 56*x + 48[]
424,1,2,x^2,3,x^2 + 2*x - 1,5,x^2 + 4*x + 4,7,x^2 - 4*x - 4,11,x^2 + 4*x -
4,13,x^2 + 6*x + 1[]
424,2,2,x^3,3,x^3 - 2*x^2 - 3*x + 2,5,x^3 - 3*x^2 - 4*x + 4,7,x^3 - 6*x^2 + 12*x
- 8,11,x^3 - 5*x^2 - 8*x + 44,13,x^3 + 6*x^2 + 5*x - 4[]
424,3,2,x^3,3,x^3 + x^2 - 3*x - 1,5,x^3 + 2*x^2 - 8*x + 4,7,x^3 + 8*x^2 + 16*x +
4,11,x^3 + 4*x^2 - 4*x - 20,13,x^3 + x^2 - 21*x - 13[]
424,4,2,x^5,3,x^5 - x^4 - 13*x^3 + 9*x^2 + 42*x - 16,5,x^5 - 5*x^4 - 8*x^3 +
56*x^2 + 4*x - 136,7,x^5 + 6*x^4 - 8*x^3 - 60*x^2 + 40*x + 64,11,x^5 - 5*x^4 -
8*x^3 + 32*x^2 + 52*x + 16,13,x^5 - 9*x^4 + 17*x^3 + 29*x^2 - 78*x + 8[]
425,1,2,x - 1,3,x,5,x,7,x + 4,11,x,13,x - 2[]
425,2,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 4,13,x - 1[]
425,3,2,x + 1,3,x + 2,5,x,7,x - 2,11,x - 2,13,x + 2[]
425,4,2,x - 1,3,x + 1,5,x,7,x - 1,11,x + 4,13,x + 1[]
425,5,2,x^2 - 3,3,x^2 + 2*x - 2,5,x^2,7,x^2 - 2*x - 2,11,x^2 - 6*x + 6,13,x^2 -
8*x + 16[]
425,6,2,x^2 - 2*x - 1,3,x^2 - 4*x + 2,5,x^2,7,x^2 - 4*x + 2,11,x^2 + 8*x +
14,13,x^2 - 8[]
425,7,2,x^4 - 2*x^3 - 4*x^2 + 8*x - 1,3,x^4 - 4*x^3 + 10*x - 2,5,x^4,7,x^4 -
10*x^3 + 32*x^2 - 38*x + 14,11,x^4 + 2*x^3 - 14*x^2 - 26*x + 2,13,x^4 - 6*x^3 -
28*x^2 + 192*x - 164[]
425,8,2,x^4 + 2*x^3 - 4*x^2 - 8*x - 1,3,x^4 + 4*x^3 - 10*x - 2,5,x^4,7,x^4 +
10*x^3 + 32*x^2 + 38*x + 14,11,x^4 + 2*x^3 - 14*x^2 - 26*x + 2,13,x^4 + 6*x^3 -
28*x^2 - 192*x - 164[]
425,9,2,x^5 + x^4 - 10*x^3 - 6*x^2 + 21*x - 3,3,x^5 - x^4 - 10*x^3 + 10*x^2 +
23*x - 25,5,x^5,7,x^5 - x^4 - 22*x^3 + 2*x^2 + 109*x + 97,11,x^5 - 4*x^4 -
22*x^3 + 120*x^2 - 156*x + 60,13,x^5 + 3*x^4 - 26*x^3 - 58*x^2 + 177*x + 227[]
425,10,2,x^5 - x^4 - 10*x^3 + 6*x^2 + 21*x + 3,3,x^5 + x^4 - 10*x^3 - 10*x^2 +
23*x + 25,5,x^5,7,x^5 + x^4 - 22*x^3 - 2*x^2 + 109*x - 97,11,x^5 - 4*x^4 -
22*x^3 + 120*x^2 - 156*x + 60,13,x^5 - 3*x^4 - 26*x^3 + 58*x^2 + 177*x - 227[]

Total time: 17.309 seconds, Total memory usage: 5.36MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 04:11:26 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [425..430] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 04:10:39 on modular  [Seed = 1904736817]
-------------------------------------

425,1,2,$.1 - 1,3,$.1,5,$.1,7,$.1 + 4,11,$.1,13,$.1 - 2[]
425,2,2,$.1 + 1,3,$.1 - 1,5,$.1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[]
425,3,2,$.1 + 1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1 - 2,13,$.1 + 2[]
425,4,2,$.1 - 1,3,$.1 + 1,5,$.1,7,$.1 - 1,11,$.1 + 4,13,$.1 + 1[]
425,5,2,$.1^2 - 3,3,$.1^2 + 2*$.1 - 2,5,$.1^2,7,$.1^2 - 2*$.1 - 2,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 8*$.1 + 16[]
425,6,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2,7,$.1^2 - 4*$.1 + 2,11,$.1^2 + 8*$.1 + 14,13,$.1^2 - 8[]
425,7,2,$.1^4 - 2*$.1^3 - 4*$.1^2 + 8*$.1 - 1,3,$.1^4 - 4*$.1^3 + 10*$.1 - 2,5,$.1^4,7,$.1^4 - 10*$.1^3 + 32*$.1^2 - 38*$.1 + 14,11,$.1^4 + 2*$.1^3 -
14*$.1^2 - 26*$.1 + 2,13,$.1^4 - 6*$.1^3 - 28*$.1^2 + 192*$.1 - 164[]
425,8,2,$.1^4 + 2*$.1^3 - 4*$.1^2 - 8*$.1 - 1,3,$.1^4 + 4*$.1^3 - 10*$.1 - 2,5,$.1^4,7,$.1^4 + 10*$.1^3 + 32*$.1^2 + 38*$.1 + 14,11,$.1^4 + 2*$.1^3 -
14*$.1^2 - 26*$.1 + 2,13,$.1^4 + 6*$.1^3 - 28*$.1^2 - 192*$.1 - 164[]
425,9,2,$.1^5 +$.1^4 - 10*$.1^3 - 6*$.1^2 + 21*$.1 - 3,3,$.1^5 - $.1^4 - 10*$.1^3 + 10*$.1^2 + 23*$.1 - 25,5,$.1^5,7,$.1^5 - $.1^4 - 22*$.1^3 + 2*$.1^2 + 109*$.1 + 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 +
3*$.1^4 - 26*$.1^3 - 58*$.1^2 + 177*$.1 + 227[]
425,10,2,$.1^5 -$.1^4 - 10*$.1^3 + 6*$.1^2 + 21*$.1 + 3,3,$.1^5 + $.1^4 - 10*$.1^3 - 10*$.1^2 + 23*$.1 + 25,5,$.1^5,7,$.1^5 + $.1^4 - 22*$.1^3 - 2*$.1^2 + 109*$.1 - 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 -
3*$.1^4 - 26*$.1^3 + 58*$.1^2 + 177*$.1 - 227[]
426,1,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x + 2,13,x[]
426,2,2,x + 1,3,x - 1,5,x - 3,7,x + 1,11,x - 3,13,x - 2[]
426,3,2,x - 1,3,x - 1,5,x - 1,7,x - 3,11,x + 3,13,x + 6[]
426,4,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 7,7,x^2 + 2*x - 17,11,x^2 -
10*x + 23,13,x^2 + 8*x + 8[]
426,5,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 - 5*x + 2,11,x^2 + x
- 4,13,x^2 - 4*x + 4[]
426,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 3*x +
10,7,x^3 - 2*x^2 - 5*x + 8,11,x^3 - 2*x^2 - 29*x + 80,13,x^3 - 2*x^2 - 24*x -
16[]
426,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - x^2 - 12*x +
4,7,x^3 + x^2 - 12*x - 4,11,x^3 - 3*x^2 - 10*x + 28,13,x^3 - 8*x^2 + 56[]
427,1,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 5,13,x - 4[]
427,2,2,x,3,x - 2,5,x - 4,7,x - 1,11,x + 2,13,x - 2[]
427,3,2,x - 1,3,x - 1,5,x + 4,7,x - 1,11,x + 3,13,x + 4[]
427,4,2,x^6 + 5*x^5 + 2*x^4 - 18*x^3 - 12*x^2 + 18*x + 5,3,x^6 - 10*x^4 - 5*x^3
+ 16*x^2 + 12*x + 1,5,x^6 + 5*x^5 - 3*x^4 - 36*x^3 - 19*x^2 + 32*x + 21,7,x^6 +
6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 6*x^5 + 5*x^4 - 15*x^3 -
14*x^2 + x + 1,13,x^6 + 13*x^5 + 15*x^4 - 368*x^3 - 1050*x^2 + 2495*x + 8275[]
427,5,2,x^6 + 5*x^5 + 2*x^4 - 22*x^3 - 30*x^2 + 9,3,x^6 + 8*x^5 + 18*x^4 - 3*x^3
- 44*x^2 - 18*x + 17,5,x^6 + 9*x^5 + 21*x^4 - 10*x^3 - 57*x^2 + 9,7,x^6 - 6*x^5
+ 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 43*x^4 + 7*x^3 + 534*x^2 - 141*x -
1635,13,x^6 + 5*x^5 - 13*x^4 + 8*x^2 - x - 1[]
427,6,2,x^7 - 4*x^6 - 3*x^5 + 26*x^4 - 12*x^3 - 38*x^2 + 23*x + 11,3,x^7 - x^6 -
12*x^5 + 9*x^4 + 37*x^3 - 18*x^2 - 19*x + 1,5,x^7 - 7*x^6 + 11*x^5 + 18*x^4 -
47*x^3 - 8*x^2 + 41*x + 4,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 +
7*x - 1,11,x^7 - x^6 - 27*x^5 + 82*x^4 - 47*x^3 - 59*x^2 + 60*x - 13,13,x^7 -
5*x^6 - 49*x^5 + 258*x^4 + 284*x^3 - 2365*x^2 + 1135*x + 2792[]
427,7,2,x^9 - 5*x^8 - 3*x^7 + 45*x^6 - 32*x^5 - 108*x^4 + 123*x^3 + 30*x^2 -
43*x + 4,3,x^9 + x^8 - 18*x^7 - 13*x^6 + 105*x^5 + 42*x^4 - 205*x^3 - 9*x^2 +
50*x + 8,5,x^9 - 9*x^8 + 13*x^7 + 78*x^6 - 193*x^5 - 190*x^4 + 693*x^3 - 14*x^2
- 768*x + 384,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 +
36*x^2 + 9*x + 1,11,x^9 - 3*x^8 - 39*x^7 + 88*x^6 + 261*x^5 - 779*x^4 + 470*x^3
+ 65*x^2 - 62*x - 8,13,x^9 - 13*x^8 + 39*x^7 + 142*x^6 - 906*x^5 + 595*x^4 +
3819*x^3 - 6580*x^2 + 804*x + 2432[]
428,1,2,x,3,x - 1,5,x - 2,7,x - 4,11,x + 3,13,x - 5[]
428,2,2,x,3,x + 1,5,x - 2,7,x + 4,11,x + 5,13,x - 1[]
428,3,2,x^2,3,x^2 + 3*x - 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 2*x +
1,13,x^2 + 4*x + 4[]
428,4,2,x^5,3,x^5 - 5*x^4 - 2*x^3 + 32*x^2 - 10*x - 43,5,x^5 + x^4 - 21*x^3 -
12*x^2 + 108*x + 24,7,x^5 - 6*x^4 - x^3 + 34*x^2 - 40,11,x^5 - 6*x^4 + 33*x^2 -
3*x - 9,13,x^5 + 8*x^4 - 23*x^3 - 185*x^2 + 236*x + 436[]

Errors: /home/mfd/gomagma: line 2: 28192 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 04:12:32 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [425..428] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 04:11:45 on modular  [Seed = 2039476857]
-------------------------------------

425,1,2,$.1 - 1,3,$.1,5,$.1,7,$.1 + 4,11,$.1,13,$.1 - 2[]
425,2,2,$.1 + 1,3,$.1 - 1,5,$.1,7,$.1 + 1,11,$.1 + 4,13,$.1 - 1[]
425,3,2,$.1 + 1,3,$.1 + 2,5,$.1,7,$.1 - 2,11,$.1 - 2,13,$.1 + 2[]
425,4,2,$.1 - 1,3,$.1 + 1,5,$.1,7,$.1 - 1,11,$.1 + 4,13,$.1 + 1[]
425,5,2,$.1^2 - 3,3,$.1^2 + 2*$.1 - 2,5,$.1^2,7,$.1^2 - 2*$.1 - 2,11,$.1^2 - 6*$.1 + 6,13,$.1^2 - 8*$.1 + 16[]
425,6,2,$.1^2 - 2*$.1 - 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2,7,$.1^2 - 4*$.1 + 2,11,$.1^2 + 8*$.1 + 14,13,$.1^2 - 8[]
425,7,2,$.1^4 - 2*$.1^3 - 4*$.1^2 + 8*$.1 - 1,3,$.1^4 - 4*$.1^3 + 10*$.1 - 2,5,$.1^4,7,$.1^4 - 10*$.1^3 + 32*$.1^2 - 38*$.1 + 14,11,$.1^4 + 2*$.1^3 -
14*$.1^2 - 26*$.1 + 2,13,$.1^4 - 6*$.1^3 - 28*$.1^2 + 192*$.1 - 164[]
425,8,2,$.1^4 + 2*$.1^3 - 4*$.1^2 - 8*$.1 - 1,3,$.1^4 + 4*$.1^3 - 10*$.1 - 2,5,$.1^4,7,$.1^4 + 10*$.1^3 + 32*$.1^2 + 38*$.1 + 14,11,$.1^4 + 2*$.1^3 -
14*$.1^2 - 26*$.1 + 2,13,$.1^4 + 6*$.1^3 - 28*$.1^2 - 192*$.1 - 164[]
425,9,2,$.1^5 +$.1^4 - 10*$.1^3 - 6*$.1^2 + 21*$.1 - 3,3,$.1^5 - $.1^4 - 10*$.1^3 + 10*$.1^2 + 23*$.1 - 25,5,$.1^5,7,$.1^5 - $.1^4 - 22*$.1^3 + 2*$.1^2 + 109*$.1 + 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 +
3*$.1^4 - 26*$.1^3 - 58*$.1^2 + 177*$.1 + 227[]
425,10,2,$.1^5 -$.1^4 - 10*$.1^3 + 6*$.1^2 + 21*$.1 + 3,3,$.1^5 + $.1^4 - 10*$.1^3 - 10*$.1^2 + 23*$.1 + 25,5,$.1^5,7,$.1^5 + $.1^4 - 22*$.1^3 - 2*$.1^2 + 109*$.1 - 97,11,$.1^5 - 4*$.1^4 - 22*$.1^3 + 120*$.1^2 - 156*$.1 + 60,13,$.1^5 -
3*$.1^4 - 26*$.1^3 + 58*$.1^2 + 177*$.1 - 227[]
426,1,2,x + 1,3,x + 1,5,x + 2,7,x - 2,11,x + 2,13,x[]
426,2,2,x + 1,3,x - 1,5,x - 3,7,x + 1,11,x - 3,13,x - 2[]
426,3,2,x - 1,3,x - 1,5,x - 1,7,x - 3,11,x + 3,13,x + 6[]
426,4,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x - 7,7,x^2 + 2*x - 17,11,x^2 -
10*x + 23,13,x^2 + 8*x + 8[]
426,5,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 - 5*x + 2,11,x^2 + x
- 4,13,x^2 - 4*x + 4[]
426,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 4*x^2 - 3*x +
10,7,x^3 - 2*x^2 - 5*x + 8,11,x^3 - 2*x^2 - 29*x + 80,13,x^3 - 2*x^2 - 24*x -
16[]
426,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - x^2 - 12*x +
4,7,x^3 + x^2 - 12*x - 4,11,x^3 - 3*x^2 - 10*x + 28,13,x^3 - 8*x^2 + 56[]
427,1,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 5,13,x - 4[]
427,2,2,x,3,x - 2,5,x - 4,7,x - 1,11,x + 2,13,x - 2[]
427,3,2,x - 1,3,x - 1,5,x + 4,7,x - 1,11,x + 3,13,x + 4[]
427,4,2,x^6 + 5*x^5 + 2*x^4 - 18*x^3 - 12*x^2 + 18*x + 5,3,x^6 - 10*x^4 - 5*x^3
+ 16*x^2 + 12*x + 1,5,x^6 + 5*x^5 - 3*x^4 - 36*x^3 - 19*x^2 + 32*x + 21,7,x^6 +
6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 6*x^5 + 5*x^4 - 15*x^3 -
14*x^2 + x + 1,13,x^6 + 13*x^5 + 15*x^4 - 368*x^3 - 1050*x^2 + 2495*x + 8275[]
427,5,2,x^6 + 5*x^5 + 2*x^4 - 22*x^3 - 30*x^2 + 9,3,x^6 + 8*x^5 + 18*x^4 - 3*x^3
- 44*x^2 - 18*x + 17,5,x^6 + 9*x^5 + 21*x^4 - 10*x^3 - 57*x^2 + 9,7,x^6 - 6*x^5
+ 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 - 43*x^4 + 7*x^3 + 534*x^2 - 141*x -
1635,13,x^6 + 5*x^5 - 13*x^4 + 8*x^2 - x - 1[]
427,6,2,x^7 - 4*x^6 - 3*x^5 + 26*x^4 - 12*x^3 - 38*x^2 + 23*x + 11,3,x^7 - x^6 -
12*x^5 + 9*x^4 + 37*x^3 - 18*x^2 - 19*x + 1,5,x^7 - 7*x^6 + 11*x^5 + 18*x^4 -
47*x^3 - 8*x^2 + 41*x + 4,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 +
7*x - 1,11,x^7 - x^6 - 27*x^5 + 82*x^4 - 47*x^3 - 59*x^2 + 60*x - 13,13,x^7 -
5*x^6 - 49*x^5 + 258*x^4 + 284*x^3 - 2365*x^2 + 1135*x + 2792[]
427,7,2,x^9 - 5*x^8 - 3*x^7 + 45*x^6 - 32*x^5 - 108*x^4 + 123*x^3 + 30*x^2 -
43*x + 4,3,x^9 + x^8 - 18*x^7 - 13*x^6 + 105*x^5 + 42*x^4 - 205*x^3 - 9*x^2 +
50*x + 8,5,x^9 - 9*x^8 + 13*x^7 + 78*x^6 - 193*x^5 - 190*x^4 + 693*x^3 - 14*x^2
- 768*x + 384,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 +
36*x^2 + 9*x + 1,11,x^9 - 3*x^8 - 39*x^7 + 88*x^6 + 261*x^5 - 779*x^4 + 470*x^3
+ 65*x^2 - 62*x - 8,13,x^9 - 13*x^8 + 39*x^7 + 142*x^6 - 906*x^5 + 595*x^4 +
3819*x^3 - 6580*x^2 + 804*x + 2432[]
428,1,2,x,3,x - 1,5,x - 2,7,x - 4,11,x + 3,13,x - 5[]
428,2,2,x,3,x + 1,5,x - 2,7,x + 4,11,x + 5,13,x - 1[]
428,3,2,x^2,3,x^2 + 3*x - 1,5,x^2 + x - 3,7,x^2 + 2*x + 1,11,x^2 - 2*x +
1,13,x^2 + 4*x + 4[]
428,4,2,x^5,3,x^5 - 5*x^4 - 2*x^3 + 32*x^2 - 10*x - 43,5,x^5 + x^4 - 21*x^3 -
12*x^2 + 108*x + 24,7,x^5 - 6*x^4 - x^3 + 34*x^2 - 40,11,x^5 - 6*x^4 + 33*x^2 -
3*x - 9,13,x^5 + 8*x^4 - 23*x^3 - 185*x^2 + 236*x + 436[]

Total time: 17.730 seconds, Total memory usage: 5.83MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 04:18:13 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [428..432] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 04:17:48 on modular  [Seed = 1805508998]
-------------------------------------

428,1,2,$.1,3,$.1 - 1,5,$.1 - 2,7,$.1 - 4,11,$.1 + 3,13,$.1 - 5[]
428,2,2,$.1,3,$.1 + 1,5,$.1 - 2,7,$.1 + 4,11,$.1 + 5,13,$.1 - 1[]
428,3,2,$.1^2,3,$.1^2 + 3*$.1 - 1,5,$.1^2 + $.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2
- 2*$.1 + 1,13,$.1^2 + 4*$.1 + 4[] 428,4,2,$.1^5,3,$.1^5 - 5*$.1^4 - 2*$.1^3 + 32*$.1^2 - 10*$.1 - 43,5,$.1^5 +
$.1^4 - 21*$.1^3 - 12*$.1^2 + 108*$.1 + 24,7,$.1^5 - 6*$.1^4 - $.1^3 + 34*$.1^2
- 40,11,$.1^5 - 6*$.1^4 + 33*$.1^2 - 3*$.1 - 9,13,$.1^5 + 8*$.1^4 - 23*$.1^3 - 185*$.1^2 + 236*$.1 + 436[] 429,1,2,x + 1,3,x + 1,5,x,7,x,11,x - 1,13,x - 1[] 429,2,2,x + 1,3,x - 1,5,x + 2,7,x,11,x + 1,13,x - 1[] 429,3,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 + 4*x + 4,11,x^2 + 2*x + 1,13,x^2 + 2*x + 1[] 429,4,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 4*x + 2,7,x^2 + 4*x - 4,11,x^2 - 2*x + 1,13,x^2 + 2*x + 1[] 429,5,2,x^3 + x^2 - 5*x - 3,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 10*x - 2,7,x^3 - 2*x^2 - 8*x + 12,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 + 3*x + 1[] 429,6,2,x^3 - 3*x^2 - x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 2*x + 2,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 + 3*x + 1[] 429,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x - 2,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 3*x^2 + 3*x - 1[] 429,8,2,x^4 + 2*x^3 - 6*x^2 - 12*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 12*x^2 - 14*x - 4,7,x^4 - 2*x^3 - 16*x^2 + 44*x - 16,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 430,1,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 4,13,x + 1[] 430,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x,13,x + 3[] 430,3,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x + 6,13,x - 5[] 430,4,2,x - 1,3,x + 2,5,x - 1,7,x + 5,11,x + 2,13,x + 5[] 430,5,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 11,11,x^2 - 2*x - 2,13,x^2 - 2*x - 11[] 430,6,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x - 2,13,x^2 + 2*x + 1[] 430,7,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x + 2,13,x^2 - 2*x - 7[] 430,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 + 6*x^2 + 5*x - 8,11,x^3 - 6*x^2 - 22*x + 136,13,x^3 + 4*x^2 - 27*x - 106[] 431,1,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x + 5,13,x + 2[] 431,2,2,x + 1,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x + 2[] 431,3,2,x^3 - x^2 - 4*x + 3,3,x^3 + x^2 - 4*x - 3,5,x^3 + 3*x^2 - 2*x - 7,7,x^3 + 6*x^2 + 12*x + 8,11,x^3,13,x^3 + 6*x^2 + 12*x + 8[] 431,4,2,x^3 - 5*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - x^2 - 10*x + 1,7,x^3 - 20*x - 8,11,x^3 + 12*x^2 + 48*x + 64,13,x^3 - 8*x^2 - 12*x + 136[] 431,5,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 3*x^3 - 4*x - 1,5,x^4 + 5*x^3 + 6*x^2 - 1,7,x^4 - 2*x^3 - 2*x^2 + 3*x + 1,11,x^4 - x^3 - 13*x^2 + 31*x - 19,13,x^4 + 5*x^3 - x^2 - 5*x - 1[] 431,6,2,x^24 - x^23 - 40*x^22 + 40*x^21 + 692*x^20 - 687*x^19 - 6790*x^18 + 6631*x^17 + 41657*x^16 - 39533*x^15 - 166175*x^14 + 150668*x^13 + 434546*x^12 - 367120*x^11 - 733353*x^10 + 555013*x^9 + 766426*x^8 - 486022*x^7 - 458392*x^6 + 216189*x^5 + 133642*x^4 - 39443*x^3 - 11021*x^2 + 2767*x + 13,3,x^24 - x^23 - 51*x^22 + 45*x^21 + 1118*x^20 - 853*x^19 - 13827*x^18 + 8872*x^17 + 106601*x^16 - 55088*x^15 - 535427*x^14 + 206199*x^13 + 1783081*x^12 - 432309*x^11 - 3938181*x^10 + 336862*x^9 + 5666150*x^8 + 485071*x^7 - 5053047*x^6 - 1363051*x^5 + 2461452*x^4 + 1177097*x^3 - 415667*x^2 - 363322*x - 62521,5,x^24 - 13*x^23 - x^22 + 693*x^21 - 2212*x^20 - 13027*x^19 + 73409*x^18 + 78062*x^17 - 1062921*x^16 + 636806*x^15 + 8076267*x^14 - 12881903*x^13 - 31663301*x^12 + 83663785*x^11 + 45711505*x^10 - 263035378*x^9 + 70497032*x^8 + 381236683*x^7 - 274310749*x^6 - 178921611*x^5 + 181598490*x^4 + 23883539*x^3 - 30789701*x^2 - 3434398*x + 738223,7,x^24 - 8*x^23 - 94*x^22 + 889*x^21 + 3211*x^20 - 41262*x^19 - 35920*x^18 + 1032968*x^17 - 571044*x^16 - 14958832*x^15 + 22590168*x^14 + 123054224*x^13 - 294152000*x^12 - 491861440*x^11 + 1902252288*x^10 + 168622848*x^9 - 5847215104*x^8 + 5061049344*x^7 + 5009858560*x^6 - 11097280512*x^5 + 7305969664*x^4 - 1900675072*x^3 - 24051712*x^2 + 100335616*x - 13238272,11,x^24 - 15*x^23 - 56*x^22 + 1718*x^21 - 967*x^20 - 85552*x^19 + 159131*x^18 + 2463154*x^17 - 5654857*x^16 - 45863834*x^15 + 103729723*x^14 + 580573026*x^13 - 1102854601*x^12 - 5039630656*x^11 + 6745640649*x^10 + 29106429742*x^9 - 21209517228*x^8 - 104340033191*x^7 + 20867246361*x^6 + 207698272456*x^5 + 35856946884*x^4 - 197939406720*x^3 - 78321571072*x^2 + 69887651200*x + 37007196736,13,x^24 - 11*x^23 - 153*x^22 + 2073*x^21 + 7799*x^20 - 162648*x^19 - 38534*x^18 + 6816228*x^17 - 11860956*x^16 - 160653936*x^15 + 537013864*x^14 + 1953872960*x^13 - 10978265728*x^12 - 5739512960*x^11 + 114862520832*x^10 - 130647495936*x^9 - 520848457216*x^8 + 1411147104256*x^7 - 56486131712*x^6 - 3959960002560*x^5 + 5582947106816*x^4 - 2083243065344*x^3 - 1377562722304*x^2 + 1279575916544*x - 244822704128[] Errors: /home/mfd/gomagma: line 2: 28218 Alarm clock /usr/local/bin/magma ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:19:09 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [428..431] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 04:18:51 on modular [Seed = 367239103] ------------------------------------- 428,1,2,$.1,3,$.1 - 1,5,$.1 - 2,7,$.1 - 4,11,$.1 + 3,13,$.1 - 5[] 428,2,2,$.1,3,$.1 + 1,5,$.1 - 2,7,$.1 + 4,11,$.1 + 5,13,$.1 - 1[] 428,3,2,$.1^2,3,$.1^2 + 3*$.1 - 1,5,$.1^2 +$.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 + 4*$.1 + 4[]
428,4,2,$.1^5,3,$.1^5 - 5*$.1^4 - 2*$.1^3 + 32*$.1^2 - 10*$.1 - 43,5,$.1^5 +$.1^4 - 21*$.1^3 - 12*$.1^2 + 108*$.1 + 24,7,$.1^5 - 6*$.1^4 -$.1^3 + 34*$.1^2 - 40,11,$.1^5 - 6*$.1^4 + 33*$.1^2 - 3*$.1 - 9,13,$.1^5 + 8*$.1^4 - 23*$.1^3 -
185*$.1^2 + 236*$.1 + 436[]
429,1,2,x + 1,3,x + 1,5,x,7,x,11,x - 1,13,x - 1[]
429,2,2,x + 1,3,x - 1,5,x + 2,7,x,11,x + 1,13,x - 1[]
429,3,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 + 4*x + 4,11,x^2 + 2*x +
1,13,x^2 + 2*x + 1[]
429,4,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 4*x + 2,7,x^2 + 4*x - 4,11,x^2 -
2*x + 1,13,x^2 + 2*x + 1[]
429,5,2,x^3 + x^2 - 5*x - 3,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 10*x -
2,7,x^3 - 2*x^2 - 8*x + 12,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 + 3*x + 1[]
429,6,2,x^3 - 3*x^2 - x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 2*x +
2,7,x^3 + 2*x^2 - 8*x + 4,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 + 3*x + 1[]
429,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x - 2,7,x^3 +
2*x^2 - 8*x + 4,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 3*x^2 + 3*x - 1[]
429,8,2,x^4 + 2*x^3 - 6*x^2 - 12*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 -
12*x^2 - 14*x - 4,7,x^4 - 2*x^3 - 16*x^2 + 44*x - 16,11,x^4 + 4*x^3 + 6*x^2 +
4*x + 1,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[]
430,1,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 4,13,x + 1[]
430,2,2,x + 1,3,x,5,x - 1,7,x + 3,11,x,13,x + 3[]
430,3,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x + 6,13,x - 5[]
430,4,2,x - 1,3,x + 2,5,x - 1,7,x + 5,11,x + 2,13,x + 5[]
430,5,2,x^2 + 2*x + 1,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x - 11,11,x^2 -
2*x - 2,13,x^2 - 2*x - 11[]
430,6,2,x^2 - 2*x + 1,3,x^2 - 6,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x -
2,13,x^2 + 2*x + 1[]
430,7,2,x^2 - 2*x + 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 4*x +
2,13,x^2 - 2*x - 7[]
430,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 + 6*x^2 + 5*x - 8,11,x^3 - 6*x^2 - 22*x + 136,13,x^3 + 4*x^2 - 27*x -
106[]
431,1,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x + 5,13,x + 2[]
431,2,2,x + 1,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x + 2[]
431,3,2,x^3 - x^2 - 4*x + 3,3,x^3 + x^2 - 4*x - 3,5,x^3 + 3*x^2 - 2*x - 7,7,x^3
+ 6*x^2 + 12*x + 8,11,x^3,13,x^3 + 6*x^2 + 12*x + 8[]
431,4,2,x^3 - 5*x + 1,3,x^3 - x^2 - 8*x + 11,5,x^3 - x^2 - 10*x + 1,7,x^3 - 20*x
- 8,11,x^3 + 12*x^2 + 48*x + 64,13,x^3 - 8*x^2 - 12*x + 136[]
431,5,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + 3*x^3 - 4*x - 1,5,x^4 + 5*x^3 + 6*x^2
- 1,7,x^4 - 2*x^3 - 2*x^2 + 3*x + 1,11,x^4 - x^3 - 13*x^2 + 31*x - 19,13,x^4 +
5*x^3 - x^2 - 5*x - 1[]
431,6,2,x^24 - x^23 - 40*x^22 + 40*x^21 + 692*x^20 - 687*x^19 - 6790*x^18 +
6631*x^17 + 41657*x^16 - 39533*x^15 - 166175*x^14 + 150668*x^13 + 434546*x^12 -
367120*x^11 - 733353*x^10 + 555013*x^9 + 766426*x^8 - 486022*x^7 - 458392*x^6 +
216189*x^5 + 133642*x^4 - 39443*x^3 - 11021*x^2 + 2767*x + 13,3,x^24 - x^23 -
51*x^22 + 45*x^21 + 1118*x^20 - 853*x^19 - 13827*x^18 + 8872*x^17 + 106601*x^16
- 55088*x^15 - 535427*x^14 + 206199*x^13 + 1783081*x^12 - 432309*x^11 -
3938181*x^10 + 336862*x^9 + 5666150*x^8 + 485071*x^7 - 5053047*x^6 - 1363051*x^5
+ 2461452*x^4 + 1177097*x^3 - 415667*x^2 - 363322*x - 62521,5,x^24 - 13*x^23 -
x^22 + 693*x^21 - 2212*x^20 - 13027*x^19 + 73409*x^18 + 78062*x^17 -
1062921*x^16 + 636806*x^15 + 8076267*x^14 - 12881903*x^13 - 31663301*x^12 +
83663785*x^11 + 45711505*x^10 - 263035378*x^9 + 70497032*x^8 + 381236683*x^7 -
274310749*x^6 - 178921611*x^5 + 181598490*x^4 + 23883539*x^3 - 30789701*x^2 -
3434398*x + 738223,7,x^24 - 8*x^23 - 94*x^22 + 889*x^21 + 3211*x^20 - 41262*x^19
- 35920*x^18 + 1032968*x^17 - 571044*x^16 - 14958832*x^15 + 22590168*x^14 +
123054224*x^13 - 294152000*x^12 - 491861440*x^11 + 1902252288*x^10 +
168622848*x^9 - 5847215104*x^8 + 5061049344*x^7 + 5009858560*x^6 -
11097280512*x^5 + 7305969664*x^4 - 1900675072*x^3 - 24051712*x^2 + 100335616*x -
13238272,11,x^24 - 15*x^23 - 56*x^22 + 1718*x^21 - 967*x^20 - 85552*x^19 +
159131*x^18 + 2463154*x^17 - 5654857*x^16 - 45863834*x^15 + 103729723*x^14 +
580573026*x^13 - 1102854601*x^12 - 5039630656*x^11 + 6745640649*x^10 +
29106429742*x^9 - 21209517228*x^8 - 104340033191*x^7 + 20867246361*x^6 +
207698272456*x^5 + 35856946884*x^4 - 197939406720*x^3 - 78321571072*x^2 +
69887651200*x + 37007196736,13,x^24 - 11*x^23 - 153*x^22 + 2073*x^21 + 7799*x^20
- 162648*x^19 - 38534*x^18 + 6816228*x^17 - 11860956*x^16 - 160653936*x^15 +
537013864*x^14 + 1953872960*x^13 - 10978265728*x^12 - 5739512960*x^11 +
114862520832*x^10 - 130647495936*x^9 - 520848457216*x^8 + 1411147104256*x^7 -
56486131712*x^6 - 3959960002560*x^5 + 5582947106816*x^4 - 2083243065344*x^3 -
1377562722304*x^2 + 1279575916544*x - 244822704128[]

Total time: 16.840 seconds, Total memory usage: 5.71MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 04:26:27 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [431..434] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 04:26:08 on modular  [Seed = 1369954808]
-------------------------------------

431,1,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 2,11,$.1 + 5,13,$.1 + 2[]
431,2,2,$.1 + 1,3,$.1 - 3,5,$.1 + 3,7,$.1 - 2,11,$.1 - 1,13,$.1 + 2[]
431,3,2,$.1^3 -$.1^2 - 4*$.1 + 3,3,$.1^3 + $.1^2 - 4*$.1 - 3,5,$.1^3 + 3*$.1^2
- 2*$.1 - 7,7,$.1^3 + 6*$.1^2 + 12*$.1 + 8,11,$.1^3,13,$.1^3 + 6*$.1^2 + 12*$.1
+ 8[]
431,4,2,$.1^3 - 5*$.1 + 1,3,$.1^3 -$.1^2 - 8*$.1 + 11,5,$.1^3 - $.1^2 - 10*$.1
+ 1,7,$.1^3 - 20*$.1 - 8,11,$.1^3 + 12*$.1^2 + 48*$.1 + 64,13,$.1^3 - 8*$.1^2 - 12*$.1 + 136[]
431,5,2,$.1^4 +$.1^3 - 3*$.1^2 -$.1 + 1,3,$.1^4 + 3*$.1^3 - 4*$.1 - 1,5,$.1^4
+ 5*$.1^3 + 6*$.1^2 - 1,7,$.1^4 - 2*$.1^3 - 2*$.1^2 + 3*$.1 + 1,11,$.1^4 -$.1^3
- 13*$.1^2 + 31*$.1 - 19,13,$.1^4 + 5*$.1^3 - $.1^2 - 5*$.1 - 1[]
431,6,2,$.1^24 -$.1^23 - 40*$.1^22 + 40*$.1^21 + 692*$.1^20 - 687*$.1^19 -
6790*$.1^18 + 6631*$.1^17 + 41657*$.1^16 - 39533*$.1^15 - 166175*$.1^14 + 150668*$.1^13 + 434546*$.1^12 - 367120*$.1^11 - 733353*$.1^10 + 555013*$.1^9 +
766426*$.1^8 - 486022*$.1^7 - 458392*$.1^6 + 216189*$.1^5 + 133642*$.1^4 - 39443*$.1^3 - 11021*$.1^2 + 2767*$.1 + 13,3,$.1^24 -$.1^23 - 51*$.1^22 + 45*$.1^21 + 1118*$.1^20 - 853*$.1^19 - 13827*$.1^18 + 8872*$.1^17 +
106601*$.1^16 - 55088*$.1^15 - 535427*$.1^14 + 206199*$.1^13 + 1783081*$.1^12 - 432309*$.1^11 - 3938181*$.1^10 + 336862*$.1^9 + 5666150*$.1^8 + 485071*$.1^7 -
5053047*$.1^6 - 1363051*$.1^5 + 2461452*$.1^4 + 1177097*$.1^3 - 415667*$.1^2 - 363322*$.1 - 62521,5,$.1^24 - 13*$.1^23 - $.1^22 + 693*$.1^21 - 2212*$.1^20 - 13027*$.1^19 + 73409*$.1^18 + 78062*$.1^17 - 1062921*$.1^16 + 636806*$.1^15 +
8076267*$.1^14 - 12881903*$.1^13 - 31663301*$.1^12 + 83663785*$.1^11 +
45711505*$.1^10 - 263035378*$.1^9 + 70497032*$.1^8 + 381236683*$.1^7 -
274310749*$.1^6 - 178921611*$.1^5 + 181598490*$.1^4 + 23883539*$.1^3 -
30789701*$.1^2 - 3434398*$.1 + 738223,7,$.1^24 - 8*$.1^23 - 94*$.1^22 + 889*$.1^21 + 3211*$.1^20 - 41262*$.1^19 - 35920*$.1^18 + 1032968*$.1^17 -
571044*$.1^16 - 14958832*$.1^15 + 22590168*$.1^14 + 123054224*$.1^13 -
294152000*$.1^12 - 491861440*$.1^11 + 1902252288*$.1^10 + 168622848*$.1^9 -
5847215104*$.1^8 + 5061049344*$.1^7 + 5009858560*$.1^6 - 11097280512*$.1^5 +
7305969664*$.1^4 - 1900675072*$.1^3 - 24051712*$.1^2 + 100335616*$.1 -
13238272,11,$.1^24 - 15*$.1^23 - 56*$.1^22 + 1718*$.1^21 - 967*$.1^20 - 85552*$.1^19 + 159131*$.1^18 + 2463154*$.1^17 - 5654857*$.1^16 - 45863834*$.1^15
+ 103729723*$.1^14 + 580573026*$.1^13 - 1102854601*$.1^12 - 5039630656*$.1^11 +
6745640649*$.1^10 + 29106429742*$.1^9 - 21209517228*$.1^8 - 104340033191*$.1^7 +
20867246361*$.1^6 + 207698272456*$.1^5 + 35856946884*$.1^4 - 197939406720*$.1^3
- 78321571072*$.1^2 + 69887651200*$.1 + 37007196736,13,$.1^24 - 11*$.1^23 -
153*$.1^22 + 2073*$.1^21 + 7799*$.1^20 - 162648*$.1^19 - 38534*$.1^18 + 6816228*$.1^17 - 11860956*$.1^16 - 160653936*$.1^15 + 537013864*$.1^14 + 1953872960*$.1^13 - 10978265728*$.1^12 - 5739512960*$.1^11 + 114862520832*$.1^10 - 130647495936*$.1^9 - 520848457216*$.1^8 + 1411147104256*$.1^7 -
56486131712*$.1^6 - 3959960002560*$.1^5 + 5582947106816*$.1^4 - 2083243065344*$.1^3 - 1377562722304*$.1^2 + 1279575916544*$.1 - 244822704128[]
432,1,2,x,3,x,5,x + 1,7,x + 3,11,x + 5,13,x - 4[]
432,2,2,x,3,x,5,x - 1,7,x + 3,11,x - 5,13,x - 4[]
432,3,2,x,3,x,5,x - 4,7,x - 3,11,x + 4,13,x - 1[]
432,4,2,x,3,x,5,x + 4,7,x - 3,11,x - 4,13,x - 1[]
432,5,2,x,3,x,5,x,7,x - 1,11,x,13,x - 5[]
432,6,2,x,3,x,5,x - 3,7,x - 1,11,x - 3,13,x + 4[]
432,7,2,x,3,x,5,x,7,x + 5,11,x,13,x + 7[]
432,8,2,x,3,x,5,x + 3,7,x - 1,11,x + 3,13,x + 4[]
433,1,2,x + 1,3,x + 2,5,x + 4,7,x + 3,11,x + 4,13,x + 5[]
433,2,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 8*x + 4,5,x^3 - 8*x + 4,7,x^3 - 7*x^2 +
11*x - 3,11,x^3 - 6*x^2 + 4*x + 4,13,x^3 - 5*x^2 - 21*x + 97[]
433,3,2,x^15 + 10*x^14 + 29*x^13 - 22*x^12 - 251*x^11 - 272*x^10 + 583*x^9 +
1252*x^8 - 186*x^7 - 1821*x^6 - 675*x^5 + 899*x^4 + 482*x^3 - 93*x^2 - 27*x -
1,3,x^15 + 8*x^14 + 7*x^13 - 92*x^12 - 221*x^11 + 232*x^10 + 1030*x^9 + 63*x^8 -
1719*x^7 - 429*x^6 + 1308*x^5 + 127*x^4 - 452*x^3 + 88*x^2 + 16*x - 4,5,x^15 +
5*x^14 - 27*x^13 - 170*x^12 + 160*x^11 + 1914*x^10 + 388*x^9 - 9870*x^8 -
5872*x^7 + 26083*x^6 + 16736*x^5 - 37759*x^4 - 18244*x^3 + 28460*x^2 + 6744*x -
8548,7,x^15 + 15*x^14 + 51*x^13 - 272*x^12 - 1975*x^11 - 212*x^10 + 22207*x^9 +
30408*x^8 - 109207*x^7 - 212799*x^6 + 274259*x^5 + 575247*x^4 - 419271*x^3 -
554748*x^2 + 403547*x - 59063,11,x^15 + 14*x^14 + 7*x^13 - 707*x^12 - 2663*x^11
+ 9425*x^10 + 64024*x^9 - 718*x^8 - 553393*x^7 - 681386*x^6 + 1691664*x^5 +
3572557*x^4 - 430092*x^3 - 4182740*x^2 - 1450688*x + 655796,13,x^15 + 9*x^14 -
54*x^13 - 600*x^12 + 885*x^11 + 14731*x^10 - 3850*x^9 - 172818*x^8 - 19607*x^7 +
1039066*x^6 + 134513*x^5 - 3101189*x^4 + 184903*x^3 + 3670090*x^2 - 1421967*x -
30529[]
433,4,2,x^16 - 7*x^15 - 5*x^14 + 129*x^13 - 125*x^12 - 929*x^11 + 1471*x^10 +
3333*x^9 - 6394*x^8 - 6443*x^7 + 13118*x^6 + 7162*x^5 - 12217*x^4 - 4691*x^3 +
3598*x^2 + 1114*x - 3,3,x^16 - 6*x^15 - 13*x^14 + 134*x^13 - 33*x^12 - 1074*x^11
+ 1074*x^10 + 4051*x^9 - 5657*x^8 - 7571*x^7 + 12986*x^6 + 6355*x^5 - 13826*x^4
- 1264*x^3 + 5720*x^2 - 680*x - 224,5,x^16 - 7*x^15 - 17*x^14 + 202*x^13 -
46*x^12 - 2060*x^11 + 2036*x^10 + 9692*x^9 - 12248*x^8 - 22667*x^7 + 29036*x^6 +
26041*x^5 - 26932*x^4 - 13736*x^3 + 7016*x^2 + 2216*x - 48,7,x^16 - 7*x^15 -
29*x^14 + 310*x^13 - 97*x^12 - 4172*x^11 + 7759*x^10 + 16632*x^9 - 54399*x^8 +
985*x^7 + 117147*x^6 - 88479*x^5 - 49471*x^4 + 73286*x^3 - 18921*x^2 - 1887*x +
636,11,x^16 - 12*x^15 - 13*x^14 + 627*x^13 - 1269*x^12 - 10221*x^11 + 29458*x^10
+ 79946*x^9 - 239097*x^8 - 375776*x^7 + 817112*x^6 + 1070885*x^5 - 938542*x^4 -
1080712*x^3 + 448064*x^2 + 319336*x - 111648,13,x^16 + 3*x^15 - 76*x^14 -
252*x^13 + 2185*x^12 + 8069*x^11 - 29472*x^10 - 125818*x^9 + 183833*x^8 +
1020236*x^7 - 354339*x^6 - 4257291*x^5 - 1094143*x^4 + 8359796*x^3 + 4913205*x^2
- 5697071*x - 4141634[]
434,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 2,13,x + 2[]
434,2,2,x - 1,3,x - 2,5,x - 2,7,x + 1,11,x + 6,13,x - 4[]
434,3,2,x - 1,3,x + 3,5,x + 3,7,x + 1,11,x - 4,13,x - 4[]
434,4,2,x - 1,3,x + 2,5,x + 2,7,x - 1,11,x + 2,13,x + 4[]
434,5,2,x - 1,3,x - 1,5,x - 3,7,x - 1,11,x,13,x + 4[]
434,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 1,5,x^2 + 2*x - 7,7,x^2 - 2*x +
1,11,x^2,13,x^2 - 8*x + 8[]
434,7,2,x^2 - 2*x + 1,3,x^2 - x - 4,5,x^2 - 3*x - 2,7,x^2 + 2*x + 1,11,x^2 - 8*x
+ 16,13,x^2 + 6*x - 8[]
434,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 5*x - 8,5,x^3 + 2*x^2 - 7*x -
4,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 2*x^2 - 32*x + 32,13,x^3 - 2*x^2 - 24*x -
16[]
434,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - x^2 - 8*x + 4,5,x^3 + x^2 - 8*x - 4,7,x^3
- 3*x^2 + 3*x - 1,11,x^3 + 4*x^2 - 20*x - 64,13,x^3 - 12*x^2 + 48*x - 64[]

Total time: 15.919 seconds, Total memory usage: 5.59MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 04:32:16 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [434..437] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 04:31:56 on modular  [Seed = 1135986007]
-------------------------------------

434,1,2,$.1 + 1,3,$.1,5,$.1,7,$.1 + 1,11,$.1 + 2,13,$.1 + 2[]
434,2,2,$.1 - 1,3,$.1 - 2,5,$.1 - 2,7,$.1 + 1,11,$.1 + 6,13,$.1 - 4[]
434,3,2,$.1 - 1,3,$.1 + 3,5,$.1 + 3,7,$.1 + 1,11,$.1 - 4,13,$.1 - 4[]
434,4,2,$.1 - 1,3,$.1 + 2,5,$.1 + 2,7,$.1 - 1,11,$.1 + 2,13,$.1 + 4[]
434,5,2,$.1 - 1,3,$.1 - 1,5,$.1 - 3,7,$.1 - 1,11,$.1,13,$.1 + 4[]
434,6,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 2*$.1 - 1,5,$.1^2 + 2*$.1 - 7,7,$.1^2 - 2*$.1 + 1,11,$.1^2,13,$.1^2 - 8*$.1 + 8[] 434,7,2,$.1^2 - 2*$.1 + 1,3,$.1^2 - $.1 - 4,5,$.1^2 - 3*$.1 - 2,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 16,13,$.1^2 + 6*$.1 - 8[] 434,8,2,$.1^3 + 3*$.1^2 + 3*$.1 + 1,3,$.1^3 + 2*$.1^2 - 5*$.1 - 8,5,$.1^3 +
2*$.1^2 - 7*$.1 - 4,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 - 2*$.1^2 - 32*$.1 +
32,13,$.1^3 - 2*$.1^2 - 24*$.1 - 16[] 434,9,2,$.1^3 - 3*$.1^2 + 3*$.1 - 1,3,$.1^3 -$.1^2 - 8*$.1 + 4,5,$.1^3 + $.1^2 - 8*$.1 - 4,7,$.1^3 - 3*$.1^2 + 3*$.1 - 1,11,$.1^3 + 4*$.1^2 - 20*$.1 -
64,13,$.1^3 - 12*$.1^2 + 48*$.1 - 64[] 435,1,2,x,3,x + 1,5,x + 1,7,x + 2,11,x - 1,13,x - 6[] 435,2,2,x,3,x - 1,5,x + 1,7,x - 2,11,x - 3,13,x - 2[] 435,3,2,x - 1,3,x - 1,5,x - 1,7,x - 4,11,x + 4,13,x - 6[] 435,4,2,x + 1,3,x - 1,5,x - 1,7,x + 4,11,x,13,x - 6[] 435,5,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 4*x + 4,13,x^2 - 4*x + 4[] 435,6,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + 2*x - 19,13,x^2 + 8*x + 11[] 435,7,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x - 16,11,x^2 + 7*x + 8,13,x^2 + 4*x + 4[] 435,8,2,x^2 + x - 5,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - 10*x + 25,13,x^2 - 21[] 435,9,2,x^3 - x^2 - 5*x + 4,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + 4*x^2 - 7*x - 14,11,x^3 - 9*x^2 + 27*x - 27,13,x^3 - 6*x^2 - x + 2[] 435,10,2,x^4 + 3*x^3 - 2*x^2 - 7*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 2*x^3 - 15*x^2 - 4*x + 4,11,x^4 + 2*x^3 - 15*x^2 + 4*x + 4,13,x^4 + 8*x^3 + 3*x^2 - 92*x - 164[] 436,1,2,x^2,3,x^2 - 8,5,x^2 - 2*x - 7,7,x^2 + 4*x + 4,11,x^2 + 6*x + 7,13,x^2[] 436,2,2,x^3,3,x^3 - 3*x - 1,5,x^3 + 6*x^2 + 9*x + 3,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 + 3*x^2 - 18*x - 3,13,x^3 + 3*x^2 - 6*x - 17[] 436,3,2,x^4,3,x^4 - 7*x^2 - x + 8,5,x^4 - 8*x^3 + 17*x^2 - 3*x - 6,7,x^4 - 5*x^3 - 10*x^2 + 45*x + 12,11,x^4 - 3*x^3 - 16*x^2 + 67*x - 58,13,x^4 - 5*x^3 - 14*x^2 + 57*x + 62[] 437,1,2,x - 2,3,x - 2,5,x - 1,7,x + 3,11,x - 5,13,x + 2[] 437,2,2,x,3,x - 2,5,x + 1,7,x + 5,11,x + 1,13,x[] 437,3,2,x^2 + 2*x + 1,3,x^2 + 3*x + 1,5,x^2 - 2*x - 4,7,x^2 - x - 11,11,x^2 + 5*x - 5,13,x^2 - 20[] 437,4,2,x^2 - 5,3,x^2 + x - 1,5,x^2 + 2*x - 4,7,x^2 + 5*x + 5,11,x^2 + 7*x + 11,13,x^2 - 20[] 437,5,2,x^2 - 2,3,x^2 + 4*x + 2,5,x^2 + 2*x - 1,7,x^2 + 2*x - 1,11,x^2 - 2*x - 1,13,x^2 - 32[] 437,6,2,x^5 + x^4 - 7*x^3 - 2*x^2 + 12*x - 4,3,x^5 + 4*x^4 - x^3 - 12*x^2 + 4,5,x^5 + x^4 - 7*x^3 - 5*x^2 + 10*x + 4,7,x^5 + 9*x^4 + 25*x^3 + 19*x^2 - 6*x - 4,11,x^5 + x^4 - 39*x^3 - 41*x^2 + 174*x + 172,13,x^5 + 10*x^4 + 29*x^3 + 16*x^2 - 24*x - 16[] 437,7,2,x^8 - 13*x^6 + 47*x^4 - 2*x^3 - 37*x^2 - 2*x + 2,3,x^8 - 5*x^7 - 4*x^6 + 45*x^5 - 16*x^4 - 121*x^3 + 71*x^2 + 96*x - 62,5,x^8 - 2*x^7 - 19*x^6 + 18*x^5 + 116*x^4 - 12*x^3 - 240*x^2 - 128*x + 16,7,x^8 - 9*x^7 + 11*x^6 + 110*x^5 - 376*x^4 + 194*x^3 + 723*x^2 - 1105*x + 449,11,x^8 - 7*x^7 - 23*x^6 + 202*x^5 + 48*x^4 - 1550*x^3 + 1315*x^2 + 2045*x - 2225,13,x^8 - 8*x^7 - 16*x^6 + 180*x^5 + 64*x^4 - 1200*x^3 - 112*x^2 + 2112*x + 1152[] 437,8,2,x^12 - 2*x^11 - 19*x^10 + 35*x^9 + 137*x^8 - 219*x^7 - 483*x^6 + 605*x^5 + 866*x^4 - 707*x^3 - 682*x^2 + 236*x + 96,3,x^12 - 7*x^11 - x^10 + 100*x^9 - 146*x^8 - 386*x^7 + 819*x^6 + 495*x^5 - 1465*x^4 - 178*x^3 + 812*x^2 + 128*x - 64,5,x^12 + x^11 - 43*x^10 - 29*x^9 + 690*x^8 + 304*x^7 - 5116*x^6 - 1600*x^5 + 17904*x^4 + 4400*x^3 - 26240*x^2 - 4736*x + 10368,7,x^12 - 14*x^11 + 44*x^10 + 199*x^9 - 1254*x^8 - 56*x^7 + 10263*x^6 - 9726*x^5 - 33184*x^4 + 43045*x^3 + 38206*x^2 - 49124*x - 5344,11,x^12 - 4*x^11 - 60*x^10 + 245*x^9 + 1130*x^8 - 5248*x^7 - 6329*x^6 + 44008*x^5 - 10772*x^4 - 119905*x^3 + 103210*x^2 + 26396*x - 16944,13,x^12 - 2*x^11 - 103*x^10 + 240*x^9 + 3836*x^8 - 10756*x^7 - 62400*x^6 + 214944*x^5 + 388784*x^4 - 1876288*x^3 - 16320*x^2 + 5750784*x - 5141504[] Total time: 18.369 seconds, Total memory usage: 5.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 04:37:47 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [437..440] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 04:37:26 on modular [Seed = 1887892799] ------------------------------------- 437,1,2,$.1 - 2,3,$.1 - 2,5,$.1 - 1,7,$.1 + 3,11,$.1 - 5,13,$.1 + 2[] 437,2,2,$.1,3,$.1 - 2,5,$.1 + 1,7,$.1 + 5,11,$.1 + 1,13,$.1[] 437,3,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - $.1 - 11,11,$.1^2 + 5*$.1 - 5,13,$.1^2 - 20[]
437,4,2,$.1^2 - 5,3,$.1^2 + $.1 - 1,5,$.1^2 + 2*$.1 - 4,7,$.1^2 + 5*$.1 + 5,11,$.1^2 + 7*$.1 + 11,13,$.1^2 - 20[]
437,5,2,$.1^2 - 2,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 - 1,7,$.1^2 + 2*$.1 - 1,11,$.1^2 - 2*$.1 - 1,13,$.1^2 - 32[]
437,6,2,$.1^5 +$.1^4 - 7*$.1^3 - 2*$.1^2 + 12*$.1 - 4,3,$.1^5 + 4*$.1^4 -$.1^3
- 12*$.1^2 + 4,5,$.1^5 + $.1^4 - 7*$.1^3 - 5*$.1^2 + 10*$.1 + 4,7,$.1^5 + 9*$.1^4 + 25*$.1^3 + 19*$.1^2 - 6*$.1 - 4,11,$.1^5 + $.1^4 - 39*$.1^3 - 41*$.1^2 + 174*$.1 + 172,13,$.1^5 + 10*$.1^4 + 29*$.1^3 + 16*$.1^2 - 24*$.1 - 16[] 437,7,2,$.1^8 - 13*$.1^6 + 47*$.1^4 - 2*$.1^3 - 37*$.1^2 - 2*$.1 + 2,3,$.1^8 -
5*$.1^7 - 4*$.1^6 + 45*$.1^5 - 16*$.1^4 - 121*$.1^3 + 71*$.1^2 + 96*$.1 - 62,5,$.1^8 - 2*$.1^7 - 19*$.1^6 + 18*$.1^5 + 116*$.1^4 - 12*$.1^3 - 240*$.1^2 -
128*$.1 + 16,7,$.1^8 - 9*$.1^7 + 11*$.1^6 + 110*$.1^5 - 376*$.1^4 + 194*$.1^3 + 723*$.1^2 - 1105*$.1 + 449,11,$.1^8 - 7*$.1^7 - 23*$.1^6 + 202*$.1^5 + 48*$.1^4
- 1550*$.1^3 + 1315*$.1^2 + 2045*$.1 - 2225,13,$.1^8 - 8*$.1^7 - 16*$.1^6 +
180*$.1^5 + 64*$.1^4 - 1200*$.1^3 - 112*$.1^2 + 2112*$.1 + 1152[] 437,8,2,$.1^12 - 2*$.1^11 - 19*$.1^10 + 35*$.1^9 + 137*$.1^8 - 219*$.1^7 - 483*$.1^6 + 605*$.1^5 + 866*$.1^4 - 707*$.1^3 - 682*$.1^2 + 236*$.1 + 96,3,$.1^12 - 7*$.1^11 -$.1^10 + 100*$.1^9 - 146*$.1^8 - 386*$.1^7 + 819*$.1^6
+ 495*$.1^5 - 1465*$.1^4 - 178*$.1^3 + 812*$.1^2 + 128*$.1 - 64,5,$.1^12 +
$.1^11 - 43*$.1^10 - 29*$.1^9 + 690*$.1^8 + 304*$.1^7 - 5116*$.1^6 - 1600*$.1^5 + 17904*$.1^4 + 4400*$.1^3 - 26240*$.1^2 - 4736*$.1 + 10368,7,$.1^12 - 14*$.1^11 + 44*$.1^10 + 199*$.1^9 - 1254*$.1^8 - 56*$.1^7 + 10263*$.1^6 - 9726*$.1^5 - 33184*$.1^4 + 43045*$.1^3 + 38206*$.1^2 - 49124*$.1 - 5344,11,$.1^12 - 4*$.1^11 - 60*$.1^10 + 245*$.1^9 + 1130*$.1^8 - 5248*$.1^7 - 6329*$.1^6 + 44008*$.1^5 - 10772*$.1^4 - 119905*$.1^3 + 103210*$.1^2 + 26396*$.1 - 16944,13,$.1^12 -
2*$.1^11 - 103*$.1^10 + 240*$.1^9 + 3836*$.1^8 - 10756*$.1^7 - 62400*$.1^6 +
214944*$.1^5 + 388784*$.1^4 - 1876288*$.1^3 - 16320*$.1^2 + 5750784*$.1 - 5141504[] 438,1,2,x + 1,3,x + 1,5,x,7,x + 2,11,x - 4,13,x + 6[] 438,2,2,x + 1,3,x - 1,5,x - 2,7,x + 2,11,x - 2,13,x - 4[] 438,3,2,x + 1,3,x - 1,5,x,7,x + 4,11,x + 6,13,x + 4[] 438,4,2,x + 1,3,x - 1,5,x + 4,7,x,11,x - 2,13,x[] 438,5,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x + 2[] 438,6,2,x - 1,3,x - 1,5,x,7,x - 2,11,x,13,x + 4[] 438,7,2,x - 1,3,x - 1,5,x,7,x + 2,11,x - 4,13,x - 4[] 438,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 + 4*x + 4,13,x^2 - 8*x + 8[] 438,9,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 2*x - 4,7,x^2 - 4*x + 4,11,x^2 - 2*x - 4,13,x^2 - 6*x + 4[] 439,1,2,x^2 + 2*x + 1,3,x^2 - x - 1,5,x^2 - x - 1,7,x^2 + 4*x + 4,11,x^2 - 2*x - 4,13,x^2 + 3*x - 9[] 439,2,2,x^9 + x^8 - 12*x^7 - 6*x^6 + 49*x^5 - x^4 - 72*x^3 + 30*x^2 + 18*x - 9,3,x^9 + 4*x^8 - 2*x^7 - 22*x^6 - 10*x^5 + 32*x^4 + 20*x^3 - 10*x^2 - 3*x + 1,5,x^9 + 12*x^8 + 48*x^7 + 41*x^6 - 184*x^5 - 370*x^4 + 161*x^3 + 676*x^2 + 17*x - 389,7,x^9 - 28*x^7 + 5*x^6 + 231*x^5 - 151*x^4 - 594*x^3 + 645*x^2 - 27*x - 9,11,x^9 + 18*x^8 + 121*x^7 + 364*x^6 + 398*x^5 - 237*x^4 - 718*x^3 - 267*x^2 + 84*x + 37,13,x^9 - 2*x^8 - 42*x^7 + 100*x^6 + 442*x^5 - 997*x^4 - 1276*x^3 + 1828*x^2 + 868*x - 823[] 439,3,2,x^25 - 4*x^24 - 31*x^23 + 138*x^22 + 389*x^21 - 2034*x^20 - 2453*x^19 + 16766*x^18 + 7126*x^17 - 84887*x^16 + 1717*x^15 + 272618*x^14 - 79978*x^13 - 552928*x^12 + 255108*x^11 + 682589*x^10 - 376568*x^9 - 476301*x^8 + 270078*x^7 + 167567*x^6 - 81530*x^5 - 24739*x^4 + 6834*x^3 + 740*x^2 - 187*x + 5,3,x^25 - 3*x^24 - 59*x^23 + 180*x^22 + 1494*x^21 - 4658*x^20 - 21258*x^19 + 68240*x^18 + 186855*x^17 - 624866*x^16 - 1049494*x^15 + 3727909*x^14 + 3753610*x^13 - 14662056*x^12 - 8177104*x^11 + 37658528*x^10 + 9484576*x^9 - 61320448*x^8 - 2806912*x^7 + 59945728*x^6 - 5250560*x^5 - 31844352*x^4 + 5380096*x^3 + 7204864*x^2 - 1499136*x - 147456,5,x^25 - 15*x^24 + 30*x^23 + 604*x^22 - 3172*x^21 - 6786*x^20 + 78027*x^19 - 41625*x^18 - 905630*x^17 + 1695144*x^16 + 5338268*x^15 - 17310085*x^14 - 12108693*x^13 + 88929934*x^12 - 29524632*x^11 - 241700856*x^10 + 243645796*x^9 + 292676933*x^8 - 544530625*x^7 + 6259017*x^6 + 436474070*x^5 - 248916049*x^4 - 12779742*x^3 + 41632573*x^2 - 9162616*x + 377804,7,x^25 - 105*x^23 + 45*x^22 + 4725*x^21 - 3988*x^20 - 119042*x^19 + 147722*x^18 + 1837131*x^17 - 2989605*x^16 - 17816646*x^15 + 36211344*x^14 + 106565798*x^13 - 270164455*x^12 - 362278764*x^11 + 1231717441*x^10 + 517244602*x^9 - 3296794753*x^8 + 439878167*x^7 + 4783749693*x^6 - 2280863566*x^5 - 3210917657*x^4 + 2290198335*x^3 + 650761693*x^2 - 705120364*x + 87118028,11,x^25 - 24*x^24 + 124*x^23 + 1490*x^22 - 18593*x^21 + 17289*x^20 + 689967*x^19 - 3299178*x^18 - 5932965*x^17 + 87626128*x^16 - 168743742*x^15 - 695091746*x^14 + 3712353144*x^13 - 3530958885*x^12 - 16822456635*x^11 + 58054450667*x^10 - 60404970235*x^9 - 41347391882*x^8 + 176320147638*x^7 - 184928168301*x^6 + 65262520376*x^5 + 24682368471*x^4 - 23786089638*x^3 + 2069636251*x^2 + 1553679254*x - 50693164,13,x^25 - x^24 - 178*x^23 + 107*x^22 + 13573*x^21 - 2481*x^20 - 579935*x^19 - 147942*x^18 + 15220868*x^17 + 10829523*x^16 - 252158087*x^15 - 299172875*x^14 + 2590040022*x^13 + 4386472844*x^12 - 15273730089*x^11 - 35295225048*x^10 + 41401147127*x^9 + 145015590316*x^8 - 7591949171*x^7 - 255305231378*x^6 - 105555649063*x^5 + 177347525591*x^4 + 111323734500*x^3 - 34356348688*x^2 - 28624753632*x - 2786136752[] 440,1,2,x,3,x,5,x + 1,7,x + 2,11,x + 1,13,x[] 440,2,2,x,3,x,5,x - 1,7,x - 4,11,x + 1,13,x - 6[] 440,3,2,x,3,x - 3,5,x - 1,7,x - 1,11,x + 1,13,x + 6[] 440,4,2,x,3,x,5,x + 1,7,x + 2,11,x - 1,13,x + 4[] 440,5,2,x^2,3,x^2 - x - 4,5,x^2 + 2*x + 1,7,x^2 - 3*x - 2,11,x^2 - 2*x + 1,13,x^2 - 2*x - 16[] 440,6,2,x^2,3,x^2 - x - 4,5,x^2 + 2*x + 1,7,x^2 - 5*x + 2,11,x^2 + 2*x + 1,13,x^2 - 6*x - 8[] 440,7,2,x^2,3,x^2 + x - 4,5,x^2 - 2*x + 1,7,x^2 + x - 4,11,x^2 - 2*x + 1,13,x^2 - 4*x + 4[] Total time: 19.090 seconds, Total memory usage: 6.21MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:22:12 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [440..443] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:21:53 on modular [Seed = 3443063242] ------------------------------------- 440,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 + 1,13,$.1[] 440,2,2,$.1,3,$.1,5,$.1 - 1,7,$.1 - 4,11,$.1 + 1,13,$.1 - 6[] 440,3,2,$.1,3,$.1 - 3,5,$.1 - 1,7,$.1 - 1,11,$.1 + 1,13,$.1 + 6[] 440,4,2,$.1,3,$.1,5,$.1 + 1,7,$.1 + 2,11,$.1 - 1,13,$.1 + 4[] 440,5,2,$.1^2,3,$.1^2 -$.1 - 4,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 3*$.1 - 2,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 2*$.1 - 16[]
440,6,2,$.1^2,3,$.1^2 - $.1 - 4,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 5*$.1 + 2,11,$.1^2
+ 2*$.1 + 1,13,$.1^2 - 6*$.1 - 8[] 440,7,2,$.1^2,3,$.1^2 +$.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 +$.1 - 4,11,$.1^2 - 2*$.1 + 1,13,$.1^2 - 4*$.1 + 4[]
441,1,2,x,3,x,5,x,7,x,11,x,13,x + 7[]
441,2,2,x,3,x,5,x,7,x,11,x,13,x - 7[]
441,3,2,x + 2,3,x,5,x - 2,7,x,11,x - 2,13,x - 1[]
441,4,2,x - 1,3,x,5,x + 2,7,x,11,x + 4,13,x - 2[]
441,5,2,x + 1,3,x,5,x,7,x,11,x + 4,13,x[]
441,6,2,x + 2,3,x,5,x + 2,7,x,11,x - 2,13,x + 1[]
441,7,2,x^2 - 7,3,x^2,5,x^2,7,x^2,11,x^2 - 28,13,x^2[]
441,8,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2,11,x^2 - 12,13,x^2 + 4*x + 4[]
441,9,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 4*x + 2,7,x^2,11,x^2 - 4*x + 4,13,x^2 + 8*x
+ 14[]
441,10,2,x^2 - 2*x - 1,3,x^2,5,x^2 + 4*x + 2,7,x^2,11,x^2 - 4*x + 4,13,x^2 - 8*x
+ 14[]
442,1,2,x + 1,3,x - 2,5,x - 2,7,x - 2,11,x - 2,13,x + 1[]
442,2,2,x - 1,3,x,5,x - 2,7,x - 4,11,x + 2,13,x + 1[]
442,3,2,x - 1,3,x - 2,5,x + 2,7,x - 2,11,x - 4,13,x + 1[]
442,4,2,x - 1,3,x - 2,5,x - 4,7,x + 4,11,x + 2,13,x + 1[]
442,5,2,x - 1,3,x,5,x + 4,7,x + 2,11,x + 2,13,x + 1[]
442,6,2,x^2 + 2*x + 1,3,x^2 - 2*x - 4,5,x^2 - 4*x + 4,7,x^2 + 2*x - 4,11,x^2 -
2*x - 4,13,x^2 - 2*x + 1[]
442,7,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 - 2,7,x^2 - 8,11,x^2 + 4*x -
4,13,x^2 - 2*x + 1[]
442,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 4*x^2 - 4*x -
20,7,x^3 - 16*x - 16,11,x^3 + 2*x^2 - 20*x - 8,13,x^3 + 3*x^2 + 3*x + 1[]
442,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 6*x + 8,5,x^3 - 4*x^2 - 2*x +
4,7,x^3,11,x^3 + 4*x^2 - 12*x - 16,13,x^3 - 3*x^2 + 3*x - 1[]
443,1,2,x,3,x - 1,5,x + 2,7,x - 2,11,x + 2,13,x + 3[]
443,2,2,x + 1,3,x + 2,5,x,7,x - 1,11,x - 3,13,x - 3[]
443,3,2,x - 1,3,x + 2,5,x - 4,7,x + 1,11,x - 5,13,x - 3[]
443,4,2,x^12 + 3*x^11 - 13*x^10 - 39*x^9 + 64*x^8 + 181*x^7 - 159*x^6 - 357*x^5
+ 226*x^4 + 264*x^3 - 156*x^2 - 20*x + 6,3,x^12 + 7*x^11 + 2*x^10 - 78*x^9 -
124*x^8 + 233*x^7 + 550*x^6 - 102*x^5 - 652*x^4 - 190*x^3 + 90*x^2 + 34*x +
1,5,x^12 + 7*x^11 - 6*x^10 - 125*x^9 - 112*x^8 + 748*x^7 + 1161*x^6 - 1633*x^5 -
3454*x^4 + 648*x^3 + 3100*x^2 + 872*x + 56,7,x^12 + 16*x^11 + 82*x^10 + x^9 -
1576*x^8 - 6340*x^7 - 9454*x^6 + 1337*x^5 + 21270*x^4 + 20898*x^3 - 2376*x^2 -
13390*x - 5422,11,x^12 + 2*x^11 - 74*x^10 - 87*x^9 + 1927*x^8 + 1329*x^7 -
21068*x^6 - 13751*x^5 + 99640*x^4 + 84998*x^3 - 158154*x^2 - 203154*x -
59638,13,x^12 + 42*x^11 + 762*x^10 + 7742*x^9 + 47304*x^8 + 168507*x^7 +
264154*x^6 - 337744*x^5 - 2278142*x^4 - 3598919*x^3 - 1085318*x^2 + 1942180*x +
773943[]
443,5,2,x^22 - x^21 - 35*x^20 + 33*x^19 + 523*x^18 - 456*x^17 - 4360*x^16 +
3428*x^15 + 22226*x^14 - 15227*x^13 - 71363*x^12 + 40569*x^11 + 143034*x^10 -
62774*x^9 - 170342*x^8 + 51992*x^7 + 107186*x^6 - 20952*x^5 - 26926*x^4 +
5536*x^3 + 1736*x^2 - 512*x + 32,3,x^22 - 8*x^21 - 13*x^20 + 258*x^19 - 277*x^18
- 3152*x^17 + 7158*x^16 + 17518*x^15 - 62601*x^14 - 35125*x^13 + 273049*x^12 -
60648*x^11 - 639542*x^10 + 402011*x^9 + 820812*x^8 - 728657*x^7 - 555145*x^6 +
619866*x^5 + 160811*x^4 - 249823*x^3 + 3908*x^2 + 38492*x - 7505,5,x^22 - 3*x^21
- 62*x^20 + 193*x^19 + 1562*x^18 - 5048*x^17 - 20653*x^16 + 69697*x^15 +
154300*x^14 - 552410*x^13 - 648452*x^12 + 2567944*x^11 + 1370328*x^10 -
6881208*x^9 - 614072*x^8 + 9965872*x^7 - 2725408*x^6 - 6560320*x^5 + 4087552*x^4
+ 727808*x^3 - 1277440*x^2 + 390144*x - 38912,7,x^22 - 12*x^21 - 24*x^20 +
825*x^19 - 1772*x^18 - 19756*x^17 + 88784*x^16 + 142763*x^15 - 1495800*x^14 +
1469332*x^13 + 9596562*x^12 - 27509624*x^11 + 1698414*x^10 + 104417834*x^9 -
189450790*x^8 + 104780356*x^7 + 88456536*x^6 - 180546416*x^5 + 124019648*x^4 -
41346880*x^3 + 5686400*x^2 + 61696*x - 48640,11,x^22 + 8*x^21 - 96*x^20 -
933*x^19 + 3101*x^18 + 44511*x^17 - 16118*x^16 - 1104161*x^15 - 1373092*x^14 +
14729830*x^13 + 36493070*x^12 - 92480016*x^11 - 387038572*x^10 + 69217042*x^9 +
1754528290*x^8 + 1648843156*x^7 - 2136261664*x^6 - 3633649248*x^5 +
105667456*x^4 + 1839810752*x^3 + 38525440*x^2 - 367278080*x + 62244352,13,x^22 -
49*x^21 + 1016*x^20 - 11182*x^19 + 62717*x^18 - 56731*x^17 - 1542348*x^16 +
9370609*x^15 - 12788700*x^14 - 82568456*x^13 + 374413256*x^12 - 228088937*x^11 -
1905863180*x^10 + 4362711726*x^9 + 406458928*x^8 - 11366848236*x^7 +
11182610208*x^6 + 483761322*x^5 - 3479002043*x^4 + 150563134*x^3 + 271225542*x^2
+ 19429200*x - 1076517[]

Total time: 18.000 seconds, Total memory usage: 5.91MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 10:28:46 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [443..446] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 10:28:30 on modular  [Seed = 4245212789]
-------------------------------------

443,1,2,$.1,3,$.1 - 1,5,$.1 + 2,7,$.1 - 2,11,$.1 + 2,13,$.1 + 3[]
443,2,2,$.1 + 1,3,$.1 + 2,5,$.1,7,$.1 - 1,11,$.1 - 3,13,$.1 - 3[]
443,3,2,$.1 - 1,3,$.1 + 2,5,$.1 - 4,7,$.1 + 1,11,$.1 - 5,13,$.1 - 3[]
443,4,2,$.1^12 + 3*$.1^11 - 13*$.1^10 - 39*$.1^9 + 64*$.1^8 + 181*$.1^7 -
159*$.1^6 - 357*$.1^5 + 226*$.1^4 + 264*$.1^3 - 156*$.1^2 - 20*$.1 + 6,3,$.1^12 + 7*$.1^11 + 2*$.1^10 - 78*$.1^9 - 124*$.1^8 + 233*$.1^7 + 550*$.1^6 - 102*$.1^5
- 652*$.1^4 - 190*$.1^3 + 90*$.1^2 + 34*$.1 + 1,5,$.1^12 + 7*$.1^11 - 6*$.1^10 - 125*$.1^9 - 112*$.1^8 + 748*$.1^7 + 1161*$.1^6 - 1633*$.1^5 - 3454*$.1^4 + 648*$.1^3 + 3100*$.1^2 + 872*$.1 + 56,7,$.1^12 + 16*$.1^11 + 82*$.1^10 +$.1^9 -
1576*$.1^8 - 6340*$.1^7 - 9454*$.1^6 + 1337*$.1^5 + 21270*$.1^4 + 20898*$.1^3 -
2376*$.1^2 - 13390*$.1 - 5422,11,$.1^12 + 2*$.1^11 - 74*$.1^10 - 87*$.1^9 +
1927*$.1^8 + 1329*$.1^7 - 21068*$.1^6 - 13751*$.1^5 + 99640*$.1^4 + 84998*$.1^3
- 158154*$.1^2 - 203154*$.1 - 59638,13,$.1^12 + 42*$.1^11 + 762*$.1^10 + 7742*$.1^9 + 47304*$.1^8 + 168507*$.1^7 + 264154*$.1^6 - 337744*$.1^5 -
2278142*$.1^4 - 3598919*$.1^3 - 1085318*$.1^2 + 1942180*$.1 + 773943[]
443,5,2,$.1^22 -$.1^21 - 35*$.1^20 + 33*$.1^19 + 523*$.1^18 - 456*$.1^17 -
4360*$.1^16 + 3428*$.1^15 + 22226*$.1^14 - 15227*$.1^13 - 71363*$.1^12 + 40569*$.1^11 + 143034*$.1^10 - 62774*$.1^9 - 170342*$.1^8 + 51992*$.1^7 +
107186*$.1^6 - 20952*$.1^5 - 26926*$.1^4 + 5536*$.1^3 + 1736*$.1^2 - 512*$.1 +
32,3,$.1^22 - 8*$.1^21 - 13*$.1^20 + 258*$.1^19 - 277*$.1^18 - 3152*$.1^17 +
7158*$.1^16 + 17518*$.1^15 - 62601*$.1^14 - 35125*$.1^13 + 273049*$.1^12 - 60648*$.1^11 - 639542*$.1^10 + 402011*$.1^9 + 820812*$.1^8 - 728657*$.1^7 -
555145*$.1^6 + 619866*$.1^5 + 160811*$.1^4 - 249823*$.1^3 + 3908*$.1^2 + 38492*$.1 - 7505,5,$.1^22 - 3*$.1^21 - 62*$.1^20 + 193*$.1^19 + 1562*$.1^18 - 5048*$.1^17 - 20653*$.1^16 + 69697*$.1^15 + 154300*$.1^14 - 552410*$.1^13 -
648452*$.1^12 + 2567944*$.1^11 + 1370328*$.1^10 - 6881208*$.1^9 - 614072*$.1^8 + 9965872*$.1^7 - 2725408*$.1^6 - 6560320*$.1^5 + 4087552*$.1^4 + 727808*$.1^3 -
1277440*$.1^2 + 390144*$.1 - 38912,7,$.1^22 - 12*$.1^21 - 24*$.1^20 + 825*$.1^19
- 1772*$.1^18 - 19756*$.1^17 + 88784*$.1^16 + 142763*$.1^15 - 1495800*$.1^14 + 1469332*$.1^13 + 9596562*$.1^12 - 27509624*$.1^11 + 1698414*$.1^10 + 104417834*$.1^9 - 189450790*$.1^8 + 104780356*$.1^7 + 88456536*$.1^6 - 180546416*$.1^5 + 124019648*$.1^4 - 41346880*$.1^3 + 5686400*$.1^2 + 61696*$.1 -
48640,11,$.1^22 + 8*$.1^21 - 96*$.1^20 - 933*$.1^19 + 3101*$.1^18 + 44511*$.1^17
- 16118*$.1^16 - 1104161*$.1^15 - 1373092*$.1^14 + 14729830*$.1^13 +
36493070*$.1^12 - 92480016*$.1^11 - 387038572*$.1^10 + 69217042*$.1^9 +
1754528290*$.1^8 + 1648843156*$.1^7 - 2136261664*$.1^6 - 3633649248*$.1^5 +
105667456*$.1^4 + 1839810752*$.1^3 + 38525440*$.1^2 - 367278080*$.1 +
62244352,13,$.1^22 - 49*$.1^21 + 1016*$.1^20 - 11182*$.1^19 + 62717*$.1^18 - 56731*$.1^17 - 1542348*$.1^16 + 9370609*$.1^15 - 12788700*$.1^14 - 82568456*$.1^13 + 374413256*$.1^12 - 228088937*$.1^11 - 1905863180*$.1^10 + 4362711726*$.1^9 + 406458928*$.1^8 - 11366848236*$.1^7 + 11182610208*$.1^6 + 483761322*$.1^5 - 3479002043*$.1^4 + 150563134*$.1^3 + 271225542*$.1^2 + 19429200*$.1 - 1076517[]
444,1,2,x,3,x + 1,5,x,7,x,11,x - 4,13,x + 2[]
444,2,2,x,3,x - 1,5,x + 2,7,x + 4,11,x + 4,13,x + 6[]
444,3,2,x^2,3,x^2 + 2*x + 1,5,x^2 + 2*x - 2,7,x^2 - 12,11,x^2 + 8*x + 16,13,x^2
- 12[]
444,4,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 6,7,x^2 - 4*x + 4,11,x^2,13,x^2 - 4*x - 20[]
445,1,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + 2*x + 1,7,x^2 - 2*x - 4,11,x^2 +
4*x - 16,13,x^2 - 4*x - 16[]
445,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 2*x + 1,7,x^2 + 2*x - 2,11,x^2,13,x^2 -
4*x + 4[]
445,3,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 - 2*x + 1,7,x^2 - 2,11,x^2 - 8*x +
16,13,x^2 - 4*x - 4[]
445,4,2,x^4 - x^3 - 5*x^2 + 7*x - 1,3,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,5,x^4 +
4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 2*x^3 - 12*x^2 + 18*x + 11,11,x^4 + 14*x^3 +
70*x^2 + 147*x + 109,13,x^4 + 5*x^3 - 14*x^2 - 10*x + 19[]
445,5,2,x^4 - x^3 - 5*x^2 + 5*x + 1,3,x^4 - 4*x^3 - 2*x^2 + 21*x - 17,5,x^4 -
4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 12*x^3 + 54*x^2 - 108*x + 81,11,x^4 - 2*x^3 -
14*x^2 + 19*x + 13,13,x^4 + 7*x^3 - 58*x - 47[]
445,6,2,x^7 + 4*x^6 - 3*x^5 - 24*x^4 - 8*x^3 + 29*x^2 + 6*x - 9,3,x^7 + 8*x^6 +
16*x^5 - 19*x^4 - 89*x^3 - 72*x^2 - 8*x + 4,5,x^7 - 7*x^6 + 21*x^5 - 35*x^4 +
35*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 16*x^6 + 94*x^5 + 236*x^4 + 189*x^3 - 96*x^2 -
76*x + 4,11,x^7 + 10*x^6 + 14*x^5 - 149*x^4 - 639*x^3 - 968*x^2 - 608*x -
128,13,x^7 + 7*x^6 - 44*x^5 - 378*x^4 - 67*x^3 + 4078*x^2 + 9196*x + 5816[]
445,7,2,x^8 - x^7 - 11*x^6 + 9*x^5 + 34*x^4 - 19*x^3 - 27*x^2 + 11*x - 1,3,x^8 -
6*x^7 + 53*x^5 - 63*x^4 - 100*x^3 + 172*x^2 - 12*x - 44,5,x^8 + 8*x^7 + 28*x^6 +
56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 6*x^7 - 12*x^6 - 102*x^5 +
11*x^4 + 536*x^3 + 244*x^2 - 856*x - 676,11,x^8 - 14*x^7 + 50*x^6 + 75*x^5 -
599*x^4 + 112*x^3 + 2192*x^2 - 704*x - 2752,13,x^8 + 7*x^7 - 40*x^6 - 270*x^5 +
475*x^4 + 2144*x^3 - 3408*x^2 + 1024*x - 64[]
446,1,2,x + 1,3,x + 1,5,x,7,x,11,x - 1,13,x + 2[]
446,2,2,x + 1,3,x + 3,5,x + 4,7,x + 4,11,x + 5,13,x + 6[]
446,3,2,x - 1,3,x - 2,5,x,7,x,11,x + 2,13,x - 4[]
446,4,2,x - 1,3,x + 1,5,x + 2,7,x + 2,11,x + 3,13,x[]
446,5,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - x^6 -
14*x^5 + 12*x^4 + 50*x^3 - 36*x^2 - 38*x + 18,5,x^7 - 2*x^6 - 22*x^5 + 42*x^4 +
92*x^3 - 256*x^2 + 174*x - 36,7,x^7 - 6*x^6 - 8*x^5 + 88*x^4 - 48*x^3 - 224*x^2
+ 80*x + 96,11,x^7 - 9*x^6 - 14*x^5 + 254*x^4 - 58*x^3 - 2028*x^2 + 394*x +
3494,13,x^7 + 2*x^6 - 64*x^5 - 78*x^4 + 1360*x^3 + 416*x^2 - 9602*x + 7056[]
446,6,2,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,3,x^8
- 4*x^7 - 12*x^6 + 54*x^5 + 34*x^4 - 204*x^3 + 6*x^2 + 160*x + 34,5,x^8 - 4*x^7
- 24*x^6 + 106*x^5 + 130*x^4 - 788*x^3 + 98*x^2 + 1596*x - 942,7,x^8 - 4*x^7 -
40*x^6 + 176*x^5 + 456*x^4 - 2512*x^3 - 496*x^2 + 11712*x - 11312,11,x^8 - 2*x^7
- 50*x^6 + 122*x^5 + 650*x^4 - 1932*x^3 - 666*x^2 + 3600*x - 126,13,x^8 - 10*x^7
- 10*x^6 + 298*x^5 - 342*x^4 - 2048*x^3 + 3682*x^2 - 612*x - 942[]

Total time: 16.010 seconds, Total memory usage: 5.92MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 10:33:47 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [446..449] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 10:33:32 on modular  [Seed = 367011788]
-------------------------------------

446,1,2,$.1 + 1,3,$.1 + 1,5,$.1,7,$.1,11,$.1 - 1,13,$.1 + 2[]
446,2,2,$.1 + 1,3,$.1 + 3,5,$.1 + 4,7,$.1 + 4,11,$.1 + 5,13,$.1 + 6[]
446,3,2,$.1 - 1,3,$.1 - 2,5,$.1,7,$.1,11,$.1 + 2,13,$.1 - 4[]
446,4,2,$.1 - 1,3,$.1 + 1,5,$.1 + 2,7,$.1 + 2,11,$.1 + 3,13,$.1[]
446,5,2,$.1^7 - 7*$.1^6 + 21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1,3,$.1^7 - $.1^6 - 14*$.1^5 + 12*$.1^4 + 50*$.1^3 - 36*$.1^2 - 38*$.1 +
18,5,$.1^7 - 2*$.1^6 - 22*$.1^5 + 42*$.1^4 + 92*$.1^3 - 256*$.1^2 + 174*$.1 - 36,7,$.1^7 - 6*$.1^6 - 8*$.1^5 + 88*$.1^4 - 48*$.1^3 - 224*$.1^2 + 80*$.1 +
96,11,$.1^7 - 9*$.1^6 - 14*$.1^5 + 254*$.1^4 - 58*$.1^3 - 2028*$.1^2 + 394*$.1 + 3494,13,$.1^7 + 2*$.1^6 - 64*$.1^5 - 78*$.1^4 + 1360*$.1^3 + 416*$.1^2 - 9602*$.1 + 7056[]
446,6,2,$.1^8 + 8*$.1^7 + 28*$.1^6 + 56*$.1^5 + 70*$.1^4 + 56*$.1^3 + 28*$.1^2 + 8*$.1 + 1,3,$.1^8 - 4*$.1^7 - 12*$.1^6 + 54*$.1^5 + 34*$.1^4 - 204*$.1^3 +
6*$.1^2 + 160*$.1 + 34,5,$.1^8 - 4*$.1^7 - 24*$.1^6 + 106*$.1^5 + 130*$.1^4 - 788*$.1^3 + 98*$.1^2 + 1596*$.1 - 942,7,$.1^8 - 4*$.1^7 - 40*$.1^6 + 176*$.1^5 +
456*$.1^4 - 2512*$.1^3 - 496*$.1^2 + 11712*$.1 - 11312,11,$.1^8 - 2*$.1^7 -
50*$.1^6 + 122*$.1^5 + 650*$.1^4 - 1932*$.1^3 - 666*$.1^2 + 3600*$.1 -
126,13,$.1^8 - 10*$.1^7 - 10*$.1^6 + 298*$.1^5 - 342*$.1^4 - 2048*$.1^3 +
3682*$.1^2 - 612*$.1 - 942[]
447,1,2,x^3 + x^2 - 2*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3,7,x^3 + 3*x^2 - 4*x -
13,11,x^3 - 3*x^2 - 4*x - 1,13,x^3 + 8*x^2 + 12*x - 8[]
447,2,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 6*x^2 + 12*x + 8,7,x^3 +
3*x^2 - 1,11,x^3 + 9*x^2 + 18*x + 9,13,x^3 - 12*x + 8[]
447,3,2,x^9 - 4*x^8 - 6*x^7 + 37*x^6 - 3*x^5 - 101*x^4 + 49*x^3 + 72*x^2 - 21*x
- 13,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x
- 1,5,x^9 - 8*x^8 + 2*x^7 + 120*x^6 - 256*x^5 - 224*x^4 + 1160*x^3 - 1216*x^2 +
480*x - 64,7,x^9 - x^8 - 29*x^7 + 32*x^6 + 222*x^5 - 293*x^4 - 313*x^3 + 435*x^2
- 144*x + 13,11,x^9 - 13*x^8 + 25*x^7 + 278*x^6 - 1046*x^5 - 1341*x^4 + 8767*x^3
- 3407*x^2 - 18734*x + 17707,13,x^9 + 2*x^8 - 68*x^7 - 72*x^6 + 1756*x^5 +
216*x^4 - 20008*x^3 + 14000*x^2 + 81472*x - 106688[]
447,4,2,x^10 - 3*x^9 - 12*x^8 + 37*x^7 + 44*x^6 - 142*x^5 - 50*x^4 + 181*x^3 -
5*x^2 - 30*x + 1,3,x^10 + 10*x^9 + 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 +
210*x^4 + 120*x^3 + 45*x^2 + 10*x + 1,5,x^10 - 4*x^9 - 34*x^8 + 132*x^7 +
392*x^6 - 1440*x^5 - 1848*x^4 + 5904*x^3 + 3488*x^2 - 6784*x - 2944,7,x^10 -
9*x^9 - 9*x^8 + 252*x^7 - 246*x^6 - 2289*x^5 + 3135*x^4 + 7363*x^3 - 8580*x^2 -
3231*x - 88,11,x^10 + 7*x^9 - 53*x^8 - 392*x^7 + 884*x^6 + 7133*x^5 - 3941*x^4 -
44019*x^3 - 15004*x^2 + 41021*x - 8900,13,x^10 - 4*x^9 - 80*x^8 + 248*x^7 +
2372*x^6 - 4632*x^5 - 31608*x^4 + 19680*x^3 + 164960*x^2 + 110144*x - 25216[]
448,1,2,x,3,x,5,x + 2,7,x + 1,11,x - 4,13,x + 2[]
448,2,2,x,3,x - 2,5,x,7,x - 1,11,x,13,x - 4[]
448,3,2,x,3,x + 2,5,x - 4,7,x - 1,11,x,13,x[]
448,4,2,x,3,x - 2,5,x,7,x + 1,11,x - 4,13,x - 4[]
448,5,2,x,3,x - 2,5,x - 4,7,x + 1,11,x,13,x[]
448,6,2,x,3,x + 2,5,x,7,x + 1,11,x,13,x - 4[]
448,7,2,x,3,x,5,x + 2,7,x - 1,11,x + 4,13,x + 2[]
448,8,2,x,3,x + 2,5,x,7,x - 1,11,x + 4,13,x - 4[]
448,9,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 2*x - 4,7,x^2 + 2*x + 1,11,x^2 + 4*x -
16,13,x^2 + 6*x + 4[]
448,10,2,x^2,3,x^2 - 2*x - 4,5,x^2 + 2*x - 4,7,x^2 - 2*x + 1,11,x^2 - 4*x -
16,13,x^2 + 6*x + 4[]
449,1,2,x^14 + 3*x^13 - 13*x^12 - 42*x^11 + 59*x^10 + 214*x^9 - 117*x^8 -
503*x^7 + 109*x^6 + 576*x^5 - 50*x^4 - 309*x^3 + 14*x^2 + 62*x - 3,3,x^14 +
5*x^13 - 11*x^12 - 84*x^11 - 4*x^10 + 452*x^9 + 260*x^8 - 1048*x^7 - 678*x^6 +
1119*x^5 + 457*x^4 - 559*x^3 - 10*x^2 + 50*x + 1,5,x^14 + 7*x^13 - 15*x^12 -
199*x^11 - 140*x^10 + 1792*x^9 + 2873*x^8 - 6770*x^7 - 15213*x^6 + 10156*x^5 +
33742*x^4 - 2190*x^3 - 30267*x^2 - 4139*x + 7679,7,x^14 + 22*x^13 + 190*x^12 +
754*x^11 + 811*x^10 - 4195*x^9 - 16603*x^8 - 20095*x^7 + 4151*x^6 + 30082*x^5 +
20539*x^4 - 3927*x^3 - 10087*x^2 - 4177*x - 567,11,x^14 + 14*x^13 + 12*x^12 -
640*x^11 - 2652*x^10 + 5733*x^9 + 48358*x^8 + 26988*x^7 - 280328*x^6 -
445385*x^5 + 389247*x^4 + 1164767*x^3 + 534702*x^2 - 79232*x - 4776,13,x^14 +
10*x^13 - 49*x^12 - 672*x^11 + 439*x^10 + 15890*x^9 + 11209*x^8 - 152535*x^7 -
224092*x^6 + 471926*x^5 + 1088176*x^4 + 371725*x^3 - 257324*x^2 - 76496*x -
1399[]
449,2,2,x^23 - 38*x^21 + x^20 + 623*x^19 - 31*x^18 - 5771*x^17 + 398*x^16 +
33229*x^15 - 2753*x^14 - 123306*x^13 + 11230*x^12 + 296022*x^11 - 28009*x^10 -
450008*x^9 + 43215*x^8 + 412760*x^7 - 40559*x^6 - 210040*x^5 + 21311*x^4 +
50781*x^3 - 5664*x^2 - 3789*x + 621,3,x^23 - 3*x^22 - 41*x^21 + 126*x^20 +
705*x^19 - 2239*x^18 - 6615*x^17 + 22000*x^16 + 36931*x^15 - 131324*x^14 -
125454*x^13 + 493823*x^12 + 253204*x^11 - 1176829*x^10 - 273386*x^9 +
1744851*x^8 + 89282*x^7 - 1530487*x^6 + 107122*x^5 + 709889*x^4 - 113406*x^3 -
130568*x^2 + 31357*x + 1052,5,x^23 - 3*x^22 - 67*x^21 + 205*x^20 + 1879*x^19 -
5847*x^18 - 28864*x^17 + 91095*x^16 + 266930*x^15 - 851395*x^14 - 1536438*x^13 +
4922437*x^12 + 5489362*x^11 - 17444495*x^10 - 11750004*x^9 + 36024274*x^8 +
13897552*x^7 - 38572189*x^6 - 7484349*x^5 + 16283982*x^4 + 563783*x^3 -
818077*x^2 - 71243*x + 46,7,x^23 - 26*x^22 + 238*x^21 - 482*x^20 - 6545*x^19 +
45377*x^18 - 30911*x^17 - 679327*x^16 + 2251007*x^15 + 2157766*x^14 -
23780381*x^13 + 25589713*x^12 + 96090845*x^11 - 241472873*x^10 - 73211795*x^9 +
769282916*x^8 - 517269912*x^7 - 912322192*x^6 + 1264824144*x^5 + 64165888*x^4 -
708731776*x^3 + 190621184*x^2 + 60660480*x + 1075200,11,x^23 - 6*x^22 - 124*x^21
+ 740*x^20 + 6220*x^19 - 37467*x^18 - 161494*x^17 + 1008144*x^16 + 2308464*x^15
- 15603673*x^14 - 17920509*x^13 + 141260947*x^12 + 71700954*x^11 -
739015112*x^10 - 162391640*x^9 + 2185091808*x^8 + 465394048*x^7 - 3543357440*x^6
- 1399362304*x^5 + 2656435200*x^4 + 1817577472*x^3 - 264945664*x^2 - 439738368*x
- 84639744,13,x^23 - 10*x^22 - 121*x^21 + 1584*x^20 + 4123*x^19 - 101054*x^18 +
62483*x^17 + 3334451*x^16 - 8140454*x^15 - 59666520*x^14 + 242531480*x^13 +
517488489*x^12 - 3599321598*x^11 - 494951422*x^10 + 28586733037*x^9 -
27400835882*x^8 - 111312873480*x^7 + 201107004784*x^6 + 134231844320*x^5 -
471865931584*x^4 + 162002751872*x^3 + 143643216128*x^2 - 22367896320*x -
6983520768[]

Total time: 14.289 seconds, Total memory usage: 5.54MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 10:41:51 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [449..452] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 10:41:31 on modular  [Seed = 234372531]
-------------------------------------

449,1,2,$.1^14 + 3*$.1^13 - 13*$.1^12 - 42*$.1^11 + 59*$.1^10 + 214*$.1^9 -
117*$.1^8 - 503*$.1^7 + 109*$.1^6 + 576*$.1^5 - 50*$.1^4 - 309*$.1^3 + 14*$.1^2 + 62*$.1 - 3,3,$.1^14 + 5*$.1^13 - 11*$.1^12 - 84*$.1^11 - 4*$.1^10 + 452*$.1^9
+ 260*$.1^8 - 1048*$.1^7 - 678*$.1^6 + 1119*$.1^5 + 457*$.1^4 - 559*$.1^3 -
10*$.1^2 + 50*$.1 + 1,5,$.1^14 + 7*$.1^13 - 15*$.1^12 - 199*$.1^11 - 140*$.1^10 + 1792*$.1^9 + 2873*$.1^8 - 6770*$.1^7 - 15213*$.1^6 + 10156*$.1^5 + 33742*$.1^4 - 2190*$.1^3 - 30267*$.1^2 - 4139*$.1 + 7679,7,$.1^14 + 22*$.1^13 + 190*$.1^12 + 754*$.1^11 + 811*$.1^10 - 4195*$.1^9 - 16603*$.1^8 - 20095*$.1^7 + 4151*$.1^6 + 30082*$.1^5 + 20539*$.1^4 - 3927*$.1^3 - 10087*$.1^2 - 4177*$.1 - 567,11,$.1^14 + 14*$.1^13 + 12*$.1^12 - 640*$.1^11 - 2652*$.1^10 + 5733*$.1^9 + 48358*$.1^8 + 26988*$.1^7 - 280328*$.1^6 - 445385*$.1^5 + 389247*$.1^4 + 1164767*$.1^3 +
534702*$.1^2 - 79232*$.1 - 4776,13,$.1^14 + 10*$.1^13 - 49*$.1^12 - 672*$.1^11 +
439*$.1^10 + 15890*$.1^9 + 11209*$.1^8 - 152535*$.1^7 - 224092*$.1^6 + 471926*$.1^5 + 1088176*$.1^4 + 371725*$.1^3 - 257324*$.1^2 - 76496*$.1 - 1399[]
449,2,2,$.1^23 - 38*$.1^21 + $.1^20 + 623*$.1^19 - 31*$.1^18 - 5771*$.1^17 +
398*$.1^16 + 33229*$.1^15 - 2753*$.1^14 - 123306*$.1^13 + 11230*$.1^12 + 296022*$.1^11 - 28009*$.1^10 - 450008*$.1^9 + 43215*$.1^8 + 412760*$.1^7 -
40559*$.1^6 - 210040*$.1^5 + 21311*$.1^4 + 50781*$.1^3 - 5664*$.1^2 - 3789*$.1 +
621,3,$.1^23 - 3*$.1^22 - 41*$.1^21 + 126*$.1^20 + 705*$.1^19 - 2239*$.1^18 -
6615*$.1^17 + 22000*$.1^16 + 36931*$.1^15 - 131324*$.1^14 - 125454*$.1^13 + 493823*$.1^12 + 253204*$.1^11 - 1176829*$.1^10 - 273386*$.1^9 + 1744851*$.1^8 +
89282*$.1^7 - 1530487*$.1^6 + 107122*$.1^5 + 709889*$.1^4 - 113406*$.1^3 - 130568*$.1^2 + 31357*$.1 + 1052,5,$.1^23 - 3*$.1^22 - 67*$.1^21 + 205*$.1^20 + 1879*$.1^19 - 5847*$.1^18 - 28864*$.1^17 + 91095*$.1^16 + 266930*$.1^15 -
851395*$.1^14 - 1536438*$.1^13 + 4922437*$.1^12 + 5489362*$.1^11 -
17444495*$.1^10 - 11750004*$.1^9 + 36024274*$.1^8 + 13897552*$.1^7 -
38572189*$.1^6 - 7484349*$.1^5 + 16283982*$.1^4 + 563783*$.1^3 - 818077*$.1^2 - 71243*$.1 + 46,7,$.1^23 - 26*$.1^22 + 238*$.1^21 - 482*$.1^20 - 6545*$.1^19 + 45377*$.1^18 - 30911*$.1^17 - 679327*$.1^16 + 2251007*$.1^15 + 2157766*$.1^14 -
23780381*$.1^13 + 25589713*$.1^12 + 96090845*$.1^11 - 241472873*$.1^10 -
73211795*$.1^9 + 769282916*$.1^8 - 517269912*$.1^7 - 912322192*$.1^6 +
1264824144*$.1^5 + 64165888*$.1^4 - 708731776*$.1^3 + 190621184*$.1^2 +
60660480*$.1 + 1075200,11,$.1^23 - 6*$.1^22 - 124*$.1^21 + 740*$.1^20 + 6220*$.1^19 - 37467*$.1^18 - 161494*$.1^17 + 1008144*$.1^16 + 2308464*$.1^15 -
15603673*$.1^14 - 17920509*$.1^13 + 141260947*$.1^12 + 71700954*$.1^11 -
739015112*$.1^10 - 162391640*$.1^9 + 2185091808*$.1^8 + 465394048*$.1^7 -
3543357440*$.1^6 - 1399362304*$.1^5 + 2656435200*$.1^4 + 1817577472*$.1^3 -
264945664*$.1^2 - 439738368*$.1 - 84639744,13,$.1^23 - 10*$.1^22 - 121*$.1^21 + 1584*$.1^20 + 4123*$.1^19 - 101054*$.1^18 + 62483*$.1^17 + 3334451*$.1^16 -
8140454*$.1^15 - 59666520*$.1^14 + 242531480*$.1^13 + 517488489*$.1^12 -
3599321598*$.1^11 - 494951422*$.1^10 + 28586733037*$.1^9 - 27400835882*$.1^8 -
111312873480*$.1^7 + 201107004784*$.1^6 + 134231844320*$.1^5 - 471865931584*$.1^4 + 162002751872*$.1^3 + 143643216128*$.1^2 - 22367896320*$.1 - 6983520768[] 450,1,2,x + 1,3,x,5,x,7,x + 2,11,x + 6,13,x - 4[] 450,2,2,x + 1,3,x,5,x,7,x + 2,11,x - 3,13,x - 4[] 450,3,2,x + 1,3,x,5,x,7,x - 4,11,x,13,x + 2[] 450,4,2,x + 1,3,x,5,x,7,x + 2,11,x + 2,13,x + 6[] 450,5,2,x - 1,3,x,5,x,7,x + 2,11,x - 6,13,x - 4[] 450,6,2,x - 1,3,x,5,x,7,x - 2,11,x + 2,13,x - 6[] 450,7,2,x - 1,3,x,5,x,7,x - 2,11,x - 3,13,x + 4[] 451,1,2,x,3,x - 1,5,x + 3,7,x - 4,11,x + 1,13,x + 6[] 451,2,2,x^5 + 2*x^4 - 5*x^3 - 10*x^2 + 4*x + 9,3,x^5 + 4*x^4 + x^3 - 8*x^2 - 6*x - 1,5,x^5 + 4*x^4 - 15*x^2 - 16*x - 3,7,x^5 + 3*x^4 - 7*x^3 - 18*x^2 + 5*x + 13,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 - x^4 - 17*x^3 + 29*x^2 + 40*x - 75[] 451,3,2,x^5 + 2*x^4 - 3*x^3 - 4*x^2 + 2*x + 1,3,x^5 - 7*x^3 - 2*x^2 + 8*x - 1,5,x^5 + 8*x^4 + 12*x^3 - 27*x^2 - 36*x + 37,7,x^5 + 5*x^4 - 9*x^3 - 52*x^2 + 17*x + 97,11,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,13,x^5 + 5*x^4 - 3*x^3 - 9*x^2 + 4*x + 1[] 451,4,2,x^10 - 4*x^9 - 6*x^8 + 38*x^7 - 7*x^6 - 105*x^5 + 74*x^4 + 77*x^3 - 74*x^2 + 8,3,x^10 - 23*x^8 + 6*x^7 + 174*x^6 - 97*x^5 - 490*x^4 + 368*x^3 + 408*x^2 - 288*x - 64,5,x^10 - 6*x^9 - 14*x^8 + 118*x^7 + 49*x^6 - 774*x^5 - 141*x^4 + 2025*x^3 + 792*x^2 - 1485*x - 837,7,x^10 - 7*x^9 - 13*x^8 + 197*x^7 - 349*x^6 - 686*x^5 + 2520*x^4 - 1520*x^3 - 1308*x^2 + 838*x + 355,11,x^10 - 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1,13,x^10 - 4*x^9 - 77*x^8 + 232*x^7 + 2019*x^6 - 3811*x^5 - 22684*x^4 + 15743*x^3 + 104057*x^2 + 26432*x - 79324[] 451,5,2,x^12 - 3*x^11 - 16*x^10 + 48*x^9 + 93*x^8 - 270*x^7 - 251*x^6 + 633*x^5 + 359*x^4 - 582*x^3 - 248*x^2 + 136*x + 32,3,x^12 - x^11 - 31*x^10 + 27*x^9 + 360*x^8 - 241*x^7 - 1941*x^6 + 746*x^5 + 4752*x^4 + 8*x^3 - 3968*x^2 - 1984*x - 256,5,x^12 - 13*x^11 + 42*x^10 + 132*x^9 - 1041*x^8 + 1195*x^7 + 4687*x^6 - 13332*x^5 + 6395*x^4 + 11677*x^3 - 11562*x^2 + 833*x + 922,7,x^12 + 7*x^11 - 31*x^10 - 287*x^9 + 159*x^8 + 3946*x^7 + 2388*x^6 - 21684*x^5 - 25156*x^4 + 36136*x^3 + 62521*x^2 + 28448*x + 4096,11,x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1,13,x^12 - 99*x^10 + 78*x^9 + 3589*x^8 - 5381*x^7 - 56370*x^6 + 116503*x^5 + 339367*x^4 - 827784*x^3 - 563400*x^2 + 1526320*x + 135344[] 452,1,2,x^3,3,x^3 + 3*x^2 - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 9*x + 9,11,x^3 - 21*x - 17,13,x^3 + 12*x^2 + 45*x + 53[] 452,2,2,x^7,3,x^7 - 3*x^6 - 12*x^5 + 33*x^4 + 40*x^3 - 98*x^2 - 16*x + 58,5,x^7 - 3*x^6 - 21*x^5 + 67*x^4 + 76*x^3 - 272*x^2 - 32*x + 240,7,x^7 - 29*x^5 + 5*x^4 + 232*x^3 - 96*x^2 - 512*x + 320,11,x^7 - 4*x^6 - 49*x^5 + 203*x^4 + 444*x^3 - 1856*x^2 - 1120*x + 4704,13,x^7 - 16*x^6 + 69*x^5 + 85*x^4 - 1124*x^3 + 1620*x^2 + 852*x - 892[] Total time: 19.920 seconds, Total memory usage: 6.44MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:46:52 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [452..455] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:46:35 on modular [Seed = 2022528950] ------------------------------------- 452,1,2,$.1^3,3,$.1^3 + 3*$.1^2 - 1,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 -
9*$.1 + 9,11,$.1^3 - 21*$.1 - 17,13,$.1^3 + 12*$.1^2 + 45*$.1 + 53[]
452,2,2,$.1^7,3,$.1^7 - 3*$.1^6 - 12*$.1^5 + 33*$.1^4 + 40*$.1^3 - 98*$.1^2 - 16*$.1 + 58,5,$.1^7 - 3*$.1^6 - 21*$.1^5 + 67*$.1^4 + 76*$.1^3 - 272*$.1^2 -
32*$.1 + 240,7,$.1^7 - 29*$.1^5 + 5*$.1^4 + 232*$.1^3 - 96*$.1^2 - 512*$.1 + 320,11,$.1^7 - 4*$.1^6 - 49*$.1^5 + 203*$.1^4 + 444*$.1^3 - 1856*$.1^2 - 1120*$.1 + 4704,13,$.1^7 - 16*$.1^6 + 69*$.1^5 + 85*$.1^4 - 1124*$.1^3 + 1620*$.1^2 + 852*$.1 - 892[] 453,1,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 - 4*x + 4,7,x^2 - 2*x + 1,11,x^2 - 4*x + 1,13,x^2 - 12[] 453,2,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 2*x + 1,11,x^2 - 6*x + 4,13,x^2 + 2*x + 1[] 453,3,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 - 3*x + 1,7,x^2 + 4*x - 1,11,x^2 - 6*x + 4,13,x^2 - 8*x + 11[] 453,4,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + x - 1,7,x^2 + 6*x + 9,11,x^2 + 6*x + 4,13,x^2 + 2*x + 1[] 453,5,2,x^3 + x^2 - 2*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 4*x - 13,7,x^3 - 2*x^2 - 8*x + 8,11,x^3 - x^2 - 16*x + 29,13,x^3 + 4*x^2 - 4*x - 8[] 453,6,2,x^5 + 3*x^4 - 6*x^3 - 18*x^2 + 8*x + 19,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 + 4*x^4 - 8*x^3 - 32*x^2 + 11*x + 49,7,x^5 + 6*x^4 - 9*x^3 - 90*x^2 - 40*x + 200,11,x^5 + 17*x^4 + 98*x^3 + 183*x^2 - 150*x - 580,13,x^5 - 4*x^4 - 45*x^3 + 164*x^2 + 480*x - 1600[] 453,7,2,x^9 - 6*x^8 + 3*x^7 + 42*x^6 - 68*x^5 - 62*x^4 + 168*x^3 - 15*x^2 - 98*x + 31,3,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,5,x^9 + 2*x^8 - 31*x^7 - 54*x^6 + 264*x^5 + 382*x^4 - 363*x^3 - 354*x^2 - 36*x + 8,7,x^9 - 14*x^8 + 53*x^7 + 96*x^6 - 1140*x^5 + 2688*x^4 - 1696*x^3 - 1664*x^2 + 2240*x - 512,11,x^9 - 2*x^8 - 46*x^7 + 86*x^6 + 193*x^5 - 124*x^4 - 193*x^3 + 36*x^2 + 43*x + 4,13,x^9 + 2*x^8 - 64*x^7 - 24*x^6 + 1376*x^5 - 1472*x^4 - 8768*x^3 + 21248*x^2 - 16384*x + 4096[] 454,1,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 2*x - 4,7,x^2 + 5*x + 5,11,x^2 + 9*x + 19,13,x^2 - 2*x - 4[] 454,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 3*x^2 - 2*x + 1,5,x^4 + 4*x^3 - 2*x^2 - 16*x - 4,7,x^4 - 2*x^3 - 13*x^2 + 14*x - 1,11,x^4 + 10*x^3 + 33*x^2 + 42*x + 17,13,x^4 + 4*x^3 - 24*x^2 - 24*x - 4[] 454,3,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + x^4 - 11*x^3 - 8*x^2 + 28*x + 8,5,x^5 - 3*x^4 - 8*x^3 + 23*x^2 + 4*x - 4,7,x^5 + 6*x^4 - 4*x^3 - 48*x^2 - 3*x + 19,11,x^5 - 7*x^4 + x^3 + 30*x^2 + 12*x - 8,13,x^5 - 3*x^4 - 32*x^3 + 11*x^2 + 54*x - 4[] 454,4,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - 4*x^6 - 9*x^5 + 48*x^4 - 11*x^3 - 92*x^2 + 28*x + 56,5,x^7 + x^6 - 20*x^5 - 9*x^4 + 86*x^3 - 10*x^2 - 52*x - 4,7,x^7 - 5*x^6 - 5*x^5 + 54*x^4 - 57*x^3 - 30*x^2 + 36*x - 7,11,x^7 - 10*x^6 - x^5 + 266*x^4 - 663*x^3 - 798*x^2 + 4076*x - 3304,13,x^7 + 5*x^6 - 30*x^5 - 231*x^4 - 480*x^3 - 352*x^2 - 72*x - 4[] 455,1,2,x - 1,3,x,5,x + 1,7,x + 1,11,x,13,x + 1[] 455,2,2,x + 1,3,x,5,x - 1,7,x + 1,11,x,13,x - 1[] 455,3,2,x^4 + x^3 - 5*x^2 - 3*x + 1,3,x^4 - 9*x^2 + 2*x + 11,5,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 - 2*x^3 - 32*x^2 + 112*x - 80,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[] 455,4,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4 - 4*x^3 - x^2 + 14*x - 9,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 + 2*x^3 - 32*x^2 - 80*x - 48,13,x^4 + 4*x^3 + 6*x^2 + 4*x + 1[] 455,5,2,x^6 - 3*x^5 - 6*x^4 + 20*x^3 + 6*x^2 - 31*x + 9,3,x^6 - 13*x^4 + 2*x^3 + 35*x^2 + 4*x - 8,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 + 2*x^5 - 40*x^4 - 80*x^3 + 368*x^2 + 448*x - 1152,13,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1[] 455,6,2,x^7 - 15*x^5 + 2*x^4 + 66*x^3 - 17*x^2 - 72*x + 19,3,x^7 - 21*x^5 + 2*x^4 + 127*x^3 - 16*x^2 - 184*x - 80,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,11,x^7 - 6*x^6 - 48*x^5 + 320*x^4 + 368*x^3 - 3712*x^2 + 2432*x + 256,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[] Total time: 16.750 seconds, Total memory usage: 5.77MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:52:29 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [455..458] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:52:10 on modular [Seed = 1788823381] ------------------------------------- 455,1,2,$.1 - 1,3,$.1,5,$.1 + 1,7,$.1 + 1,11,$.1,13,$.1 + 1[] 455,2,2,$.1 + 1,3,$.1,5,$.1 - 1,7,$.1 + 1,11,$.1,13,$.1 - 1[] 455,3,2,$.1^4 + $.1^3 - 5*$.1^2 - 3*$.1 + 1,3,$.1^4 - 9*$.1^2 + 2*$.1 +
11,5,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 +
1,11,$.1^4 - 2*$.1^3 - 32*$.1^2 + 112*$.1 - 80,13,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1[]
455,4,2,$.1^4 - 3*$.1^3 - $.1^2 + 5*$.1 + 1,3,$.1^4 - 4*$.1^3 - $.1^2 + 14*$.1 -
9,5,$.1^4 - 4*$.1^3 + 6*$.1^2 - 4*$.1 + 1,7,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 +
1,11,$.1^4 + 2*$.1^3 - 32*$.1^2 - 80*$.1 - 48,13,$.1^4 + 4*$.1^3 + 6*$.1^2 + 4*$.1 + 1[]
455,5,2,$.1^6 - 3*$.1^5 - 6*$.1^4 + 20*$.1^3 + 6*$.1^2 - 31*$.1 + 9,3,$.1^6 - 13*$.1^4 + 2*$.1^3 + 35*$.1^2 + 4*$.1 - 8,5,$.1^6 - 6*$.1^5 + 15*$.1^4 -
20*$.1^3 + 15*$.1^2 - 6*$.1 + 1,7,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1,11,$.1^6 + 2*$.1^5 - 40*$.1^4 - 80*$.1^3 + 368*$.1^2 +
448*$.1 - 1152,13,$.1^6 - 6*$.1^5 + 15*$.1^4 - 20*$.1^3 + 15*$.1^2 - 6*$.1 + 1[] 455,6,2,$.1^7 - 15*$.1^5 + 2*$.1^4 + 66*$.1^3 - 17*$.1^2 - 72*$.1 + 19,3,$.1^7 -
21*$.1^5 + 2*$.1^4 + 127*$.1^3 - 16*$.1^2 - 184*$.1 - 80,5,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,7,$.1^7 - 7*$.1^6 +
21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1,11,$.1^7 - 6*$.1^6 - 48*$.1^5 + 320*$.1^4 + 368*$.1^3 - 3712*$.1^2 + 2432*$.1 + 256,13,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1[] 456,1,2,x,3,x + 1,5,x - 4,7,x - 4,11,x + 4,13,x + 4[] 456,2,2,x,3,x - 1,5,x - 2,7,x,11,x,13,x - 2[] 456,3,2,x,3,x - 1,5,x + 3,7,x + 3,11,x + 1,13,x + 2[] 456,4,2,x,3,x + 1,5,x - 1,7,x + 3,11,x + 5,13,x + 2[] 456,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 10,7,x^2 + 3*x - 8,11,x^2 - 3*x - 8,13,x^2 - 12*x + 36[] 456,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 - x - 4,7,x^2 - x - 4,11,x^2 - 7*x + 8,13,x^2 + 2*x - 16[] 457,1,2,x^2 - x - 1,3,x^2 - x - 1,5,x^2 + 4*x + 4,7,x^2 + x - 1,11,x^2 + 10*x + 25,13,x^2 - 9*x + 19[] 457,2,2,x^15 + 10*x^14 + 27*x^13 - 43*x^12 - 324*x^11 - 310*x^10 + 917*x^9 + 1910*x^8 - 330*x^7 - 3170*x^6 - 1281*x^5 + 1917*x^4 + 1110*x^3 - 506*x^2 - 232*x + 79,3,x^15 + 12*x^14 + 41*x^13 - 53*x^12 - 629*x^11 - 1007*x^10 + 1640*x^9 + 6449*x^8 + 3861*x^7 - 7351*x^6 - 10000*x^5 - 498*x^4 + 3853*x^3 + 938*x^2 - 275*x - 7,5,x^15 + 9*x^14 - 3*x^13 - 220*x^12 - 306*x^11 + 2107*x^10 + 4204*x^9 - 9949*x^8 - 22795*x^7 + 23452*x^6 + 56696*x^5 - 22253*x^4 - 55753*x^3 - 1526*x^2 + 9110*x + 1561,7,x^15 + 15*x^14 + 44*x^13 - 384*x^12 - 2576*x^11 - 615*x^10 + 30656*x^9 + 62493*x^8 - 94313*x^7 - 359632*x^6 + 26522*x^5 + 792762*x^4 + 205877*x^3 - 757233*x^2 - 155241*x + 243999,11,x^15 - 3*x^14 - 81*x^13 + 184*x^12 + 2489*x^11 - 2926*x^10 - 38009*x^9 - 2039*x^8 + 274479*x^7 + 326299*x^6 - 543677*x^5 - 1424824*x^4 - 1022219*x^3 - 129316*x^2 + 137450*x + 42709,13,x^15 + 22*x^14 + 134*x^13 - 480*x^12 - 9388*x^11 - 35576*x^10 + 42716*x^9 + 724698*x^8 + 2107635*x^7 + 1206799*x^6 - 6877134*x^5 - 18724263*x^4 - 21377048*x^3 - 12207240*x^2 - 3224610*x - 288757[] 457,3,2,x^20 - 6*x^19 - 12*x^18 + 130*x^17 - 25*x^16 - 1135*x^15 + 1068*x^14 + 5145*x^13 - 6910*x^12 - 12965*x^11 + 21043*x^10 + 17930*x^9 - 33307*x^8 - 12486*x^7 + 25549*x^6 + 3888*x^5 - 7077*x^4 - 927*x^3 + 255*x^2 + 6*x - 1,3,x^20 - 9*x^19 + 214*x^17 - 417*x^16 - 1941*x^15 + 6028*x^14 + 7936*x^13 - 39328*x^12 - 8993*x^11 + 141030*x^10 - 42579*x^9 - 287729*x^8 + 177855*x^7 + 317230*x^6 - 269642*x^5 - 156890*x^4 + 177939*x^3 + 12672*x^2 - 42176*x + 8336,5,x^20 - 11*x^19 + 7*x^18 + 328*x^17 - 1046*x^16 - 2665*x^15 + 15558*x^14 + 1385*x^13 - 95561*x^12 + 71734*x^11 + 286142*x^10 - 331613*x^9 - 433461*x^8 + 597630*x^7 + 325064*x^6 - 466163*x^5 - 111002*x^4 + 140752*x^3 + 11056*x^2 - 9232*x - 32,7,x^20 - 8*x^19 - 38*x^18 + 437*x^17 + 128*x^16 - 8783*x^15 + 12109*x^14 + 76044*x^13 - 202104*x^12 - 201942*x^11 + 1199771*x^10 - 750096*x^9 - 2289999*x^8 + 4040094*x^7 - 1174475*x^6 - 2581213*x^5 + 2947740*x^4 - 1324351*x^3 + 281816*x^2 - 25808*x + 736,11,x^20 - 9*x^19 - 66*x^18 + 819*x^17 + 680*x^16 - 26518*x^15 + 29864*x^14 + 408361*x^13 - 867122*x^12 - 3196750*x^11 + 9189590*x^10 + 12207587*x^9 - 45833068*x^8 - 20554064*x^7 + 106973755*x^6 + 24030413*x^5 - 117010702*x^4 - 31879529*x^3 + 48557012*x^2 + 18575440*x - 923198,13,x^20 - 3*x^19 - 115*x^18 + 294*x^17 + 5278*x^16 - 11782*x^15 - 122582*x^14 + 252976*x^13 + 1518121*x^12 - 3112978*x^11 - 9712412*x^10 + 20968864*x^9 + 28564321*x^8 - 67741911*x^7 - 34086000*x^6 + 97762415*x^5 + 8431877*x^4 - 52934837*x^3 + 5096834*x^2 + 8376084*x - 1627048[] 458,1,2,x + 1,3,x + 3,5,x - 1,7,x + 2,11,x - 1,13,x - 2[] 458,2,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 1,13,x + 2[] 458,3,2,x^2 + 2*x + 1,3,x^2,5,x^2 - x - 3,7,x^2 + 3*x - 1,11,x^2 + 2*x - 12,13,x^2 + 8*x + 16[] 458,4,2,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,3,x^7 - 4*x^6 - 6*x^5 + 31*x^4 + 12*x^3 - 77*x^2 - 10*x + 59,5,x^7 - x^6 - 30*x^5 + 40*x^4 + 216*x^3 - 400*x^2 + 192,7,x^7 - 7*x^6 - 11*x^5 + 156*x^4 - 176*x^3 - 497*x^2 + 551*x + 524,11,x^7 - 6*x^6 - 12*x^5 + 57*x^4 + 76*x^3 - 107*x^2 - 144*x - 27,13,x^7 - 9*x^6 - 27*x^5 + 344*x^4 + 96*x^3 - 3199*x^2 - 535*x + 1742[] 458,5,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 - 2*x^8 - 20*x^7 + 41*x^6 + 112*x^5 - 241*x^4 - 160*x^3 + 385*x^2 + 28*x - 112,5,x^9 - 4*x^8 - 26*x^7 + 107*x^6 + 214*x^5 - 944*x^4 - 456*x^3 + 2736*x^2 - 832*x + 64,7,x^9 - 6*x^8 - 21*x^7 + 164*x^6 - 121*x^5 - 277*x^4 + 74*x^3 + 82*x^2 - 15*x - 2,11,x^9 + 6*x^8 - 50*x^7 - 317*x^6 + 678*x^5 + 4981*x^4 - 944*x^3 - 22589*x^2 - 22614*x - 4436,13,x^9 - 11*x^8 - 19*x^7 + 544*x^6 - 1144*x^5 - 5361*x^4 + 24641*x^3 - 32662*x^2 + 12432*x + 896[] Total time: 18.440 seconds, Total memory usage: 6.24MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 10:59:54 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [458..461] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 10:59:38 on modular [Seed = 2238753146] ------------------------------------- 458,1,2,$.1 + 1,3,$.1 + 3,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 2[] 458,2,2,$.1 - 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 4,11,$.1 + 1,13,$.1 + 2[] 458,3,2,$.1^2 + 2*$.1 + 1,3,$.1^2,5,$.1^2 -$.1 - 3,7,$.1^2 + 3*$.1 - 1,11,$.1^2 + 2*$.1 - 12,13,$.1^2 + 8*$.1 + 16[]
458,4,2,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1,3,$.1^7 - 4*$.1^6 - 6*$.1^5 + 31*$.1^4 + 12*$.1^3 - 77*$.1^2 - 10*$.1 +
59,5,$.1^7 -$.1^6 - 30*$.1^5 + 40*$.1^4 + 216*$.1^3 - 400*$.1^2 + 192,7,$.1^7 - 7*$.1^6 - 11*$.1^5 + 156*$.1^4 - 176*$.1^3 - 497*$.1^2 + 551*$.1 + 524,11,$.1^7
- 6*$.1^6 - 12*$.1^5 + 57*$.1^4 + 76*$.1^3 - 107*$.1^2 - 144*$.1 - 27,13,$.1^7 - 9*$.1^6 - 27*$.1^5 + 344*$.1^4 + 96*$.1^3 - 3199*$.1^2 - 535*$.1 + 1742[] 458,5,2,$.1^9 - 9*$.1^8 + 36*$.1^7 - 84*$.1^6 + 126*$.1^5 - 126*$.1^4 + 84*$.1^3
- 36*$.1^2 + 9*$.1 - 1,3,$.1^9 - 2*$.1^8 - 20*$.1^7 + 41*$.1^6 + 112*$.1^5 - 241*$.1^4 - 160*$.1^3 + 385*$.1^2 + 28*$.1 - 112,5,$.1^9 - 4*$.1^8 - 26*$.1^7 +
107*$.1^6 + 214*$.1^5 - 944*$.1^4 - 456*$.1^3 + 2736*$.1^2 - 832*$.1 +
64,7,$.1^9 - 6*$.1^8 - 21*$.1^7 + 164*$.1^6 - 121*$.1^5 - 277*$.1^4 + 74*$.1^3 + 82*$.1^2 - 15*$.1 - 2,11,$.1^9 + 6*$.1^8 - 50*$.1^7 - 317*$.1^6 + 678*$.1^5 +
4981*$.1^4 - 944*$.1^3 - 22589*$.1^2 - 22614*$.1 - 4436,13,$.1^9 - 11*$.1^8 -
19*$.1^7 + 544*$.1^6 - 1144*$.1^5 - 5361*$.1^4 + 24641*$.1^3 - 32662*$.1^2 +
12432*$.1 + 896[] 459,1,2,x - 1,3,x,5,x + 1,7,x + 2,11,x,13,x + 5[] 459,2,2,x + 2,3,x,5,x + 4,7,x - 1,11,x - 6,13,x - 1[] 459,3,2,x,3,x,5,x - 3,7,x - 2,11,x + 3,13,x - 2[] 459,4,2,x - 2,3,x,5,x + 2,7,x - 4,11,x - 3,13,x - 7[] 459,5,2,x - 2,3,x,5,x - 4,7,x - 1,11,x + 6,13,x - 1[] 459,6,2,x,3,x,5,x + 3,7,x - 2,11,x - 3,13,x - 2[] 459,7,2,x + 2,3,x,5,x - 2,7,x - 4,11,x + 3,13,x - 7[] 459,8,2,x + 1,3,x,5,x - 1,7,x + 2,11,x,13,x + 5[] 459,9,2,x^2 - x - 1,3,x^2,5,x^2 + 3*x + 1,7,x^2 + 3*x - 9,11,x^2 + 8*x + 11,13,x^2 - 2*x - 4[] 459,10,2,x^2 + x - 1,3,x^2,5,x^2 - 3*x + 1,7,x^2 + 3*x - 9,11,x^2 - 8*x + 11,13,x^2 - 2*x - 4[] 459,11,2,x^2 - x - 3,3,x^2,5,x^2 - 5*x + 3,7,x^2 - 3*x - 1,11,x^2 - 6*x + 9,13,x^2 + 6*x - 4[] 459,12,2,x^2 + x - 3,3,x^2,5,x^2 + 5*x + 3,7,x^2 - 3*x - 1,11,x^2 + 6*x + 9,13,x^2 + 6*x - 4[] 459,13,2,x^3 + x^2 - 7*x - 9,3,x^3,5,x^3 + 3*x^2 - 5*x - 3,7,x^3 + 4*x^2 - 12*x - 36,11,x^3 + 4*x^2 - 16*x - 48,13,x^3 - x^2 - 21*x + 29[] 459,14,2,x^3 - x^2 - 7*x + 9,3,x^3,5,x^3 - 3*x^2 - 5*x + 3,7,x^3 + 4*x^2 - 12*x - 36,11,x^3 - 4*x^2 - 16*x + 48,13,x^3 - x^2 - 21*x + 29[] 460,1,2,x,3,x,5,x + 1,7,x + 1,11,x - 6,13,x - 6[] 460,2,2,x,3,x - 3,5,x + 1,7,x - 2,11,x,13,x + 3[] 460,3,2,x,3,x - 1,5,x + 1,7,x + 4,11,x + 6,13,x + 1[] 460,4,2,x,3,x + 1,5,x - 1,7,x + 2,11,x + 4,13,x - 1[] 460,5,2,x^2,3,x^2 - x - 4,5,x^2 - 2*x + 1,7,x^2 - x - 4,11,x^2 - 4*x + 4,13,x^2 + 3*x - 2[] 461,1,2,x^2 + x - 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x - 4,11,x^2 - 5,13,x^2 + 2*x + 1[] 461,2,2,x^3 + 2*x^2 - x - 1,3,x^3 - 7*x + 7,5,x^3 + x^2 - 9*x - 1,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 + 9*x^2 + 20*x + 13,13,x^3 + 4*x^2 - 11*x - 1[] 461,3,2,x^7 - 8*x^5 + x^4 + 18*x^3 - 2*x^2 - 12*x + 1,3,x^7 + 3*x^6 - 5*x^5 - 19*x^4 - 8*x^3 + 8*x^2 + 2*x - 1,5,x^7 + 4*x^6 - 2*x^5 - 26*x^4 - 33*x^3 - 9*x^2 + 3*x + 1,7,x^7 + 5*x^6 - 17*x^5 - 104*x^4 + 17*x^3 + 445*x^2 + 153*x - 289,11,x^7 + 7*x^6 - 10*x^5 - 119*x^4 - 170*x^3 - 48*x^2 + 17*x - 1,13,x^7 - 2*x^6 - 46*x^5 + 72*x^4 + 457*x^3 - 180*x^2 - 242*x - 43[] 461,4,2,x^26 - 3*x^25 - 41*x^24 + 126*x^23 + 726*x^22 - 2303*x^21 - 7266*x^20 + 24054*x^19 + 45144*x^18 - 158550*x^17 - 179824*x^16 + 687620*x^15 + 456511*x^14 - 1985932*x^13 - 703693*x^12 + 3785104*x^11 + 571532*x^10 - 4624305*x^9 - 111938*x^8 + 3430214*x^7 - 156745*x^6 - 1399829*x^5 + 108715*x^4 + 249906*x^3 - 21297*x^2 - 6102*x + 223,3,x^26 - 8*x^25 - 25*x^24 + 350*x^23 - 67*x^22 - 6375*x^21 + 9131*x^20 + 62591*x^19 - 142101*x^18 - 354222*x^17 + 1131262*x^16 + 1100229*x^15 - 5439111*x^14 - 1179040*x^13 + 16616042*x^12 - 3766381*x^11 - 32549826*x^10 + 16848027*x^9 + 40027314*x^8 - 29339246*x^7 - 28984472*x^6 + 26997218*x^5 + 10382911*x^4 - 12846388*x^3 - 637663*x^2 + 2482812*x - 412364,5,x^26 - x^25 - 81*x^24 + 89*x^23 + 2834*x^22 - 3337*x^21 - 56369*x^20 + 69650*x^19 + 706674*x^18 - 899724*x^17 - 5857374*x^16 + 7559751*x^15 + 32782433*x^14 - 42250384*x^13 - 124348564*x^12 + 157850099*x^11 + 315862226*x^10 - 390387594*x^9 - 520297841*x^8 + 621732909*x^7 + 519864632*x^6 - 602181344*x^5 - 272562048*x^4 + 314042258*x^3 + 48441044*x^2 - 63929748*x + 3703649,7,x^26 - 10*x^25 - 60*x^24 + 871*x^23 + 794*x^22 - 31920*x^21 + 24932*x^20 + 646295*x^19 - 1052609*x^18 - 8001190*x^17 + 17074484*x^16 + 63570421*x^15 - 155447227*x^14 - 333095634*x^13 + 860725592*x^12 + 1174538237*x^11 - 2928391388*x^10 - 2824918032*x^9 + 5914395816*x^8 + 4532213984*x^7 - 6445957683*x^6 - 4306115742*x^5 + 3059587300*x^4 + 1793364464*x^3 - 439165584*x^2 - 254287328*x - 21295936,11,x^26 - 22*x^25 + 83*x^24 + 1560*x^23 - 14351*x^22 - 13740*x^21 + 588900*x^20 - 1405048*x^19 - 9844007*x^18 + 47950725*x^17 + 50344062*x^16 - 653138686*x^15 + 502380513*x^14 + 4333954341*x^13 - 8056737769*x^12 - 12971428871*x^11 + 41885314760*x^10 + 7218265149*x^9 - 97024228874*x^8 + 35476022484*x^7 + 96414098848*x^6 - 43009973890*x^5 - 50612978091*x^4 + 12228864075*x^3 + 12784976002*x^2 + 796292595*x - 328816693,13,x^26 - 6*x^25 - 182*x^24 + 1159*x^23 + 13772*x^22 - 95371*x^21 - 560750*x^20 + 4411668*x^19 + 13010037*x^18 - 126932023*x^17 - 155796755*x^16 + 2365313943*x^15 + 222285283*x^14 - 28723004920*x^13 + 20894083248*x^12 + 221761328032*x^11 - 311581537600*x^10 - 1012055432256*x^9 + 2157421019008*x^8 + 2184332068096*x^7 - 7839979669504*x^6 + 412493474816*x^5 + 13389378247680*x^4 - 9398097330176*x^3 - 6029370896384*x^2 + 8993424179200*x - 2762166648832[] Total time: 16.299 seconds, Total memory usage: 5.93MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:21:10 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [461..464] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:20:52 on modular [Seed = 3460032831] ------------------------------------- 461,1,2,$.1^2 + $.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 5,7,$.1^2 + 2*$.1 -
4,11,$.1^2 - 5,13,$.1^2 + 2*$.1 + 1[] 461,2,2,$.1^3 + 2*$.1^2 -$.1 - 1,3,$.1^3 - 7*$.1 + 7,5,$.1^3 +$.1^2 - 9*$.1 - 1,7,$.1^3 + 3*$.1^2 + 3*$.1 + 1,11,$.1^3 + 9*$.1^2 + 20*$.1 + 13,13,$.1^3 +
4*$.1^2 - 11*$.1 - 1[]
461,3,2,$.1^7 - 8*$.1^5 + $.1^4 + 18*$.1^3 - 2*$.1^2 - 12*$.1 + 1,3,$.1^7 + 3*$.1^6 - 5*$.1^5 - 19*$.1^4 - 8*$.1^3 + 8*$.1^2 + 2*$.1 - 1,5,$.1^7 + 4*$.1^6 - 2*$.1^5 - 26*$.1^4 - 33*$.1^3 - 9*$.1^2 + 3*$.1 + 1,7,$.1^7 + 5*$.1^6 - 17*$.1^5 - 104*$.1^4 + 17*$.1^3 + 445*$.1^2 + 153*$.1 - 289,11,$.1^7 + 7*$.1^6 - 10*$.1^5
- 119*$.1^4 - 170*$.1^3 - 48*$.1^2 + 17*$.1 - 1,13,$.1^7 - 2*$.1^6 - 46*$.1^5 + 72*$.1^4 + 457*$.1^3 - 180*$.1^2 - 242*$.1 - 43[] 461,4,2,$.1^26 - 3*$.1^25 - 41*$.1^24 + 126*$.1^23 + 726*$.1^22 - 2303*$.1^21 - 7266*$.1^20 + 24054*$.1^19 + 45144*$.1^18 - 158550*$.1^17 - 179824*$.1^16 +
687620*$.1^15 + 456511*$.1^14 - 1985932*$.1^13 - 703693*$.1^12 + 3785104*$.1^11 + 571532*$.1^10 - 4624305*$.1^9 - 111938*$.1^8 + 3430214*$.1^7 - 156745*$.1^6 -
1399829*$.1^5 + 108715*$.1^4 + 249906*$.1^3 - 21297*$.1^2 - 6102*$.1 + 223,3,$.1^26 - 8*$.1^25 - 25*$.1^24 + 350*$.1^23 - 67*$.1^22 - 6375*$.1^21 + 9131*$.1^20 + 62591*$.1^19 - 142101*$.1^18 - 354222*$.1^17 + 1131262*$.1^16 +
1100229*$.1^15 - 5439111*$.1^14 - 1179040*$.1^13 + 16616042*$.1^12 -
3766381*$.1^11 - 32549826*$.1^10 + 16848027*$.1^9 + 40027314*$.1^8 -
29339246*$.1^7 - 28984472*$.1^6 + 26997218*$.1^5 + 10382911*$.1^4 -
12846388*$.1^3 - 637663*$.1^2 + 2482812*$.1 - 412364,5,$.1^26 - $.1^25 - 81*$.1^24 + 89*$.1^23 + 2834*$.1^22 - 3337*$.1^21 - 56369*$.1^20 + 69650*$.1^19 + 706674*$.1^18 - 899724*$.1^17 - 5857374*$.1^16 + 7559751*$.1^15 + 32782433*$.1^14 - 42250384*$.1^13 - 124348564*$.1^12 + 157850099*$.1^11 + 315862226*$.1^10 - 390387594*$.1^9 - 520297841*$.1^8 + 621732909*$.1^7 + 519864632*$.1^6 - 602181344*$.1^5 - 272562048*$.1^4 + 314042258*$.1^3 + 48441044*$.1^2 - 63929748*$.1 + 3703649,7,$.1^26 - 10*$.1^25 - 60*$.1^24 +
871*$.1^23 + 794*$.1^22 - 31920*$.1^21 + 24932*$.1^20 + 646295*$.1^19 - 1052609*$.1^18 - 8001190*$.1^17 + 17074484*$.1^16 + 63570421*$.1^15 - 155447227*$.1^14 - 333095634*$.1^13 + 860725592*$.1^12 + 1174538237*$.1^11 - 2928391388*$.1^10 - 2824918032*$.1^9 + 5914395816*$.1^8 + 4532213984*$.1^7 - 6445957683*$.1^6 - 4306115742*$.1^5 + 3059587300*$.1^4 + 1793364464*$.1^3 - 439165584*$.1^2 - 254287328*$.1 - 21295936,11,$.1^26 - 22*$.1^25 + 83*$.1^24 +
1560*$.1^23 - 14351*$.1^22 - 13740*$.1^21 + 588900*$.1^20 - 1405048*$.1^19 - 9844007*$.1^18 + 47950725*$.1^17 + 50344062*$.1^16 - 653138686*$.1^15 + 502380513*$.1^14 + 4333954341*$.1^13 - 8056737769*$.1^12 - 12971428871*$.1^11 + 41885314760*$.1^10 + 7218265149*$.1^9 - 97024228874*$.1^8 + 35476022484*$.1^7 + 96414098848*$.1^6 - 43009973890*$.1^5 - 50612978091*$.1^4 + 12228864075*$.1^3 + 12784976002*$.1^2 + 796292595*$.1 - 328816693,13,$.1^26 - 6*$.1^25 - 182*$.1^24
+ 1159*$.1^23 + 13772*$.1^22 - 95371*$.1^21 - 560750*$.1^20 + 4411668*$.1^19 + 13010037*$.1^18 - 126932023*$.1^17 - 155796755*$.1^16 + 2365313943*$.1^15 + 222285283*$.1^14 - 28723004920*$.1^13 + 20894083248*$.1^12 + 221761328032*$.1^11 - 311581537600*$.1^10 - 1012055432256*$.1^9 + 2157421019008*$.1^8 +
2184332068096*$.1^7 - 7839979669504*$.1^6 + 412493474816*$.1^5 + 13389378247680*$.1^4 - 9398097330176*$.1^3 - 6029370896384*$.1^2 +
8993424179200*$.1 - 2762166648832[] 462,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x + 1,13,x + 2[] 462,2,2,x + 1,3,x + 1,5,x - 2,7,x + 1,11,x - 1,13,x - 2[] 462,3,2,x + 1,3,x + 1,5,x + 2,7,x - 1,11,x - 1,13,x - 2[] 462,4,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 1,13,x - 6[] 462,5,2,x - 1,3,x + 1,5,x + 4,7,x - 1,11,x + 1,13,x + 6[] 462,6,2,x - 1,3,x - 1,5,x - 2,7,x + 1,11,x - 1,13,x + 2[] 462,7,2,x - 1,3,x - 1,5,x,7,x - 1,11,x + 1,13,x - 2[] 462,8,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 12,7,x^2 - 2*x + 1,11,x^2 - 2*x + 1,13,x^2 - 4*x + 4[] 463,1,2,x^16 + 9*x^15 + 17*x^14 - 70*x^13 - 282*x^12 + 7*x^11 + 1223*x^10 + 1073*x^9 - 2045*x^8 - 2946*x^7 + 1137*x^6 + 2847*x^5 + 88*x^4 - 954*x^3 - 47*x^2 + 118*x - 9,3,x^16 + 6*x^15 - 10*x^14 - 113*x^13 - 38*x^12 + 756*x^11 + 674*x^10 - 2299*x^9 - 2327*x^8 + 3496*x^7 + 2916*x^6 - 2854*x^5 - 1321*x^4 + 1115*x^3 + 125*x^2 - 151*x + 17,5,x^16 + 16*x^15 + 84*x^14 + 39*x^13 - 1210*x^12 - 4138*x^11 - 1410*x^10 + 16780*x^9 + 27638*x^8 - 8560*x^7 - 49341*x^6 - 20011*x^5 + 23715*x^4 + 12698*x^3 - 3322*x^2 - 355*x + 75,7,x^16 + 10*x^15 - 4*x^14 - 305*x^13 - 525*x^12 + 3091*x^11 + 7597*x^10 - 12200*x^9 - 33924*x^8 + 20827*x^7 + 52761*x^6 - 11881*x^5 - 27051*x^4 + 1806*x^3 + 3512*x^2 - 395*x + 9,11,x^16 + 7*x^15 - 69*x^14 - 471*x^13 + 2127*x^12 + 12574*x^11 - 39019*x^10 - 165746*x^9 + 448793*x^8 + 1057645*x^7 - 2970725*x^6 - 2325341*x^5 + 8806405*x^4 - 2477609*x^3 - 3318103*x^2 + 735353*x + 419003,13,x^16 + 17*x^15 + 29*x^14 - 948*x^13 - 4829*x^12 + 13057*x^11 + 126050*x^10 + 49398*x^9 - 1183509*x^8 - 1969668*x^7 + 3199115*x^6 + 10003714*x^5 + 5302860*x^4 - 4889311*x^3 - 6512429*x^2 - 2575705*x - 350517[] 463,2,2,x^22 - 8*x^21 - x^20 + 161*x^19 - 281*x^18 - 1216*x^17 + 3523*x^16 + 3859*x^15 - 19383*x^14 - 1030*x^13 + 56835*x^12 - 26406*x^11 - 90387*x^10 + 71356*x^9 + 71796*x^8 - 76057*x^7 - 22452*x^6 + 32959*x^5 + 1404*x^4 - 4772*x^3 - 174*x^2 + 237*x + 25,3,x^22 - 4*x^21 - 40*x^20 + 175*x^19 + 634*x^18 - 3196*x^17 - 4882*x^16 + 31685*x^15 + 15943*x^14 - 185800*x^13 + 17462*x^12 + 658774*x^11 - 317425*x^10 - 1385913*x^9 + 1058217*x^8 + 1616727*x^7 - 1650803*x^6 - 853772*x^5 + 1229264*x^4 + 27760*x^3 - 336304*x^2 + 87744*x - 6080,5,x^22 - 14*x^21 + 30*x^20 + 429*x^19 - 2232*x^18 - 2804*x^17 + 39278*x^16 - 37660*x^15 - 291072*x^14 + 650216*x^13 + 804651*x^12 - 3585845*x^11 + 758887*x^10 + 8250140*x^9 - 7478252*x^8 - 6369965*x^7 + 10268643*x^6 + 264580*x^5 - 4629944*x^4 + 762336*x^3 + 677968*x^2 - 51776*x - 27584,7,x^22 - 2*x^21 - 76*x^20 + 181*x^19 + 2301*x^18 - 6343*x^17 - 35541*x^16 + 113608*x^15 + 295698*x^14 - 1144665*x^13 - 1238901*x^12 + 6708483*x^11 + 1472515*x^10 - 22688648*x^9 + 7199360*x^8 + 41794201*x^7 - 29091175*x^6 - 35510916*x^5 + 38151008*x^4 + 6047480*x^3 - 16528576*x^2 + 4477728*x - 17728,11,x^22 - 3*x^21 - 113*x^20 + 343*x^19 + 5117*x^18 - 15366*x^17 - 121755*x^16 + 349548*x^15 + 1699863*x^14 - 4397687*x^13 - 14931055*x^12 + 31550965*x^11 + 85507127*x^10 - 126103999*x^9 - 314041293*x^8 + 247288771*x^7 + 673005607*x^6 - 136356452*x^5 - 675381584*x^4 - 101740656*x^3 + 217744368*x^2 + 59584960*x - 5641024,13,x^22 - 13*x^21 - 75*x^20 + 1644*x^19 - 881*x^18 - 77769*x^17 + 225146*x^16 + 1714666*x^15 - 8239929*x^14 - 15611588*x^13 + 137556583*x^12 - 31493298*x^11 - 1124303704*x^10 + 1647535345*x^9 + 3696411261*x^8 - 10524859959*x^7 + 1100329357*x^6 + 19814686542*x^5 - 21136903324*x^4 + 4162677720*x^3 + 3672221712*x^2 - 1509576416*x + 54642112[] 464,1,2,x,3,x - 1,5,x + 3,7,x + 2,11,x - 3,13,x + 5[] 464,2,2,x,3,x + 1,5,x - 1,7,x + 2,11,x + 3,13,x + 1[] 464,3,2,x,3,x - 1,5,x - 1,7,x - 2,11,x - 3,13,x + 1[] 464,4,2,x,3,x + 1,5,x - 3,7,x - 4,11,x + 3,13,x - 5[] 464,5,2,x,3,x + 2,5,x + 2,7,x + 4,11,x - 6,13,x - 2[] 464,6,2,x,3,x - 3,5,x - 3,7,x + 4,11,x - 1,13,x + 3[] 464,7,2,x,3,x - 3,5,x + 3,7,x - 2,11,x - 1,13,x - 3[] 464,8,2,x^2,3,x^2 - 2*x - 1,5,x^2 + 2*x - 7,7,x^2 - 8*x + 16,11,x^2 - 2*x - 1,13,x^2 + 2*x - 31[] 464,9,2,x^2,3,x^2 + 2*x - 1,5,x^2 + 2*x + 1,7,x^2 - 8,11,x^2 + 2*x - 1,13,x^2 + 2*x - 7[] 464,10,2,x^3,3,x^3 + 2*x^2 - 5*x - 8,5,x^3 - 4*x^2 - 3*x + 10,7,x^3,11,x^3 + 2*x^2 - 29*x - 80,13,x^3 - 4*x^2 - 19*x + 2[] Total time: 18.170 seconds, Total memory usage: 6.45MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:28:23 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [464..467] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:28:07 on modular [Seed = 468598424] ------------------------------------- 464,1,2,$.1,3,$.1 - 1,5,$.1 + 3,7,$.1 + 2,11,$.1 - 3,13,$.1 + 5[] 464,2,2,$.1,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 + 3,13,$.1 + 1[] 464,3,2,$.1,3,$.1 - 1,5,$.1 - 1,7,$.1 - 2,11,$.1 - 3,13,$.1 + 1[] 464,4,2,$.1,3,$.1 + 1,5,$.1 - 3,7,$.1 - 4,11,$.1 + 3,13,$.1 - 5[] 464,5,2,$.1,3,$.1 + 2,5,$.1 + 2,7,$.1 + 4,11,$.1 - 6,13,$.1 - 2[] 464,6,2,$.1,3,$.1 - 3,5,$.1 - 3,7,$.1 + 4,11,$.1 - 1,13,$.1 + 3[] 464,7,2,$.1,3,$.1 - 3,5,$.1 + 3,7,$.1 - 2,11,$.1 - 1,13,$.1 - 3[] 464,8,2,$.1^2,3,$.1^2 - 2*$.1 - 1,5,$.1^2 + 2*$.1 - 7,7,$.1^2 - 8*$.1 +
16,11,$.1^2 - 2*$.1 - 1,13,$.1^2 + 2*$.1 - 31[]
464,9,2,$.1^2,3,$.1^2 + 2*$.1 - 1,5,$.1^2 + 2*$.1 + 1,7,$.1^2 - 8,11,$.1^2 + 2*$.1 - 1,13,$.1^2 + 2*$.1 - 7[]
464,10,2,$.1^3,3,$.1^3 + 2*$.1^2 - 5*$.1 - 8,5,$.1^3 - 4*$.1^2 - 3*$.1 + 10,7,$.1^3,11,$.1^3 + 2*$.1^2 - 29*$.1 - 80,13,$.1^3 - 4*$.1^2 - 19*$.1 + 2[]
465,1,2,x - 1,3,x + 1,5,x - 1,7,x + 2,11,x + 4,13,x[]
465,2,2,x + 1,3,x - 1,5,x - 1,7,x + 4,11,x + 4,13,x - 2[]
465,3,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 6*x + 6,11,x^2 - 4*x -
8,13,x^2 + 6*x + 6[]
465,4,2,x^2 + 2*x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 4*x + 2,11,x^2 -
8,13,x^2 + 8*x + 14[]
465,5,2,x^3 - x^2 - 5*x + 3,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 8*x^2 + 16*x - 6,11,x^3 - 2*x^2 - 20*x + 24,13,x^3 - 4*x^2 + 6[]
465,6,2,x^3 - 3*x^2 - x + 5,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 2*x^2 - 12*x - 10,11,x^3 - 2*x^2 - 12*x + 8,13,x^3 + 6*x^2 + 8*x - 2[]
465,7,2,x^3 - x^2 - 3*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 2*x^2 - 2*x + 2,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 2*x^2 - 22*x + 2[]
465,8,2,x^4 - 2*x^3 - 6*x^2 + 12*x - 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 -
4*x^3 + 6*x^2 - 4*x + 1,7,x^4 - 4*x^3 - 10*x^2 + 46*x - 32,11,x^4 - 6*x^3 -
12*x^2 + 56*x + 32,13,x^4 - 2*x^3 - 50*x^2 + 94*x + 4[]
466,1,2,x + 1,3,x - 2,5,x,7,x,11,x - 2,13,x - 2[]
466,2,2,x - 1,3,x - 1,5,x,7,x - 2,11,x,13,x - 5[]
466,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 3*x - 5,5,x^3 - 5*x^2 + 4*x +
5,7,x^3 - 3*x^2 - 10*x + 25,11,x^3 - 8*x^2 + 17*x - 5,13,x^3 + 5*x^2 - 9*x - 5[]
466,4,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 4*x^2 + 3*x - 1,5,x^3 + 7*x^2 + 14*x +
7,7,x^3 + x^2 - 16*x - 29,11,x^3 + 10*x^2 + 17*x - 41,13,x^3 + 7*x^2 + 7*x - 7[]
466,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 8*x^3 + x^2 + 5*x -
1,5,x^5 + 5*x^4 - 4*x^3 - 37*x^2 - 24*x + 16,7,x^5 + 5*x^4 - 10*x^3 - 47*x^2 +
36*x - 4,11,x^5 + 12*x^4 + 33*x^3 - 71*x^2 - 320*x - 76,13,x^5 - 5*x^4 - 26*x^3
+ 74*x^2 + 73*x + 11[]
466,6,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - x^5 - 13*x^4 +
10*x^3 + 43*x^2 - 12*x - 36,5,x^6 - 7*x^5 + 4*x^4 + 47*x^3 - 52*x^2 - 66*x +
64,7,x^6 + 3*x^5 - 18*x^4 - 33*x^3 + 42*x^2 + 72*x + 16,11,x^6 - 6*x^5 - 31*x^4
+ 221*x^3 - 56*x^2 - 796*x + 64,13,x^6 - 2*x^5 - 24*x^4 + 6*x^3 + 171*x^2 +
212*x + 52[]
467,1,2,x,3,x + 3,5,x - 2,7,x - 1,11,x - 4,13,x + 6[]
467,2,2,x^12 + 5*x^11 - 3*x^10 - 46*x^9 - 28*x^8 + 144*x^7 + 140*x^6 - 182*x^5 -
197*x^4 + 102*x^3 + 104*x^2 - 22*x - 17,3,x^12 + 3*x^11 - 11*x^10 - 35*x^9 +
39*x^8 + 137*x^7 - 48*x^6 - 212*x^5 + 5*x^4 + 121*x^3 + 16*x^2 - 12*x + 1,5,x^12
+ 7*x^11 - 92*x^9 - 169*x^8 + 187*x^7 + 773*x^6 + 653*x^5 + 21*x^4 - 197*x^3 -
74*x^2 - 4*x + 1,7,x^12 + 12*x^11 + 30*x^10 - 183*x^9 - 1201*x^8 - 2087*x^7 +
1097*x^6 + 7291*x^5 + 5601*x^4 - 4034*x^3 - 6862*x^2 - 2643*x - 269,11,x^12 +
6*x^11 - 38*x^10 - 240*x^9 + 409*x^8 + 3134*x^7 - 159*x^6 - 14588*x^5 -
13297*x^4 + 16338*x^3 + 33221*x^2 + 19331*x + 3845,13,x^12 + 29*x^11 + 339*x^10
+ 1964*x^9 + 4955*x^8 - 3998*x^7 - 61729*x^6 - 174010*x^5 - 239727*x^4 -
170293*x^3 - 55755*x^2 - 6048*x + 27[]
467,3,2,x^26 - 5*x^25 - 30*x^24 + 181*x^23 + 338*x^22 - 2813*x^21 - 1420*x^20 +
24571*x^19 - 4052*x^18 - 132574*x^17 + 73889*x^16 + 457016*x^15 - 370842*x^14 -
1004824*x^13 + 992642*x^12 + 1361654*x^11 - 1526411*x^10 - 1049992*x^9 +
1309411*x^8 + 383566*x^7 - 569750*x^6 - 29300*x^5 + 105328*x^4 - 5888*x^3 -
6944*x^2 + 448*x + 128,3,x^26 - 4*x^25 - 46*x^24 + 196*x^23 + 893*x^22 -
4154*x^21 - 9443*x^20 + 49915*x^19 + 57965*x^18 - 374373*x^17 - 196608*x^16 +
1818054*x^15 + 249133*x^14 - 5741255*x^13 + 547597*x^12 + 11551260*x^11 -
2428841*x^10 - 14158547*x^9 + 3083763*x^8 + 9839699*x^7 - 1135144*x^6 -
3499562*x^5 - 199898*x^4 + 469317*x^3 + 73469*x^2 - 16172*x - 3151,5,x^26 -
3*x^25 - 88*x^24 + 282*x^23 + 3293*x^22 - 11295*x^21 - 68205*x^20 + 252251*x^19
+ 852605*x^18 - 3451561*x^17 - 6582044*x^16 + 29965190*x^15 + 30905167*x^14 -
165685764*x^13 - 84525874*x^12 + 573092728*x^11 + 130984024*x^10 -
1193054512*x^9 - 146599680*x^8 + 1387791296*x^7 + 202913280*x^6 - 773243904*x^5
- 172236288*x^4 + 142046208*x^3 + 31006720*x^2 - 7929856*x - 1220608,7,x^26 -
11*x^25 - 48*x^24 + 911*x^23 - 237*x^22 - 30439*x^21 + 58280*x^20 + 530524*x^19
- 1552763*x^18 - 5213022*x^17 + 20094626*x^16 + 29129121*x^15 - 147617188*x^14 -
90880344*x^13 + 638793969*x^12 + 182147970*x^11 - 1621148858*x^10 -
456119623*x^9 + 2307815904*x^8 + 1136598134*x^7 - 1394567530*x^6 -
1251108627*x^5 - 186732226*x^4 + 107562639*x^3 + 42029309*x^2 + 4788605*x +
153911,11,x^26 - 170*x^24 + 60*x^23 + 12429*x^22 - 8628*x^21 - 511399*x^20 +
522410*x^19 + 13007513*x^18 - 17371744*x^17 - 211346041*x^16 + 346903909*x^15 +
2184972859*x^14 - 4270849060*x^13 - 13785736442*x^12 + 31948079796*x^11 +
47565552664*x^10 - 136506612320*x^9 - 63934259328*x^8 + 286039610304*x^7 -
23226979712*x^6 - 193807726848*x^5 + 1930760192*x^4 + 44769953792*x^3 +
10725629952*x^2 + 465903616*x - 33923072,13,x^26 - 47*x^25 + 901*x^24 -
8210*x^23 + 18582*x^22 + 334227*x^21 - 3290814*x^20 + 7720356*x^19 +
56998590*x^18 - 443724985*x^17 + 655975590*x^16 + 4770587780*x^15 -
23477796337*x^14 + 14328650996*x^13 + 169189717890*x^12 - 475812982626*x^11 -
27477167834*x^10 + 2218007529808*x^9 - 3372965479433*x^8 - 1428631387058*x^7 +
8642602458407*x^6 - 7173300791221*x^5 - 1144500659319*x^4 + 3299643594404*x^3 -
114001961373*x^2 - 484815751724*x - 51049532452[]

Total time: 16.090 seconds, Total memory usage: 5.97MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 11:36:42 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [467..470] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 11:36:22 on modular  [Seed = 1070210221]
-------------------------------------

467,1,2,$.1,3,$.1 + 3,5,$.1 - 2,7,$.1 - 1,11,$.1 - 4,13,$.1 + 6[]
467,2,2,$.1^12 + 5*$.1^11 - 3*$.1^10 - 46*$.1^9 - 28*$.1^8 + 144*$.1^7 +
140*$.1^6 - 182*$.1^5 - 197*$.1^4 + 102*$.1^3 + 104*$.1^2 - 22*$.1 - 17,3,$.1^12 + 3*$.1^11 - 11*$.1^10 - 35*$.1^9 + 39*$.1^8 + 137*$.1^7 - 48*$.1^6 - 212*$.1^5
+ 5*$.1^4 + 121*$.1^3 + 16*$.1^2 - 12*$.1 + 1,5,$.1^12 + 7*$.1^11 - 92*$.1^9 - 169*$.1^8 + 187*$.1^7 + 773*$.1^6 + 653*$.1^5 + 21*$.1^4 - 197*$.1^3 - 74*$.1^2
- 4*$.1 + 1,7,$.1^12 + 12*$.1^11 + 30*$.1^10 - 183*$.1^9 - 1201*$.1^8 -
2087*$.1^7 + 1097*$.1^6 + 7291*$.1^5 + 5601*$.1^4 - 4034*$.1^3 - 6862*$.1^2 -
2643*$.1 - 269,11,$.1^12 + 6*$.1^11 - 38*$.1^10 - 240*$.1^9 + 409*$.1^8 +
3134*$.1^7 - 159*$.1^6 - 14588*$.1^5 - 13297*$.1^4 + 16338*$.1^3 + 33221*$.1^2 +
19331*$.1 + 3845,13,$.1^12 + 29*$.1^11 + 339*$.1^10 + 1964*$.1^9 + 4955*$.1^8 -
3998*$.1^7 - 61729*$.1^6 - 174010*$.1^5 - 239727*$.1^4 - 170293*$.1^3 - 55755*$.1^2 - 6048*$.1 + 27[] 467,3,2,$.1^26 - 5*$.1^25 - 30*$.1^24 + 181*$.1^23 + 338*$.1^22 - 2813*$.1^21 - 1420*$.1^20 + 24571*$.1^19 - 4052*$.1^18 - 132574*$.1^17 + 73889*$.1^16 +
457016*$.1^15 - 370842*$.1^14 - 1004824*$.1^13 + 992642*$.1^12 + 1361654*$.1^11 - 1526411*$.1^10 - 1049992*$.1^9 + 1309411*$.1^8 + 383566*$.1^7 - 569750*$.1^6 -
29300*$.1^5 + 105328*$.1^4 - 5888*$.1^3 - 6944*$.1^2 + 448*$.1 + 128,3,$.1^26 -
4*$.1^25 - 46*$.1^24 + 196*$.1^23 + 893*$.1^22 - 4154*$.1^21 - 9443*$.1^20 +
49915*$.1^19 + 57965*$.1^18 - 374373*$.1^17 - 196608*$.1^16 + 1818054*$.1^15 + 249133*$.1^14 - 5741255*$.1^13 + 547597*$.1^12 + 11551260*$.1^11 - 2428841*$.1^10 - 14158547*$.1^9 + 3083763*$.1^8 + 9839699*$.1^7 - 1135144*$.1^6
- 3499562*$.1^5 - 199898*$.1^4 + 469317*$.1^3 + 73469*$.1^2 - 16172*$.1 - 3151,5,$.1^26 - 3*$.1^25 - 88*$.1^24 + 282*$.1^23 + 3293*$.1^22 - 11295*$.1^21 - 68205*$.1^20 + 252251*$.1^19 + 852605*$.1^18 - 3451561*$.1^17 - 6582044*$.1^16 +
29965190*$.1^15 + 30905167*$.1^14 - 165685764*$.1^13 - 84525874*$.1^12 +
573092728*$.1^11 + 130984024*$.1^10 - 1193054512*$.1^9 - 146599680*$.1^8 +
1387791296*$.1^7 + 202913280*$.1^6 - 773243904*$.1^5 - 172236288*$.1^4 +
142046208*$.1^3 + 31006720*$.1^2 - 7929856*$.1 - 1220608,7,$.1^26 - 11*$.1^25 - 48*$.1^24 + 911*$.1^23 - 237*$.1^22 - 30439*$.1^21 + 58280*$.1^20 +
530524*$.1^19 - 1552763*$.1^18 - 5213022*$.1^17 + 20094626*$.1^16 +
29129121*$.1^15 - 147617188*$.1^14 - 90880344*$.1^13 + 638793969*$.1^12 +
182147970*$.1^11 - 1621148858*$.1^10 - 456119623*$.1^9 + 2307815904*$.1^8 +
1136598134*$.1^7 - 1394567530*$.1^6 - 1251108627*$.1^5 - 186732226*$.1^4 +
107562639*$.1^3 + 42029309*$.1^2 + 4788605*$.1 + 153911,11,$.1^26 - 170*$.1^24 + 60*$.1^23 + 12429*$.1^22 - 8628*$.1^21 - 511399*$.1^20 + 522410*$.1^19 +
13007513*$.1^18 - 17371744*$.1^17 - 211346041*$.1^16 + 346903909*$.1^15 +
2184972859*$.1^14 - 4270849060*$.1^13 - 13785736442*$.1^12 + 31948079796*$.1^11
+ 47565552664*$.1^10 - 136506612320*$.1^9 - 63934259328*$.1^8 + 286039610304*$.1^7 - 23226979712*$.1^6 - 193807726848*$.1^5 + 1930760192*$.1^4 + 44769953792*$.1^3 + 10725629952*$.1^2 + 465903616*$.1 - 33923072,13,$.1^26 - 47*$.1^25 + 901*$.1^24 - 8210*$.1^23 + 18582*$.1^22 + 334227*$.1^21 -
3290814*$.1^20 + 7720356*$.1^19 + 56998590*$.1^18 - 443724985*$.1^17 +
655975590*$.1^16 + 4770587780*$.1^15 - 23477796337*$.1^14 + 14328650996*$.1^13 +
169189717890*$.1^12 - 475812982626*$.1^11 - 27477167834*$.1^10 + 2218007529808*$.1^9 - 3372965479433*$.1^8 - 1428631387058*$.1^7 +
8642602458407*$.1^6 - 7173300791221*$.1^5 - 1144500659319*$.1^4 + 3299643594404*$.1^3 - 114001961373*$.1^2 - 484815751724*$.1 - 51049532452[]
468,1,2,x,3,x,5,x - 4,7,x - 4,11,x + 4,13,x + 1[]
468,2,2,x,3,x,5,x + 4,7,x - 4,11,x - 4,13,x + 1[]
468,3,2,x,3,x,5,x + 2,7,x + 2,11,x - 2,13,x + 1[]
468,4,2,x,3,x,5,x,7,x - 2,11,x,13,x - 1[]
468,5,2,x,3,x,5,x - 4,7,x + 2,11,x - 4,13,x - 1[]
469,1,2,x - 1,3,x - 1,5,x + 3,7,x + 1,11,x,13,x + 1[]
469,2,2,x + 1,3,x + 3,5,x - 1,7,x + 1,11,x,13,x - 3[]
469,3,2,x^2 - x - 4,3,x^2 + x - 4,5,x^2 + 3*x - 2,7,x^2 - 2*x + 1,11,x^2 - 8*x +
16,13,x^2 + 7*x + 8[]
469,4,2,x^2 - 2*x + 1,3,x^2 + x - 4,5,x^2 + x - 4,7,x^2 - 2*x + 1,11,x^2 - 8*x +
16,13,x^2 - 9*x + 16[]
469,5,2,x^3 + x^2 - 3*x - 1,3,x^3 + x^2 - 5*x - 1,5,x^3 + 9*x^2 + 27*x +
27,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 12*x^2 + 48*x + 64,13,x^3 - 5*x^2 - 5*x +
17[]
469,6,2,x^3 + 3*x^2 - 3,3,x^3 + 3*x^2 - 1,5,x^3 - 3*x^2 + 3,7,x^3 - 3*x^2 + 3*x
- 1,11,x^3 + 6*x^2 - 9*x - 51,13,x^3 + 3*x^2 - 6*x - 17[]
469,7,2,x^5 - 2*x^4 - 5*x^3 + 9*x^2 + 3*x - 4,3,x^5 + 2*x^4 - 5*x^3 - 9*x^2 +
3*x + 4,5,x^5 + 4*x^4 - 5*x^3 - 19*x^2 + 9*x + 18,7,x^5 + 5*x^4 + 10*x^3 +
10*x^2 + 5*x + 1,11,x^5 + 16*x^4 + 77*x^3 + 27*x^2 - 620*x - 1024,13,x^5 + 4*x^4
- 41*x^3 - 99*x^2 + 477*x + 216[]
469,8,2,x^7 - x^6 - 12*x^5 + 9*x^4 + 43*x^3 - 17*x^2 - 44*x - 11,3,x^7 - 6*x^6 +
x^5 + 51*x^4 - 85*x^3 - 12*x^2 + 80*x - 32,5,x^7 - 6*x^6 - 3*x^5 + 73*x^4 -
95*x^3 - 144*x^2 + 350*x - 178,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2
+ 7*x - 1,11,x^7 - 8*x^6 - 7*x^5 + 83*x^4 + 164*x^3 + 72*x^2 - 28*x - 16,13,x^7
+ 8*x^6 + x^5 - 113*x^4 - 151*x^3 + 362*x^2 + 374*x - 394[]
469,9,2,x^9 + x^8 - 13*x^7 - 10*x^6 + 53*x^5 + 28*x^4 - 69*x^3 - 12*x^2 + 12*x +
1,3,x^9 - 8*x^8 + 12*x^7 + 47*x^6 - 122*x^5 - 67*x^4 + 297*x^3 - 12*x^2 - 192*x
+ 32,5,x^9 - 8*x^8 + 6*x^7 + 87*x^6 - 176*x^5 - 177*x^4 + 507*x^3 + 88*x^2 -
334*x - 82,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2
+ 9*x + 1,11,x^9 - 18*x^8 + 107*x^7 - 147*x^6 - 712*x^5 + 1952*x^4 + 1140*x^3 -
4896*x^2 - 256*x + 2048,13,x^9 - 4*x^8 - 68*x^7 + 157*x^6 + 1678*x^5 - 781*x^4 -
15613*x^3 - 12902*x^2 + 30374*x + 36406[]
470,1,2,x + 1,3,x - 1,5,x + 1,7,x + 1,11,x + 3,13,x + 5[]
470,2,2,x + 1,3,x - 1,5,x - 1,7,x + 1,11,x - 3,13,x - 5[]
470,3,2,x + 1,3,x + 1,5,x - 1,7,x + 1,11,x - 1,13,x + 5[]
470,4,2,x - 1,3,x - 1,5,x + 1,7,x - 5,11,x + 3,13,x - 5[]
470,5,2,x - 1,3,x + 1,5,x + 1,7,x + 3,11,x + 5,13,x + 1[]
470,6,2,x - 1,3,x + 3,5,x - 1,7,x + 3,11,x + 1,13,x + 1[]
470,7,2,x^2 + 2*x + 1,3,x^2 - x - 5,5,x^2 - 2*x + 1,7,x^2 - 8*x + 16,11,x^2 +
5*x + 1,13,x^2 - 2*x - 20[]
470,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 6*x - 1,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 -
3*x^2 - 12*x + 16,11,x^3 - 12*x - 15,13,x^3 - 3*x^2 - 18*x + 4[]
470,9,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - 5*x + 12,5,x^3 + 3*x^2 + 3*x +
1,7,x^3,11,x^3 - 5*x^2 - 15*x + 72,13,x^3 - 32*x - 40[]
470,10,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 2*x^2 - 4*x + 7,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - x^2 - 12*x + 16,11,x^3 - 4*x - 1,13,x^3 + x^2 - 6*x - 4[]

Total time: 19.350 seconds, Total memory usage: 6.56MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 11:40:31 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [470..473] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 11:40:13 on modular  [Seed = 685574737]
-------------------------------------

470,1,2,$.1 + 1,3,$.1 - 1,5,$.1 + 1,7,$.1 + 1,11,$.1 + 3,13,$.1 + 5[]
470,2,2,$.1 + 1,3,$.1 - 1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 3,13,$.1 - 5[]
470,3,2,$.1 + 1,3,$.1 + 1,5,$.1 - 1,7,$.1 + 1,11,$.1 - 1,13,$.1 + 5[]
470,4,2,$.1 - 1,3,$.1 - 1,5,$.1 + 1,7,$.1 - 5,11,$.1 + 3,13,$.1 - 5[]
470,5,2,$.1 - 1,3,$.1 + 1,5,$.1 + 1,7,$.1 + 3,11,$.1 + 5,13,$.1 + 1[]
470,6,2,$.1 - 1,3,$.1 + 3,5,$.1 - 1,7,$.1 + 3,11,$.1 + 1,13,$.1 + 1[]
470,7,2,$.1^2 + 2*$.1 + 1,3,$.1^2 -$.1 - 5,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 8*$.1
+ 16,11,$.1^2 + 5*$.1 + 1,13,$.1^2 - 2*$.1 - 20[]
470,8,2,$.1^3 + 3*$.1^2 + 3*$.1 + 1,3,$.1^3 - 6*$.1 - 1,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3 - 3*$.1^2 - 12*$.1 + 16,11,$.1^3 - 12*$.1 - 15,13,$.1^3 -
3*$.1^2 - 18*$.1 + 4[]
470,9,2,$.1^3 - 3*$.1^2 + 3*$.1 - 1,3,$.1^3 - 3*$.1^2 - 5*$.1 + 12,5,$.1^3 + 3*$.1^2 + 3*$.1 + 1,7,$.1^3,11,$.1^3 - 5*$.1^2 - 15*$.1 + 72,13,$.1^3 - 32*$.1 - 40[] 470,10,2,$.1^3 - 3*$.1^2 + 3*$.1 - 1,3,$.1^3 - 2*$.1^2 - 4*$.1 + 7,5,$.1^3 -
3*$.1^2 + 3*$.1 - 1,7,$.1^3 -$.1^2 - 12*$.1 + 16,11,$.1^3 - 4*$.1 - 1,13,$.1^3
+ $.1^2 - 6*$.1 - 4[]
471,1,2,x + 1,3,x + 1,5,x + 2,7,x - 3,11,x,13,x - 1[]
471,2,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 6*x + 9,11,x^2 + x -
11,13,x^2 + 3*x + 1[]
471,3,2,x^3 - 4*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 +
3*x^2 + 3*x + 1,11,x^3 + 5*x^2 + 3*x - 8,13,x^3 + 2*x^2 - 30*x - 29[]
471,4,2,x^9 - 2*x^8 - 11*x^7 + 19*x^6 + 39*x^5 - 53*x^4 - 49*x^3 + 45*x^2 + 14*x
- 1,3,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x
+ 1,5,x^9 - 8*x^8 + x^7 + 122*x^6 - 214*x^5 - 330*x^4 + 728*x^3 + 380*x^2 -
648*x - 324,7,x^9 + 2*x^8 - 43*x^7 - 88*x^6 + 528*x^5 + 1152*x^4 - 1472*x^3 -
3264*x^2 - 384*x + 256,11,x^9 - 7*x^8 - 37*x^7 + 328*x^6 + 64*x^5 - 3696*x^4 +
4160*x^3 + 8320*x^2 - 14592*x + 5632,13,x^9 + x^8 - 77*x^7 - 30*x^6 + 2012*x^5 -
104*x^4 - 19440*x^3 + 5088*x^2 + 40512*x + 17536[]
471,5,2,x^12 + x^11 - 20*x^10 - 17*x^9 + 149*x^8 + 106*x^7 - 500*x^6 - 294*x^5 +
711*x^4 + 349*x^3 - 290*x^2 - 173*x - 15,3,x^12 - 12*x^11 + 66*x^10 - 220*x^9 +
495*x^8 - 792*x^7 + 924*x^6 - 792*x^5 + 495*x^4 - 220*x^3 + 66*x^2 - 12*x +
1,5,x^12 - 4*x^11 - 33*x^10 + 140*x^9 + 334*x^8 - 1590*x^7 - 1164*x^6 + 7376*x^5
+ 8*x^4 - 12456*x^3 + 4748*x^2 + 2096*x - 400,7,x^12 - 8*x^11 - 34*x^10 +
404*x^9 + 9*x^8 - 6916*x^7 + 9824*x^6 + 43904*x^5 - 100224*x^4 - 60608*x^3 +
249728*x^2 - 92928*x - 37376,11,x^12 + x^11 - 87*x^10 - 116*x^9 + 2752*x^8 +
4304*x^7 - 38464*x^6 - 65664*x^5 + 224512*x^4 + 385024*x^3 - 418816*x^2 -
499712*x + 393216,13,x^12 - 15*x^11 + 12*x^10 + 753*x^9 - 3031*x^8 - 6440*x^7 +
46816*x^6 - 17968*x^5 - 195232*x^4 + 233984*x^3 + 145152*x^2 - 297216*x +
80384[]
472,1,2,x,3,x + 3,5,x + 1,7,x - 3,11,x + 4,13,x - 6[]
472,2,2,x,3,x + 1,5,x + 1,7,x - 1,11,x - 4,13,x - 2[]
472,3,2,x,3,x - 2,5,x - 2,7,x - 1,11,x - 1,13,x + 1[]
472,4,2,x,3,x - 3,5,x + 3,7,x - 3,11,x - 6,13,x + 6[]
472,5,2,x,3,x + 1,5,x + 1,7,x - 1,11,x,13,x + 2[]
472,6,2,x^4,3,x^4 + x^3 - 5*x^2 + 1,5,x^4 + 3*x^3 - 11*x^2 - 20*x + 43,7,x^4 +
9*x^3 + 11*x^2 - 78*x - 169,11,x^4 + 4*x^3 - 36*x^2 - 72*x + 368,13,x^4 + 10*x^3
+ 12*x^2 - 64*x + 16[]
472,7,2,x^6,3,x^6 + x^5 - 15*x^4 - 16*x^3 + 51*x^2 + 30*x - 56,5,x^6 - 7*x^5 -
3*x^4 + 118*x^3 - 279*x^2 + 180*x + 4,7,x^6 + 4*x^5 - 18*x^4 - 93*x^3 - 51*x^2 +
157*x + 128,11,x^6 + 3*x^5 - 30*x^4 - 56*x^3 + 264*x^2 + 224*x - 512,13,x^6 -
9*x^5 + 144*x^3 - 120*x^2 - 496*x + 32[]
473,1,2,x + 2,3,x - 1,5,x + 1,7,x,11,x + 1,13,x + 2[]
473,2,2,x^2 - x - 1,3,x^2 + 4*x + 4,5,x^2 - 2*x - 4,7,x^2 - 5,11,x^2 + 2*x +
1,13,x^2 - 20[]
473,3,2,x^2 - x - 1,3,x^2 + 2*x - 4,5,x^2 - 2*x - 4,7,x^2 + 4*x - 1,11,x^2 - 2*x
+ 1,13,x^2 + 12*x + 36[]
473,4,2,x^5 - x^4 - 6*x^3 + 5*x^2 + x - 1,3,x^5 + 3*x^4 - 7*x^3 - 19*x^2 + 4*x +
1,5,x^5 + 6*x^4 + 3*x^3 - 19*x^2 + x + 1,7,x^5 + 15*x^4 + 71*x^3 + 53*x^2 -
420*x - 799,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 + x^4 - 15*x^3 -
14*x^2 + 19*x + 7[]
473,5,2,x^5 + 3*x^4 - 4*x^3 - 13*x^2 + 3*x + 9,3,x^5 + x^4 - 9*x^3 - 7*x^2 + 2*x
+ 1,5,x^5 + 4*x^4 - 7*x^3 - 41*x^2 - 43*x - 11,7,x^5 + 9*x^4 + 23*x^3 + 9*x^2 -
30*x - 25,11,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,13,x^5 + 9*x^4 - x^3 -
132*x^2 - 117*x + 193[]
473,6,2,x^9 - 4*x^8 - 5*x^7 + 36*x^6 - 20*x^5 - 65*x^4 + 66*x^3 + 4*x^2 - 8*x +
1,3,x^9 - 5*x^8 - 4*x^7 + 52*x^6 - 47*x^5 - 108*x^4 + 148*x^3 + 43*x^2 - 82*x -
4,5,x^9 - 25*x^7 + 13*x^6 + 179*x^5 - 143*x^4 - 374*x^3 + 424*x^2 - 40*x -
16,7,x^9 - 19*x^8 + 140*x^7 - 482*x^6 + 627*x^5 + 570*x^4 - 2324*x^3 + 1223*x^2
+ 1580*x - 1368,11,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 -
36*x^2 + 9*x - 1,13,x^9 - 11*x^8 - 5*x^7 + 436*x^6 - 1613*x^5 + 957*x^4 +
3732*x^3 - 4212*x^2 - 1360*x + 992[]
473,7,2,x^11 + x^10 - 17*x^9 - 15*x^8 + 102*x^7 + 77*x^6 - 255*x^5 - 150*x^4 +
248*x^3 + 59*x^2 - 93*x + 18,3,x^11 - 6*x^10 - 7*x^9 + 94*x^8 - 53*x^7 - 483*x^6
+ 524*x^5 + 873*x^4 - 1135*x^3 - 260*x^2 + 364*x + 64,5,x^11 - 3*x^10 - 31*x^9 +
82*x^8 + 354*x^7 - 824*x^6 - 1773*x^5 + 3616*x^4 + 3412*x^3 - 5976*x^2 - 768*x +
864,7,x^11 - 17*x^10 + 96*x^9 - 92*x^8 - 1043*x^7 + 3448*x^6 - 142*x^5 -
12971*x^4 + 13700*x^3 + 4760*x^2 - 6848*x + 1024,11,x^11 + 11*x^10 + 55*x^9 +
165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x +
1,13,x^11 - 11*x^10 - 15*x^9 + 478*x^8 - 649*x^7 - 5829*x^6 + 10608*x^5 +
21112*x^4 - 20096*x^3 - 31984*x^2 - 5312*x + 384[]

Total time: 17.389 seconds, Total memory usage: 5.87MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 11:47:27 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [473..476] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 11:47:07 on modular  [Seed = 1605009216]
-------------------------------------

473,1,2,$.1 + 2,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 + 1,13,$.1 + 2[]
473,2,2,$.1^2 -$.1 - 1,3,$.1^2 + 4*$.1 + 4,5,$.1^2 - 2*$.1 - 4,7,$.1^2 - 5,11,$.1^2 + 2*$.1 + 1,13,$.1^2 - 20[]
473,3,2,$.1^2 -$.1 - 1,3,$.1^2 + 2*$.1 - 4,5,$.1^2 - 2*$.1 - 4,7,$.1^2 + 4*$.1
- 1,11,$.1^2 - 2*$.1 + 1,13,$.1^2 + 12*$.1 + 36[]
473,4,2,$.1^5 -$.1^4 - 6*$.1^3 + 5*$.1^2 + $.1 - 1,3,$.1^5 + 3*$.1^4 - 7*$.1^3
- 19*$.1^2 + 4*$.1 + 1,5,$.1^5 + 6*$.1^4 + 3*$.1^3 - 19*$.1^2 + $.1 + 1,7,$.1^5
+ 15*$.1^4 + 71*$.1^3 + 53*$.1^2 - 420*$.1 - 799,11,$.1^5 + 5*$.1^4 + 10*$.1^3 + 10*$.1^2 + 5*$.1 + 1,13,$.1^5 + $.1^4 - 15*$.1^3 - 14*$.1^2 + 19*$.1 + 7[]
473,5,2,$.1^5 + 3*$.1^4 - 4*$.1^3 - 13*$.1^2 + 3*$.1 + 9,3,$.1^5 + $.1^4 - 9*$.1^3 - 7*$.1^2 + 2*$.1 + 1,5,$.1^5 + 4*$.1^4 - 7*$.1^3 - 41*$.1^2 - 43*$.1 - 11,7,$.1^5 + 9*$.1^4 + 23*$.1^3 + 9*$.1^2 - 30*$.1 - 25,11,$.1^5 - 5*$.1^4 +
10*$.1^3 - 10*$.1^2 + 5*$.1 - 1,13,$.1^5 + 9*$.1^4 -$.1^3 - 132*$.1^2 - 117*$.1
+ 193[]
473,6,2,$.1^9 - 4*$.1^8 - 5*$.1^7 + 36*$.1^6 - 20*$.1^5 - 65*$.1^4 + 66*$.1^3 + 4*$.1^2 - 8*$.1 + 1,3,$.1^9 - 5*$.1^8 - 4*$.1^7 + 52*$.1^6 - 47*$.1^5 -
108*$.1^4 + 148*$.1^3 + 43*$.1^2 - 82*$.1 - 4,5,$.1^9 - 25*$.1^7 + 13*$.1^6 + 179*$.1^5 - 143*$.1^4 - 374*$.1^3 + 424*$.1^2 - 40*$.1 - 16,7,$.1^9 - 19*$.1^8 +
140*$.1^7 - 482*$.1^6 + 627*$.1^5 + 570*$.1^4 - 2324*$.1^3 + 1223*$.1^2 +
1580*$.1 - 1368,11,$.1^9 - 9*$.1^8 + 36*$.1^7 - 84*$.1^6 + 126*$.1^5 - 126*$.1^4 + 84*$.1^3 - 36*$.1^2 + 9*$.1 - 1,13,$.1^9 - 11*$.1^8 - 5*$.1^7 + 436*$.1^6 -
1613*$.1^5 + 957*$.1^4 + 3732*$.1^3 - 4212*$.1^2 - 1360*$.1 + 992[] 473,7,2,$.1^11 + $.1^10 - 17*$.1^9 - 15*$.1^8 + 102*$.1^7 + 77*$.1^6 - 255*$.1^5
- 150*$.1^4 + 248*$.1^3 + 59*$.1^2 - 93*$.1 + 18,3,$.1^11 - 6*$.1^10 - 7*$.1^9 + 94*$.1^8 - 53*$.1^7 - 483*$.1^6 + 524*$.1^5 + 873*$.1^4 - 1135*$.1^3 - 260*$.1^2
+ 364*$.1 + 64,5,$.1^11 - 3*$.1^10 - 31*$.1^9 + 82*$.1^8 + 354*$.1^7 - 824*$.1^6 - 1773*$.1^5 + 3616*$.1^4 + 3412*$.1^3 - 5976*$.1^2 - 768*$.1 + 864,7,$.1^11 - 17*$.1^10 + 96*$.1^9 - 92*$.1^8 - 1043*$.1^7 + 3448*$.1^6 - 142*$.1^5 - 12971*$.1^4 + 13700*$.1^3 + 4760*$.1^2 - 6848*$.1 + 1024,11,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3
+ 55*$.1^2 + 11*$.1 + 1,13,$.1^11 - 11*$.1^10 - 15*$.1^9 + 478*$.1^8 - 649*$.1^7 - 5829*$.1^6 + 10608*$.1^5 + 21112*$.1^4 - 20096*$.1^3 - 31984*$.1^2 - 5312*$.1 + 384[] 474,1,2,x + 1,3,x + 1,5,x - 2,7,x + 3,11,x + 5,13,x + 1[] 474,2,2,x + 1,3,x - 1,5,x + 2,7,x + 1,11,x + 5,13,x + 1[] 474,3,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + x - 7,7,x^2 - x - 7,11,x^2,13,x^2[] 474,4,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 3*x + 1,7,x^2 + x - 11,11,x^2 - 8*x + 16,13,x^2 + 4*x - 16[] 474,5,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - x + 2,7,x^3 - 4*x + 1,11,x^3 - x^2 - 12*x + 16,13,x^3 + x^2 - 12*x - 16[] 474,6,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - x^3 - 19*x^2 + 20*x - 4,7,x^4 - 4*x^3 - 12*x^2 + 55*x - 24,11,x^4 - 5*x^3 - 40*x^2 + 192*x + 64,13,x^4 - 9*x^3 + 2*x^2 + 112*x - 128[] 475,1,2,x,3,x - 2,5,x,7,x - 1,11,x - 3,13,x - 4[] 475,2,2,x - 1,3,x,5,x,7,x + 2,11,x + 4,13,x - 2[] 475,3,2,x + 1,3,x,5,x,7,x - 2,11,x + 4,13,x + 2[] 475,4,2,x^3 + x^2 - 3*x - 1,3,x^3 + 2*x^2 - 4*x - 4,5,x^3,7,x^3 - 16*x - 16,11,x^3 + 8*x^2 + 8*x - 16,13,x^3 + 8*x^2 + 12*x + 4[] 475,5,2,x^3 + 4*x^2 + 3*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3,7,x^3 - 7*x - 7,11,x^3 - x^2 - 16*x - 13,13,x^3 + 5*x^2 + 6*x + 1[] 475,6,2,x^3 - 2*x^2 - 3*x + 5,3,x^3 - 2*x^2 - 3*x + 5,5,x^3,7,x^3 - 4*x^2 + x + 1,11,x^3 - x^2 - 4*x - 1,13,x^3 - 3*x^2 - 36*x + 103[] 475,7,2,x^3 - 4*x^2 + 3*x + 1,3,x^3 - 2*x^2 - x + 1,5,x^3,7,x^3 - 7*x + 7,11,x^3 - x^2 - 16*x - 13,13,x^3 - 5*x^2 + 6*x - 1[] 475,8,2,x^3 + 2*x^2 - 3*x - 5,3,x^3 + 2*x^2 - 3*x - 5,5,x^3,7,x^3 + 4*x^2 + x - 1,11,x^3 - x^2 - 4*x - 1,13,x^3 + 3*x^2 - 36*x - 103[] 475,9,2,x^4 - 2*x^3 - 6*x^2 + 8*x + 9,3,x^4 + 2*x^3 - 8*x^2 - 16*x - 4,5,x^4,7,x^4 + 4*x^3 - 16*x^2 - 48*x + 32,11,x^4 - 4*x^3 - 16*x^2 + 32*x + 48,13,x^4 + 2*x^3 - 24*x^2 - 32*x + 20[] 475,10,2,x^6 - 10*x^4 + 27*x^2 - 16,3,x^6 - 16*x^4 + 60*x^2 - 16,5,x^6,7,x^6 - 19*x^4 + 104*x^2 - 144,11,x^6 - 2*x^5 - 31*x^4 + 56*x^3 + 232*x^2 - 384*x + 144,13,x^6 - 28*x^4 + 236*x^2 - 576[] 476,1,2,x^2,3,x^2 + x - 3,5,x^2 - x - 3,7,x^2 + 2*x + 1,11,x^2 - 8*x + 16,13,x^2 + 2*x - 12[] 476,2,2,x^2,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 + 2*x + 1,11,x^2 + 6*x + 4,13,x^2 + 2*x - 4[] 476,3,2,x^2,3,x^2 + 3*x - 1,5,x^2 + 3*x - 1,7,x^2 - 2*x + 1,11,x^2 - 2*x - 12,13,x^2 + 6*x - 4[] 476,4,2,x^2,3,x^2 - x - 3,5,x^2 + x - 3,7,x^2 - 2*x + 1,11,x^2,13,x^2 - 6*x - 4[] Total time: 19.250 seconds, Total memory usage: 6.67MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 11:51:02 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [476..479] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 11:50:46 on modular [Seed = 1220372666] ------------------------------------- 476,1,2,$.1^2,3,$.1^2 +$.1 - 3,5,$.1^2 -$.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 8*$.1 + 16,13,$.1^2 + 2*$.1 - 12[]
476,2,2,$.1^2,3,$.1^2 + $.1 - 1,5,$.1^2 + $.1 - 1,7,$.1^2 + 2*$.1 + 1,11,$.1^2 +
6*$.1 + 4,13,$.1^2 + 2*$.1 - 4[] 476,3,2,$.1^2,3,$.1^2 + 3*$.1 - 1,5,$.1^2 + 3*$.1 - 1,7,$.1^2 - 2*$.1 +
1,11,$.1^2 - 2*$.1 - 12,13,$.1^2 + 6*$.1 - 4[]
476,4,2,$.1^2,3,$.1^2 - $.1 - 3,5,$.1^2 + $.1 - 3,7,$.1^2 - 2*$.1 + 1,11,$.1^2,13,$.1^2 - 6*$.1 - 4[]
477,1,2,x - 1,3,x,5,x,7,x + 4,11,x,13,x + 3[]
477,2,2,x^3 - x^2 - 3*x + 1,3,x^3,5,x^3 - 2*x^2 - 4*x + 4,7,x^3 - 4*x^2 +
4,11,x^3 - 4*x^2 - 4*x + 20,13,x^3 - 3*x^2 + 3*x - 1[]
477,3,2,x^4 + 3*x^3 - x^2 - 5*x + 1,3,x^4,5,x^4 + 4*x^3 - x^2 - 14*x - 9,7,x^4 -
7*x^2 + 4*x + 1,11,x^4 + 8*x^3 + 8*x^2 - 40*x - 48,13,x^4 + 6*x^3 - 21*x^2 -
106*x + 93[]
477,4,2,x^4 - 3*x^3 - x^2 + 5*x + 1,3,x^4,5,x^4 - 4*x^3 - x^2 + 14*x - 9,7,x^4 -
7*x^2 + 4*x + 1,11,x^4 - 8*x^3 + 8*x^2 + 40*x - 48,13,x^4 + 6*x^3 - 21*x^2 -
106*x + 93[]
477,5,2,x^4 + 3*x^3 - x^2 - 7*x - 3,3,x^4,5,x^4 + 2*x^3 - 11*x^2 - 32*x -
21,7,x^4 + 4*x^3 - 7*x^2 - 44*x - 43,11,x^4 + 6*x^3 - 28*x^2 - 232*x -
336,13,x^4 + 6*x^3 - 9*x^2 - 70*x + 1[]
477,6,2,x^5 - 10*x^3 + 22*x - 5,3,x^5,5,x^5 - 19*x^3 - 6*x^2 + 67*x + 2,7,x^5 -
4*x^4 - 23*x^3 + 92*x^2 + 117*x - 472,11,x^5 + 2*x^4 - 28*x^3 - 72*x^2 + 16*x +
64,13,x^5 - 8*x^4 - 13*x^3 + 136*x^2 + 101*x - 110[]
478,1,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 4*x^2 - 5*x - 1,5,x^4 +
3*x^3 - 2*x^2 - 10*x - 5,7,x^4 + 2*x^3 - 8*x^2 - 9*x + 13,11,x^4 + 3*x^3 -
26*x^2 - 46*x + 103,13,x^4 + 3*x^3 - 17*x^2 + 11*x + 7[]
478,2,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 6*x^3 + 10*x^2 + 3*x - 1,5,x^4 +
7*x^3 + 10*x^2 - 16*x - 31,7,x^4 + 6*x^3 - 8*x^2 - 101*x - 149,11,x^4 + 3*x^3 -
30*x^2 - 44*x + 179,13,x^4 + 9*x^3 - 5*x^2 - 213*x - 451[]
478,3,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 2*x^4 - 6*x^3 + 11*x^2 +
7*x - 12,5,x^5 - 3*x^4 - 4*x^3 + 12*x^2 + 5*x - 6,7,x^5 - 4*x^4 - 2*x^3 + 21*x^2
- 15*x - 4,11,x^5 - 5*x^4 - 6*x^3 + 28*x^2 + 15*x - 16,13,x^5 - x^4 - 23*x^3 +
69*x^2 - 57*x + 8[]
478,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 2*x^5 - 12*x^4
+ 19*x^3 + 35*x^2 - 32*x - 32,5,x^6 - 5*x^5 - 6*x^4 + 50*x^3 - 33*x^2 - 44*x +
28,7,x^6 - 26*x^4 + 5*x^3 + 71*x^2 - 48*x + 8,11,x^6 - 5*x^5 - 18*x^4 + 130*x^3
- 133*x^2 - 200*x + 232,13,x^6 - 3*x^5 - 53*x^4 + 131*x^3 + 563*x^2 - 334*x -
1186[]
479,1,2,x^8 + 2*x^7 - 6*x^6 - 11*x^5 + 10*x^4 + 17*x^3 - 4*x^2 - 7*x - 1,3,x^8 +
3*x^7 - 4*x^6 - 15*x^5 + x^4 + 16*x^3 + 2*x^2 - 4*x - 1,5,x^8 + 4*x^7 - 2*x^6 -
24*x^5 - 21*x^4 + 17*x^3 + 27*x^2 + 10*x + 1,7,x^8 + 4*x^7 - 6*x^6 - 44*x^5 -
49*x^4 + 19*x^3 + 49*x^2 + 14*x - 1,11,x^8 + 5*x^7 - 11*x^6 - 84*x^5 - 112*x^4 -
43*x^3 + 7*x^2 + 7*x + 1,13,x^8 + 9*x^7 + 23*x^6 - 10*x^5 - 116*x^4 - 107*x^3 +
99*x^2 + 177*x + 61[]
479,2,2,x^32 - 3*x^31 - 49*x^30 + 150*x^29 + 1068*x^28 - 3349*x^27 - 13663*x^26
+ 44102*x^25 + 114017*x^24 - 381227*x^23 - 652363*x^22 + 2278423*x^21 +
2617329*x^20 - 9659993*x^19 - 7391907*x^18 + 29333039*x^17 + 14485613*x^16 -
63589225*x^15 - 18892591*x^14 + 96842403*x^13 + 14744217*x^12 - 100301909*x^11 -
4507611*x^10 + 66698107*x^9 - 2210691*x^8 - 25684834*x^7 + 2153748*x^6 +
4689118*x^5 - 470371*x^4 - 268239*x^3 + 38414*x^2 - 242*x - 7,3,x^32 - 5*x^31 -
63*x^30 + 344*x^29 + 1704*x^28 - 10494*x^27 - 25595*x^26 + 187357*x^25 +
227445*x^24 - 2177843*x^23 - 1114189*x^22 + 17365061*x^21 + 1360454*x^20 -
97608556*x^19 + 18763008*x^18 + 392002532*x^17 - 137548311*x^16 -
1129433662*x^15 + 478309511*x^14 + 2325377139*x^13 - 985918389*x^12 -
3375402978*x^11 + 1221010481*x^10 + 3357623855*x^9 - 830495510*x^8 -
2164167195*x^7 + 208967933*x^6 + 805018305*x^5 + 56962584*x^4 - 128835824*x^3 -
31102484*x^2 - 398028*x + 139187,5,x^32 - 6*x^31 - 99*x^30 + 650*x^29 +
4176*x^28 - 31187*x^27 - 95978*x^26 + 874153*x^25 + 1230170*x^24 - 15896279*x^23
- 6371926*x^22 + 196883940*x^21 - 55851768*x^20 - 1695138243*x^19 +
1356000015*x^18 + 10151496640*x^17 - 12573160105*x^16 - 41443199854*x^15 +
69699610005*x^14 + 109264004022*x^13 - 248513470559*x^12 - 160056140840*x^11 +
570181911365*x^10 + 46587939531*x^9 - 809089270013*x^8 + 237355977983*x^7 +
650249928390*x^6 - 376623575384*x^5 - 241458556798*x^4 + 219821395723*x^3 +
12651006597*x^2 - 45139203778*x + 9151995329,7,x^32 - 8*x^31 - 125*x^30 +
1172*x^29 + 6124*x^28 - 74777*x^27 - 127164*x^26 + 2715765*x^25 - 396922*x^24 -
61390141*x^23 + 85340794*x^22 + 880387964*x^21 - 2177495446*x^20 -
7632833373*x^19 + 29456135743*x^18 + 31292238770*x^17 - 236954544803*x^16 +
58898064532*x^15 + 1100884700503*x^14 - 1315047166956*x^13 - 2445524896771*x^12
+ 5854903619054*x^11 + 191611506123*x^10 - 10294527175039*x^9 +
7720989332953*x^8 + 4916583932917*x^7 - 8596797576802*x^6 + 1645938589520*x^5 +
2700693624016*x^4 - 1440448082017*x^3 - 49317177497*x^2 + 159770207746*x -
23508342337,11,x^32 - 11*x^31 - 170*x^30 + 2265*x^29 + 10788*x^28 - 202568*x^27
- 225464*x^26 + 10290626*x^25 - 8512681*x^24 - 325230593*x^23 + 705680039*x^22 +
6543689371*x^21 - 22177538499*x^20 - 80731840869*x^19 + 404699138729*x^18 +
502086529171*x^17 - 4606709368897*x^16 + 545099209698*x^15 + 32350430642653*x^14
- 34722746983061*x^13 - 128353862486880*x^12 + 258847478402279*x^11 +
203773531088353*x^10 - 868283210528113*x^9 + 261837256912342*x^8 +
1229973469625787*x^7 - 1201747716097153*x^6 - 291619684645047*x^5 +
859061505759179*x^4 - 253385721770497*x^3 - 141315750945463*x^2 +
88787782173691*x - 12184098128923,13,x^32 - 13*x^31 - 207*x^30 + 3306*x^29 +
16128*x^28 - 368777*x^27 - 429085*x^26 + 23712447*x^25 - 17477467*x^24 -
971341690*x^23 + 1881302792*x^22 + 26443688640*x^21 - 74652373648*x^20 -
484433337312*x^19 + 1739050092352*x^18 + 5919946586624*x^17 -
25974846256640*x^16 - 46921286472704*x^15 + 254028258181120*x^14 +
229645967859712*x^13 - 1621563037339648*x^12 - 642474047692800*x^11 +
6660436956053504*x^10 + 877802533945344*x^9 - 17084262354649088*x^8 -
307470387642368*x^7 + 25775286115368960*x^6 - 470173925507072*x^5 -
20398713754091520*x^4 + 1055820137627648*x^3 + 6892854760701952*x^2 -
698012942729216*x - 415848749596672[]

Total time: 16.219 seconds, Total memory usage: 5.84MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:01:59 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [479..482] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 12:01:36 on modular  [Seed = 2640871673]
-------------------------------------

479,1,2,$.1^8 + 2*$.1^7 - 6*$.1^6 - 11*$.1^5 + 10*$.1^4 + 17*$.1^3 - 4*$.1^2 - 7*$.1 - 1,3,$.1^8 + 3*$.1^7 - 4*$.1^6 - 15*$.1^5 + $.1^4 + 16*$.1^3 + 2*$.1^2 - 4*$.1 - 1,5,$.1^8 + 4*$.1^7 - 2*$.1^6 - 24*$.1^5 - 21*$.1^4 + 17*$.1^3 +
27*$.1^2 + 10*$.1 + 1,7,$.1^8 + 4*$.1^7 - 6*$.1^6 - 44*$.1^5 - 49*$.1^4 + 19*$.1^3 + 49*$.1^2 + 14*$.1 - 1,11,$.1^8 + 5*$.1^7 - 11*$.1^6 - 84*$.1^5 -
112*$.1^4 - 43*$.1^3 + 7*$.1^2 + 7*$.1 + 1,13,$.1^8 + 9*$.1^7 + 23*$.1^6 - 10*$.1^5 - 116*$.1^4 - 107*$.1^3 + 99*$.1^2 + 177*$.1 + 61[]
479,2,2,$.1^32 - 3*$.1^31 - 49*$.1^30 + 150*$.1^29 + 1068*$.1^28 - 3349*$.1^27 -
13663*$.1^26 + 44102*$.1^25 + 114017*$.1^24 - 381227*$.1^23 - 652363*$.1^22 + 2278423*$.1^21 + 2617329*$.1^20 - 9659993*$.1^19 - 7391907*$.1^18 + 29333039*$.1^17 + 14485613*$.1^16 - 63589225*$.1^15 - 18892591*$.1^14 + 96842403*$.1^13 + 14744217*$.1^12 - 100301909*$.1^11 - 4507611*$.1^10 + 66698107*$.1^9 - 2210691*$.1^8 - 25684834*$.1^7 + 2153748*$.1^6 + 4689118*$.1^5
- 470371*$.1^4 - 268239*$.1^3 + 38414*$.1^2 - 242*$.1 - 7,3,$.1^32 - 5*$.1^31 -
63*$.1^30 + 344*$.1^29 + 1704*$.1^28 - 10494*$.1^27 - 25595*$.1^26 + 187357*$.1^25 + 227445*$.1^24 - 2177843*$.1^23 - 1114189*$.1^22 + 17365061*$.1^21 + 1360454*$.1^20 - 97608556*$.1^19 + 18763008*$.1^18 + 392002532*$.1^17 - 137548311*$.1^16 - 1129433662*$.1^15 + 478309511*$.1^14 + 2325377139*$.1^13 - 985918389*$.1^12 - 3375402978*$.1^11 + 1221010481*$.1^10 + 3357623855*$.1^9 - 830495510*$.1^8 - 2164167195*$.1^7 + 208967933*$.1^6 + 805018305*$.1^5 + 56962584*$.1^4 - 128835824*$.1^3 - 31102484*$.1^2 - 398028*$.1
+ 139187,5,$.1^32 - 6*$.1^31 - 99*$.1^30 + 650*$.1^29 + 4176*$.1^28 - 31187*$.1^27 - 95978*$.1^26 + 874153*$.1^25 + 1230170*$.1^24 - 15896279*$.1^23 -
6371926*$.1^22 + 196883940*$.1^21 - 55851768*$.1^20 - 1695138243*$.1^19 +
1356000015*$.1^18 + 10151496640*$.1^17 - 12573160105*$.1^16 - 41443199854*$.1^15
+ 69699610005*$.1^14 + 109264004022*$.1^13 - 248513470559*$.1^12 - 160056140840*$.1^11 + 570181911365*$.1^10 + 46587939531*$.1^9 -
809089270013*$.1^8 + 237355977983*$.1^7 + 650249928390*$.1^6 - 376623575384*$.1^5 - 241458556798*$.1^4 + 219821395723*$.1^3 + 12651006597*$.1^2 - 45139203778*$.1 + 9151995329,7,$.1^32 - 8*$.1^31 - 125*$.1^30 + 1172*$.1^29 +
6124*$.1^28 - 74777*$.1^27 - 127164*$.1^26 + 2715765*$.1^25 - 396922*$.1^24 - 61390141*$.1^23 + 85340794*$.1^22 + 880387964*$.1^21 - 2177495446*$.1^20 - 7632833373*$.1^19 + 29456135743*$.1^18 + 31292238770*$.1^17 -
236954544803*$.1^16 + 58898064532*$.1^15 + 1100884700503*$.1^14 - 1315047166956*$.1^13 - 2445524896771*$.1^12 + 5854903619054*$.1^11 +
191611506123*$.1^10 - 10294527175039*$.1^9 + 7720989332953*$.1^8 + 4916583932917*$.1^7 - 8596797576802*$.1^6 + 1645938589520*$.1^5 +
2700693624016*$.1^4 - 1440448082017*$.1^3 - 49317177497*$.1^2 + 159770207746*$.1
- 23508342337,11,$.1^32 - 11*$.1^31 - 170*$.1^30 + 2265*$.1^29 + 10788*$.1^28 - 202568*$.1^27 - 225464*$.1^26 + 10290626*$.1^25 - 8512681*$.1^24 - 325230593*$.1^23 + 705680039*$.1^22 + 6543689371*$.1^21 - 22177538499*$.1^20 - 80731840869*$.1^19 + 404699138729*$.1^18 + 502086529171*$.1^17 -
4606709368897*$.1^16 + 545099209698*$.1^15 + 32350430642653*$.1^14 - 34722746983061*$.1^13 - 128353862486880*$.1^12 + 258847478402279*$.1^11 +
203773531088353*$.1^10 - 868283210528113*$.1^9 + 261837256912342*$.1^8 + 1229973469625787*$.1^7 - 1201747716097153*$.1^6 - 291619684645047*$.1^5 +
859061505759179*$.1^4 - 253385721770497*$.1^3 - 141315750945463*$.1^2 + 88787782173691*$.1 - 12184098128923,13,$.1^32 - 13*$.1^31 - 207*$.1^30 + 3306*$.1^29 + 16128*$.1^28 - 368777*$.1^27 - 429085*$.1^26 + 23712447*$.1^25 -
17477467*$.1^24 - 971341690*$.1^23 + 1881302792*$.1^22 + 26443688640*$.1^21 -
74652373648*$.1^20 - 484433337312*$.1^19 + 1739050092352*$.1^18 + 5919946586624*$.1^17 - 25974846256640*$.1^16 - 46921286472704*$.1^15 +
254028258181120*$.1^14 + 229645967859712*$.1^13 - 1621563037339648*$.1^12 - 642474047692800*$.1^11 + 6660436956053504*$.1^10 + 877802533945344*$.1^9 -
17084262354649088*$.1^8 - 307470387642368*$.1^7 + 25775286115368960*$.1^6 - 470173925507072*$.1^5 - 20398713754091520*$.1^4 + 1055820137627648*$.1^3 +
6892854760701952*$.1^2 - 698012942729216*$.1 - 415848749596672[]
480,1,2,x,3,x + 1,5,x + 1,7,x,11,x + 4,13,x - 2[]
480,2,2,x,3,x + 1,5,x - 1,7,x,11,x,13,x - 2[]
480,3,2,x,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[]
480,4,2,x,3,x - 1,5,x + 1,7,x - 4,11,x + 4,13,x - 6[]
480,5,2,x,3,x + 1,5,x + 1,7,x + 4,11,x - 4,13,x - 6[]
480,6,2,x,3,x + 1,5,x - 1,7,x + 4,11,x,13,x + 2[]
480,7,2,x,3,x - 1,5,x - 1,7,x,11,x,13,x - 2[]
480,8,2,x,3,x - 1,5,x - 1,7,x - 4,11,x,13,x + 2[]
481,1,2,x - 1,3,x,5,x + 2,7,x - 2,11,x + 2,13,x + 1[]
481,2,2,x^7 + 5*x^6 + 2*x^5 - 21*x^4 - 25*x^3 + 8*x^2 + 13*x - 2,3,x^7 - x^6 -
11*x^5 + 7*x^4 + 39*x^3 - 6*x^2 - 46*x - 19,5,x^7 + 4*x^6 - 13*x^5 - 42*x^4 +
83*x^3 + 99*x^2 - 227*x + 94,7,x^7 + 8*x^6 - 5*x^5 - 147*x^4 - 126*x^3 + 621*x^2
+ 405*x - 243,11,x^7 + 13*x^6 + 38*x^5 - 83*x^4 - 427*x^3 - 434*x^2 - 71*x +
37,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[]
481,3,2,x^7 + x^6 - 8*x^5 - 7*x^4 + 17*x^3 + 12*x^2 - 9*x - 6,3,x^7 + 7*x^6 +
13*x^5 - 5*x^4 - 29*x^3 - 10*x^2 + 10*x + 1,5,x^7 + 2*x^6 - 19*x^5 - 38*x^4 +
73*x^3 + 195*x^2 + 105*x + 12,7,x^7 + 2*x^6 - 15*x^5 - 11*x^4 + 64*x^3 - 27*x^2
- 21*x + 11,11,x^7 + 13*x^6 + 40*x^5 - 87*x^4 - 461*x^3 + 60*x^2 + 1035*x +
423,13,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1[]
481,4,2,x^11 - 3*x^10 - 14*x^9 + 45*x^8 + 64*x^7 - 237*x^6 - 99*x^5 + 529*x^4 -
7*x^3 - 460*x^2 + 67*x + 110,3,x^11 - x^10 - 23*x^9 + 19*x^8 + 191*x^7 - 106*x^6
- 702*x^5 + 153*x^4 + 1016*x^3 + 144*x^2 - 160*x - 32,5,x^11 - 4*x^10 - 29*x^9 +
128*x^8 + 223*x^7 - 1259*x^6 - 243*x^5 + 4516*x^4 - 2112*x^3 - 4300*x^2 + 3492*x
- 640,7,x^11 - 4*x^10 - 27*x^9 + 115*x^8 + 174*x^7 - 923*x^6 - 157*x^5 +
2419*x^4 - 704*x^3 - 1246*x^2 + 126*x + 2,11,x^11 - 21*x^10 + 138*x^9 + 5*x^8 -
3767*x^7 + 13336*x^6 + 5591*x^5 - 102581*x^4 + 126638*x^3 + 89244*x^2 - 150718*x
+ 21938,13,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 +
330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1[]
481,5,2,x^11 - 3*x^10 - 12*x^9 + 39*x^8 + 38*x^7 - 149*x^6 - 23*x^5 + 175*x^4 -
5*x^3 - 48*x^2 + 5*x + 2,3,x^11 - 5*x^10 - 11*x^9 + 83*x^8 - 9*x^7 - 418*x^6 +
314*x^5 + 709*x^4 - 692*x^3 - 192*x^2 + 128*x + 32,5,x^11 - 2*x^10 - 27*x^9 +
64*x^8 + 177*x^7 - 491*x^6 - 127*x^5 + 706*x^4 + 40*x^3 - 268*x^2 - 92*x -
8,7,x^11 - 45*x^9 + 13*x^8 + 694*x^7 - 379*x^6 - 4269*x^5 + 3371*x^4 + 8922*x^3
- 9110*x^2 + 486*x + 262,11,x^11 - 11*x^10 + 30*x^9 + 77*x^8 - 503*x^7 + 440*x^6
+ 1621*x^5 - 3413*x^4 + 848*x^3 + 2084*x^2 - 1058*x + 102,13,x^11 - 11*x^10 +
55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 +
11*x - 1[]
482,1,2,x + 1,3,x + 2,5,x + 1,7,x - 1,11,x - 4,13,x + 2[]
482,2,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 +
6*x + 9,13,x^2 + 7*x + 11[]
482,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 5*x - 2,5,x^3 - 2*x^2 - 4*x +
7,7,x^3 + 9*x^2 + 27*x + 27,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 + 5*x^2 - 11*x -
2[]
482,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 2*x^5 - 10*x^4
+ 16*x^3 + 26*x^2 - 30*x - 13,5,x^6 + 5*x^5 - 9*x^4 - 56*x^3 + 20*x^2 + 128*x -
48,7,x^6 - 10*x^5 + 22*x^4 + 44*x^3 - 172*x^2 + 118*x - 23,11,x^6 + 4*x^5 -
17*x^4 - 48*x^3 + 104*x^2 + 128*x - 192,13,x^6 - 9*x^5 + 16*x^4 + 49*x^3 -
178*x^2 + 165*x - 45[]

Errors: /home/mfd/gomagma: line 2: 11145 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:02:53 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [479..481] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 12:02:33 on modular  [Seed = 2238748728]
-------------------------------------

479,1,2,$.1^8 + 2*$.1^7 - 6*$.1^6 - 11*$.1^5 + 10*$.1^4 + 17*$.1^3 - 4*$.1^2 - 7*$.1 - 1,3,$.1^8 + 3*$.1^7 - 4*$.1^6 - 15*$.1^5 + $.1^4 + 16*$.1^3 + 2*$.1^2 - 4*$.1 - 1,5,$.1^8 + 4*$.1^7 - 2*$.1^6 - 24*$.1^5 - 21*$.1^4 + 17*$.1^3 +
27*$.1^2 + 10*$.1 + 1,7,$.1^8 + 4*$.1^7 - 6*$.1^6 - 44*$.1^5 - 49*$.1^4 + 19*$.1^3 + 49*$.1^2 + 14*$.1 - 1,11,$.1^8 + 5*$.1^7 - 11*$.1^6 - 84*$.1^5 -
112*$.1^4 - 43*$.1^3 + 7*$.1^2 + 7*$.1 + 1,13,$.1^8 + 9*$.1^7 + 23*$.1^6 - 10*$.1^5 - 116*$.1^4 - 107*$.1^3 + 99*$.1^2 + 177*$.1 + 61[]
479,2,2,$.1^32 - 3*$.1^31 - 49*$.1^30 + 150*$.1^29 + 1068*$.1^28 - 3349*$.1^27 -
13663*$.1^26 + 44102*$.1^25 + 114017*$.1^24 - 381227*$.1^23 - 652363*$.1^22 + 2278423*$.1^21 + 2617329*$.1^20 - 9659993*$.1^19 - 7391907*$.1^18 + 29333039*$.1^17 + 14485613*$.1^16 - 63589225*$.1^15 - 18892591*$.1^14 + 96842403*$.1^13 + 14744217*$.1^12 - 100301909*$.1^11 - 4507611*$.1^10 + 66698107*$.1^9 - 2210691*$.1^8 - 25684834*$.1^7 + 2153748*$.1^6 + 4689118*$.1^5
- 470371*$.1^4 - 268239*$.1^3 + 38414*$.1^2 - 242*$.1 - 7,3,$.1^32 - 5*$.1^31 -
63*$.1^30 + 344*$.1^29 + 1704*$.1^28 - 10494*$.1^27 - 25595*$.1^26 + 187357*$.1^25 + 227445*$.1^24 - 2177843*$.1^23 - 1114189*$.1^22 + 17365061*$.1^21 + 1360454*$.1^20 - 97608556*$.1^19 + 18763008*$.1^18 + 392002532*$.1^17 - 137548311*$.1^16 - 1129433662*$.1^15 + 478309511*$.1^14 + 2325377139*$.1^13 - 985918389*$.1^12 - 3375402978*$.1^11 + 1221010481*$.1^10 + 3357623855*$.1^9 - 830495510*$.1^8 - 2164167195*$.1^7 + 208967933*$.1^6 + 805018305*$.1^5 + 56962584*$.1^4 - 128835824*$.1^3 - 31102484*$.1^2 - 398028*$.1
+ 139187,5,$.1^32 - 6*$.1^31 - 99*$.1^30 + 650*$.1^29 + 4176*$.1^28 - 31187*$.1^27 - 95978*$.1^26 + 874153*$.1^25 + 1230170*$.1^24 - 15896279*$.1^23 -
6371926*$.1^22 + 196883940*$.1^21 - 55851768*$.1^20 - 1695138243*$.1^19 +
1356000015*$.1^18 + 10151496640*$.1^17 - 12573160105*$.1^16 - 41443199854*$.1^15
+ 69699610005*$.1^14 + 109264004022*$.1^13 - 248513470559*$.1^12 - 160056140840*$.1^11 + 570181911365*$.1^10 + 46587939531*$.1^9 -
809089270013*$.1^8 + 237355977983*$.1^7 + 650249928390*$.1^6 - 376623575384*$.1^5 - 241458556798*$.1^4 + 219821395723*$.1^3 + 12651006597*$.1^2 - 45139203778*$.1 + 9151995329,7,$.1^32 - 8*$.1^31 - 125*$.1^30 + 1172*$.1^29 +
6124*$.1^28 - 74777*$.1^27 - 127164*$.1^26 + 2715765*$.1^25 - 396922*$.1^24 - 61390141*$.1^23 + 85340794*$.1^22 + 880387964*$.1^21 - 2177495446*$.1^20 - 7632833373*$.1^19 + 29456135743*$.1^18 + 31292238770*$.1^17 -
236954544803*$.1^16 + 58898064532*$.1^15 + 1100884700503*$.1^14 - 1315047166956*$.1^13 - 2445524896771*$.1^12 + 5854903619054*$.1^11 +
191611506123*$.1^10 - 10294527175039*$.1^9 + 7720989332953*$.1^8 + 4916583932917*$.1^7 - 8596797576802*$.1^6 + 1645938589520*$.1^5 +
2700693624016*$.1^4 - 1440448082017*$.1^3 - 49317177497*$.1^2 + 159770207746*$.1
- 23508342337,11,$.1^32 - 11*$.1^31 - 170*$.1^30 + 2265*$.1^29 + 10788*$.1^28 - 202568*$.1^27 - 225464*$.1^26 + 10290626*$.1^25 - 8512681*$.1^24 - 325230593*$.1^23 + 705680039*$.1^22 + 6543689371*$.1^21 - 22177538499*$.1^20 - 80731840869*$.1^19 + 404699138729*$.1^18 + 502086529171*$.1^17 -
4606709368897*$.1^16 + 545099209698*$.1^15 + 32350430642653*$.1^14 - 34722746983061*$.1^13 - 128353862486880*$.1^12 + 258847478402279*$.1^11 +
203773531088353*$.1^10 - 868283210528113*$.1^9 + 261837256912342*$.1^8 + 1229973469625787*$.1^7 - 1201747716097153*$.1^6 - 291619684645047*$.1^5 +
859061505759179*$.1^4 - 253385721770497*$.1^3 - 141315750945463*$.1^2 + 88787782173691*$.1 - 12184098128923,13,$.1^32 - 13*$.1^31 - 207*$.1^30 + 3306*$.1^29 + 16128*$.1^28 - 368777*$.1^27 - 429085*$.1^26 + 23712447*$.1^25 -
17477467*$.1^24 - 971341690*$.1^23 + 1881302792*$.1^22 + 26443688640*$.1^21 -
74652373648*$.1^20 - 484433337312*$.1^19 + 1739050092352*$.1^18 + 5919946586624*$.1^17 - 25974846256640*$.1^16 - 46921286472704*$.1^15 +
254028258181120*$.1^14 + 229645967859712*$.1^13 - 1621563037339648*$.1^12 - 642474047692800*$.1^11 + 6660436956053504*$.1^10 + 877802533945344*$.1^9 -
17084262354649088*$.1^8 - 307470387642368*$.1^7 + 25775286115368960*$.1^6 - 470173925507072*$.1^5 - 20398713754091520*$.1^4 + 1055820137627648*$.1^3 +
6892854760701952*$.1^2 - 698012942729216*$.1 - 415848749596672[]
480,1,2,x,3,x + 1,5,x + 1,7,x,11,x + 4,13,x - 2[]
480,2,2,x,3,x + 1,5,x - 1,7,x,11,x,13,x - 2[]
480,3,2,x,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[]
480,4,2,x,3,x - 1,5,x + 1,7,x - 4,11,x + 4,13,x - 6[]
480,5,2,x,3,x + 1,5,x + 1,7,x + 4,11,x - 4,13,x - 6[]
480,6,2,x,3,x + 1,5,x - 1,7,x + 4,11,x,13,x + 2[]
480,7,2,x,3,x - 1,5,x - 1,7,x,11,x,13,x - 2[]
480,8,2,x,3,x - 1,5,x - 1,7,x - 4,11,x,13,x + 2[]
481,1,2,x - 1,3,x,5,x + 2,7,x - 2,11,x + 2,13,x + 1[]
481,2,2,x^7 + 5*x^6 + 2*x^5 - 21*x^4 - 25*x^3 + 8*x^2 + 13*x - 2,3,x^7 - x^6 -
11*x^5 + 7*x^4 + 39*x^3 - 6*x^2 - 46*x - 19,5,x^7 + 4*x^6 - 13*x^5 - 42*x^4 +
83*x^3 + 99*x^2 - 227*x + 94,7,x^7 + 8*x^6 - 5*x^5 - 147*x^4 - 126*x^3 + 621*x^2
+ 405*x - 243,11,x^7 + 13*x^6 + 38*x^5 - 83*x^4 - 427*x^3 - 434*x^2 - 71*x +
37,13,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[]
481,3,2,x^7 + x^6 - 8*x^5 - 7*x^4 + 17*x^3 + 12*x^2 - 9*x - 6,3,x^7 + 7*x^6 +
13*x^5 - 5*x^4 - 29*x^3 - 10*x^2 + 10*x + 1,5,x^7 + 2*x^6 - 19*x^5 - 38*x^4 +
73*x^3 + 195*x^2 + 105*x + 12,7,x^7 + 2*x^6 - 15*x^5 - 11*x^4 + 64*x^3 - 27*x^2
- 21*x + 11,11,x^7 + 13*x^6 + 40*x^5 - 87*x^4 - 461*x^3 + 60*x^2 + 1035*x +
423,13,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1[]
481,4,2,x^11 - 3*x^10 - 14*x^9 + 45*x^8 + 64*x^7 - 237*x^6 - 99*x^5 + 529*x^4 -
7*x^3 - 460*x^2 + 67*x + 110,3,x^11 - x^10 - 23*x^9 + 19*x^8 + 191*x^7 - 106*x^6
- 702*x^5 + 153*x^4 + 1016*x^3 + 144*x^2 - 160*x - 32,5,x^11 - 4*x^10 - 29*x^9 +
128*x^8 + 223*x^7 - 1259*x^6 - 243*x^5 + 4516*x^4 - 2112*x^3 - 4300*x^2 + 3492*x
- 640,7,x^11 - 4*x^10 - 27*x^9 + 115*x^8 + 174*x^7 - 923*x^6 - 157*x^5 +
2419*x^4 - 704*x^3 - 1246*x^2 + 126*x + 2,11,x^11 - 21*x^10 + 138*x^9 + 5*x^8 -
3767*x^7 + 13336*x^6 + 5591*x^5 - 102581*x^4 + 126638*x^3 + 89244*x^2 - 150718*x
+ 21938,13,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 +
330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1[]
481,5,2,x^11 - 3*x^10 - 12*x^9 + 39*x^8 + 38*x^7 - 149*x^6 - 23*x^5 + 175*x^4 -
5*x^3 - 48*x^2 + 5*x + 2,3,x^11 - 5*x^10 - 11*x^9 + 83*x^8 - 9*x^7 - 418*x^6 +
314*x^5 + 709*x^4 - 692*x^3 - 192*x^2 + 128*x + 32,5,x^11 - 2*x^10 - 27*x^9 +
64*x^8 + 177*x^7 - 491*x^6 - 127*x^5 + 706*x^4 + 40*x^3 - 268*x^2 - 92*x -
8,7,x^11 - 45*x^9 + 13*x^8 + 694*x^7 - 379*x^6 - 4269*x^5 + 3371*x^4 + 8922*x^3
- 9110*x^2 + 486*x + 262,11,x^11 - 11*x^10 + 30*x^9 + 77*x^8 - 503*x^7 + 440*x^6
+ 1621*x^5 - 3413*x^4 + 848*x^3 + 2084*x^2 - 1058*x + 102,13,x^11 - 11*x^10 +
55*x^9 - 165*x^8 + 330*x^7 - 462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 +
11*x - 1[]

Total time: 19.090 seconds, Total memory usage: 6.38MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:07:03 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [481..484] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 12:06:46 on modular  [Seed = 2340329273]
-------------------------------------

481,1,2,$.1 - 1,3,$.1,5,$.1 + 2,7,$.1 - 2,11,$.1 + 2,13,$.1 + 1[]
481,2,2,$.1^7 + 5*$.1^6 + 2*$.1^5 - 21*$.1^4 - 25*$.1^3 + 8*$.1^2 + 13*$.1 - 2,3,$.1^7 - $.1^6 - 11*$.1^5 + 7*$.1^4 + 39*$.1^3 - 6*$.1^2 - 46*$.1 -
19,5,$.1^7 + 4*$.1^6 - 13*$.1^5 - 42*$.1^4 + 83*$.1^3 + 99*$.1^2 - 227*$.1 + 94,7,$.1^7 + 8*$.1^6 - 5*$.1^5 - 147*$.1^4 - 126*$.1^3 + 621*$.1^2 + 405*$.1 -
243,11,$.1^7 + 13*$.1^6 + 38*$.1^5 - 83*$.1^4 - 427*$.1^3 - 434*$.1^2 - 71*$.1 + 37,13,$.1^7 + 7*$.1^6 + 21*$.1^5 + 35*$.1^4 + 35*$.1^3 + 21*$.1^2 + 7*$.1 + 1[]
481,3,2,$.1^7 +$.1^6 - 8*$.1^5 - 7*$.1^4 + 17*$.1^3 + 12*$.1^2 - 9*$.1 - 6,3,$.1^7 + 7*$.1^6 + 13*$.1^5 - 5*$.1^4 - 29*$.1^3 - 10*$.1^2 + 10*$.1 +
1,5,$.1^7 + 2*$.1^6 - 19*$.1^5 - 38*$.1^4 + 73*$.1^3 + 195*$.1^2 + 105*$.1 + 12,7,$.1^7 + 2*$.1^6 - 15*$.1^5 - 11*$.1^4 + 64*$.1^3 - 27*$.1^2 - 21*$.1 +
11,11,$.1^7 + 13*$.1^6 + 40*$.1^5 - 87*$.1^4 - 461*$.1^3 + 60*$.1^2 + 1035*$.1 + 423,13,$.1^7 - 7*$.1^6 + 21*$.1^5 - 35*$.1^4 + 35*$.1^3 - 21*$.1^2 + 7*$.1 - 1[]
481,4,2,$.1^11 - 3*$.1^10 - 14*$.1^9 + 45*$.1^8 + 64*$.1^7 - 237*$.1^6 -
99*$.1^5 + 529*$.1^4 - 7*$.1^3 - 460*$.1^2 + 67*$.1 + 110,3,$.1^11 - $.1^10 - 23*$.1^9 + 19*$.1^8 + 191*$.1^7 - 106*$.1^6 - 702*$.1^5 + 153*$.1^4 + 1016*$.1^3
+ 144*$.1^2 - 160*$.1 - 32,5,$.1^11 - 4*$.1^10 - 29*$.1^9 + 128*$.1^8 +
223*$.1^7 - 1259*$.1^6 - 243*$.1^5 + 4516*$.1^4 - 2112*$.1^3 - 4300*$.1^2 +
3492*$.1 - 640,7,$.1^11 - 4*$.1^10 - 27*$.1^9 + 115*$.1^8 + 174*$.1^7 -
923*$.1^6 - 157*$.1^5 + 2419*$.1^4 - 704*$.1^3 - 1246*$.1^2 + 126*$.1 +
2,11,$.1^11 - 21*$.1^10 + 138*$.1^9 + 5*$.1^8 - 3767*$.1^7 + 13336*$.1^6 +
5591*$.1^5 - 102581*$.1^4 + 126638*$.1^3 + 89244*$.1^2 - 150718*$.1 + 21938,13,$.1^11 + 11*$.1^10 + 55*$.1^9 + 165*$.1^8 + 330*$.1^7 + 462*$.1^6 + 462*$.1^5 + 330*$.1^4 + 165*$.1^3 + 55*$.1^2 + 11*$.1 + 1[]
481,5,2,$.1^11 - 3*$.1^10 - 12*$.1^9 + 39*$.1^8 + 38*$.1^7 - 149*$.1^6 -
23*$.1^5 + 175*$.1^4 - 5*$.1^3 - 48*$.1^2 + 5*$.1 + 2,3,$.1^11 - 5*$.1^10 - 11*$.1^9 + 83*$.1^8 - 9*$.1^7 - 418*$.1^6 + 314*$.1^5 + 709*$.1^4 - 692*$.1^3 -
192*$.1^2 + 128*$.1 + 32,5,$.1^11 - 2*$.1^10 - 27*$.1^9 + 64*$.1^8 + 177*$.1^7 - 491*$.1^6 - 127*$.1^5 + 706*$.1^4 + 40*$.1^3 - 268*$.1^2 - 92*$.1 - 8,7,$.1^11 -
45*$.1^9 + 13*$.1^8 + 694*$.1^7 - 379*$.1^6 - 4269*$.1^5 + 3371*$.1^4 +
8922*$.1^3 - 9110*$.1^2 + 486*$.1 + 262,11,$.1^11 - 11*$.1^10 + 30*$.1^9 +
77*$.1^8 - 503*$.1^7 + 440*$.1^6 + 1621*$.1^5 - 3413*$.1^4 + 848*$.1^3 +
2084*$.1^2 - 1058*$.1 + 102,13,$.1^11 - 11*$.1^10 + 55*$.1^9 - 165*$.1^8 +
330*$.1^7 - 462*$.1^6 + 462*$.1^5 - 330*$.1^4 + 165*$.1^3 - 55*$.1^2 + 11*$.1 - 1[] 482,1,2,x + 1,3,x + 2,5,x + 1,7,x - 1,11,x - 4,13,x + 2[] 482,2,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 + 6*x + 9,13,x^2 + 7*x + 11[] 482,3,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 2*x^2 - 5*x - 2,5,x^3 - 2*x^2 - 4*x + 7,7,x^3 + 9*x^2 + 27*x + 27,11,x^3 + 2*x^2 - 11*x + 4,13,x^3 + 5*x^2 - 11*x - 2[] 482,4,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 2*x^5 - 10*x^4 + 16*x^3 + 26*x^2 - 30*x - 13,5,x^6 + 5*x^5 - 9*x^4 - 56*x^3 + 20*x^2 + 128*x - 48,7,x^6 - 10*x^5 + 22*x^4 + 44*x^3 - 172*x^2 + 118*x - 23,11,x^6 + 4*x^5 - 17*x^4 - 48*x^3 + 104*x^2 + 128*x - 192,13,x^6 - 9*x^5 + 16*x^4 + 49*x^3 - 178*x^2 + 165*x - 45[] 482,5,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x - 1,3,x^9 - 4*x^8 - 12*x^7 + 58*x^6 + 24*x^5 - 252*x^4 + 97*x^3 + 336*x^2 - 244*x - 16,5,x^9 - 5*x^8 - 18*x^7 + 113*x^6 + 23*x^5 - 662*x^4 + 628*x^3 + 296*x^2 - 272*x - 32,7,x^9 - 6*x^8 - 15*x^7 + 126*x^6 + 42*x^5 - 854*x^4 + 19*x^3 + 2278*x^2 + 117*x - 1732,11,x^9 - 2*x^8 - 57*x^7 + 74*x^6 + 1020*x^5 - 984*x^4 - 6048*x^3 + 6208*x^2 + 6400*x - 6656,13,x^9 - 5*x^8 - 66*x^7 + 275*x^6 + 1352*x^5 - 3351*x^4 - 13353*x^3 + 7280*x^2 + 49580*x + 35936[] 483,1,2,x - 2,3,x - 1,5,x - 4,7,x + 1,11,x + 5,13,x + 2[] 483,2,2,x - 2,3,x - 1,5,x,7,x - 1,11,x - 1,13,x - 2[] 483,3,2,x^2 + x - 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 + 2*x + 1,11,x^2 - 5,13,x^2 + 7*x + 11[] 483,4,2,x^2 - x - 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 - 2*x + 1,11,x^2 - 5,13,x^2 + 7*x + 1[] 483,5,2,x^2 + x - 3,3,x^2 - 2*x + 1,5,x^2 + 5*x + 3,7,x^2 + 2*x + 1,11,x^2 + 10*x + 25,13,x^2 - x - 3[] 483,6,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 + 5*x + 5,7,x^2 - 2*x + 1,11,x^2 + 2*x - 19,13,x^2 + 7*x + 11[] 483,7,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 - 5*x + 5,7,x^2 - 2*x + 1,11,x^2 - 2*x + 1,13,x^2 + x - 1[] 483,8,2,x^3 - 6*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 - 3*x + 6,7,x^3 + 3*x^2 + 3*x + 1,11,x^3 - 6*x^2 - 3*x + 20,13,x^3 - 9*x^2 + 15*x - 6[] 483,9,2,x^4 - 2*x^3 - 4*x^2 + 5*x + 2,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 5*x^3 - 3*x^2 + 38*x - 32,7,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,11,x^4 - x^3 - 17*x^2 - 19*x + 4,13,x^4 - 7*x^3 - 17*x^2 + 164*x - 188[] 483,10,2,x^4 - 6*x^2 + x + 2,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 - 5*x^3 - x^2 + 14*x + 8,7,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,11,x^4 + 5*x^3 - 9*x^2 - 65*x - 68,13,x^4 - 7*x^3 - 11*x^2 + 152*x - 236[] 484,1,2,x,3,x - 1,5,x + 3,7,x + 2,11,x,13,x - 4[] 484,2,2,x^2,3,x^2 - x - 8,5,x^2 - 3*x - 6,7,x^2,11,x^2,13,x^2[] 484,3,2,x^2,3,x^2 + 3*x + 1,5,x^2 + x - 1,7,x^2 + x - 11,11,x^2,13,x^2 - 7*x + 11[] 484,4,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 6*x + 9,7,x^2 - 12,11,x^2,13,x^2 - 27[] 484,5,2,x^2,3,x^2 + 3*x + 1,5,x^2 + x - 1,7,x^2 - x - 11,11,x^2,13,x^2 + 7*x + 11[] Total time: 17.229 seconds, Total memory usage: 6.08MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:11:08 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [484..487] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:10:52 on modular [Seed = 2773532205] ------------------------------------- 484,1,2,$.1,3,$.1 - 1,5,$.1 + 3,7,$.1 + 2,11,$.1,13,$.1 - 4[] 484,2,2,$.1^2,3,$.1^2 -$.1 - 8,5,$.1^2 - 3*$.1 - 6,7,$.1^2,11,$.1^2,13,$.1^2[] 484,3,2,$.1^2,3,$.1^2 + 3*$.1 + 1,5,$.1^2 +$.1 - 1,7,$.1^2 +$.1 -
11,11,$.1^2,13,$.1^2 - 7*$.1 + 11[] 484,4,2,$.1^2,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - 6*$.1 + 9,7,$.1^2 - 12,11,$.1^2,13,$.1^2 - 27[] 484,5,2,$.1^2,3,$.1^2 + 3*$.1 + 1,5,$.1^2 +$.1 - 1,7,$.1^2 -$.1 -
11,11,$.1^2,13,$.1^2 + 7*$.1 + 11[] 485,1,2,x,3,x + 2,5,x + 1,7,x + 1,11,x + 3,13,x - 5[] 485,2,2,x,3,x,5,x - 1,7,x + 1,11,x - 1,13,x - 1[] 485,3,2,x^2 - 5,3,x^2 - x - 1,5,x^2 + 2*x + 1,7,x^2 - 8*x + 16,11,x^2 + 6*x + 4,13,x^2 - 5*x + 5[] 485,4,2,x^2 - 2*x + 1,3,x^2 - x - 7,5,x^2 - 2*x + 1,7,x^2,11,x^2 - 2*x - 28,13,x^2 - 7*x + 5[] 485,5,2,x^3 + 2*x^2 - 5*x - 8,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 - 5*x^2 + 2*x + 10,11,x^3 - 5*x^2 + 8,13,x^3 + x^2 - 24*x + 20[] 485,6,2,x^4 + x^3 - 4*x^2 - 2*x + 3,3,x^4 + 4*x^3 - 7*x + 3,5,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,7,x^4 + 3*x^3 - 5*x^2 - 5*x - 1,11,x^4 + 16*x^3 + 92*x^2 + 225*x + 197,13,x^4 + 4*x^3 - 22*x^2 - 84*x - 43[] 485,7,2,x^6 + x^5 - 9*x^4 - 9*x^3 + 17*x^2 + 14*x + 1,3,x^6 + x^5 - 9*x^4 - 9*x^3 + 8*x^2 + 8*x + 1,5,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,7,x^6 - 3*x^5 - 35*x^4 + 115*x^3 + 241*x^2 - 928*x + 448,11,x^6 - 6*x^5 - 12*x^4 + 113*x^3 - 141*x^2 + 42*x + 4,13,x^6 - x^5 - 17*x^4 + 4*x^3 + 73*x^2 + 45*x + 7[] 485,8,2,x^7 + x^6 - 9*x^5 - 7*x^4 + 23*x^3 + 12*x^2 - 15*x - 8,3,x^7 + 6*x^6 + 2*x^5 - 41*x^4 - 51*x^3 + 48*x^2 + 68*x + 16,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 + 10*x^6 + 14*x^5 - 142*x^4 - 504*x^3 - 191*x^2 + 1022*x + 982,11,x^7 - 5*x^6 - 24*x^5 + 165*x^4 - 156*x^3 - 481*x^2 + 996*x - 504,13,x^7 + 9*x^6 - 14*x^5 - 234*x^4 + 61*x^3 + 1837*x^2 - 736*x - 2428[] 485,9,2,x^7 - 2*x^6 - 10*x^5 + 18*x^4 + 26*x^3 - 35*x^2 - 21*x + 7,3,x^7 - 9*x^6 + 21*x^5 + 29*x^4 - 182*x^3 + 218*x^2 - 19*x - 68,5,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,7,x^7 - 3*x^6 - 23*x^5 + 45*x^4 + 191*x^3 - 106*x^2 - 592*x - 352,11,x^7 - 6*x^6 - 12*x^5 + 145*x^4 - 297*x^3 + 106*x^2 + 148*x - 32,13,x^7 - 5*x^6 - 47*x^5 + 226*x^4 + 441*x^3 - 1327*x^2 - 2955*x - 1438[] 486,1,2,x + 1,3,x,5,x,7,x + 1,11,x + 6,13,x + 1[] 486,2,2,x + 1,3,x,5,x + 3,7,x - 2,11,x,13,x + 4[] 486,3,2,x + 1,3,x,5,x - 3,7,x + 4,11,x - 6,13,x - 2[] 486,4,2,x - 1,3,x,5,x,7,x + 1,11,x - 6,13,x + 1[] 486,5,2,x - 1,3,x,5,x - 3,7,x - 2,11,x,13,x + 4[] 486,6,2,x - 1,3,x,5,x + 3,7,x + 4,11,x + 6,13,x - 2[] 486,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3,5,x^3 - 9*x - 9,7,x^3 - 6*x^2 + 3*x + 19,11,x^3 - 9*x - 9,13,x^3 - 6*x^2 - 24*x + 136[] 486,8,2,x^3 - 3*x^2 + 3*x - 1,3,x^3,5,x^3 - 9*x + 9,7,x^3 - 6*x^2 + 3*x + 19,11,x^3 - 9*x + 9,13,x^3 - 6*x^2 - 24*x + 136[] 487,1,2,x^2,3,x^2 + x - 3,5,x^2 - 3*x - 1,7,x^2 - 13,11,x^2 + 2*x + 1,13,x^2 - 9*x + 17[] 487,2,2,x^2,3,x^2 - 3*x - 1,5,x^2 - x - 3,7,x^2 + 2*x + 1,11,x^2 - 4*x - 9,13,x^2 - 3*x - 1[] 487,3,2,x^3 - 5*x + 3,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 6*x^2 + 12*x - 8,7,x^3 - 6*x^2 + 12*x - 8,11,x^3 - 4*x^2 - 36*x + 152,13,x^3 + 6*x^2 + 12*x + 8[] 487,4,2,x^16 - 7*x^15 - 5*x^14 + 131*x^13 - 132*x^12 - 977*x^11 + 1666*x^10 + 3671*x^9 - 8191*x^8 - 7212*x^7 + 20571*x^6 + 6937*x^5 - 27100*x^4 - 2748*x^3 + 17207*x^2 + 360*x - 3825,3,x^16 + 4*x^15 - 27*x^14 - 120*x^13 + 254*x^12 + 1398*x^11 - 784*x^10 - 7896*x^9 - 1793*x^8 + 21749*x^7 + 15439*x^6 - 24655*x^5 - 26442*x^4 + 5641*x^3 + 10500*x^2 - 148*x - 1224,5,x^16 - 9*x^15 - 17*x^14 + 326*x^13 - 155*x^12 - 4490*x^11 + 4421*x^10 + 30506*x^9 - 25817*x^8 - 110435*x^7 + 40289*x^6 + 185308*x^5 + 24592*x^4 - 73975*x^3 - 14792*x^2 - 108*x + 72,7,x^16 - x^15 - 65*x^14 + 62*x^13 + 1599*x^12 - 1579*x^11 - 18837*x^10 + 19796*x^9 + 108749*x^8 - 122733*x^7 - 268709*x^6 + 330038*x^5 + 155861*x^4 - 236191*x^3 + 20622*x^2 + 20672*x - 632,11,x^16 - x^15 - 60*x^14 + 115*x^13 + 1231*x^12 - 3266*x^11 - 9620*x^10 + 32513*x^9 + 30643*x^8 - 148399*x^7 - 20214*x^6 + 327721*x^5 - 86790*x^4 - 317637*x^3 + 153178*x^2 + 89832*x - 50616,13,x^16 - 4*x^15 - 106*x^14 + 364*x^13 + 4612*x^12 - 13192*x^11 - 105021*x^10 + 245349*x^9 + 1320155*x^8 - 2540046*x^7 - 8851982*x^6 + 15030336*x^5 + 27662566*x^4 - 49136445*x^3 - 24458970*x^2 + 67586632*x - 26544200[] 487,5,2,x^17 + 8*x^16 + 7*x^15 - 97*x^14 - 239*x^13 + 327*x^12 + 1500*x^11 + 70*x^10 - 3964*x^9 - 2280*x^8 + 4849*x^7 + 4192*x^6 - 2492*x^5 - 2765*x^4 + 364*x^3 + 588*x^2 - 16,3,x^17 + 6*x^16 - 12*x^15 - 126*x^14 - 28*x^13 + 966*x^12 + 843*x^11 - 3526*x^10 - 3777*x^9 + 7023*x^8 + 6916*x^7 - 8306*x^6 - 5364*x^5 + 5495*x^4 + 1085*x^3 - 1358*x^2 + 162*x - 1,5,x^17 + 19*x^16 + 132*x^15 + 297*x^14 - 1001*x^13 - 7281*x^12 - 13237*x^11 + 8658*x^10 + 62929*x^9 + 64801*x^8 - 33491*x^7 - 87085*x^6 - 12860*x^5 + 37682*x^4 + 10983*x^3 - 4959*x^2 - 1836*x - 81,7,x^17 + 11*x^16 - x^15 - 412*x^14 - 1166*x^13 + 4148*x^12 + 20568*x^11 - 8760*x^10 - 144166*x^9 - 81902*x^8 + 488378*x^7 + 521494*x^6 - 803370*x^5 - 1136782*x^4 + 581809*x^3 + 1043038*x^2 - 135633*x - 337347,11,x^17 + 11*x^16 - 50*x^15 - 939*x^14 - 446*x^13 + 29897*x^12 + 69242*x^11 - 440580*x^10 - 1628456*x^9 + 2744029*x^8 + 16876622*x^7 + 39618*x^6 - 80051629*x^5 - 69160750*x^4 + 130895976*x^3 + 190034733*x^2 + 24632784*x - 17408851,13,x^17 + 12*x^16 - 45*x^15 - 1078*x^14 - 1845*x^13 + 29816*x^12 + 126839*x^11 - 175735*x^10 - 1911940*x^9 - 2693463*x^8 + 5037822*x^7 + 17181885*x^6 + 11294537*x^5 - 13465343*x^4 - 25963998*x^3 - 16440181*x^2 - 4592586*x - 454771[] Total time: 16.039 seconds, Total memory usage: 5.89MB ************** MAGMA ***************** Host px1wh.vc.shawcable.net. (24.69.255.202) Time: Sun Nov 30 12:18:29 2003 Input: CP:=CharacteristicPolynomial; DH:=DualHeckeOperator; for N in [487..490] do A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1))))); for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5)); C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13)); B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13]; printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print []; end for; end for; Output: Magma V2.10-6 Sun Nov 30 2003 12:18:11 on modular [Seed = 3609382544] ------------------------------------- 487,1,2,$.1^2,3,$.1^2 +$.1 - 3,5,$.1^2 - 3*$.1 - 1,7,$.1^2 - 13,11,$.1^2 +
2*$.1 + 1,13,$.1^2 - 9*$.1 + 17[] 487,2,2,$.1^2,3,$.1^2 - 3*$.1 - 1,5,$.1^2 -$.1 - 3,7,$.1^2 + 2*$.1 + 1,11,$.1^2 - 4*$.1 - 9,13,$.1^2 - 3*$.1 - 1[]
487,3,2,$.1^3 - 5*$.1 + 3,3,$.1^3 - 6*$.1^2 + 12*$.1 - 8,5,$.1^3 - 6*$.1^2 + 12*$.1 - 8,7,$.1^3 - 6*$.1^2 + 12*$.1 - 8,11,$.1^3 - 4*$.1^2 - 36*$.1 +
152,13,$.1^3 + 6*$.1^2 + 12*$.1 + 8[] 487,4,2,$.1^16 - 7*$.1^15 - 5*$.1^14 + 131*$.1^13 - 132*$.1^12 - 977*$.1^11 + 1666*$.1^10 + 3671*$.1^9 - 8191*$.1^8 - 7212*$.1^7 + 20571*$.1^6 + 6937*$.1^5 - 27100*$.1^4 - 2748*$.1^3 + 17207*$.1^2 + 360*$.1 - 3825,3,$.1^16 + 4*$.1^15 - 27*$.1^14 - 120*$.1^13 + 254*$.1^12 + 1398*$.1^11 - 784*$.1^10 - 7896*$.1^9 - 1793*$.1^8 + 21749*$.1^7 + 15439*$.1^6 - 24655*$.1^5 - 26442*$.1^4 + 5641*$.1^3 + 10500*$.1^2 - 148*$.1 - 1224,5,$.1^16 - 9*$.1^15 - 17*$.1^14 + 326*$.1^13 - 155*$.1^12 - 4490*$.1^11 + 4421*$.1^10 + 30506*$.1^9 - 25817*$.1^8 -
110435*$.1^7 + 40289*$.1^6 + 185308*$.1^5 + 24592*$.1^4 - 73975*$.1^3 - 14792*$.1^2 - 108*$.1 + 72,7,$.1^16 - $.1^15 - 65*$.1^14 + 62*$.1^13 + 1599*$.1^12 - 1579*$.1^11 - 18837*$.1^10 + 19796*$.1^9 + 108749*$.1^8 -
122733*$.1^7 - 268709*$.1^6 + 330038*$.1^5 + 155861*$.1^4 - 236191*$.1^3 + 20622*$.1^2 + 20672*$.1 - 632,11,$.1^16 - $.1^15 - 60*$.1^14 + 115*$.1^13 + 1231*$.1^12 - 3266*$.1^11 - 9620*$.1^10 + 32513*$.1^9 + 30643*$.1^8 -
148399*$.1^7 - 20214*$.1^6 + 327721*$.1^5 - 86790*$.1^4 - 317637*$.1^3 + 153178*$.1^2 + 89832*$.1 - 50616,13,$.1^16 - 4*$.1^15 - 106*$.1^14 + 364*$.1^13 + 4612*$.1^12 - 13192*$.1^11 - 105021*$.1^10 + 245349*$.1^9 + 1320155*$.1^8 -
2540046*$.1^7 - 8851982*$.1^6 + 15030336*$.1^5 + 27662566*$.1^4 - 49136445*$.1^3 - 24458970*$.1^2 + 67586632*$.1 - 26544200[] 487,5,2,$.1^17 + 8*$.1^16 + 7*$.1^15 - 97*$.1^14 - 239*$.1^13 + 327*$.1^12 + 1500*$.1^11 + 70*$.1^10 - 3964*$.1^9 - 2280*$.1^8 + 4849*$.1^7 + 4192*$.1^6 - 2492*$.1^5 - 2765*$.1^4 + 364*$.1^3 + 588*$.1^2 - 16,3,$.1^17 + 6*$.1^16 - 12*$.1^15 - 126*$.1^14 - 28*$.1^13 + 966*$.1^12 + 843*$.1^11 - 3526*$.1^10 - 3777*$.1^9 + 7023*$.1^8 + 6916*$.1^7 - 8306*$.1^6 - 5364*$.1^5 + 5495*$.1^4 + 1085*$.1^3 - 1358*$.1^2 + 162*$.1 - 1,5,$.1^17 + 19*$.1^16 + 132*$.1^15 + 297*$.1^14 - 1001*$.1^13 - 7281*$.1^12 - 13237*$.1^11 + 8658*$.1^10 +
62929*$.1^9 + 64801*$.1^8 - 33491*$.1^7 - 87085*$.1^6 - 12860*$.1^5 + 37682*$.1^4 + 10983*$.1^3 - 4959*$.1^2 - 1836*$.1 - 81,7,$.1^17 + 11*$.1^16 -$.1^15 - 412*$.1^14 - 1166*$.1^13 + 4148*$.1^12 + 20568*$.1^11 - 8760*$.1^10 - 144166*$.1^9 - 81902*$.1^8 + 488378*$.1^7 + 521494*$.1^6 - 803370*$.1^5 -
1136782*$.1^4 + 581809*$.1^3 + 1043038*$.1^2 - 135633*$.1 - 337347,11,$.1^17 + 11*$.1^16 - 50*$.1^15 - 939*$.1^14 - 446*$.1^13 + 29897*$.1^12 + 69242*$.1^11 - 440580*$.1^10 - 1628456*$.1^9 + 2744029*$.1^8 + 16876622*$.1^7 + 39618*$.1^6 -
80051629*$.1^5 - 69160750*$.1^4 + 130895976*$.1^3 + 190034733*$.1^2 +
24632784*$.1 - 17408851,13,$.1^17 + 12*$.1^16 - 45*$.1^15 - 1078*$.1^14 - 1845*$.1^13 + 29816*$.1^12 + 126839*$.1^11 - 175735*$.1^10 - 1911940*$.1^9 -
2693463*$.1^8 + 5037822*$.1^7 + 17181885*$.1^6 + 11294537*$.1^5 - 13465343*$.1^4 - 25963998*$.1^3 - 16440181*$.1^2 - 4592586*$.1 - 454771[]
488,1,2,x^2,3,x^2,5,x^2 + 2*x + 1,7,x^2 + 2*x - 1,11,x^2 + 2*x - 17,13,x^2 + 6*x
+ 1[]
488,2,2,x^3,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + x^2 - 5*x - 1,7,x^3 + 7*x^2 + 13*x +
5,11,x^3 + 3*x^2 - x - 5,13,x^3 + 5*x^2 - 5*x - 17[]
488,3,2,x^4,3,x^4 - x^3 - 7*x^2 + 4*x + 8,5,x^4 + 2*x^3 - 11*x^2 - 4*x +
16,7,x^4 - 7*x^3 + 12*x^2 - 3*x - 1,11,x^4 - 2*x^3 - 11*x^2 + 14*x - 4,13,x^4 -
4*x^3 - 19*x^2 + 10*x + 4[]
488,4,2,x^6,3,x^6 - 3*x^5 - 9*x^4 + 26*x^3 + 16*x^2 - 52*x + 16,5,x^6 - 5*x^5 -
11*x^4 + 77*x^3 - 26*x^2 - 192*x + 128,7,x^6 - 6*x^5 - 7*x^4 + 69*x^3 - 22*x^2 -
117*x - 36,11,x^6 - 3*x^5 - 31*x^4 + 109*x^3 + 182*x^2 - 932*x + 736,13,x^6 -
7*x^5 - 41*x^4 + 355*x^3 - 116*x^2 - 2584*x + 3688[]
489,1,2,x^4 + 2*x^3 - 2*x^2 - 3*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 +
3*x^3 - 5*x^2 - 19*x - 11,7,x^4 + 10*x^3 + 35*x^2 + 50*x + 25,11,x^4 + 8*x^3 +
3*x^2 - 62*x - 89,13,x^4 + 14*x^3 + 60*x^2 + 82*x + 19[]
489,2,2,x^5 + 2*x^4 - 4*x^3 - 7*x^2 + 3*x + 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 +
5*x + 1,5,x^5 + 3*x^4 - 5*x^3 - 21*x^2 - 17*x - 4,7,x^5 + 4*x^4 - 9*x^3 - 20*x^2
+ 37*x - 14,11,x^5 + 10*x^4 + 21*x^3 - 78*x^2 - 355*x - 362,13,x^5 - 10*x^4 +
24*x^3 + 2*x^2 - 25*x - 8[]
489,3,2,x^8 - 4*x^7 - 6*x^6 + 35*x^5 - 86*x^3 + 36*x^2 + 39*x - 19,3,x^8 + 8*x^7
+ 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 - 5*x^7 - 10*x^6 +
66*x^5 - x^4 - 174*x^3 + 32*x^2 + 105*x - 19,7,x^8 - 4*x^7 - 22*x^6 + 84*x^5 +
155*x^4 - 516*x^3 - 382*x^2 + 768*x + 305,11,x^8 - 14*x^7 + 45*x^6 + 244*x^5 -
2181*x^4 + 6108*x^3 - 6696*x^2 + 320*x + 3008,13,x^8 + 14*x^7 + 32*x^6 - 290*x^5
- 1225*x^4 + 676*x^3 + 7720*x^2 + 9728*x + 3392[]
489,4,2,x^10 - x^9 - 16*x^8 + 15*x^7 + 87*x^6 - 72*x^5 - 188*x^4 + 125*x^3 +
132*x^2 - 55*x + 4,3,x^10 - 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 +
210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1,5,x^10 + x^9 - 28*x^8 - 16*x^7 + 277*x^6 +
26*x^5 - 1134*x^4 + 371*x^3 + 1509*x^2 - 850*x - 56,7,x^10 - 14*x^9 + 58*x^8 +
36*x^7 - 829*x^6 + 1558*x^5 + 1442*x^4 - 5932*x^3 + 1305*x^2 + 5666*x -
2384,11,x^10 - 4*x^9 - 45*x^8 + 108*x^7 + 669*x^6 - 306*x^5 - 2712*x^4 - 624*x^3
+ 2432*x^2 + 640*x - 512,13,x^10 - 16*x^9 + 64*x^8 + 182*x^7 - 1761*x^6 +
2746*x^5 + 4384*x^4 - 11696*x^3 - 2624*x^2 + 12160*x + 2048[]
490,1,2,x + 1,3,x - 1,5,x + 1,7,x,11,x + 6,13,x + 4[]
490,2,2,x + 1,3,x - 2,5,x + 1,7,x,11,x - 3,13,x - 1[]
490,3,2,x + 1,3,x + 2,5,x - 1,7,x,11,x - 3,13,x + 1[]
490,4,2,x + 1,3,x + 1,5,x - 1,7,x,11,x + 6,13,x - 4[]
490,5,2,x - 1,3,x + 2,5,x + 1,7,x,11,x - 3,13,x - 5[]
490,6,2,x - 1,3,x - 3,5,x + 1,7,x,11,x + 2,13,x[]
490,7,2,x - 1,3,x + 2,5,x + 1,7,x,11,x + 4,13,x + 2[]
490,8,2,x - 1,3,x,5,x - 1,7,x,11,x - 4,13,x - 6[]
490,9,2,x - 1,3,x - 2,5,x - 1,7,x,11,x - 3,13,x + 5[]
490,10,2,x - 1,3,x - 2,5,x - 1,7,x,11,x + 4,13,x - 2[]
490,11,2,x - 1,3,x + 3,5,x - 1,7,x,11,x + 2,13,x[]
490,12,2,x^2 + 2*x + 1,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2,11,x^2 - 4*x -
4,13,x^2 - 4*x - 4[]
490,13,2,x^2 + 2*x + 1,3,x^2 - 4*x + 2,5,x^2 - 2*x + 1,7,x^2,11,x^2 - 4*x -
4,13,x^2 + 4*x - 4[]

Total time: 17.270 seconds, Total memory usage: 6.42MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:23:02 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [490..493] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 12:22:41 on modular  [Seed = 3275152310]
-------------------------------------

490,1,2,$.1 + 1,3,$.1 - 1,5,$.1 + 1,7,$.1,11,$.1 + 6,13,$.1 + 4[]
490,2,2,$.1 + 1,3,$.1 - 2,5,$.1 + 1,7,$.1,11,$.1 - 3,13,$.1 - 1[]
490,3,2,$.1 + 1,3,$.1 + 2,5,$.1 - 1,7,$.1,11,$.1 - 3,13,$.1 + 1[]
490,4,2,$.1 + 1,3,$.1 + 1,5,$.1 - 1,7,$.1,11,$.1 + 6,13,$.1 - 4[]
490,5,2,$.1 - 1,3,$.1 + 2,5,$.1 + 1,7,$.1,11,$.1 - 3,13,$.1 - 5[]
490,6,2,$.1 - 1,3,$.1 - 3,5,$.1 + 1,7,$.1,11,$.1 + 2,13,$.1[]
490,7,2,$.1 - 1,3,$.1 + 2,5,$.1 + 1,7,$.1,11,$.1 + 4,13,$.1 + 2[]
490,8,2,$.1 - 1,3,$.1,5,$.1 - 1,7,$.1,11,$.1 - 4,13,$.1 - 6[]
490,9,2,$.1 - 1,3,$.1 - 2,5,$.1 - 1,7,$.1,11,$.1 - 3,13,$.1 + 5[]
490,10,2,$.1 - 1,3,$.1 - 2,5,$.1 - 1,7,$.1,11,$.1 + 4,13,$.1 - 2[]
490,11,2,$.1 - 1,3,$.1 + 3,5,$.1 - 1,7,$.1,11,$.1 + 2,13,$.1[]
490,12,2,$.1^2 + 2*$.1 + 1,3,$.1^2 + 4*$.1 + 2,5,$.1^2 + 2*$.1 +
1,7,$.1^2,11,$.1^2 - 4*$.1 - 4,13,$.1^2 - 4*$.1 - 4[] 490,13,2,$.1^2 + 2*$.1 + 1,3,$.1^2 - 4*$.1 + 2,5,$.1^2 - 2*$.1 + 1,7,$.1^2,11,$.1^2 - 4*$.1 - 4,13,$.1^2 + 4*$.1 - 4[]
491,1,2,x^2 - x - 1,3,x^2 + x - 1,5,x^2 + x - 1,7,x^2 - x - 11,11,x^2 + 3*x +
1,13,x^2 + 8*x + 11[]
491,2,2,x^10 + 3*x^9 - 7*x^8 - 25*x^7 + 10*x^6 + 60*x^5 + 3*x^4 - 45*x^3 - 2*x^2
+ 7*x - 1,3,x^10 + 4*x^9 - 8*x^8 - 41*x^7 + 8*x^6 + 115*x^5 + 37*x^4 - 52*x^3 -
7*x^2 + 8*x - 1,5,x^10 + 9*x^9 + 17*x^8 - 54*x^7 - 191*x^6 - 8*x^5 + 389*x^4 +
169*x^3 - 139*x^2 - 16*x + 4,7,x^10 + 6*x^9 + x^8 - 47*x^7 - 55*x^6 + 94*x^5 +
163*x^4 - 19*x^3 - 121*x^2 - 48*x - 4,11,x^10 + 3*x^9 - 40*x^8 - 120*x^7 +
416*x^6 + 1119*x^5 - 1621*x^4 - 2979*x^3 + 2233*x^2 - 149*x + 1,13,x^10 + 15*x^9
+ 72*x^8 + 73*x^7 - 299*x^6 - 570*x^5 + 106*x^4 + 547*x^3 + 63*x^2 - 95*x + 11[]
491,3,2,x^29 - 49*x^27 + x^26 + 1068*x^25 - 39*x^24 - 13655*x^23 + 658*x^22 +
113723*x^21 - 6306*x^20 - 647801*x^19 + 37953*x^18 + 2578721*x^17 - 150115*x^16
- 7201417*x^15 + 398246*x^14 + 13959112*x^13 - 711934*x^12 - 18310154*x^11 +
839798*x^10 + 15574775*x^9 - 585854*x^8 - 8065060*x^7 + 132680*x^6 + 2339280*x^5
+ 83968*x^4 - 350400*x^3 - 36608*x^2 + 20992*x + 3584,3,x^29 - 5*x^28 - 51*x^27
+ 285*x^26 + 1074*x^25 - 7083*x^24 - 11671*x^23 + 101035*x^22 + 61012*x^21 -
916051*x^20 + 9358*x^19 + 5521492*x^18 - 2268766*x^17 - 22476158*x^16 +
15564692*x^15 + 61480703*x^14 - 55671561*x^13 - 110117294*x^12 + 119536861*x^11
+ 122122439*x^10 - 155573079*x^9 - 74561960*x^8 + 116894326*x^7 + 18045557*x^6 -
45284459*x^5 + 1071678*x^4 + 7240653*x^3 - 382097*x^2 - 378798*x - 20629,5,x^29
- 12*x^28 - 25*x^27 + 827*x^26 - 1385*x^25 - 23115*x^24 + 79578*x^23 +
322515*x^22 - 1736444*x^21 - 1973332*x^20 + 20894215*x^19 - 4080535*x^18 -
149899042*x^17 + 153502827*x^16 + 634768721*x^15 - 1098785934*x^14 -
1416285283*x^13 + 3910213899*x^12 + 857385707*x^11 - 7264915276*x^10 +
2451049126*x^9 + 6205475492*x^8 - 4251009756*x^7 - 1575152001*x^6 +
1562591587*x^5 + 181201045*x^4 - 196190120*x^3 - 21924992*x^2 + 3942016*x +
447296,7,x^29 - 3*x^28 - 136*x^27 + 412*x^26 + 8115*x^25 - 24880*x^24 -
279700*x^23 + 870828*x^22 + 6168083*x^21 - 19594692*x^20 - 91046243*x^19 +
297033872*x^18 + 914234208*x^17 - 3089629912*x^16 - 6223062620*x^15 +
22032007040*x^14 + 28147738144*x^13 - 105800264928*x^12 - 81947049408*x^11 +
329785114368*x^10 + 150613360384*x^9 - 626925014528*x^8 - 190515703808*x^7 +
653954707456*x^6 + 202447900672*x^5 - 298738786304*x^4 - 127617892352*x^3 +
7909670912*x^2 + 3912368128*x + 142475264,11,x^29 - 174*x^27 + 3*x^26 +
13387*x^25 - 5*x^24 - 600700*x^23 - 31244*x^22 + 17457958*x^21 + 2480297*x^20 -
345012431*x^19 - 93873749*x^18 + 4734024421*x^17 + 2100989175*x^16 -
45173732357*x^15 - 29743014907*x^14 + 294544324496*x^13 + 270822348921*x^12 -
1252941801030*x^11 - 1561412678711*x^10 + 3116139977050*x^9 + 5404743012046*x^8
- 3123372493282*x^7 - 9890918895463*x^6 - 2551461338584*x^5 + 6416553573185*x^4
+ 5849603936438*x^3 + 1895405070433*x^2 + 209949016511*x - 2521936469,13,x^29 -
35*x^28 + 375*x^27 + 738*x^26 - 43178*x^25 + 223154*x^24 + 1278098*x^23 -
15300869*x^22 + 8339177*x^21 + 416021113*x^20 - 1204667595*x^19 -
5693819640*x^18 + 28847903406*x^17 + 38959400842*x^16 - 368828569445*x^15 -
73831634315*x^14 + 3009910729081*x^13 - 745404787749*x^12 - 16858747455882*x^11
+ 5330362373840*x^10 + 66058381678064*x^9 - 8825110202864*x^8 -
173388274625185*x^7 - 32275281536103*x^6 + 264595714433913*x^5 +
138838988426446*x^4 - 164090391440550*x^3 - 127318042428327*x^2 +
19583693385928*x + 23545612672057[]
492,1,2,x,3,x + 1,5,x,7,x + 2,11,x + 1,13,x + 2[]
492,2,2,x,3,x - 1,5,x + 2,7,x + 4,11,x + 5,13,x - 4[]
492,3,2,x^2,3,x^2 + 2*x + 1,5,x^2 + 4*x - 2,7,x^2 - 4*x - 2,11,x^2 + 2*x -
5,13,x^2 - 4*x - 2[]
492,4,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 2*x - 2,7,x^2 - 2*x - 2,11,x^2 - 4*x +
1,13,x^2 + 2*x - 2[]
493,1,2,x + 1,3,x,5,x + 2,7,x + 5,11,x,13,x - 7[]
493,2,2,x + 1,3,x + 3,5,x - 1,7,x + 2,11,x - 3,13,x - 1[]
493,3,2,x^2 - 2*x + 1,3,x^2 + x - 4,5,x^2 - 3*x - 2,7,x^2 - 5*x + 2,11,x^2 - x -
4,13,x^2 - 17[]
493,4,2,x^4 - 2*x^3 - 6*x^2 + 12*x - 1,3,x^4 - 3*x^3 - 7*x^2 + 27*x - 16,5,x^4 -
3*x^3 - 3*x^2 + 7*x + 2,7,x^4 - x^3 - 6*x^2 + 4*x + 4,11,x^4 - 15*x^3 + 79*x^2 -
171*x + 128,13,x^4 + 2*x^3 - 20*x^2 + 10*x - 1[]
493,5,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 3,3,x^5 + 2*x^4 - 5*x^3 - 10*x^2 +
1,5,x^5 + x^4 - 18*x^3 - 31*x^2 + 21*x + 41,7,x^5 + 4*x^4 - 16*x^3 - 65*x^2 +
14*x + 83,11,x^5 + 14*x^4 + 52*x^3 - 69*x^2 - 738*x - 1081,13,x^5 + 8*x^4 +
18*x^3 + x^2 - 26*x - 7[]
493,6,2,x^6 - 5*x^5 + 3*x^4 + 16*x^3 - 20*x^2 + 1,3,x^6 - 2*x^5 - 11*x^4 +
14*x^3 + 38*x^2 - 15*x - 26,5,x^6 - x^5 - 24*x^4 + 37*x^3 + 133*x^2 - 293*x +
142,7,x^6 - 2*x^5 - 18*x^4 + 47*x^3 + 8*x^2 - 93*x + 58,11,x^6 - 32*x^4 - 19*x^3
+ 180*x^2 + 203*x - 26,13,x^6 + 6*x^5 - 6*x^4 - 87*x^3 - 96*x^2 + 177*x + 262[]
493,7,2,x^8 - 3*x^7 - 10*x^6 + 29*x^5 + 37*x^4 - 88*x^3 - 65*x^2 + 80*x +
51,3,x^8 - 6*x^7 + x^6 + 44*x^5 - 42*x^4 - 85*x^3 + 80*x^2 + 42*x - 8,5,x^8 -
x^7 - 26*x^6 + 31*x^5 + 203*x^4 - 251*x^3 - 514*x^2 + 580*x + 168,7,x^8 - 3*x^7
- 20*x^6 + 41*x^5 + 121*x^4 - 101*x^3 - 109*x^2 + 106*x - 22,11,x^8 - 10*x^7 +
4*x^6 + 195*x^5 - 438*x^4 - 477*x^3 + 1604*x^2 - 386*x + 24,13,x^8 - 3*x^7 -
38*x^6 + 179*x^5 + 43*x^4 - 1333*x^3 + 2205*x^2 - 1088*x + 128[]
493,8,2,x^10 + 5*x^9 - 3*x^8 - 44*x^7 - 25*x^6 + 119*x^5 + 98*x^4 - 116*x^3 -
94*x^2 + 28*x + 11,3,x^10 + 9*x^9 + 22*x^8 - 16*x^7 - 115*x^6 - 54*x^5 + 155*x^4
+ 95*x^3 - 65*x^2 - 24*x + 2,5,x^10 + 4*x^9 - 22*x^8 - 85*x^7 + 173*x^6 +
565*x^5 - 707*x^4 - 1316*x^3 + 1435*x^2 + 456*x - 484,7,x^10 + 4*x^9 - 30*x^8 -
123*x^7 + 264*x^6 + 1127*x^5 - 752*x^4 - 3078*x^3 + 1496*x^2 + 1880*x -
1000,11,x^10 + 19*x^9 + 115*x^8 + 32*x^7 - 2393*x^6 - 9046*x^5 - 5030*x^4 +
37325*x^3 + 87481*x^2 + 70032*x + 16258,13,x^10 + x^9 - 87*x^8 - 82*x^7 +
2761*x^6 + 2132*x^5 - 39298*x^4 - 20799*x^3 + 238099*x^2 + 57204*x - 413528[]

Total time: 20.809 seconds, Total memory usage: 7.12MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:34:05 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [493..496] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 12:33:45 on modular  [Seed = 4212059414]
-------------------------------------

493,1,2,$.1 + 1,3,$.1,5,$.1 + 2,7,$.1 + 5,11,$.1,13,$.1 - 7[]
493,2,2,$.1 + 1,3,$.1 + 3,5,$.1 - 1,7,$.1 + 2,11,$.1 - 3,13,$.1 - 1[]
493,3,2,$.1^2 - 2*$.1 + 1,3,$.1^2 +$.1 - 4,5,$.1^2 - 3*$.1 - 2,7,$.1^2 - 5*$.1
+ 2,11,$.1^2 -$.1 - 4,13,$.1^2 - 17[] 493,4,2,$.1^4 - 2*$.1^3 - 6*$.1^2 + 12*$.1 - 1,3,$.1^4 - 3*$.1^3 - 7*$.1^2 +
27*$.1 - 16,5,$.1^4 - 3*$.1^3 - 3*$.1^2 + 7*$.1 + 2,7,$.1^4 - $.1^3 - 6*$.1^2 +
4*$.1 + 4,11,$.1^4 - 15*$.1^3 + 79*$.1^2 - 171*$.1 + 128,13,$.1^4 + 2*$.1^3 - 20*$.1^2 + 10*$.1 - 1[] 493,5,2,$.1^5 + 2*$.1^4 - 5*$.1^3 - 7*$.1^2 + 7*$.1 + 3,3,$.1^5 + 2*$.1^4 -
5*$.1^3 - 10*$.1^2 + 1,5,$.1^5 +$.1^4 - 18*$.1^3 - 31*$.1^2 + 21*$.1 + 41,7,$.1^5 + 4*$.1^4 - 16*$.1^3 - 65*$.1^2 + 14*$.1 + 83,11,$.1^5 + 14*$.1^4 +
52*$.1^3 - 69*$.1^2 - 738*$.1 - 1081,13,$.1^5 + 8*$.1^4 + 18*$.1^3 + $.1^2 - 26*$.1 - 7[]
493,6,2,$.1^6 - 5*$.1^5 + 3*$.1^4 + 16*$.1^3 - 20*$.1^2 + 1,3,$.1^6 - 2*$.1^5 - 11*$.1^4 + 14*$.1^3 + 38*$.1^2 - 15*$.1 - 26,5,$.1^6 - $.1^5 - 24*$.1^4 +
37*$.1^3 + 133*$.1^2 - 293*$.1 + 142,7,$.1^6 - 2*$.1^5 - 18*$.1^4 + 47*$.1^3 + 8*$.1^2 - 93*$.1 + 58,11,$.1^6 - 32*$.1^4 - 19*$.1^3 + 180*$.1^2 + 203*$.1 -
26,13,$.1^6 + 6*$.1^5 - 6*$.1^4 - 87*$.1^3 - 96*$.1^2 + 177*$.1 + 262[]
493,7,2,$.1^8 - 3*$.1^7 - 10*$.1^6 + 29*$.1^5 + 37*$.1^4 - 88*$.1^3 - 65*$.1^2 + 80*$.1 + 51,3,$.1^8 - 6*$.1^7 + $.1^6 + 44*$.1^5 - 42*$.1^4 - 85*$.1^3 +
80*$.1^2 + 42*$.1 - 8,5,$.1^8 -$.1^7 - 26*$.1^6 + 31*$.1^5 + 203*$.1^4 - 251*$.1^3 - 514*$.1^2 + 580*$.1 + 168,7,$.1^8 - 3*$.1^7 - 20*$.1^6 + 41*$.1^5 +
121*$.1^4 - 101*$.1^3 - 109*$.1^2 + 106*$.1 - 22,11,$.1^8 - 10*$.1^7 + 4*$.1^6 + 195*$.1^5 - 438*$.1^4 - 477*$.1^3 + 1604*$.1^2 - 386*$.1 + 24,13,$.1^8 - 3*$.1^7
- 38*$.1^6 + 179*$.1^5 + 43*$.1^4 - 1333*$.1^3 + 2205*$.1^2 - 1088*$.1 + 128[]
493,8,2,$.1^10 + 5*$.1^9 - 3*$.1^8 - 44*$.1^7 - 25*$.1^6 + 119*$.1^5 + 98*$.1^4 - 116*$.1^3 - 94*$.1^2 + 28*$.1 + 11,3,$.1^10 + 9*$.1^9 + 22*$.1^8 - 16*$.1^7 -
115*$.1^6 - 54*$.1^5 + 155*$.1^4 + 95*$.1^3 - 65*$.1^2 - 24*$.1 + 2,5,$.1^10 + 4*$.1^9 - 22*$.1^8 - 85*$.1^7 + 173*$.1^6 + 565*$.1^5 - 707*$.1^4 - 1316*$.1^3 +
1435*$.1^2 + 456*$.1 - 484,7,$.1^10 + 4*$.1^9 - 30*$.1^8 - 123*$.1^7 + 264*$.1^6 + 1127*$.1^5 - 752*$.1^4 - 3078*$.1^3 + 1496*$.1^2 + 1880*$.1 - 1000,11,$.1^10 + 19*$.1^9 + 115*$.1^8 + 32*$.1^7 - 2393*$.1^6 - 9046*$.1^5 - 5030*$.1^4 + 37325*$.1^3 + 87481*$.1^2 + 70032*$.1 + 16258,13,$.1^10 +$.1^9 - 87*$.1^8 - 82*$.1^7 + 2761*$.1^6 + 2132*$.1^5 - 39298*$.1^4 - 20799*$.1^3 + 238099*$.1^2 + 57204*$.1 - 413528[]
494,1,2,x + 1,3,x + 1,5,x - 1,7,x + 1,11,x,13,x + 1[]
494,2,2,x + 1,3,x,5,x - 2,7,x - 4,11,x - 4,13,x + 1[]
494,3,2,x + 1,3,x - 3,5,x + 3,7,x - 3,11,x,13,x + 1[]
494,4,2,x - 1,3,x + 1,5,x + 1,7,x + 3,11,x + 4,13,x - 1[]
494,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 3*x^2 - 6*x - 17,5,x^3 - 3*x^2 - 18*x +
57,7,x^3 + 6*x^2 - 24,11,x^3 + 3*x^2 - 18*x - 57,13,x^3 + 3*x^2 + 3*x + 1[]
494,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 6*x - 7,5,x^3 - x^2 - 6*x + 7,7,x^3
- 2*x^2 - 24*x + 56,11,x^3 + x^2 - 6*x - 7,13,x^3 - 3*x^2 + 3*x - 1[]
494,7,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 5*x^2 + 6*x - 1,5,x^3 - 5*x^2 + 6*x -
1,7,x^3 + 2*x^2 - 8*x - 8,11,x^3 + x^2 - 30*x - 43,13,x^3 + 3*x^2 + 3*x + 1[]
494,8,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 2*x^3 - 5*x^2 + 7*x + 5,5,x^4 -
2*x^3 - 9*x^2 + 11*x - 3,7,x^4 - 7*x^3 + 6*x^2 + 24*x - 8,11,x^4 - x^3 - 22*x^2
+ 35*x + 12,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[]
495,1,2,x + 1,3,x,5,x + 1,7,x,11,x - 1,13,x - 2[]
495,2,2,x^2 + 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 + 2*x +
1,13,x^2 + 8*x + 8[]
495,3,2,x^2 - 3,3,x^2,5,x^2 - 2*x + 1,7,x^2 - 4*x + 4,11,x^2 - 2*x + 1,13,x^2 -
4*x - 8[]
495,4,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 4*x - 4,11,x^2 - 2*x +
1,13,x^2 - 32[]
495,5,2,x^3 - x^2 - 5*x + 1,3,x^3,5,x^3 + 3*x^2 + 3*x + 1,7,x^3 - 16*x +
16,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 2*x^2 - 12*x - 8[]
495,6,2,x^4 + 2*x^3 - 6*x^2 - 10*x + 3,3,x^4,5,x^4 + 4*x^3 + 6*x^2 + 4*x +
1,7,x^4 - 4*x^3 - 16*x^2 + 64*x - 36,11,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,13,x^4 -
8*x^3 - 8*x^2 + 168*x - 292[]
495,7,2,x^4 - 2*x^3 - 6*x^2 + 10*x + 3,3,x^4,5,x^4 - 4*x^3 + 6*x^2 - 4*x +
1,7,x^4 - 4*x^3 - 16*x^2 + 64*x - 36,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 -
8*x^3 - 8*x^2 + 168*x - 292[]
496,1,2,x,3,x,5,x + 3,7,x - 3,11,x + 2,13,x + 4[]
496,2,2,x,3,x - 2,5,x - 1,7,x - 3,11,x - 2,13,x + 2[]
496,3,2,x,3,x - 2,5,x - 2,7,x,11,x + 2,13,x - 4[]
496,4,2,x,3,x - 2,5,x + 3,7,x - 1,11,x - 6,13,x - 2[]
496,5,2,x,3,x,5,x - 1,7,x + 3,11,x + 6,13,x + 4[]
496,6,2,x,3,x,5,x + 2,7,x,11,x,13,x - 2[]
496,7,2,x^2,3,x^2 + 4*x + 4,5,x^2 - 3*x - 6,7,x^2 + x - 8,11,x^2 - 4*x +
4,13,x^2 - 2*x - 32[]
496,8,2,x^2,3,x^2 - 2*x - 4,5,x^2 - 2*x + 1,7,x^2 - 4*x - 1,11,x^2 + 4*x +
4,13,x^2 + 2*x - 4[]
496,9,2,x^2,3,x^2 + 2*x - 2,5,x^2 - 12,7,x^2 + 4*x + 4,11,x^2 - 6*x + 6,13,x^2 +
2*x - 26[]
496,10,2,x^3,3,x^3 + 2*x^2 - 6*x - 8,5,x^3 + 3*x^2 - 4*x - 4,7,x^3 + 5*x^2 - 8*x
- 44,11,x^3 + 8*x^2 + 6*x - 44,13,x^3 - 2*x^2 - 14*x + 32[]

Total time: 19.719 seconds, Total memory usage: 6.62MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:37:24 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [496..499] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 12:37:08 on modular  [Seed = 3910990905]
-------------------------------------

496,1,2,$.1,3,$.1,5,$.1 + 3,7,$.1 - 3,11,$.1 + 2,13,$.1 + 4[]
496,2,2,$.1,3,$.1 - 2,5,$.1 - 1,7,$.1 - 3,11,$.1 - 2,13,$.1 + 2[]
496,3,2,$.1,3,$.1 - 2,5,$.1 - 2,7,$.1,11,$.1 + 2,13,$.1 - 4[]
496,4,2,$.1,3,$.1 - 2,5,$.1 + 3,7,$.1 - 1,11,$.1 - 6,13,$.1 - 2[]
496,5,2,$.1,3,$.1,5,$.1 - 1,7,$.1 + 3,11,$.1 + 6,13,$.1 + 4[]
496,6,2,$.1,3,$.1,5,$.1 + 2,7,$.1,11,$.1,13,$.1 - 2[]
496,7,2,$.1^2,3,$.1^2 + 4*$.1 + 4,5,$.1^2 - 3*$.1 - 6,7,$.1^2 + $.1 - 8,11,$.1^2
- 4*$.1 + 4,13,$.1^2 - 2*$.1 - 32[] 496,8,2,$.1^2,3,$.1^2 - 2*$.1 - 4,5,$.1^2 - 2*$.1 + 1,7,$.1^2 - 4*$.1 -
1,11,$.1^2 + 4*$.1 + 4,13,$.1^2 + 2*$.1 - 4[]
496,9,2,$.1^2,3,$.1^2 + 2*$.1 - 2,5,$.1^2 - 12,7,$.1^2 + 4*$.1 + 4,11,$.1^2 - 6*$.1 + 6,13,$.1^2 + 2*$.1 - 26[]
496,10,2,$.1^3,3,$.1^3 + 2*$.1^2 - 6*$.1 - 8,5,$.1^3 + 3*$.1^2 - 4*$.1 - 4,7,$.1^3 + 5*$.1^2 - 8*$.1 - 44,11,$.1^3 + 8*$.1^2 + 6*$.1 - 44,13,$.1^3 -
2*$.1^2 - 14*$.1 + 32[]
497,1,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 1,13,x + 3[]
497,2,2,x^2 + 2*x + 1,3,x^2 + 2*x - 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 2*x +
1,13,x^2 + 2*x - 17[]
497,3,2,x^8 - 12*x^6 + 42*x^4 + 4*x^3 - 44*x^2 - 8*x + 1,3,x^8 - 5*x^7 - x^6 +
33*x^5 - 25*x^4 - 53*x^3 + 57*x^2 - 3*x - 2,5,x^8 - 2*x^7 - 20*x^6 + 32*x^5 +
112*x^4 - 152*x^3 - 160*x^2 + 176*x + 32,7,x^8 + 8*x^7 + 28*x^6 + 56*x^5 +
70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,11,x^8 + x^7 - 31*x^6 - 43*x^5 + 227*x^4 +
431*x^3 - 105*x^2 - 537*x - 236,13,x^8 - 9*x^7 + 3*x^6 + 125*x^5 - 151*x^4 -
307*x^3 + 347*x^2 + x - 8[]
497,4,2,x^9 + 2*x^8 - 9*x^7 - 16*x^6 + 26*x^5 + 36*x^4 - 28*x^3 - 19*x^2 + 10*x
+ 1,3,x^9 + 7*x^8 + 8*x^7 - 36*x^6 - 75*x^5 + 19*x^4 + 99*x^3 + 49*x^2 + 3*x -
1,5,x^9 + 4*x^8 - 17*x^7 - 82*x^6 + 52*x^5 + 524*x^4 + 329*x^3 - 928*x^2 -
1344*x - 496,7,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 +
36*x^2 + 9*x + 1,11,x^9 - x^8 - 69*x^7 - 3*x^6 + 1580*x^5 + 1536*x^4 - 12656*x^3
- 21296*x^2 + 16832*x + 35648,13,x^9 + 15*x^8 + 61*x^7 - 115*x^6 - 1516*x^5 -
4144*x^4 - 4392*x^3 - 1376*x^2 + 288*x + 64[]
497,5,2,x^15 - 2*x^14 - 24*x^13 + 46*x^12 + 224*x^11 - 406*x^10 - 1026*x^9 +
1731*x^8 + 2373*x^7 - 3662*x^6 - 2504*x^5 + 3488*x^4 + 818*x^3 - 1062*x^2 - 54*x
+ 27,3,x^15 - 5*x^14 - 22*x^13 + 134*x^12 + 150*x^11 - 1360*x^10 - 207*x^9 +
6723*x^8 - 1448*x^7 - 17210*x^6 + 5407*x^5 + 21721*x^4 - 4821*x^3 - 10775*x^2 -
942*x + 656,5,x^15 - 57*x^13 + 22*x^12 + 1268*x^11 - 1004*x^10 - 13807*x^9 +
16352*x^8 + 73900*x^7 - 115416*x^6 - 161608*x^5 + 327976*x^4 + 44080*x^3 -
219888*x^2 + 10368*x + 15552,7,x^15 - 15*x^14 + 105*x^13 - 455*x^12 + 1365*x^11
- 3003*x^10 + 5005*x^9 - 6435*x^8 + 6435*x^7 - 5005*x^6 + 3003*x^5 - 1365*x^4 +
455*x^3 - 105*x^2 + 15*x - 1,11,x^15 - 5*x^14 - 87*x^13 + 483*x^12 + 2427*x^11 -
16499*x^10 - 17121*x^9 + 227697*x^8 - 187868*x^7 - 995056*x^6 + 1794832*x^5 +
587792*x^4 - 3364544*x^3 + 2528064*x^2 - 539136*x - 27648,13,x^15 - 5*x^14 -
111*x^13 + 551*x^12 + 4623*x^11 - 22427*x^10 - 92267*x^9 + 419999*x^8 +
958290*x^7 - 3691576*x^6 - 5251560*x^5 + 13177968*x^4 + 13337824*x^3 -
10126080*x^2 - 2121344*x - 83968[]
498,1,2,x + 1,3,x - 1,5,x - 2,7,x - 4,11,x,13,x[]
498,2,2,x + 1,3,x - 1,5,x + 1,7,x + 4,11,x - 3,13,x + 6[]
498,3,2,x^2 + 2*x + 1,3,x^2 - 2*x + 1,5,x^2 + 3*x - 3,7,x^2 - x -
5,11,x^2,13,x^2 - 7*x + 7[]
498,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 3*x - 2,7,x^2,11,x^2 - x -
4,13,x^2 - 4*x + 4[]
498,5,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 5*x + 5,7,x^2 + 3*x - 9,11,x^2 +
4*x - 16,13,x^2 + 7*x + 11[]
498,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 12*x - 7,7,x^3 +
3*x^2 - 9*x - 4,11,x^3 + 3*x^2 - 24*x - 64,13,x^3 + 3*x^2 - 15*x - 46[]
498,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 -
2*x^3 - 8*x^2 + 11*x + 14,7,x^4 - x^3 - 21*x^2 + 52*x - 32,11,x^4 + x^3 - 28*x^2
- 16*x + 128,13,x^4 - 7*x^3 - 31*x^2 + 202*x + 112[]
499,1,2,x^2 + x - 1,3,x^2 - 5,5,x^2 + 5*x + 5,7,x^2 + 2*x + 1,11,x^2 + 2*x -
19,13,x^2 - 45[]
499,2,2,x^16 + 5*x^15 - 11*x^14 - 85*x^13 + 9*x^12 + 548*x^11 + 293*x^10 -
1718*x^9 - 1408*x^8 + 2735*x^7 + 2662*x^6 - 2058*x^5 - 2241*x^4 + 585*x^3 +
738*x^2 - 54*x - 81,3,x^16 + 5*x^15 - 14*x^14 - 98*x^13 + 18*x^12 + 617*x^11 +
258*x^10 - 1767*x^9 - 985*x^8 + 2671*x^7 + 1338*x^6 - 2241*x^5 - 719*x^4 +
1008*x^3 + 68*x^2 - 194*x + 35,5,x^16 + 20*x^15 + 149*x^14 + 408*x^13 - 651*x^12
- 6586*x^11 - 11148*x^10 + 15067*x^9 + 66330*x^8 + 32190*x^7 - 110780*x^6 -
126154*x^5 + 51365*x^4 + 119462*x^3 + 17428*x^2 - 33621*x - 11849,7,x^16 +
4*x^15 - 63*x^14 - 248*x^13 + 1575*x^12 + 6076*x^11 - 19859*x^10 - 74491*x^9 +
132137*x^8 + 473816*x^7 - 440367*x^6 - 1450597*x^5 + 618118*x^4 + 1720867*x^3 -
165914*x^2 - 583503*x - 27953,11,x^16 + 18*x^15 + 61*x^14 - 734*x^13 - 5949*x^12
- 1787*x^11 + 112530*x^10 + 308694*x^9 - 502294*x^8 - 2986329*x^7 - 822966*x^6 +
11116513*x^5 + 10278876*x^4 - 17684787*x^3 - 22277034*x^2 + 9519653*x +
14162251,13,x^16 + 14*x^15 - 2*x^14 - 819*x^13 - 2570*x^12 + 15509*x^11 +
81665*x^10 - 79401*x^9 - 977484*x^8 - 677266*x^7 + 4767550*x^6 + 8109124*x^5 -
5223609*x^4 - 21003732*x^3 - 14674885*x^2 - 1340222*x + 1007372[]
499,3,2,x^23 - 4*x^22 - 26*x^21 + 117*x^20 + 268*x^19 - 1447*x^18 - 1325*x^17 +
9859*x^16 + 2497*x^15 - 40388*x^14 + 4836*x^13 + 101760*x^12 - 34790*x^11 -
154579*x^10 + 72287*x^9 + 132753*x^8 - 68227*x^7 - 57242*x^6 + 26996*x^5 +
11011*x^4 - 4109*x^3 - 660*x^2 + 172*x - 8,3,x^23 - x^22 - 47*x^21 + 49*x^20 +
938*x^19 - 1009*x^18 - 10386*x^17 + 11358*x^16 + 70051*x^15 - 76320*x^14 -
298353*x^13 + 315080*x^12 + 809095*x^11 - 799217*x^10 - 1383405*x^9 +
1226888*x^8 + 1441343*x^7 - 1105750*x^6 - 847011*x^5 + 553800*x^4 + 237620*x^3 -
138504*x^2 - 21632*x + 11776,5,x^23 - 25*x^22 + 242*x^21 - 958*x^20 - 774*x^19 +
21179*x^18 - 62625*x^17 - 51232*x^16 + 653345*x^15 - 982565*x^14 - 1702705*x^13
+ 6480859*x^12 - 2790244*x^11 - 12328951*x^10 + 15243330*x^9 + 5901074*x^8 -
17613142*x^7 + 3290507*x^6 + 6617092*x^5 - 1954498*x^4 - 959061*x^3 + 184141*x^2
+ 60531*x + 2043,7,x^23 - 2*x^22 - 86*x^21 + 184*x^20 + 3066*x^19 - 7094*x^18 -
58500*x^17 + 149025*x^16 + 639920*x^15 - 1857955*x^14 - 3908486*x^13 +
14016231*x^12 + 10726921*x^11 - 61960310*x^10 + 7490888*x^9 + 142825764*x^8 -
113008621*x^7 - 110238725*x^6 + 187850257*x^5 - 72076130*x^4 - 8718240*x^3 +
8461496*x^2 - 99136*x - 226112,11,x^23 - 10*x^22 - 72*x^21 + 886*x^20 +
1948*x^19 - 32143*x^18 - 23119*x^17 + 609371*x^16 + 72764*x^15 - 6373481*x^14 +
989180*x^13 + 35884388*x^12 - 11126828*x^11 - 102770942*x^10 + 41074754*x^9 +
151249934*x^8 - 69690257*x^7 - 109156833*x^6 + 56283273*x^5 + 30315234*x^4 -
18273116*x^3 + 309656*x^2 + 689184*x - 35136,13,x^23 - 14*x^22 - 53*x^21 +
1501*x^20 - 1370*x^19 - 65954*x^18 + 176723*x^17 + 1526698*x^16 - 5948323*x^15 -
19654349*x^14 + 104348794*x^13 + 128901988*x^12 - 1074468215*x^11 -
162469082*x^10 + 6631301500*x^9 - 3526175718*x^8 - 23451765391*x^7 +
24981860880*x^6 + 39771509500*x^5 - 68805809440*x^4 - 7449698960*x^3 +
67995404512*x^2 - 44128976704*x + 8912473984[]

Total time: 16.670 seconds, Total memory usage: 6.50MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:47:39 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [499..452] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 12:47:36 on modular  [Seed = 99620654]
-------------------------------------

Total time: 3.019 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 12:48:27 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [499..502] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 12:48:11 on modular  [Seed = 234364741]
-------------------------------------

499,1,2,$.1^2 +$.1 - 1,3,$.1^2 - 5,5,$.1^2 + 5*$.1 + 5,7,$.1^2 + 2*$.1 + 1,11,$.1^2 + 2*$.1 - 19,13,$.1^2 - 45[]
499,2,2,$.1^16 + 5*$.1^15 - 11*$.1^14 - 85*$.1^13 + 9*$.1^12 + 548*$.1^11 +
293*$.1^10 - 1718*$.1^9 - 1408*$.1^8 + 2735*$.1^7 + 2662*$.1^6 - 2058*$.1^5 -
2241*$.1^4 + 585*$.1^3 + 738*$.1^2 - 54*$.1 - 81,3,$.1^16 + 5*$.1^15 - 14*$.1^14 - 98*$.1^13 + 18*$.1^12 + 617*$.1^11 + 258*$.1^10 - 1767*$.1^9 - 985*$.1^8 + 2671*$.1^7 + 1338*$.1^6 - 2241*$.1^5 - 719*$.1^4 + 1008*$.1^3 + 68*$.1^2 - 194*$.1 + 35,5,$.1^16 + 20*$.1^15 + 149*$.1^14 + 408*$.1^13 - 651*$.1^12 - 6586*$.1^11 - 11148*$.1^10 + 15067*$.1^9 + 66330*$.1^8 + 32190*$.1^7 -
110780*$.1^6 - 126154*$.1^5 + 51365*$.1^4 + 119462*$.1^3 + 17428*$.1^2 - 33621*$.1 - 11849,7,$.1^16 + 4*$.1^15 - 63*$.1^14 - 248*$.1^13 + 1575*$.1^12 + 6076*$.1^11 - 19859*$.1^10 - 74491*$.1^9 + 132137*$.1^8 + 473816*$.1^7 -
440367*$.1^6 - 1450597*$.1^5 + 618118*$.1^4 + 1720867*$.1^3 - 165914*$.1^2 - 583503*$.1 - 27953,11,$.1^16 + 18*$.1^15 + 61*$.1^14 - 734*$.1^13 - 5949*$.1^12 - 1787*$.1^11 + 112530*$.1^10 + 308694*$.1^9 - 502294*$.1^8 - 2986329*$.1^7 -
822966*$.1^6 + 11116513*$.1^5 + 10278876*$.1^4 - 17684787*$.1^3 - 22277034*$.1^2 + 9519653*$.1 + 14162251,13,$.1^16 + 14*$.1^15 - 2*$.1^14 - 819*$.1^13 -
2570*$.1^12 + 15509*$.1^11 + 81665*$.1^10 - 79401*$.1^9 - 977484*$.1^8 - 677266*$.1^7 + 4767550*$.1^6 + 8109124*$.1^5 - 5223609*$.1^4 - 21003732*$.1^3 -
14674885*$.1^2 - 1340222*$.1 + 1007372[]
499,3,2,$.1^23 - 4*$.1^22 - 26*$.1^21 + 117*$.1^20 + 268*$.1^19 - 1447*$.1^18 -
1325*$.1^17 + 9859*$.1^16 + 2497*$.1^15 - 40388*$.1^14 + 4836*$.1^13 + 101760*$.1^12 - 34790*$.1^11 - 154579*$.1^10 + 72287*$.1^9 + 132753*$.1^8 -
68227*$.1^7 - 57242*$.1^6 + 26996*$.1^5 + 11011*$.1^4 - 4109*$.1^3 - 660*$.1^2 +
172*$.1 - 8,3,$.1^23 - $.1^22 - 47*$.1^21 + 49*$.1^20 + 938*$.1^19 - 1009*$.1^18 - 10386*$.1^17 + 11358*$.1^16 + 70051*$.1^15 - 76320*$.1^14 - 298353*$.1^13 +
315080*$.1^12 + 809095*$.1^11 - 799217*$.1^10 - 1383405*$.1^9 + 1226888*$.1^8 + 1441343*$.1^7 - 1105750*$.1^6 - 847011*$.1^5 + 553800*$.1^4 + 237620*$.1^3 -
138504*$.1^2 - 21632*$.1 + 11776,5,$.1^23 - 25*$.1^22 + 242*$.1^21 - 958*$.1^20
- 774*$.1^19 + 21179*$.1^18 - 62625*$.1^17 - 51232*$.1^16 + 653345*$.1^15 - 982565*$.1^14 - 1702705*$.1^13 + 6480859*$.1^12 - 2790244*$.1^11 - 12328951*$.1^10 + 15243330*$.1^9 + 5901074*$.1^8 - 17613142*$.1^7 + 3290507*$.1^6 + 6617092*$.1^5 - 1954498*$.1^4 - 959061*$.1^3 + 184141*$.1^2 +
60531*$.1 + 2043,7,$.1^23 - 2*$.1^22 - 86*$.1^21 + 184*$.1^20 + 3066*$.1^19 -
7094*$.1^18 - 58500*$.1^17 + 149025*$.1^16 + 639920*$.1^15 - 1857955*$.1^14 - 3908486*$.1^13 + 14016231*$.1^12 + 10726921*$.1^11 - 61960310*$.1^10 + 7490888*$.1^9 + 142825764*$.1^8 - 113008621*$.1^7 - 110238725*$.1^6 + 187850257*$.1^5 - 72076130*$.1^4 - 8718240*$.1^3 + 8461496*$.1^2 - 99136*$.1 -
226112,11,$.1^23 - 10*$.1^22 - 72*$.1^21 + 886*$.1^20 + 1948*$.1^19 - 32143*$.1^18 - 23119*$.1^17 + 609371*$.1^16 + 72764*$.1^15 - 6373481*$.1^14 +
989180*$.1^13 + 35884388*$.1^12 - 11126828*$.1^11 - 102770942*$.1^10 +
41074754*$.1^9 + 151249934*$.1^8 - 69690257*$.1^7 - 109156833*$.1^6 +
56283273*$.1^5 + 30315234*$.1^4 - 18273116*$.1^3 + 309656*$.1^2 + 689184*$.1 - 35136,13,$.1^23 - 14*$.1^22 - 53*$.1^21 + 1501*$.1^20 - 1370*$.1^19 -
65954*$.1^18 + 176723*$.1^17 + 1526698*$.1^16 - 5948323*$.1^15 - 19654349*$.1^14 + 104348794*$.1^13 + 128901988*$.1^12 - 1074468215*$.1^11 - 162469082*$.1^10 + 6631301500*$.1^9 - 3526175718*$.1^8 - 23451765391*$.1^7 + 24981860880*$.1^6 + 39771509500*$.1^5 - 68805809440*$.1^4 - 7449698960*$.1^3 + 67995404512*$.1^2 - 44128976704*$.1 + 8912473984[]
500,1,2,x^2,3,x^2 - x - 1,5,x^2,7,x^2 - 4*x - 1,11,x^2 - 5,13,x^2 - 9*x + 19[]
500,2,2,x^2,3,x^2 + x - 1,5,x^2,7,x^2 + 4*x - 1,11,x^2 - 5,13,x^2 + 9*x + 19[]
500,3,2,x^4,3,x^4 - 13*x^2 + 31,5,x^4,7,x^4 - 23*x^2 + 31,11,x^4 - 40*x^2 +
400,13,x^4 - 48*x^2 + 496[]
501,1,2,x - 1,3,x + 1,5,x + 4,7,x - 4,11,x - 4,13,x - 6[]
501,2,2,x^5 - 5*x^3 + 4*x + 1,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,5,x^5 +
x^4 - 9*x^3 - 2*x^2 + 17*x - 1,7,x^5 + 4*x^4 - 3*x^3 - 29*x^2 - 37*x - 13,11,x^5
+ 7*x^4 - 3*x^3 - 92*x^2 - 101*x + 121,13,x^5 + 8*x^4 - x^3 - 66*x^2 - 48*x +
17[]
501,3,2,x^5 + 4*x^4 + x^3 - 8*x^2 - 2*x + 3,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 +
5*x - 1,5,x^5 + 9*x^4 + 25*x^3 + 12*x^2 - 39*x - 37,7,x^5 + 4*x^4 - 15*x^3 -
49*x^2 + 55*x + 83,11,x^5 + 15*x^4 + 69*x^3 + 36*x^2 - 447*x - 761,13,x^5 -
41*x^3 - 32*x^2 + 412*x + 687[]
501,4,2,x^8 + 3*x^7 - 10*x^6 - 34*x^5 + 17*x^4 + 100*x^3 + 43*x^2 - 21*x -
7,3,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 -
x^7 - 21*x^6 + 18*x^5 + 91*x^4 - 117*x^3 - 18*x^2 + 48*x - 2,7,x^8 - 31*x^6 +
7*x^5 + 175*x^4 + 59*x^3 - 224*x^2 - 160*x - 16,11,x^8 - 5*x^7 - 23*x^6 +
104*x^5 + 151*x^4 - 547*x^3 - 460*x^2 + 700*x + 500,13,x^8 - 61*x^6 - 10*x^5 +
1088*x^4 - 237*x^3 - 6922*x^2 + 3828*x + 9224[]
501,5,2,x^8 - 3*x^7 - 8*x^6 + 28*x^5 + 9*x^4 - 64*x^3 + 17*x^2 + 23*x + 1,3,x^8
- 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,5,x^8 - 7*x^7 +
7*x^6 + 50*x^5 - 125*x^4 + 9*x^3 + 196*x^2 - 124*x - 18,7,x^8 + 4*x^7 - 19*x^6 -
65*x^5 + 63*x^4 + 255*x^3 + 84*x^2 - 48*x - 16,11,x^8 - 13*x^7 + 41*x^6 +
104*x^5 - 691*x^4 + 435*x^3 + 1804*x^2 - 1316*x - 1596,13,x^8 - 37*x^6 - 52*x^5
+ 320*x^4 + 973*x^3 + 994*x^2 + 412*x + 56[]
502,1,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 5*x + 3,7,x^2 + 2*x + 1,11,x^2 -
6*x + 9,13,x^2 - 13[]
502,2,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 3*x + 1,7,x^2 + 4*x - 1,11,x^2 +
6*x + 9,13,x^2 + 2*x + 1[]
502,3,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + x^4 - 7*x^3 - 4*x^2 +
6*x - 1,5,x^5 + 6*x^4 + 6*x^3 - 18*x^2 - 25*x + 7,7,x^5 + x^4 - 19*x^3 - 18*x^2
+ 78*x + 73,11,x^5 + 4*x^4 - 29*x^3 - 76*x^2 + 160*x - 64,13,x^5 + 7*x^4 - 7*x^3
- 100*x^2 - 6*x + 373[]
502,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 2*x^4 - 9*x^3 + 14*x^2 +
16*x - 8,5,x^5 - 7*x^4 + 9*x^3 + 24*x^2 - 52*x + 24,7,x^5 - x^4 - 19*x^3 +
28*x^2 + 80*x - 137,11,x^5 - 7*x^4 + 13*x^3 - 10*x - 1,13,x^5 - 4*x^4 - 23*x^3 +
138*x^2 - 200*x + 72[]
502,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - x^5 - 16*x^4 +
9*x^3 + 74*x^2 - 8*x - 88,5,x^6 + x^5 - 14*x^4 - 3*x^3 + 44*x^2 - 36*x + 8,7,x^6
- 6*x^5 - 7*x^4 + 90*x^3 - 146*x^2 + 72*x - 11,11,x^6 - x^5 - 30*x^4 + 23*x^3 +
280*x^2 - 112*x - 832,13,x^6 + 5*x^5 - 24*x^4 - 141*x^3 - 78*x^2 + 360*x + 392[]

Total time: 15.839 seconds, Total memory usage: 6.14MB

************** MAGMA *****************
Host c-67-160-217-111.client.comcast.net. (67.160.217.111)
Time: Sun Nov 30 14:09:33 2003

Input: 2+2

Output: Magma V2.10-6     Sun Nov 30 2003 14:09:30 on modular  [Seed = 451896674]
-------------------------------------

4

Total time: 3.059 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host c-67-160-217-111.client.comcast.net. (67.160.217.111)
Time: Sun Nov 30 14:09:36 2003

Input: 2+2

Output: Magma V2.10-6     Sun Nov 30 2003 14:09:33 on modular  [Seed = 434923110]
-------------------------------------

4

Total time: 3.019 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host c-67-160-217-111.client.comcast.net. (67.160.217.111)
Time: Sun Nov 30 14:09:56 2003

Input: 2+2+2

Output: Magma V2.10-6     Sun Nov 30 2003 14:09:53 on modular  [Seed = 201225368]
-------------------------------------

6

Total time: 2.909 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host c-67-160-217-111.client.comcast.net. (67.160.217.111)
Time: Sun Nov 30 14:12:07 2003

Input: 2+2+2

Output: Magma V2.10-6     Sun Nov 30 2003 14:12:04 on modular  [Seed = 719279164]
-------------------------------------

6

Total time: 3.009 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:23:09 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=14;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;

Output: Magma V2.10-6     Sun Nov 30 2003 14:23:06 on modular  [Seed = 2824721440]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
14,1,2,x + 1,3,x + 2,5,x,7,x - 1,11,x,13,x + 4[]

Total time: 3.319 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:25:00 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [503..507] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 14:24:37 on modular  [Seed = 3609373488]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
503,1,2,x - 1,3,x - 1,5,x + 2,7,x + 3,11,x - 1,13,x - 1[]
503,2,2,x - 1,3,x - 3,5,x + 2,7,x - 3,11,x - 3,13,x - 5[]
503,3,2,x + 1,3,x - 1,5,x + 4,7,x + 3,11,x - 5,13,x - 1[]
503,4,2,x^3 - 5*x + 3,3,x^3 - x^2 - 4*x + 3,5,x^3,7,x^3 - x^2 - 8*x + 3,11,x^3 -
11*x^2 + 36*x - 35,13,x^3 - 5*x^2 - 2*x + 25[]
503,5,2,x^10 + 4*x^9 - 4*x^8 - 31*x^7 - 13*x^6 + 66*x^5 + 56*x^4 - 37*x^3 -
46*x^2 - 8*x + 1,3,x^10 + 8*x^9 + 18*x^8 - 10*x^7 - 85*x^6 - 75*x^5 + 54*x^4 +
86*x^3 + 5*x^2 - 14*x + 1,5,x^10 + x^9 - 11*x^8 - 7*x^7 + 41*x^6 + 7*x^5 -
59*x^4 + 16*x^3 + 18*x^2 - 9*x + 1,7,x^10 + 5*x^9 - 9*x^8 - 64*x^7 + 8*x^6 +
228*x^5 + 23*x^4 - 214*x^3 + 86*x^2 - 4*x - 1,11,x^10 + 3*x^9 - 41*x^8 - 80*x^7
+ 515*x^6 + 537*x^5 - 1961*x^4 - 1781*x^3 + 1973*x^2 + 1920*x + 311,13,x^10 +
18*x^9 + 120*x^8 + 307*x^7 - 212*x^6 - 2777*x^5 - 4882*x^4 - 481*x^3 + 5985*x^2
+ 4107*x - 19[]
503,6,2,x^26 - 4*x^25 - 36*x^24 + 154*x^23 + 554*x^22 - 2577*x^21 - 4772*x^20 +
24652*x^19 + 25321*x^18 - 149131*x^17 - 86017*x^16 + 595540*x^15 + 189834*x^14 -
1589003*x^13 - 278156*x^12 + 2799707*x^11 + 297701*x^10 - 3137915*x^9 -
283355*x^8 + 2081504*x^7 + 236065*x^6 - 725019*x^5 - 120174*x^4 + 115872*x^3 +
24760*x^2 - 6437*x - 1583,3,x^26 - 4*x^25 - 52*x^24 + 211*x^23 + 1175*x^22 -
4814*x^21 - 15259*x^20 + 62449*x^19 + 127340*x^18 - 509651*x^17 - 726005*x^16 +
2735786*x^15 + 2939963*x^14 - 9813106*x^13 - 8635730*x^12 + 23403122*x^11 +
18323065*x^10 - 36123133*x^9 - 27001213*x^8 + 34013592*x^7 + 25434027*x^6 -
17328663*x^5 - 13187700*x^4 + 3683025*x^3 + 2752584*x^2 - 219997*x -
113513,5,x^26 - 9*x^25 - 71*x^24 + 873*x^23 + 1333*x^22 - 35769*x^21 +
27305*x^20 + 795330*x^19 - 1730386*x^18 - 10082887*x^17 + 35969747*x^16 +
64971026*x^15 - 407126924*x^14 - 30144880*x^13 + 2659470320*x^12 -
2703014464*x^11 - 9170377216*x^10 + 19446722944*x^9 + 9083193856*x^8 -
57597089792*x^7 + 35068894208*x^6 + 60235479040*x^5 - 94082748416*x^4 +
22315384832*x^3 + 39809548288*x^2 - 32069681152*x + 7351042048,7,x^26 - 11*x^25
- 63*x^24 + 1107*x^23 + 43*x^22 - 44446*x^21 + 93217*x^20 + 898238*x^19 -
3273637*x^18 - 9066021*x^17 + 53508259*x^16 + 26089563*x^15 - 476783660*x^14 +
340019836*x^13 + 2258493746*x^12 - 3638899633*x^11 - 4488923464*x^10 +
13313053218*x^9 - 1189588910*x^8 - 17825595396*x^7 + 10116673017*x^6 +
8032872453*x^5 - 6538139464*x^4 - 992741156*x^3 + 848600087*x^2 + 172525027*x +
5803441,11,x^26 + 17*x^25 - 19*x^24 - 1993*x^23 - 9318*x^22 + 69343*x^21 +
684361*x^20 + 171574*x^19 - 17790495*x^18 - 58741228*x^17 + 140418152*x^16 +
1195749823*x^15 + 1337713907*x^14 - 7963423904*x^13 - 26524346571*x^12 -
2437492147*x^11 + 127147119393*x^10 + 220655004639*x^9 - 72117070449*x^8 -
683061933795*x^7 - 791478601478*x^6 + 76774743603*x^5 + 1080817421692*x^4 +
1209958900604*x^3 + 658913392984*x^2 + 184269684053*x + 21107618035,13,x^26 -
14*x^25 - 120*x^24 + 2386*x^23 + 3454*x^22 - 168492*x^21 + 136722*x^20 +
6506843*x^19 - 11822453*x^18 - 153132460*x^17 + 344794423*x^16 + 2326590816*x^15
- 5339743095*x^14 - 23621117551*x^13 + 47008122323*x^12 + 162052333548*x^11 -
225426275374*x^10 - 725968713666*x^9 + 471071882753*x^8 + 1883475205603*x^7 +
51373051032*x^6 - 2118085970313*x^5 - 982189476223*x^4 + 528503780175*x^3 +
396000550123*x^2 + 39464838428*x - 4565810269[]
504,1,2,x,3,x,5,x + 2,7,x + 1,11,x + 2,13,x - 2[]
504,2,2,x,3,x,5,x - 2,7,x - 1,11,x - 6,13,x + 6[]
504,3,2,x,3,x,5,x + 2,7,x + 1,11,x - 4,13,x - 2[]
504,4,2,x,3,x,5,x - 2,7,x + 1,11,x - 2,13,x - 2[]
504,5,2,x,3,x,5,x + 2,7,x - 1,11,x + 6,13,x + 6[]
504,6,2,x,3,x,5,x + 2,7,x + 1,11,x,13,x + 2[]
504,7,2,x,3,x,5,x + 2,7,x - 1,11,x,13,x - 6[]
504,8,2,x,3,x,5,x - 4,7,x - 1,11,x,13,x[]
505,1,2,x - 1,3,x,5,x + 1,7,x,11,x + 2,13,x - 2[]
505,2,2,x^6 + 3*x^5 - 4*x^4 - 17*x^3 - 5*x^2 + 13*x + 5,3,x^6 + x^5 - 9*x^4 -
8*x^3 + 15*x^2 + 7*x - 8,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x +
1,7,x^6 + 2*x^5 - 25*x^4 - 39*x^3 + 133*x^2 + 111*x - 232,11,x^6 + 11*x^5 +
17*x^4 - 192*x^3 - 799*x^2 - 737*x + 362,13,x^6 + 3*x^5 - 39*x^4 - 33*x^3 +
480*x^2 - 479*x - 298[]
505,3,2,x^8 + 5*x^7 + x^6 - 26*x^5 - 27*x^4 + 30*x^3 + 46*x^2 + 9*x - 1,3,x^8 +
11*x^7 + 43*x^6 + 62*x^5 - 11*x^4 - 91*x^3 - 34*x^2 + 16*x + 4,5,x^8 - 8*x^7 +
28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,7,x^8 + 12*x^7 + 37*x^6 -
65*x^5 - 553*x^4 - 979*x^3 - 418*x^2 + 384*x + 284,11,x^8 + 9*x^7 - 27*x^6 -
400*x^5 - 219*x^4 + 4817*x^3 + 7176*x^2 - 12232*x - 16784,13,x^8 + 7*x^7 -
43*x^6 - 215*x^5 + 790*x^4 + 925*x^3 - 3070*x^2 - 1092*x + 3064[]
505,4,2,x^9 - 2*x^8 - 12*x^7 + 21*x^6 + 47*x^5 - 61*x^4 - 72*x^3 + 43*x^2 + 34*x
- 1,3,x^9 - x^8 - 17*x^7 + 14*x^6 + 91*x^5 - 57*x^4 - 180*x^3 + 88*x^2 + 108*x -
52,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x +
1,7,x^9 - 39*x^7 + 13*x^6 + 521*x^5 - 329*x^4 - 2644*x^3 + 2292*x^2 + 3636*x -
3620,11,x^9 - 11*x^8 + 13*x^7 + 224*x^6 - 711*x^5 - 787*x^4 + 5064*x^3 -
3288*x^2 - 3632*x + 1040,13,x^9 + x^8 - 65*x^7 - 131*x^6 + 1286*x^5 + 3317*x^4 -
8768*x^3 - 25672*x^2 + 18784*x + 60880[]
505,5,2,x^9 - 2*x^8 - 10*x^7 + 19*x^6 + 31*x^5 - 57*x^4 - 28*x^3 + 57*x^2 - 6*x
- 7,3,x^9 - 7*x^8 + 7*x^7 + 44*x^6 - 87*x^5 - 63*x^4 + 210*x^3 - 28*x^2 - 116*x
+ 28,5,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x
- 1,7,x^9 - 6*x^8 - 5*x^7 + 67*x^6 - 37*x^5 - 119*x^4 + 62*x^3 + 48*x^2 - 12*x -
4,11,x^9 - 3*x^8 - 33*x^7 + 98*x^6 + 233*x^5 - 567*x^4 - 504*x^3 + 888*x^2 +
80*x - 224,13,x^9 - 3*x^8 - 41*x^7 + 35*x^6 + 556*x^5 + 561*x^4 - 836*x^3 -
832*x^2 + 400*x - 16[]
506,1,2,x + 1,3,x + 2,5,x - 1,7,x + 1,11,x + 1,13,x - 3[]
506,2,2,x + 1,3,x,5,x + 3,7,x - 3,11,x + 1,13,x - 5[]
506,3,2,x + 1,3,x + 2,5,x - 3,7,x - 5,11,x - 1,13,x + 1[]
506,4,2,x + 1,3,x,5,x + 1,7,x - 1,11,x - 1,13,x + 7[]
506,5,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 1,13,x + 1[]
506,6,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x - 1,13,x + 3[]

Errors: /home/mfd/gomagma: line 2: 11717 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:26:05 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [503..506] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 14:25:42 on modular  [Seed = 3241458405]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
503,1,2,x - 1,3,x - 1,5,x + 2,7,x + 3,11,x - 1,13,x - 1[]
503,2,2,x - 1,3,x - 3,5,x + 2,7,x - 3,11,x - 3,13,x - 5[]
503,3,2,x + 1,3,x - 1,5,x + 4,7,x + 3,11,x - 5,13,x - 1[]
503,4,2,x^3 - 5*x + 3,3,x^3 - x^2 - 4*x + 3,5,x^3,7,x^3 - x^2 - 8*x + 3,11,x^3 -
11*x^2 + 36*x - 35,13,x^3 - 5*x^2 - 2*x + 25[]
503,5,2,x^10 + 4*x^9 - 4*x^8 - 31*x^7 - 13*x^6 + 66*x^5 + 56*x^4 - 37*x^3 -
46*x^2 - 8*x + 1,3,x^10 + 8*x^9 + 18*x^8 - 10*x^7 - 85*x^6 - 75*x^5 + 54*x^4 +
86*x^3 + 5*x^2 - 14*x + 1,5,x^10 + x^9 - 11*x^8 - 7*x^7 + 41*x^6 + 7*x^5 -
59*x^4 + 16*x^3 + 18*x^2 - 9*x + 1,7,x^10 + 5*x^9 - 9*x^8 - 64*x^7 + 8*x^6 +
228*x^5 + 23*x^4 - 214*x^3 + 86*x^2 - 4*x - 1,11,x^10 + 3*x^9 - 41*x^8 - 80*x^7
+ 515*x^6 + 537*x^5 - 1961*x^4 - 1781*x^3 + 1973*x^2 + 1920*x + 311,13,x^10 +
18*x^9 + 120*x^8 + 307*x^7 - 212*x^6 - 2777*x^5 - 4882*x^4 - 481*x^3 + 5985*x^2
+ 4107*x - 19[]
503,6,2,x^26 - 4*x^25 - 36*x^24 + 154*x^23 + 554*x^22 - 2577*x^21 - 4772*x^20 +
24652*x^19 + 25321*x^18 - 149131*x^17 - 86017*x^16 + 595540*x^15 + 189834*x^14 -
1589003*x^13 - 278156*x^12 + 2799707*x^11 + 297701*x^10 - 3137915*x^9 -
283355*x^8 + 2081504*x^7 + 236065*x^6 - 725019*x^5 - 120174*x^4 + 115872*x^3 +
24760*x^2 - 6437*x - 1583,3,x^26 - 4*x^25 - 52*x^24 + 211*x^23 + 1175*x^22 -
4814*x^21 - 15259*x^20 + 62449*x^19 + 127340*x^18 - 509651*x^17 - 726005*x^16 +
2735786*x^15 + 2939963*x^14 - 9813106*x^13 - 8635730*x^12 + 23403122*x^11 +
18323065*x^10 - 36123133*x^9 - 27001213*x^8 + 34013592*x^7 + 25434027*x^6 -
17328663*x^5 - 13187700*x^4 + 3683025*x^3 + 2752584*x^2 - 219997*x -
113513,5,x^26 - 9*x^25 - 71*x^24 + 873*x^23 + 1333*x^22 - 35769*x^21 +
27305*x^20 + 795330*x^19 - 1730386*x^18 - 10082887*x^17 + 35969747*x^16 +
64971026*x^15 - 407126924*x^14 - 30144880*x^13 + 2659470320*x^12 -
2703014464*x^11 - 9170377216*x^10 + 19446722944*x^9 + 9083193856*x^8 -
57597089792*x^7 + 35068894208*x^6 + 60235479040*x^5 - 94082748416*x^4 +
22315384832*x^3 + 39809548288*x^2 - 32069681152*x + 7351042048,7,x^26 - 11*x^25
- 63*x^24 + 1107*x^23 + 43*x^22 - 44446*x^21 + 93217*x^20 + 898238*x^19 -
3273637*x^18 - 9066021*x^17 + 53508259*x^16 + 26089563*x^15 - 476783660*x^14 +
340019836*x^13 + 2258493746*x^12 - 3638899633*x^11 - 4488923464*x^10 +
13313053218*x^9 - 1189588910*x^8 - 17825595396*x^7 + 10116673017*x^6 +
8032872453*x^5 - 6538139464*x^4 - 992741156*x^3 + 848600087*x^2 + 172525027*x +
5803441,11,x^26 + 17*x^25 - 19*x^24 - 1993*x^23 - 9318*x^22 + 69343*x^21 +
684361*x^20 + 171574*x^19 - 17790495*x^18 - 58741228*x^17 + 140418152*x^16 +
1195749823*x^15 + 1337713907*x^14 - 7963423904*x^13 - 26524346571*x^12 -
2437492147*x^11 + 127147119393*x^10 + 220655004639*x^9 - 72117070449*x^8 -
683061933795*x^7 - 791478601478*x^6 + 76774743603*x^5 + 1080817421692*x^4 +
1209958900604*x^3 + 658913392984*x^2 + 184269684053*x + 21107618035,13,x^26 -
14*x^25 - 120*x^24 + 2386*x^23 + 3454*x^22 - 168492*x^21 + 136722*x^20 +
6506843*x^19 - 11822453*x^18 - 153132460*x^17 + 344794423*x^16 + 2326590816*x^15
- 5339743095*x^14 - 23621117551*x^13 + 47008122323*x^12 + 162052333548*x^11 -
225426275374*x^10 - 725968713666*x^9 + 471071882753*x^8 + 1883475205603*x^7 +
51373051032*x^6 - 2118085970313*x^5 - 982189476223*x^4 + 528503780175*x^3 +
396000550123*x^2 + 39464838428*x - 4565810269[]
504,1,2,x,3,x,5,x + 2,7,x + 1,11,x + 2,13,x - 2[]
504,2,2,x,3,x,5,x - 2,7,x - 1,11,x - 6,13,x + 6[]
504,3,2,x,3,x,5,x + 2,7,x + 1,11,x - 4,13,x - 2[]
504,4,2,x,3,x,5,x - 2,7,x + 1,11,x - 2,13,x - 2[]
504,5,2,x,3,x,5,x + 2,7,x - 1,11,x + 6,13,x + 6[]
504,6,2,x,3,x,5,x + 2,7,x + 1,11,x,13,x + 2[]
504,7,2,x,3,x,5,x + 2,7,x - 1,11,x,13,x - 6[]
504,8,2,x,3,x,5,x - 4,7,x - 1,11,x,13,x[]
505,1,2,x - 1,3,x,5,x + 1,7,x,11,x + 2,13,x - 2[]
505,2,2,x^6 + 3*x^5 - 4*x^4 - 17*x^3 - 5*x^2 + 13*x + 5,3,x^6 + x^5 - 9*x^4 -
8*x^3 + 15*x^2 + 7*x - 8,5,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x +
1,7,x^6 + 2*x^5 - 25*x^4 - 39*x^3 + 133*x^2 + 111*x - 232,11,x^6 + 11*x^5 +
17*x^4 - 192*x^3 - 799*x^2 - 737*x + 362,13,x^6 + 3*x^5 - 39*x^4 - 33*x^3 +
480*x^2 - 479*x - 298[]
505,3,2,x^8 + 5*x^7 + x^6 - 26*x^5 - 27*x^4 + 30*x^3 + 46*x^2 + 9*x - 1,3,x^8 +
11*x^7 + 43*x^6 + 62*x^5 - 11*x^4 - 91*x^3 - 34*x^2 + 16*x + 4,5,x^8 - 8*x^7 +
28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,7,x^8 + 12*x^7 + 37*x^6 -
65*x^5 - 553*x^4 - 979*x^3 - 418*x^2 + 384*x + 284,11,x^8 + 9*x^7 - 27*x^6 -
400*x^5 - 219*x^4 + 4817*x^3 + 7176*x^2 - 12232*x - 16784,13,x^8 + 7*x^7 -
43*x^6 - 215*x^5 + 790*x^4 + 925*x^3 - 3070*x^2 - 1092*x + 3064[]
505,4,2,x^9 - 2*x^8 - 12*x^7 + 21*x^6 + 47*x^5 - 61*x^4 - 72*x^3 + 43*x^2 + 34*x
- 1,3,x^9 - x^8 - 17*x^7 + 14*x^6 + 91*x^5 - 57*x^4 - 180*x^3 + 88*x^2 + 108*x -
52,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x +
1,7,x^9 - 39*x^7 + 13*x^6 + 521*x^5 - 329*x^4 - 2644*x^3 + 2292*x^2 + 3636*x -
3620,11,x^9 - 11*x^8 + 13*x^7 + 224*x^6 - 711*x^5 - 787*x^4 + 5064*x^3 -
3288*x^2 - 3632*x + 1040,13,x^9 + x^8 - 65*x^7 - 131*x^6 + 1286*x^5 + 3317*x^4 -
8768*x^3 - 25672*x^2 + 18784*x + 60880[]
505,5,2,x^9 - 2*x^8 - 10*x^7 + 19*x^6 + 31*x^5 - 57*x^4 - 28*x^3 + 57*x^2 - 6*x
- 7,3,x^9 - 7*x^8 + 7*x^7 + 44*x^6 - 87*x^5 - 63*x^4 + 210*x^3 - 28*x^2 - 116*x
+ 28,5,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 + 9*x
- 1,7,x^9 - 6*x^8 - 5*x^7 + 67*x^6 - 37*x^5 - 119*x^4 + 62*x^3 + 48*x^2 - 12*x -
4,11,x^9 - 3*x^8 - 33*x^7 + 98*x^6 + 233*x^5 - 567*x^4 - 504*x^3 + 888*x^2 +
80*x - 224,13,x^9 - 3*x^8 - 41*x^7 + 35*x^6 + 556*x^5 + 561*x^4 - 836*x^3 -
832*x^2 + 400*x - 16[]
506,1,2,x + 1,3,x + 2,5,x - 1,7,x + 1,11,x + 1,13,x - 3[]
506,2,2,x + 1,3,x,5,x + 3,7,x - 3,11,x + 1,13,x - 5[]
506,3,2,x + 1,3,x + 2,5,x - 3,7,x - 5,11,x - 1,13,x + 1[]
506,4,2,x + 1,3,x,5,x + 1,7,x - 1,11,x - 1,13,x + 7[]
506,5,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 1,13,x + 1[]
506,6,2,x - 1,3,x + 2,5,x + 1,7,x + 1,11,x - 1,13,x + 3[]
506,7,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 6*x + 17,5,x^3 - 3*x^2 + 3,7,x^3 -
12*x - 8,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 + 3*x^2 - 6*x - 17[]
506,8,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 2*x + 5,5,x^3 + 7*x^2 + 8*x -
15,7,x^3 - 20*x + 8,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 - 5*x^2 - 2*x + 15[]
506,9,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + x^3 - 6*x^2 - 3*x + 8,5,x^4 -
2*x^3 - 11*x^2 + 23*x - 1,7,x^4 - 3*x^3 - 8*x^2 + 20*x - 8,11,x^4 - 4*x^3 +
6*x^2 - 4*x + 1,13,x^4 - 6*x^3 - 21*x^2 + 103*x + 137[]
506,10,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 12*x^3 + 13*x^2 +
22*x - 8,5,x^5 - 4*x^4 - 7*x^3 + 31*x^2 + x - 18,7,x^5 - x^4 - 24*x^3 + 4*x^2 +
88*x - 64,11,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,13,x^5 - 10*x^4 - 23*x^3 +
377*x^2 + 33*x - 3578[]

Total time: 22.860 seconds, Total memory usage: 7.07MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:37:08 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [507..510] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 14:36:45 on modular  [Seed = 4262168353]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
507,1,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x + 2,13,x[]
507,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 2,13,x[]
507,3,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x[]
507,4,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 3,11,x^2 - 12,13,x^2[]
507,5,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 12,11,x^2 - 12,13,x^2[]
507,6,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 + 3*x - 2,11,x^2 + 4*x
+ 4,13,x^2[]
507,7,2,x^2 + x - 4,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 - 3*x - 2,11,x^2 - 4*x
+ 4,13,x^2[]
507,8,2,x^2 - 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 - 4*x +
4,13,x^2[]
507,9,2,x^3 + 3*x^2 - 4*x - 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 6*x^2 + 5*x -
13,7,x^3 + 2*x^2 - x - 1,11,x^3 + 5*x^2 - 8*x - 41,13,x^3[]
507,10,2,x^3 - 3*x^2 - 4*x + 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 6*x^2 + 5*x +
13,7,x^3 - 2*x^2 - x + 1,11,x^3 - 5*x^2 - 8*x + 41,13,x^3[]
507,11,2,x^3 - x^2 - 2*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 3*x +
1,7,x^3 - 10*x^2 + 31*x - 29,11,x^3 + x^2 - 30*x - 43,13,x^3[]
507,12,2,x^3 + x^2 - 2*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 4*x^2 + 3*x -
1,7,x^3 + 10*x^2 + 31*x + 29,11,x^3 - x^2 - 30*x + 43,13,x^3[]
508,1,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 5*x +
5,13,x^2 - 7*x + 11[]
508,2,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 4*x + 4,7,x^2 - 20,11,x^2 - x - 11,13,x^2 +
5*x - 5[]
508,3,2,x^3,3,x^3 - x^2 - 6*x - 3,5,x^3 - 4*x^2 + x + 3,7,x^3 - 7*x^2 + 12*x -
3,11,x^3 - 2*x^2 - 5*x + 9,13,x^3 + 7*x^2 + 10*x + 3[]
508,4,2,x^3,3,x^3 + 3*x^2 - 1,5,x^3 - 9*x + 9,7,x^3 + 3*x^2 - 6*x - 17,11,x^3 +
6*x^2 - 9*x - 51,13,x^3 + 3*x^2 - 6*x - 17[]
509,1,2,x^14 + 3*x^13 - 11*x^12 - 36*x^11 + 43*x^10 + 161*x^9 - 70*x^8 - 337*x^7
+ 29*x^6 + 336*x^5 + 40*x^4 - 139*x^3 - 36*x^2 + 12*x + 3,3,x^14 + 5*x^13 -
11*x^12 - 81*x^11 + 8*x^10 + 438*x^9 + 183*x^8 - 1032*x^7 - 579*x^6 + 1074*x^5 +
579*x^4 - 417*x^3 - 172*x^2 + 29*x + 11,5,x^14 + 5*x^13 - 17*x^12 - 121*x^11 -
3*x^10 + 866*x^9 + 897*x^8 - 2207*x^7 - 3776*x^6 + 1189*x^5 + 4603*x^4 + 984*x^3
- 1708*x^2 - 736*x - 16,7,x^14 + 17*x^13 + 96*x^12 + 61*x^11 - 1535*x^10 -
6288*x^9 - 6227*x^8 + 16783*x^7 + 47959*x^6 + 26599*x^5 - 43785*x^4 - 69420*x^3
- 33088*x^2 - 4384*x - 64,11,x^14 + 20*x^13 + 129*x^12 + 28*x^11 - 3389*x^10 -
14314*x^9 - 2747*x^8 + 135745*x^7 + 385001*x^6 + 194812*x^5 - 1097552*x^4 -
2779576*x^3 - 3033711*x^2 - 1660621*x - 371677,13,x^14 + 6*x^13 - 70*x^12 -
566*x^11 + 780*x^10 + 15417*x^9 + 23838*x^8 - 122059*x^7 - 422348*x^6 -
172234*x^5 + 768087*x^4 + 624287*x^3 - 531991*x^2 - 344123*x + 199459[]
509,2,2,x^28 - 3*x^27 - 44*x^26 + 135*x^25 + 847*x^24 - 2674*x^23 - 9369*x^22 +
30699*x^21 + 65714*x^20 - 226429*x^19 - 303558*x^18 + 1123948*x^17 + 922806*x^16
- 3822074*x^15 - 1752519*x^14 + 8879314*x^13 + 1675588*x^12 - 13751763*x^11 +
382971*x^10 + 13397267*x^9 - 2958134*x^8 - 7169500*x^7 + 3056380*x^6 +
1305763*x^5 - 1072947*x^4 + 245723*x^3 - 24485*x^2 + 1114*x - 19,3,x^28 - 5*x^27
- 48*x^26 + 272*x^25 + 931*x^24 - 6405*x^23 - 8850*x^22 + 85759*x^21 +
31965*x^20 - 721317*x^19 + 164032*x^18 + 3972999*x^17 - 2503752*x^16 -
14475994*x^15 + 13508475*x^14 + 34330526*x^13 - 41204799*x^12 - 50312318*x^11 +
75928604*x^10 + 39824769*x^9 - 82931046*x^8 - 9371818*x^7 + 49394521*x^6 -
6602510*x^5 - 13320545*x^4 + 3321297*x^3 + 1196222*x^2 - 267183*x - 31583,5,x^28
- x^27 - 86*x^26 + 100*x^25 + 3226*x^24 - 4251*x^23 - 69315*x^22 + 101474*x^21 +
941574*x^20 - 1508877*x^19 - 8418071*x^18 + 14621274*x^17 + 49979838*x^16 -
93690681*x^15 - 194106206*x^14 + 394225378*x^13 + 473294393*x^12 -
1060961763*x^11 - 669570897*x^10 + 1744938012*x^9 + 465995781*x^8 -
1643052709*x^7 - 73313109*x^6 + 799280568*x^5 - 66191620*x^4 - 163204400*x^3 +
24714384*x^2 + 6775680*x - 395200,7,x^28 - 19*x^27 + 59*x^26 + 1046*x^25 -
7773*x^24 - 12799*x^23 + 266239*x^22 - 328866*x^21 - 4320998*x^20 +
12180077*x^19 + 36055653*x^18 - 165902683*x^17 - 133267136*x^16 +
1240417261*x^15 - 83325840*x^14 - 5674708476*x^13 + 2619605547*x^12 +
16832782791*x^11 - 10032388939*x^10 - 33338640274*x^9 + 18249500769*x^8 +
43742965431*x^7 - 16307228095*x^6 - 35600041583*x^5 + 5188671857*x^4 +
15282505552*x^3 + 865161736*x^2 - 2359400544*x - 427287872,11,x^28 - 24*x^27 +
109*x^26 + 1716*x^25 - 17505*x^24 - 16702*x^23 + 774057*x^22 - 1728287*x^21 -
15056563*x^20 + 66368896*x^19 + 114572412*x^18 - 1020245916*x^17 +
300125641*x^16 + 7751456251*x^15 - 10332794825*x^14 - 29149056508*x^13 +
66040834520*x^12 + 42954791184*x^11 - 195283700736*x^10 + 32381865088*x^9 +
287532490752*x^8 - 180086084096*x^7 - 188919045888*x^6 + 200298798080*x^5 +
28612415488*x^4 - 81634443264*x^3 + 12479713280*x^2 + 11091165184*x -
3179560960,13,x^28 - 8*x^27 - 186*x^26 + 1570*x^25 + 14590*x^24 - 133651*x^23 -
620848*x^22 + 6506217*x^21 + 14924456*x^20 - 200543250*x^19 - 167804839*x^18 +
4081257155*x^17 - 801119881*x^16 - 55212568969*x^15 + 56352951195*x^14 +
482890261616*x^13 - 864977589548*x^12 - 2496581876256*x^11 + 6925120183312*x^10
+ 5504434047296*x^9 - 30250690896192*x^8 + 8697521814528*x^7 +
63084344508672*x^6 - 63829683296256*x^5 - 35153013180416*x^4 +
78367682740224*x^3 - 20830072713216*x^2 - 18202017693696*x + 8555162042368[]

Errors: /home/mfd/gomagma: line 2: 11756 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:38:01 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [507..509] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 14:37:49 on modular  [Seed = 3927937781]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
507,1,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x + 2,13,x[]
507,2,2,x + 1,3,x + 1,5,x - 1,7,x + 2,11,x - 2,13,x[]
507,3,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x[]
507,4,2,x^2,3,x^2 + 2*x + 1,5,x^2 - 12,7,x^2 - 3,11,x^2 - 12,13,x^2[]
507,5,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 12,11,x^2 - 12,13,x^2[]
507,6,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 + 3*x - 2,7,x^2 + 3*x - 2,11,x^2 + 4*x
+ 4,13,x^2[]
507,7,2,x^2 + x - 4,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 - 3*x - 2,11,x^2 - 4*x
+ 4,13,x^2[]
507,8,2,x^2 - 2*x - 1,3,x^2 - 2*x + 1,5,x^2 - 8,7,x^2 - 8,11,x^2 - 4*x +
4,13,x^2[]
507,9,2,x^3 + 3*x^2 - 4*x - 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 6*x^2 + 5*x -
13,7,x^3 + 2*x^2 - x - 1,11,x^3 + 5*x^2 - 8*x - 41,13,x^3[]
507,10,2,x^3 - 3*x^2 - 4*x + 13,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 6*x^2 + 5*x +
13,7,x^3 - 2*x^2 - x + 1,11,x^3 - 5*x^2 - 8*x + 41,13,x^3[]
507,11,2,x^3 - x^2 - 2*x + 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 4*x^2 + 3*x +
1,7,x^3 - 10*x^2 + 31*x - 29,11,x^3 + x^2 - 30*x - 43,13,x^3[]
507,12,2,x^3 + x^2 - 2*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 4*x^2 + 3*x -
1,7,x^3 + 10*x^2 + 31*x + 29,11,x^3 - x^2 - 30*x + 43,13,x^3[]
508,1,2,x^2,3,x^2 - 4*x + 4,5,x^2 - 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 5*x +
5,13,x^2 - 7*x + 11[]
508,2,2,x^2,3,x^2 + 2*x - 4,5,x^2 + 4*x + 4,7,x^2 - 20,11,x^2 - x - 11,13,x^2 +
5*x - 5[]
508,3,2,x^3,3,x^3 - x^2 - 6*x - 3,5,x^3 - 4*x^2 + x + 3,7,x^3 - 7*x^2 + 12*x -
3,11,x^3 - 2*x^2 - 5*x + 9,13,x^3 + 7*x^2 + 10*x + 3[]
508,4,2,x^3,3,x^3 + 3*x^2 - 1,5,x^3 - 9*x + 9,7,x^3 + 3*x^2 - 6*x - 17,11,x^3 +
6*x^2 - 9*x - 51,13,x^3 + 3*x^2 - 6*x - 17[]
509,1,2,x^14 + 3*x^13 - 11*x^12 - 36*x^11 + 43*x^10 + 161*x^9 - 70*x^8 - 337*x^7
+ 29*x^6 + 336*x^5 + 40*x^4 - 139*x^3 - 36*x^2 + 12*x + 3,3,x^14 + 5*x^13 -
11*x^12 - 81*x^11 + 8*x^10 + 438*x^9 + 183*x^8 - 1032*x^7 - 579*x^6 + 1074*x^5 +
579*x^4 - 417*x^3 - 172*x^2 + 29*x + 11,5,x^14 + 5*x^13 - 17*x^12 - 121*x^11 -
3*x^10 + 866*x^9 + 897*x^8 - 2207*x^7 - 3776*x^6 + 1189*x^5 + 4603*x^4 + 984*x^3
- 1708*x^2 - 736*x - 16,7,x^14 + 17*x^13 + 96*x^12 + 61*x^11 - 1535*x^10 -
6288*x^9 - 6227*x^8 + 16783*x^7 + 47959*x^6 + 26599*x^5 - 43785*x^4 - 69420*x^3
- 33088*x^2 - 4384*x - 64,11,x^14 + 20*x^13 + 129*x^12 + 28*x^11 - 3389*x^10 -
14314*x^9 - 2747*x^8 + 135745*x^7 + 385001*x^6 + 194812*x^5 - 1097552*x^4 -
2779576*x^3 - 3033711*x^2 - 1660621*x - 371677,13,x^14 + 6*x^13 - 70*x^12 -
566*x^11 + 780*x^10 + 15417*x^9 + 23838*x^8 - 122059*x^7 - 422348*x^6 -
172234*x^5 + 768087*x^4 + 624287*x^3 - 531991*x^2 - 344123*x + 199459[]
509,2,2,x^28 - 3*x^27 - 44*x^26 + 135*x^25 + 847*x^24 - 2674*x^23 - 9369*x^22 +
30699*x^21 + 65714*x^20 - 226429*x^19 - 303558*x^18 + 1123948*x^17 + 922806*x^16
- 3822074*x^15 - 1752519*x^14 + 8879314*x^13 + 1675588*x^12 - 13751763*x^11 +
382971*x^10 + 13397267*x^9 - 2958134*x^8 - 7169500*x^7 + 3056380*x^6 +
1305763*x^5 - 1072947*x^4 + 245723*x^3 - 24485*x^2 + 1114*x - 19,3,x^28 - 5*x^27
- 48*x^26 + 272*x^25 + 931*x^24 - 6405*x^23 - 8850*x^22 + 85759*x^21 +
31965*x^20 - 721317*x^19 + 164032*x^18 + 3972999*x^17 - 2503752*x^16 -
14475994*x^15 + 13508475*x^14 + 34330526*x^13 - 41204799*x^12 - 50312318*x^11 +
75928604*x^10 + 39824769*x^9 - 82931046*x^8 - 9371818*x^7 + 49394521*x^6 -
6602510*x^5 - 13320545*x^4 + 3321297*x^3 + 1196222*x^2 - 267183*x - 31583,5,x^28
- x^27 - 86*x^26 + 100*x^25 + 3226*x^24 - 4251*x^23 - 69315*x^22 + 101474*x^21 +
941574*x^20 - 1508877*x^19 - 8418071*x^18 + 14621274*x^17 + 49979838*x^16 -
93690681*x^15 - 194106206*x^14 + 394225378*x^13 + 473294393*x^12 -
1060961763*x^11 - 669570897*x^10 + 1744938012*x^9 + 465995781*x^8 -
1643052709*x^7 - 73313109*x^6 + 799280568*x^5 - 66191620*x^4 - 163204400*x^3 +
24714384*x^2 + 6775680*x - 395200,7,x^28 - 19*x^27 + 59*x^26 + 1046*x^25 -
7773*x^24 - 12799*x^23 + 266239*x^22 - 328866*x^21 - 4320998*x^20 +
12180077*x^19 + 36055653*x^18 - 165902683*x^17 - 133267136*x^16 +
1240417261*x^15 - 83325840*x^14 - 5674708476*x^13 + 2619605547*x^12 +
16832782791*x^11 - 10032388939*x^10 - 33338640274*x^9 + 18249500769*x^8 +
43742965431*x^7 - 16307228095*x^6 - 35600041583*x^5 + 5188671857*x^4 +
15282505552*x^3 + 865161736*x^2 - 2359400544*x - 427287872,11,x^28 - 24*x^27 +
109*x^26 + 1716*x^25 - 17505*x^24 - 16702*x^23 + 774057*x^22 - 1728287*x^21 -
15056563*x^20 + 66368896*x^19 + 114572412*x^18 - 1020245916*x^17 +
300125641*x^16 + 7751456251*x^15 - 10332794825*x^14 - 29149056508*x^13 +
66040834520*x^12 + 42954791184*x^11 - 195283700736*x^10 + 32381865088*x^9 +
287532490752*x^8 - 180086084096*x^7 - 188919045888*x^6 + 200298798080*x^5 +
28612415488*x^4 - 81634443264*x^3 + 12479713280*x^2 + 11091165184*x -
3179560960,13,x^28 - 8*x^27 - 186*x^26 + 1570*x^25 + 14590*x^24 - 133651*x^23 -
620848*x^22 + 6506217*x^21 + 14924456*x^20 - 200543250*x^19 - 167804839*x^18 +
4081257155*x^17 - 801119881*x^16 - 55212568969*x^15 + 56352951195*x^14 +
482890261616*x^13 - 864977589548*x^12 - 2496581876256*x^11 + 6925120183312*x^10
+ 5504434047296*x^9 - 30250690896192*x^8 + 8697521814528*x^7 +
63084344508672*x^6 - 63829683296256*x^5 - 35153013180416*x^4 +
78367682740224*x^3 - 20830072713216*x^2 - 18202017693696*x + 8555162042368[]

Total time: 11.839 seconds, Total memory usage: 5.01MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:47:52 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [510..513] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 14:47:28 on modular  [Seed = 217676365]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
510,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x - 4[]
510,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 4,13,x[]
510,3,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x,13,x - 4[]
510,4,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 4,13,x + 2[]
510,5,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x + 2[]
510,6,2,x - 1,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[]
510,7,2,x - 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x + 4[]
510,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 24,11,x^2,13,x^2 -
4*x - 20[]
511,1,2,x^3 - x^2 - 4*x - 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 3*x^2 + 3*x +
1,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 3*x^2 - 36*x + 103[]
511,2,2,x^3 - 5*x + 1,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 3*x^2 - 2*x + 3,7,x^3 -
3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 - 5*x^2 - 14*x + 73[]
511,3,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 7*x - 1,3,x^6 - x^5 - 6*x^4 + 4*x^3 +
8*x^2 - 1,5,x^6 + 2*x^5 - 15*x^4 - 29*x^3 + 46*x^2 + 59*x - 59,7,x^6 + 6*x^5 +
15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 9*x^5 - 135*x^3 + 729*x - 729,13,x^6
+ 4*x^5 - 27*x^4 - 104*x^3 + 35*x^2 + 301*x + 131[]
511,4,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 11*x + 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 -
10*x^2 + 4*x + 3,5,x^6 + 6*x^5 + 5*x^4 - 15*x^3 - 4*x^2 + 11*x - 3,7,x^6 - 6*x^5
+ 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 + 5*x^5 - 12*x^4 - 59*x^3 + 52*x^2 +
109*x - 93,13,x^6 - 35*x^4 - 6*x^3 + 285*x^2 + 59*x + 3[]
511,5,2,x^9 - 2*x^8 - 10*x^7 + 18*x^6 + 33*x^5 - 50*x^4 - 40*x^3 + 45*x^2 + 17*x
- 11,3,x^9 + x^8 - 22*x^7 - 30*x^6 + 138*x^5 + 250*x^4 - 167*x^3 - 480*x^2 -
144*x + 64,5,x^9 - 7*x^8 - 7*x^7 + 139*x^6 - 203*x^5 - 448*x^4 + 1101*x^3 -
283*x^2 - 401*x + 59,7,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 +
84*x^3 - 36*x^2 + 9*x - 1,11,x^9 + 5*x^8 - 82*x^7 - 463*x^6 + 1854*x^5 +
13253*x^4 - 3763*x^3 - 114484*x^2 - 137676*x + 35704,13,x^9 + x^8 - 47*x^7 -
32*x^6 + 685*x^5 + 215*x^4 - 3440*x^3 + 406*x^2 + 4081*x - 341[]
511,6,2,x^10 - 4*x^9 - 9*x^8 + 50*x^7 + 4*x^6 - 194*x^5 + 123*x^4 + 224*x^3 -
231*x^2 + 11*x + 27,3,x^10 + x^9 - 34*x^8 - 28*x^7 + 440*x^6 + 278*x^5 -
2679*x^4 - 1138*x^3 + 7540*x^2 + 1576*x - 7520,5,x^10 - x^9 - 39*x^8 + 45*x^7 +
509*x^6 - 680*x^5 - 2299*x^4 + 3603*x^3 + 925*x^2 - 2281*x + 554,7,x^10 + 10*x^9
+ 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x +
1,11,x^10 - 5*x^9 - 28*x^8 + 125*x^7 + 328*x^6 - 943*x^5 - 1957*x^4 + 1574*x^3 +
4044*x^2 + 2008*x + 288,13,x^10 + x^9 - 71*x^8 - 4*x^7 + 1351*x^6 - 1271*x^5 -
3902*x^4 + 2902*x^3 + 3459*x^2 - 1357*x - 1094[]
512,1,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 + 8*x + 16,11,x^2 - 2,13,x^2 - 8[]
512,2,2,x^2,3,x^2 - 2,5,x^2 + 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 + 12*x + 36[]
512,3,2,x^2,3,x^2 + 4*x + 2,5,x^2,7,x^2,11,x^2 + 4*x - 14,13,x^2[]
512,4,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2,13,x^2 - 8[]
512,5,2,x^2,3,x^2 - 2,5,x^2 - 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 - 12*x + 36[]
512,6,2,x^2,3,x^2 - 4*x + 2,5,x^2,7,x^2,11,x^2 - 4*x - 14,13,x^2[]
512,7,2,x^4,3,x^4 - 12*x^2 + 36,5,x^4 - 24*x^2 + 144,7,x^4 - 16*x^2 + 64,11,x^4
- 12*x^2 + 36,13,x^4 - 24*x^2 + 144[]

Errors: /home/mfd/gomagma: line 2: 11805 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:48:31 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [510..512] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 14:48:11 on modular  [Seed = 885080670]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
510,1,2,x + 1,3,x + 1,5,x + 1,7,x - 2,11,x + 4,13,x - 4[]
510,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 4,13,x[]
510,3,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x,13,x - 4[]
510,4,2,x - 1,3,x + 1,5,x + 1,7,x + 4,11,x + 4,13,x + 2[]
510,5,2,x - 1,3,x + 1,5,x - 1,7,x,11,x - 4,13,x + 2[]
510,6,2,x - 1,3,x - 1,5,x + 1,7,x,11,x - 4,13,x - 2[]
510,7,2,x - 1,3,x - 1,5,x - 1,7,x - 2,11,x,13,x + 4[]
510,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 24,11,x^2,13,x^2 -
4*x - 20[]
511,1,2,x^3 - x^2 - 4*x - 1,3,x^3,5,x^3 + x^2 - 4*x + 1,7,x^3 + 3*x^2 + 3*x +
1,11,x^3 - 4*x^2 - 12*x + 40,13,x^3 - 3*x^2 - 36*x + 103[]
511,2,2,x^3 - 5*x + 1,3,x^3 - 6*x^2 + 12*x - 8,5,x^3 - 3*x^2 - 2*x + 3,7,x^3 -
3*x^2 + 3*x - 1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 - 5*x^2 - 14*x + 73[]
511,3,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 7*x - 1,3,x^6 - x^5 - 6*x^4 + 4*x^3 +
8*x^2 - 1,5,x^6 + 2*x^5 - 15*x^4 - 29*x^3 + 46*x^2 + 59*x - 59,7,x^6 + 6*x^5 +
15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,11,x^6 + 9*x^5 - 135*x^3 + 729*x - 729,13,x^6
+ 4*x^5 - 27*x^4 - 104*x^3 + 35*x^2 + 301*x + 131[]
511,4,2,x^6 + 3*x^5 - 3*x^4 - 12*x^3 + 11*x + 3,3,x^6 + 5*x^5 + 4*x^4 - 10*x^3 -
10*x^2 + 4*x + 3,5,x^6 + 6*x^5 + 5*x^4 - 15*x^3 - 4*x^2 + 11*x - 3,7,x^6 - 6*x^5
+ 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,11,x^6 + 5*x^5 - 12*x^4 - 59*x^3 + 52*x^2 +
109*x - 93,13,x^6 - 35*x^4 - 6*x^3 + 285*x^2 + 59*x + 3[]
511,5,2,x^9 - 2*x^8 - 10*x^7 + 18*x^6 + 33*x^5 - 50*x^4 - 40*x^3 + 45*x^2 + 17*x
- 11,3,x^9 + x^8 - 22*x^7 - 30*x^6 + 138*x^5 + 250*x^4 - 167*x^3 - 480*x^2 -
144*x + 64,5,x^9 - 7*x^8 - 7*x^7 + 139*x^6 - 203*x^5 - 448*x^4 + 1101*x^3 -
283*x^2 - 401*x + 59,7,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 +
84*x^3 - 36*x^2 + 9*x - 1,11,x^9 + 5*x^8 - 82*x^7 - 463*x^6 + 1854*x^5 +
13253*x^4 - 3763*x^3 - 114484*x^2 - 137676*x + 35704,13,x^9 + x^8 - 47*x^7 -
32*x^6 + 685*x^5 + 215*x^4 - 3440*x^3 + 406*x^2 + 4081*x - 341[]
511,6,2,x^10 - 4*x^9 - 9*x^8 + 50*x^7 + 4*x^6 - 194*x^5 + 123*x^4 + 224*x^3 -
231*x^2 + 11*x + 27,3,x^10 + x^9 - 34*x^8 - 28*x^7 + 440*x^6 + 278*x^5 -
2679*x^4 - 1138*x^3 + 7540*x^2 + 1576*x - 7520,5,x^10 - x^9 - 39*x^8 + 45*x^7 +
509*x^6 - 680*x^5 - 2299*x^4 + 3603*x^3 + 925*x^2 - 2281*x + 554,7,x^10 + 10*x^9
+ 45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x +
1,11,x^10 - 5*x^9 - 28*x^8 + 125*x^7 + 328*x^6 - 943*x^5 - 1957*x^4 + 1574*x^3 +
4044*x^2 + 2008*x + 288,13,x^10 + x^9 - 71*x^8 - 4*x^7 + 1351*x^6 - 1271*x^5 -
3902*x^4 + 2902*x^3 + 3459*x^2 - 1357*x - 1094[]
512,1,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 + 8*x + 16,11,x^2 - 2,13,x^2 - 8[]
512,2,2,x^2,3,x^2 - 2,5,x^2 + 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 + 12*x + 36[]
512,3,2,x^2,3,x^2 + 4*x + 2,5,x^2,7,x^2,11,x^2 + 4*x - 14,13,x^2[]
512,4,2,x^2,3,x^2 - 2,5,x^2 - 8,7,x^2 - 8*x + 16,11,x^2 - 2,13,x^2 - 8[]
512,5,2,x^2,3,x^2 - 2,5,x^2 - 4*x + 4,7,x^2 - 8,11,x^2 - 18,13,x^2 - 12*x + 36[]
512,6,2,x^2,3,x^2 - 4*x + 2,5,x^2,7,x^2,11,x^2 - 4*x - 14,13,x^2[]
512,7,2,x^4,3,x^4 - 12*x^2 + 36,5,x^4 - 24*x^2 + 144,7,x^4 - 16*x^2 + 64,11,x^4
- 12*x^2 + 36,13,x^4 - 24*x^2 + 144[]

Total time: 19.739 seconds, Total memory usage: 7.03MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 14:52:43 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [513..515] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 14:52:29 on modular  [Seed = 668095051]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
513,1,2,x - 1,3,x,5,x,7,x + 2,11,x + 5,13,x + 4[]
513,2,2,x + 1,3,x,5,x,7,x + 2,11,x - 5,13,x + 4[]
513,3,2,x^2 - 3,3,x^2,5,x^2 - 12,7,x^2 + 8*x + 16,11,x^2 - 27,13,x^2 + 8*x +
16[]
513,4,2,x^3 + x^2 - 4*x - 1,3,x^3,5,x^3 + 5*x^2 + 4*x - 3,7,x^3 - x^2 - 6*x -
3,11,x^3 + 8*x^2 + 15*x - 3,13,x^3 + x^2 - 6*x + 3[]
513,5,2,x^3 - 3*x^2 + 3,3,x^3,5,x^3 - 3*x^2 + 3,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 -
27*x + 27,13,x^3 + 3*x^2 - 24*x + 1[]
513,6,2,x^3 - x^2 - 4*x + 1,3,x^3,5,x^3 - 5*x^2 + 4*x + 3,7,x^3 - x^2 - 6*x -
3,11,x^3 - 8*x^2 + 15*x + 3,13,x^3 + x^2 - 6*x + 3[]
513,7,2,x^3 + 3*x^2 - 3,3,x^3,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 - 6*x + 1,11,x^3 -
27*x - 27,13,x^3 + 3*x^2 - 24*x + 1[]
513,8,2,x^4 - 6*x^2 + 3,3,x^4,5,x^4 - 12*x^2 + 12,7,x^4 - 8*x^3 + 12*x^2 + 16*x
+ 4,11,x^4 - 18*x^2 + 27,13,x^4 - 8*x^3 + 24*x^2 - 32*x + 16[]
513,9,2,x^4 - 8*x^2 + 13,3,x^4,5,x^4 - 20*x^2 + 52,7,x^4 - 12*x^3 + 48*x^2 -
72*x + 36,11,x^4 - 24*x^2 + 117,13,x^4 - 24*x^2 + 144[]
514,1,2,x - 1,3,x,5,x + 2,7,x + 4,11,x + 4,13,x + 2[]
514,2,2,x - 1,3,x + 2,5,x + 2,7,x - 2,11,x + 4,13,x + 2[]
514,3,2,x^2 + 2*x + 1,3,x^2 - 6,5,x^2 - 6,7,x^2 + 4*x + 4,11,x^2,13,x^2 + 4*x -
20[]
514,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 - 4*x^2 + 2*x +
2,7,x^3 - 6*x^2 + 8*x - 2,11,x^3 - 10*x^2 + 28*x - 20,13,x^3 + 6*x^2 - 4*x - 8[]
514,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 - 8*x^3 + 6*x - 2,5,x^5 +
4*x^4 - 8*x^3 - 48*x^2 - 48*x - 8,7,x^5 + 4*x^4 - 6*x^3 - 20*x^2 + 18*x +
2,11,x^5 + 14*x^4 + 52*x^3 - 56*x^2 - 592*x - 688,13,x^5 - 2*x^4 - 28*x^3 -
16*x^2 + 64*x - 16[]
514,6,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 +
9*x - 1,3,x^9 - 2*x^8 - 20*x^7 + 40*x^6 + 116*x^5 - 226*x^4 - 204*x^3 + 376*x^2
+ 96*x - 176,5,x^9 - 4*x^8 - 22*x^7 + 86*x^6 + 174*x^5 - 612*x^4 - 576*x^3 +
1440*x^2 + 640*x - 16,7,x^9 + 4*x^8 - 26*x^7 - 74*x^6 + 282*x^5 + 350*x^4 -
1220*x^3 - 68*x^2 + 820*x + 244,11,x^9 - 12*x^8 + 16*x^7 + 252*x^6 - 604*x^5 -
2176*x^4 + 4976*x^3 + 10144*x^2 - 13248*x - 22208,13,x^9 - 6*x^8 - 52*x^7 +
264*x^6 + 976*x^5 - 3280*x^4 - 6976*x^3 + 8960*x^2 + 3840*x - 2816[]
515,1,2,x^4 + x^3 - 3*x^2 - x + 1,3,x^4 + x^3 - 3*x^2 - x + 1,5,x^4 - 4*x^3 +
6*x^2 - 4*x + 1,7,x^4 + 3*x^3 - 7*x^2 - 27*x - 19,11,x^4 + 9*x^3 + 22*x^2 + 6*x
- 19,13,x^4 + 11*x^3 + 35*x^2 + 13*x - 61[]
515,2,2,x^8 + 2*x^7 - 9*x^6 - 16*x^5 + 25*x^4 + 36*x^3 - 21*x^2 - 18*x + 9,3,x^8
+ 3*x^7 - 13*x^6 - 37*x^5 + 43*x^4 + 98*x^3 - 68*x^2 - 72*x + 48,5,x^8 + 8*x^7 +
28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 11*x^7 + 28*x^6 -
58*x^5 - 247*x^4 + 30*x^3 + 406*x^2 + 189*x + 3,11,x^8 - 5*x^7 - 30*x^6 +
116*x^5 + 363*x^4 - 662*x^3 - 1940*x^2 - 72*x + 1296,13,x^8 + 23*x^7 + 204*x^6 +
860*x^5 + 1657*x^4 + 900*x^3 - 720*x^2 - 243*x + 81[]
515,3,2,x^9 - x^8 - 14*x^7 + 12*x^6 + 64*x^5 - 45*x^4 - 107*x^3 + 64*x^2 + 52*x
- 24,3,x^9 - 3*x^8 - 11*x^7 + 34*x^6 + 37*x^5 - 113*x^4 - 57*x^3 + 121*x^2 +
44*x - 5,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 +
9*x + 1,7,x^9 - 9*x^8 - 5*x^7 + 267*x^6 - 745*x^5 - 432*x^4 + 3620*x^3 -
1696*x^2 - 4544*x + 2816,11,x^9 - x^8 - 34*x^7 + 42*x^6 + 325*x^5 - 374*x^4 -
1072*x^3 + 1176*x^2 + 1088*x - 1152,13,x^9 - 23*x^8 + 197*x^7 - 691*x^6 +
115*x^5 + 5478*x^4 - 10800*x^3 - 4680*x^2 + 27840*x - 17600[]
515,4,2,x^14 + x^13 - 22*x^12 - 18*x^11 + 188*x^10 + 120*x^9 - 778*x^8 - 354*x^7
+ 1574*x^6 + 400*x^5 - 1345*x^4 - 43*x^3 + 284*x^2 + 20*x - 8,3,x^14 - x^13 -
33*x^12 + 36*x^11 + 411*x^10 - 499*x^9 - 2353*x^8 + 3237*x^7 + 5790*x^6 -
9331*x^5 - 3658*x^4 + 8340*x^3 - 856*x^2 - 784*x - 64,5,x^14 - 14*x^13 + 91*x^12
- 364*x^11 + 1001*x^10 - 2002*x^9 + 3003*x^8 - 3432*x^7 + 3003*x^6 - 2002*x^5 +
1001*x^4 - 364*x^3 + 91*x^2 - 14*x + 1,7,x^14 - 9*x^13 - 22*x^12 + 384*x^11 -
227*x^10 - 6064*x^9 + 10238*x^8 + 41915*x^7 - 103699*x^6 - 102808*x^5 +
416876*x^4 - 89376*x^3 - 556032*x^2 + 516096*x - 131072,11,x^14 - 3*x^13 -
94*x^12 + 248*x^11 + 3407*x^10 - 8104*x^9 - 60376*x^8 + 131624*x^7 + 543632*x^6
- 1088576*x^5 - 2309824*x^4 + 4184960*x^3 + 3551744*x^2 - 5865472*x +
524288,13,x^14 - 21*x^13 + 108*x^12 + 518*x^11 - 5725*x^10 + 1638*x^9 +
101086*x^8 - 159853*x^7 - 827345*x^6 + 1778544*x^5 + 3078652*x^4 - 7484472*x^3 -
3309040*x^2 + 9757248*x - 3492224[]

Total time: 13.389 seconds, Total memory usage: 4.96MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 15:38:37 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [516..518] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 15:38:17 on modular  [Seed = 2340348323]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
516,1,2,x,3,x + 1,5,x - 3,7,x + 1,11,x + 1,13,x - 7[]
516,2,2,x,3,x + 1,5,x + 2,7,x - 2,11,x + 3,13,x + 1[]
516,3,2,x,3,x - 1,5,x,7,x,11,x + 2,13,x - 6[]
516,4,2,x,3,x - 1,5,x - 3,7,x - 5,11,x + 3,13,x + 1[]
516,5,2,x^2,3,x^2 + 2*x + 1,5,x^2 + x - 8,7,x^2 + x - 8,11,x^2 - 5*x - 2,13,x^2
+ 3*x - 6[]
516,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 - x - 14,7,x^2 + x - 14,11,x^2 - 10*x +
25,13,x^2 + 2*x + 1[]
517,1,2,x - 2,3,x + 1,5,x - 3,7,x - 4,11,x + 1,13,x[]
517,2,2,x,3,x - 3,5,x - 3,7,x + 2,11,x - 1,13,x + 2[]
517,3,2,x - 2,3,x + 1,5,x + 3,7,x + 2,11,x - 1,13,x[]
517,4,2,x^2 - 2,3,x^2 - 6*x + 9,5,x^2 + 2*x - 1,7,x^2 - 2,11,x^2 + 2*x +
1,13,x^2 - 2[]
517,5,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 - 2,7,x^2 + 6*x + 9,11,x^2 + 2*x +
1,13,x^2 + 2*x - 1[]
517,6,2,x^2 - 2*x - 1,3,x^2 - 4*x + 2,5,x^2 + 4*x + 2,7,x^2 + 2*x - 7,11,x^2 -
2*x + 1,13,x^2 - 2*x - 1[]
517,7,2,x^2 + 2*x - 2,3,x^2 + 2*x + 1,5,x^2 - 3,7,x^2 - 2*x - 2,11,x^2 - 2*x +
1,13,x^2 + 6*x + 6[]
517,8,2,x^3 - x^2 - 5*x + 1,3,x^3 - 4*x + 2,5,x^3 - 2*x^2 - 2*x + 2,7,x^3 -
5*x^2 + 5*x + 1,11,x^3 + 3*x^2 + 3*x + 1,13,x^3 - 5*x^2 - 13*x + 25[]
517,9,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + 4*x^2 - 2*x - 14,5,x^3 + 2*x^2 - 4*x -
6,7,x^3 + x^2 - 19*x - 37,11,x^3 - 3*x^2 + 3*x - 1,13,x^3 + 3*x^2 - 5*x - 3[]
517,10,2,x^10 + 6*x^9 + 3*x^8 - 40*x^7 - 56*x^6 + 79*x^5 + 148*x^4 - 41*x^3 -
112*x^2 - 8*x + 4,3,x^10 + 7*x^9 + 6*x^8 - 48*x^7 - 78*x^6 + 92*x^5 + 139*x^4 -
99*x^3 - 30*x^2 + 20*x - 2,5,x^10 + 3*x^9 - 27*x^8 - 85*x^7 + 212*x^6 + 734*x^5
- 490*x^4 - 2096*x^3 + 384*x^2 + 1776*x - 416,7,x^10 + 9*x^9 - 182*x^7 - 262*x^6
+ 1254*x^5 + 2215*x^4 - 3393*x^3 - 5552*x^2 + 3216*x + 4036,11,x^10 + 10*x^9 +
45*x^8 + 120*x^7 + 210*x^6 + 252*x^5 + 210*x^4 + 120*x^3 + 45*x^2 + 10*x +
1,13,x^10 + 5*x^9 - 71*x^8 - 353*x^7 + 1646*x^6 + 8676*x^5 - 12964*x^4 -
85184*x^3 + 4096*x^2 + 284672*x + 212992[]
517,11,2,x^10 - 3*x^9 - 13*x^8 + 41*x^7 + 54*x^6 - 189*x^5 - 75*x^4 + 345*x^3 +
x^2 - 206*x + 36,3,x^10 - 2*x^9 - 18*x^8 + 32*x^7 + 114*x^6 - 182*x^5 - 295*x^4
+ 420*x^3 + 256*x^2 - 298*x - 24,5,x^10 - 4*x^9 - 31*x^8 + 134*x^7 + 242*x^6 -
1374*x^5 + 204*x^4 + 3840*x^3 - 3792*x^2 + 704*x + 192,7,x^10 - 7*x^9 - 14*x^8 +
150*x^7 + 26*x^6 - 970*x^5 - 21*x^4 + 2351*x^3 + 370*x^2 - 1900*x - 736,11,x^10
- 10*x^9 + 45*x^8 - 120*x^7 + 210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 -
10*x + 1,13,x^10 + 11*x^9 - 13*x^8 - 487*x^7 - 936*x^6 + 5120*x^5 + 13272*x^4 -
18944*x^3 - 47104*x^2 + 28672*x + 32768[]
518,1,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 - 8,7,x^2 + 2*x + 1,11,x^2 - 8,13,x^2 -
8*x + 16[]
518,2,2,x^2 - 2*x + 1,3,x^2 - 2*x - 2,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x -
8,13,x^2 - 4*x - 8[]
518,3,2,x^2 - 2*x + 1,3,x^2 + 3*x + 1,5,x^2 + 3*x + 1,7,x^2 + 2*x + 1,11,x^2 +
3*x + 1,13,x^2 + 7*x + 1[]
518,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 5*x + 2,5,x^3 + 3*x^2 - x - 2,7,x^3
+ 3*x^2 + 3*x + 1,11,x^3 - 5*x^2 - 31*x + 148,13,x^3 + 11*x^2 + 35*x + 26[]
518,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 7*x + 8,5,x^3 - 3*x^2 - 7*x +
20,7,x^3 - 3*x^2 + 3*x - 1,11,x^3 + 3*x^2 - 7*x - 20,13,x^3 - 11*x^2 + 33*x -
28[]
518,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - x^4 - 11*x^3 + 12*x^2 +
24*x - 28,5,x^5 + 3*x^4 - 15*x^3 - 20*x^2 + 80*x - 48,7,x^5 - 5*x^4 + 10*x^3 -
10*x^2 + 5*x - 1,11,x^5 - 5*x^4 - 23*x^3 + 104*x^2 + 32*x - 96,13,x^5 - 5*x^4 -
31*x^3 + 164*x^2 - 104*x + 16[]

Total time: 19.549 seconds, Total memory usage: 6.30MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 15:43:29 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [519..521] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 15:43:14 on modular  [Seed = 2740374224]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
519,1,2,x^3 - 3*x - 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 -
3,11,x^3 - 3*x^2 - 9*x + 3,13,x^3 + 3*x^2 - 3[]
519,2,2,x^3 + 2*x^2 - x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + 5*x^2 + 6*x +
1,7,x^3 + x^2 - 2*x - 1,11,x^3 + 9*x^2 + 27*x + 27,13,x^3 + 3*x^2 - 4*x + 1[]
519,3,2,x^11 - 3*x^10 - 12*x^9 + 39*x^8 + 43*x^7 - 165*x^6 - 45*x^5 + 271*x^4 -
29*x^3 - 134*x^2 + 60*x - 7,3,x^11 - 11*x^10 + 55*x^9 - 165*x^8 + 330*x^7 -
462*x^6 + 462*x^5 - 330*x^4 + 165*x^3 - 55*x^2 + 11*x - 1,5,x^11 - 9*x^10 +
7*x^9 + 150*x^8 - 451*x^7 - 80*x^6 + 1582*x^5 - 1057*x^4 - 951*x^3 + 439*x^2 +
44*x + 1,7,x^11 + 3*x^10 - 48*x^9 - 95*x^8 + 850*x^7 + 712*x^6 - 6576*x^5 +
672*x^4 + 19328*x^3 - 14208*x^2 - 7680*x + 6400,11,x^11 - 13*x^10 + 26*x^9 +
254*x^8 - 882*x^7 - 1402*x^6 + 5473*x^5 + 5337*x^4 - 9513*x^3 - 11475*x^2 -
2673*x + 243,13,x^11 + x^10 - 75*x^9 + 38*x^8 + 1873*x^7 - 2994*x^6 - 16349*x^5
+ 39962*x^4 + 25166*x^3 - 114923*x^2 + 44392*x + 30524[]
519,4,2,x^12 + 2*x^11 - 19*x^10 - 37*x^9 + 128*x^8 + 244*x^7 - 352*x^6 - 664*x^5
+ 316*x^4 + 597*x^3 - 24*x^2 - 27*x + 1,3,x^12 + 12*x^11 + 66*x^10 + 220*x^9 +
495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x +
1,5,x^12 - x^11 - 49*x^10 + 42*x^9 + 919*x^8 - 688*x^7 - 8144*x^6 + 5699*x^5 +
33691*x^4 - 25057*x^3 - 52812*x^2 + 45721*x + 3682,7,x^12 - 3*x^11 - 62*x^10 +
191*x^9 + 1330*x^8 - 4400*x^7 - 10800*x^6 + 43744*x^5 + 11904*x^4 - 160512*x^3 +
147968*x^2 + 14592*x - 45056,11,x^12 + 7*x^11 - 70*x^10 - 518*x^9 + 1690*x^8 +
13518*x^7 - 17063*x^6 - 148531*x^5 + 86035*x^4 + 654861*x^3 - 379109*x^2 -
944217*x + 699092,13,x^12 - 13*x^11 - 29*x^10 + 956*x^9 - 1391*x^8 - 25788*x^7 +
70723*x^6 + 317924*x^5 - 1116722*x^4 - 1779475*x^3 + 7471394*x^2 + 3542620*x -
17962376[]
520,1,2,x,3,x,5,x + 1,7,x,11,x + 4,13,x + 1[]
520,2,2,x,3,x - 2,5,x - 1,7,x,11,x - 2,13,x - 1[]
520,3,2,x^2,3,x^2 + 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 12,11,x^2 - 2*x - 2,13,x^2 -
2*x + 1[]
520,4,2,x^2,3,x^2 - 6,5,x^2 - 2*x + 1,7,x^2 - 4*x + 4,11,x^2 + 4*x - 2,13,x^2 +
2*x + 1[]
520,5,2,x^2,3,x^2 - 2*x - 4,5,x^2 + 2*x + 1,7,x^2,11,x^2 - 6*x + 4,13,x^2 + 2*x
+ 1[]
520,6,2,x^2,3,x^2 + 2*x - 2,5,x^2 + 2*x + 1,7,x^2 - 12,11,x^2 + 6*x + 6,13,x^2 -
2*x + 1[]
520,7,2,x^2,3,x^2 + 4*x + 2,5,x^2 - 2*x + 1,7,x^2 + 4*x + 4,11,x^2 - 18,13,x^2 +
2*x + 1[]
521,1,2,x^14 + 2*x^13 - 13*x^12 - 25*x^11 + 63*x^10 + 115*x^9 - 142*x^8 -
242*x^7 + 151*x^6 + 238*x^5 - 65*x^4 - 104*x^3 + 2*x^2 + 17*x + 3,3,x^14 +
5*x^13 - 9*x^12 - 73*x^11 - 8*x^10 + 358*x^9 + 250*x^8 - 654*x^7 - 659*x^6 +
261*x^5 + 453*x^4 + 76*x^3 - 67*x^2 - 28*x - 3,5,x^14 + 3*x^13 - 27*x^12 -
92*x^11 + 203*x^10 + 917*x^9 - 126*x^8 - 3265*x^7 - 2489*x^6 + 3061*x^5 +
4750*x^4 + 1154*x^3 - 1150*x^2 - 742*x - 125,7,x^14 + 20*x^13 + 150*x^12 +
433*x^11 - 468*x^10 - 6502*x^9 - 16175*x^8 - 10267*x^7 + 20750*x^6 + 34650*x^5 +
2014*x^4 - 23989*x^3 - 9725*x^2 + 4904*x + 2705,11,x^14 + 14*x^13 + 27*x^12 -
415*x^11 - 1800*x^10 + 3153*x^9 + 25012*x^8 + 4014*x^7 - 128407*x^6 - 89151*x^5
+ 268529*x^4 + 194251*x^3 - 252739*x^2 - 114889*x + 91151,13,x^14 + 12*x^13 -
6*x^12 - 482*x^11 - 596*x^10 + 8095*x^9 + 11752*x^8 - 73271*x^7 - 83440*x^6 +
370837*x^5 + 224073*x^4 - 947320*x^3 - 71804*x^2 + 867673*x - 233169[]
521,2,2,x^29 - x^28 - 50*x^27 + 49*x^26 + 1112*x^25 - 1061*x^24 - 14511*x^23 +
13387*x^22 + 123412*x^21 - 109286*x^20 - 718385*x^19 + 606113*x^18 +
2924033*x^17 - 2333576*x^16 - 8348401*x^15 + 6263323*x^14 + 16508066*x^13 -
11605772*x^12 - 21923563*x^11 + 14498124*x^10 + 18478199*x^9 - 11710480*x^8 -
8913548*x^7 + 5683110*x^6 + 1973213*x^5 - 1428489*x^4 - 75206*x^3 + 126742*x^2 -
12580*x - 647,3,x^29 - 3*x^28 - 57*x^27 + 175*x^26 + 1416*x^25 - 4478*x^24 -
20174*x^23 + 66310*x^22 + 182503*x^21 - 631731*x^20 - 1095179*x^19 +
4074814*x^18 + 4405585*x^17 - 18242234*x^16 - 11594711*x^15 + 57146460*x^14 +
18034386*x^13 - 124534362*x^12 - 9245398*x^11 + 184711504*x^10 - 21908590*x^9 -
178114686*x^8 + 50841804*x^7 + 101705076*x^6 - 45772420*x^5 - 27285314*x^4 +
18445740*x^3 + 700184*x^2 - 2236414*x + 374662,5,x^29 + x^28 - 93*x^27 - 66*x^26
+ 3823*x^25 + 1579*x^24 - 91624*x^23 - 10829*x^22 + 1420077*x^21 - 238337*x^20 -
14904844*x^19 + 6557662*x^18 + 107682638*x^17 - 74932098*x^16 - 532623473*x^15 +
498953610*x^14 + 1754721156*x^13 - 2051596488*x^12 - 3637268440*x^11 +
5122275040*x^10 + 4290498968*x^9 - 7224726888*x^8 - 2565373648*x^7 +
5076815504*x^6 + 1157607376*x^5 - 1770925392*x^4 - 462474672*x^3 + 226762208*x^2
+ 79303760*x + 3136144,7,x^29 - 26*x^28 + 208*x^27 + 289*x^26 - 13280*x^25 +
53478*x^24 + 204431*x^23 - 2005201*x^22 + 1462262*x^21 + 29700020*x^20 -
81771174*x^19 - 191231711*x^18 + 1094992267*x^17 - 38121866*x^16 -
7383820445*x^15 + 8959022328*x^14 + 25477695022*x^13 - 61134642580*x^12 -
26202204398*x^11 + 187428285440*x^10 - 101854421698*x^9 - 241529892404*x^8 +
332867888996*x^7 - 13818864698*x^6 - 248812651082*x^5 + 209175022120*x^4 -
75571529386*x^3 + 12084102956*x^2 - 455251218*x - 47545450,11,x^29 - 14*x^28 -
93*x^27 + 2129*x^26 + 140*x^25 - 135155*x^24 + 331784*x^23 + 4556450*x^22 -
19422179*x^21 - 83302355*x^20 + 551616537*x^19 + 627686815*x^18 -
9017563715*x^17 + 4657820187*x^16 + 85585238423*x^15 - 145901558052*x^14 -
420994270592*x^13 + 1314952125184*x^12 + 514875597056*x^11 - 5466825958272*x^10
+ 3891170455808*x^9 + 9141854047232*x^8 - 14919589138944*x^7 - 300972565504*x^6
+ 14214404550656*x^5 - 7807168249856*x^4 - 2711152517120*x^3 + 3185594138624*x^2
- 485356765184*x - 86829105152,13,x^29 - 10*x^28 - 162*x^27 + 1922*x^26 +
10072*x^25 - 159569*x^24 - 252918*x^23 + 7516917*x^22 - 2038966*x^21 -
221821171*x^20 + 321260227*x^19 + 4264114414*x^18 - 10043549048*x^17 -
53506778471*x^16 + 173919337229*x^15 + 418988055918*x^14 - 1892913448712*x^13 -
1698838015528*x^12 + 13244949039648*x^11 - 587911453592*x^10 -
57787247954956*x^9 + 42542040694952*x^8 + 141091798290056*x^7 -
198684083332764*x^6 - 127811810086032*x^5 + 375712136581416*x^4 -
117523168109860*x^3 - 208034047032508*x^2 + 186714211552040*x - 45824749347532[]

Total time: 14.729 seconds, Total memory usage: 5.61MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 18:54:53 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [522..525] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 18:54:30 on modular  [Seed = 2957315209]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
522,1,2,x + 1,3,x,5,x - 3,7,x + 5,11,x + 4,13,x + 6[]
522,2,2,x + 1,3,x,5,x - 2,7,x - 4,11,x,13,x - 2[]
522,3,2,x + 1,3,x,5,x + 3,7,x + 1,11,x,13,x - 2[]
522,4,2,x + 1,3,x,5,x - 1,7,x - 1,11,x - 2,13,x[]
522,5,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 6,13,x + 4[]
522,6,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 3,13,x + 1[]
522,7,2,x - 1,3,x,5,x + 2,7,x - 4,11,x,13,x - 2[]
522,8,2,x - 1,3,x,5,x - 3,7,x + 1,11,x,13,x - 2[]
522,9,2,x - 1,3,x,5,x + 3,7,x + 5,11,x - 4,13,x + 6[]
522,10,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 6,13,x[]
522,11,2,x - 1,3,x,5,x + 2,7,x,11,x - 4,13,x - 6[]
522,12,2,x - 1,3,x,5,x - 3,7,x + 2,11,x - 1,13,x - 3[]
522,13,2,x - 1,3,x,5,x - 3,7,x - 5,11,x + 6,13,x + 4[]
523,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2,13,x^2 +
x - 11[]
523,2,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 72*x^11 + 308*x^10 + 492*x^9 -
587*x^8 - 1283*x^7 + 418*x^6 + 1526*x^5 + 33*x^4 - 774*x^3 - 85*x^2 + 141*x +
8,3,x^15 + 3*x^14 - 17*x^13 - 50*x^12 + 111*x^11 + 312*x^10 - 349*x^9 - 897*x^8
+ 543*x^7 + 1180*x^6 - 401*x^5 - 623*x^4 + 181*x^3 + 114*x^2 - 33*x - 2,5,x^15 +
19*x^14 + 140*x^13 + 442*x^12 + 24*x^11 - 4077*x^10 - 11810*x^9 - 10832*x^8 +
8722*x^7 + 23778*x^6 + 9378*x^5 - 9987*x^4 - 8231*x^3 - 341*x^2 + 1043*x +
218,7,x^15 + x^14 - 65*x^13 - 71*x^12 + 1622*x^11 + 2079*x^10 - 19593*x^9 -
29759*x^8 + 114951*x^7 + 207182*x^6 - 263534*x^5 - 598861*x^4 + 4063*x^3 +
322280*x^2 + 37779*x - 2744,11,x^15 + 7*x^14 - 85*x^13 - 719*x^12 + 2007*x^11 +
26554*x^10 + 7728*x^9 - 410286*x^8 - 784569*x^7 + 2121922*x^6 + 7495618*x^5 +
1560600*x^4 - 15953890*x^3 - 15090096*x^2 + 3265879*x + 6017216,13,x^15 +
15*x^14 + 10*x^13 - 909*x^12 - 4293*x^11 + 12207*x^10 + 129405*x^9 + 140948*x^8
- 1181467*x^7 - 3470111*x^6 + 1369276*x^5 + 16369458*x^4 + 13960211*x^3 -
18909210*x^2 - 29808448*x - 7023157[]
523,3,2,x^26 - 9*x^25 - x^24 + 231*x^23 - 464*x^22 - 2306*x^21 + 7763*x^20 +
10298*x^19 - 60057*x^18 - 8015*x^17 + 266789*x^16 - 125796*x^15 - 723565*x^14 +
622138*x^13 + 1202991*x^12 - 1407289*x^11 - 1178824*x^10 + 1766306*x^9 +
617378*x^8 - 1241966*x^7 - 135947*x^6 + 462396*x^5 + 400*x^4 - 78680*x^3 +
2576*x^2 + 4032*x - 384,3,x^26 - 4*x^25 - 49*x^24 + 208*x^23 + 1012*x^22 -
4663*x^21 - 11396*x^20 + 59094*x^19 + 75007*x^18 - 466388*x^17 - 280600*x^16 +
2381986*x^15 + 472857*x^14 - 7939604*x^13 + 309652*x^12 + 17086537*x^11 -
2646657*x^10 - 23178878*x^9 + 3952698*x^8 + 19159320*x^7 - 1998424*x^6 -
9145408*x^5 - 112256*x^4 + 2223616*x^3 + 295296*x^2 - 196608*x - 42496,5,x^26 -
21*x^25 + 133*x^24 + 189*x^23 - 5652*x^22 + 16091*x^21 + 67148*x^20 -
424783*x^19 + 1108*x^18 + 4494594*x^17 - 6685702*x^16 - 23809605*x^15 +
66301197*x^14 + 54241804*x^13 - 319227622*x^12 + 53568465*x^11 + 861747737*x^10
- 640623368*x^9 - 1250489090*x^8 + 1587993980*x^7 + 684118440*x^6 -
1736185744*x^5 + 365192256*x^4 + 648584256*x^3 - 446921856*x^2 + 106382592*x -
8750592,7,x^26 - 3*x^25 - 100*x^24 + 332*x^23 + 4188*x^22 - 15475*x^21 -
95119*x^20 + 398414*x^19 + 1260778*x^18 - 6247004*x^17 - 9578508*x^16 +
62051571*x^15 + 34312880*x^14 - 393739786*x^13 + 27090636*x^12 + 1572077681*x^11
- 741916832*x^10 - 3800557726*x^9 + 2763329261*x^8 + 5217039801*x^7 -
4505859008*x^6 - 3750173443*x^5 + 3257166390*x^4 + 1371874260*x^3 -
941636161*x^2 - 224401796*x + 68725316,11,x^26 - 11*x^25 - 87*x^24 + 1307*x^23 +
2074*x^22 - 65149*x^21 + 34467*x^20 + 1783337*x^19 - 2908355*x^18 -
29305733*x^17 + 69754523*x^16 + 294503313*x^15 - 899355720*x^14 -
1734222972*x^13 + 6832413781*x^12 + 5021134610*x^11 - 30319565127*x^10 -
1070558006*x^9 + 72749481441*x^8 - 27663976900*x^7 - 79359825114*x^6 +
46389402198*x^5 + 28335287243*x^4 - 17095836984*x^3 - 2526515156*x^2 +
1622311536*x - 135464256,13,x^26 - 14*x^25 - 96*x^24 + 2136*x^23 + 383*x^22 -
132080*x^21 + 301427*x^20 + 4199329*x^19 - 16468009*x^18 - 70566834*x^17 +
412698712*x^16 + 520810586*x^15 - 5699369592*x^14 + 968098975*x^13 +
45100198785*x^12 - 45073381925*x^11 - 203890014853*x^10 + 327499828693*x^9 +
499671005301*x^8 - 1128758701394*x^7 - 551108498487*x^6 + 1984720955197*x^5 +
55147303448*x^4 - 1628923185473*x^3 + 220929697737*x^2 + 473723308718*x -
30230457287[]
524,1,2,x,3,x - 1,5,x + 2,7,x + 3,11,x,13,x - 1[]
524,2,2,x^2,3,x^2 + 3*x + 1,5,x^2 - x - 1,7,x^2 + x - 1,11,x^2 + 5*x + 5,13,x^2
+ 3*x - 9[]
524,3,2,x^4,3,x^4 - x^3 - 12*x^2 + 7*x + 29,5,x^4 + 3*x^3 - 9*x^2 - 16*x +
24,7,x^4 + x^3 - 18*x^2 - 11*x + 43,11,x^4 + 3*x^3 - 15*x^2 - 24*x + 36,13,x^4 +
x^3 - 66*x^2 - 27*x + 1023[]
524,4,2,x^4,3,x^4 - 3*x^3 - 2*x^2 + 6*x + 3,5,x^4 - 2*x^3 - 13*x^2 + 30*x -
3,7,x^4 - 7*x^3 + 10*x^2 + 18*x - 37,11,x^4 - 12*x^3 + 41*x^2 - 16*x - 79,13,x^4
+ x^3 - 8*x^2 + 9[]
525,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x,13,x - 6[]
525,2,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 4,13,x - 2[]
525,3,2,x - 1,3,x + 1,5,x,7,x - 1,11,x + 6,13,x - 2[]
525,4,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 6,13,x + 2[]
525,5,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 6*x +
9,13,x^2 + 2*x - 12[]
525,6,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 2*x -
19,13,x^2 + 6*x + 4[]
525,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x - 16,13,x^2 -
20[]
525,8,2,x^2 - 3*x + 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 2*x -
19,13,x^2 - 6*x + 4[]
525,9,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 6*x +
9,13,x^2 - 2*x - 12[]

Errors: /home/mfd/gomagma: line 2: 12479 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 18:55:47 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [522..524] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 18:55:30 on modular  [Seed = 3275128766]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
522,1,2,x + 1,3,x,5,x - 3,7,x + 5,11,x + 4,13,x + 6[]
522,2,2,x + 1,3,x,5,x - 2,7,x - 4,11,x,13,x - 2[]
522,3,2,x + 1,3,x,5,x + 3,7,x + 1,11,x,13,x - 2[]
522,4,2,x + 1,3,x,5,x - 1,7,x - 1,11,x - 2,13,x[]
522,5,2,x + 1,3,x,5,x + 1,7,x - 1,11,x + 6,13,x + 4[]
522,6,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 3,13,x + 1[]
522,7,2,x - 1,3,x,5,x + 2,7,x - 4,11,x,13,x - 2[]
522,8,2,x - 1,3,x,5,x - 3,7,x + 1,11,x,13,x - 2[]
522,9,2,x - 1,3,x,5,x + 3,7,x + 5,11,x - 4,13,x + 6[]
522,10,2,x - 1,3,x,5,x + 3,7,x + 3,11,x + 6,13,x[]
522,11,2,x - 1,3,x,5,x + 2,7,x,11,x - 4,13,x - 6[]
522,12,2,x - 1,3,x,5,x - 3,7,x + 2,11,x - 1,13,x - 3[]
522,13,2,x - 1,3,x,5,x - 3,7,x - 5,11,x + 6,13,x + 4[]
523,1,2,x^2 + 3*x + 1,3,x^2 + 3*x + 1,5,x^2 - 5,7,x^2 + 2*x + 1,11,x^2,13,x^2 +
x - 11[]
523,2,2,x^15 + 6*x^14 - 2*x^13 - 71*x^12 - 72*x^11 + 308*x^10 + 492*x^9 -
587*x^8 - 1283*x^7 + 418*x^6 + 1526*x^5 + 33*x^4 - 774*x^3 - 85*x^2 + 141*x +
8,3,x^15 + 3*x^14 - 17*x^13 - 50*x^12 + 111*x^11 + 312*x^10 - 349*x^9 - 897*x^8
+ 543*x^7 + 1180*x^6 - 401*x^5 - 623*x^4 + 181*x^3 + 114*x^2 - 33*x - 2,5,x^15 +
19*x^14 + 140*x^13 + 442*x^12 + 24*x^11 - 4077*x^10 - 11810*x^9 - 10832*x^8 +
8722*x^7 + 23778*x^6 + 9378*x^5 - 9987*x^4 - 8231*x^3 - 341*x^2 + 1043*x +
218,7,x^15 + x^14 - 65*x^13 - 71*x^12 + 1622*x^11 + 2079*x^10 - 19593*x^9 -
29759*x^8 + 114951*x^7 + 207182*x^6 - 263534*x^5 - 598861*x^4 + 4063*x^3 +
322280*x^2 + 37779*x - 2744,11,x^15 + 7*x^14 - 85*x^13 - 719*x^12 + 2007*x^11 +
26554*x^10 + 7728*x^9 - 410286*x^8 - 784569*x^7 + 2121922*x^6 + 7495618*x^5 +
1560600*x^4 - 15953890*x^3 - 15090096*x^2 + 3265879*x + 6017216,13,x^15 +
15*x^14 + 10*x^13 - 909*x^12 - 4293*x^11 + 12207*x^10 + 129405*x^9 + 140948*x^8
- 1181467*x^7 - 3470111*x^6 + 1369276*x^5 + 16369458*x^4 + 13960211*x^3 -
18909210*x^2 - 29808448*x - 7023157[]
523,3,2,x^26 - 9*x^25 - x^24 + 231*x^23 - 464*x^22 - 2306*x^21 + 7763*x^20 +
10298*x^19 - 60057*x^18 - 8015*x^17 + 266789*x^16 - 125796*x^15 - 723565*x^14 +
622138*x^13 + 1202991*x^12 - 1407289*x^11 - 1178824*x^10 + 1766306*x^9 +
617378*x^8 - 1241966*x^7 - 135947*x^6 + 462396*x^5 + 400*x^4 - 78680*x^3 +
2576*x^2 + 4032*x - 384,3,x^26 - 4*x^25 - 49*x^24 + 208*x^23 + 1012*x^22 -
4663*x^21 - 11396*x^20 + 59094*x^19 + 75007*x^18 - 466388*x^17 - 280600*x^16 +
2381986*x^15 + 472857*x^14 - 7939604*x^13 + 309652*x^12 + 17086537*x^11 -
2646657*x^10 - 23178878*x^9 + 3952698*x^8 + 19159320*x^7 - 1998424*x^6 -
9145408*x^5 - 112256*x^4 + 2223616*x^3 + 295296*x^2 - 196608*x - 42496,5,x^26 -
21*x^25 + 133*x^24 + 189*x^23 - 5652*x^22 + 16091*x^21 + 67148*x^20 -
424783*x^19 + 1108*x^18 + 4494594*x^17 - 6685702*x^16 - 23809605*x^15 +
66301197*x^14 + 54241804*x^13 - 319227622*x^12 + 53568465*x^11 + 861747737*x^10
- 640623368*x^9 - 1250489090*x^8 + 1587993980*x^7 + 684118440*x^6 -
1736185744*x^5 + 365192256*x^4 + 648584256*x^3 - 446921856*x^2 + 106382592*x -
8750592,7,x^26 - 3*x^25 - 100*x^24 + 332*x^23 + 4188*x^22 - 15475*x^21 -
95119*x^20 + 398414*x^19 + 1260778*x^18 - 6247004*x^17 - 9578508*x^16 +
62051571*x^15 + 34312880*x^14 - 393739786*x^13 + 27090636*x^12 + 1572077681*x^11
- 741916832*x^10 - 3800557726*x^9 + 2763329261*x^8 + 5217039801*x^7 -
4505859008*x^6 - 3750173443*x^5 + 3257166390*x^4 + 1371874260*x^3 -
941636161*x^2 - 224401796*x + 68725316,11,x^26 - 11*x^25 - 87*x^24 + 1307*x^23 +
2074*x^22 - 65149*x^21 + 34467*x^20 + 1783337*x^19 - 2908355*x^18 -
29305733*x^17 + 69754523*x^16 + 294503313*x^15 - 899355720*x^14 -
1734222972*x^13 + 6832413781*x^12 + 5021134610*x^11 - 30319565127*x^10 -
1070558006*x^9 + 72749481441*x^8 - 27663976900*x^7 - 79359825114*x^6 +
46389402198*x^5 + 28335287243*x^4 - 17095836984*x^3 - 2526515156*x^2 +
1622311536*x - 135464256,13,x^26 - 14*x^25 - 96*x^24 + 2136*x^23 + 383*x^22 -
132080*x^21 + 301427*x^20 + 4199329*x^19 - 16468009*x^18 - 70566834*x^17 +
412698712*x^16 + 520810586*x^15 - 5699369592*x^14 + 968098975*x^13 +
45100198785*x^12 - 45073381925*x^11 - 203890014853*x^10 + 327499828693*x^9 +
499671005301*x^8 - 1128758701394*x^7 - 551108498487*x^6 + 1984720955197*x^5 +
55147303448*x^4 - 1628923185473*x^3 + 220929697737*x^2 + 473723308718*x -
30230457287[]
524,1,2,x,3,x - 1,5,x + 2,7,x + 3,11,x,13,x - 1[]
524,2,2,x^2,3,x^2 + 3*x + 1,5,x^2 - x - 1,7,x^2 + x - 1,11,x^2 + 5*x + 5,13,x^2
+ 3*x - 9[]
524,3,2,x^4,3,x^4 - x^3 - 12*x^2 + 7*x + 29,5,x^4 + 3*x^3 - 9*x^2 - 16*x +
24,7,x^4 + x^3 - 18*x^2 - 11*x + 43,11,x^4 + 3*x^3 - 15*x^2 - 24*x + 36,13,x^4 +
x^3 - 66*x^2 - 27*x + 1023[]
524,4,2,x^4,3,x^4 - 3*x^3 - 2*x^2 + 6*x + 3,5,x^4 - 2*x^3 - 13*x^2 + 30*x -
3,7,x^4 - 7*x^3 + 10*x^2 + 18*x - 37,11,x^4 - 12*x^3 + 41*x^2 - 16*x - 79,13,x^4
+ x^3 - 8*x^2 + 9[]

Total time: 16.569 seconds, Total memory usage: 5.81MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 19:04:00 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [525..527] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:03:44 on modular  [Seed = 1270804773]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
525,1,2,x + 1,3,x + 1,5,x,7,x + 1,11,x,13,x - 6[]
525,2,2,x - 1,3,x + 1,5,x,7,x - 1,11,x - 4,13,x - 2[]
525,3,2,x - 1,3,x + 1,5,x,7,x - 1,11,x + 6,13,x - 2[]
525,4,2,x + 1,3,x - 1,5,x,7,x + 1,11,x + 6,13,x + 2[]
525,5,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 6*x +
9,13,x^2 + 2*x - 12[]
525,6,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 2*x -
19,13,x^2 + 6*x + 4[]
525,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 - 4*x - 16,13,x^2 -
20[]
525,8,2,x^2 - 3*x + 1,3,x^2 - 2*x + 1,5,x^2,7,x^2 + 2*x + 1,11,x^2 + 2*x -
19,13,x^2 - 6*x + 4[]
525,9,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2,7,x^2 - 2*x + 1,11,x^2 + 6*x +
9,13,x^2 - 2*x - 12[]
525,10,2,x^3 - x^2 - 5*x + 1,3,x^3 + 3*x^2 + 3*x + 1,5,x^3,7,x^3 + 3*x^2 + 3*x +
1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 + 6*x^2 - 4*x - 8[]
525,11,2,x^3 + x^2 - 5*x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3,7,x^3 - 3*x^2 + 3*x -
1,11,x^3 - 6*x^2 + 12*x - 8,13,x^3 - 6*x^2 - 4*x + 8[]
526,1,2,x^2 + 2*x + 1,3,x^2 - 8,5,x^2 - 6*x + 7,7,x^2 - 4*x - 4,11,x^2,13,x^2 +
4*x + 4[]
526,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - x^3 - 4*x^2 + 2*x + 3,5,x^4 +
5*x^3 + 4*x^2 - 8*x - 9,7,x^4 + x^3 - 12*x^2 + 12*x + 1,11,x^4 + 8*x^3 + 11*x^2
- 42*x - 89,13,x^4 - 6*x^2 - x + 7[]
526,3,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 5*x^3 + 6*x^2 - 1,5,x^4 + 7*x^3 +
10*x^2 - 16*x - 31,7,x^4 + 5*x^3 - 10*x^2 - 50*x - 25,11,x^4 + 8*x^3 - 5*x^2 -
154*x - 281,13,x^4 + 12*x^3 + 48*x^2 + 77*x + 41[]
526,4,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5 + 3*x^4 - 4*x^3 - 10*x^2 +
7*x + 4,5,x^5 - x^4 - 12*x^3 + 12*x^2 + 21*x - 8,7,x^5 + 7*x^4 - 90*x^2 - 181*x
- 56,11,x^5 - 8*x^4 - 9*x^3 + 166*x^2 - 209*x - 92,13,x^5 - 2*x^4 - 54*x^3 +
67*x^2 + 561*x + 394[]
526,5,2,x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1,3,x^6 - 3*x^5 - 6*x^4 +
20*x^3 + 3*x^2 - 32*x + 16,5,x^6 - 5*x^5 + x^4 + 21*x^3 - 11*x^2 - 22*x -
1,7,x^6 - 5*x^5 - 2*x^4 + 24*x^3 - 19*x^2 - 4*x + 4,11,x^6 - 4*x^5 - 9*x^4 +
50*x^3 - 17*x^2 - 96*x + 64,13,x^6 - 36*x^4 - 27*x^3 + 309*x^2 + 376*x - 124[]
527,1,2,x^2 - x - 1,3,x^2 - 5,5,x^2,7,x^2 - 2*x - 4,11,x^2 + 8*x + 11,13,x^2 +
2*x - 4[]
527,2,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,3,x^5 + 3*x^4 - 3*x^3 - 11*x^2 +
2*x + 7,5,x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 18*x + 9,7,x^5 + 4*x^4 + x^3 - 9*x^2 -
7*x - 1,11,x^5 + 2*x^4 - 26*x^3 - x^2 + 118*x - 77,13,x^5 + 15*x^4 + 78*x^3 +
175*x^2 + 165*x + 53[]
527,3,2,x^7 + x^6 - 8*x^5 - 8*x^4 + 15*x^3 + 13*x^2 - 8*x - 5,3,x^7 + 3*x^6 -
7*x^5 - 23*x^4 + 2*x^3 + 33*x^2 + 22*x + 4,5,x^7 + 6*x^6 + 5*x^5 - 29*x^4 -
54*x^3 + 8*x^2 + 60*x + 23,7,x^7 + 10*x^6 + 30*x^5 + 11*x^4 - 80*x^3 - 98*x^2 -
5*x + 19,11,x^7 - 38*x^5 - 25*x^4 + 408*x^3 + 549*x^2 - 898*x - 1412,13,x^7 +
9*x^6 + 10*x^5 - 97*x^4 - 277*x^3 - 123*x^2 + 218*x + 164[]
527,4,2,x^11 + 2*x^10 - 17*x^9 - 34*x^8 + 101*x^7 + 202*x^6 - 238*x^5 - 469*x^4
+ 182*x^3 + 295*x^2 - 83*x - 3,3,x^11 - 7*x^10 + 3*x^9 + 71*x^8 - 105*x^7 -
252*x^6 + 472*x^5 + 388*x^4 - 741*x^3 - 302*x^2 + 330*x + 139,5,x^11 - 6*x^10 -
30*x^9 + 217*x^8 + 276*x^7 - 2917*x^6 - 404*x^5 + 17936*x^4 - 5320*x^3 -
49088*x^2 + 17152*x + 46272,7,x^11 - 8*x^10 - 21*x^9 + 305*x^8 - 237*x^7 -
3483*x^6 + 6828*x^5 + 11052*x^4 - 32712*x^3 + 1504*x^2 + 28576*x - 4928,11,x^11
- 12*x^10 + 411*x^8 - 609*x^7 - 5455*x^6 + 8507*x^5 + 32317*x^4 - 39900*x^3 -
63546*x^2 + 71648*x - 6729,13,x^11 - 17*x^10 + 58*x^9 + 491*x^8 - 3815*x^7 +
4485*x^6 + 24590*x^5 - 57012*x^4 - 30624*x^3 + 98976*x^2 + 43488*x - 15424[]
527,5,2,x^16 - 3*x^15 - 22*x^14 + 70*x^13 + 179*x^12 - 631*x^11 - 642*x^10 +
2789*x^9 + 792*x^8 - 6335*x^7 + 903*x^6 + 6928*x^5 - 3096*x^4 - 2631*x^3 +
2063*x^2 - 344*x - 11,3,x^16 - 3*x^15 - 34*x^14 + 102*x^13 + 444*x^12 -
1341*x^11 - 2785*x^10 + 8642*x^9 + 8401*x^8 - 28364*x^7 - 10183*x^6 + 44605*x^5
+ 2730*x^4 - 29441*x^3 - 966*x^2 + 7148*x + 1008,5,x^16 - 4*x^15 - 57*x^14 +
249*x^13 + 1172*x^12 - 5894*x^11 - 9730*x^10 + 65513*x^9 + 14914*x^8 -
336400*x^7 + 164680*x^6 + 663056*x^5 - 440640*x^4 - 529088*x^3 + 302976*x^2 +
133120*x - 67584,7,x^16 - 8*x^15 - 48*x^14 + 477*x^13 + 722*x^12 - 10702*x^11 -
3811*x^10 + 118555*x^9 + 15646*x^8 - 721168*x^7 - 217504*x^6 + 2353408*x^5 +
1536384*x^4 - 3198336*x^3 - 3539200*x^2 - 278272*x + 456704,11,x^16 + 6*x^15 -
81*x^14 - 519*x^13 + 2237*x^12 + 16810*x^11 - 21684*x^10 - 252558*x^9 -
35799*x^8 + 1779801*x^7 + 1694694*x^6 - 5021831*x^5 - 7678550*x^4 + 2811663*x^3
+ 9030698*x^2 + 3399132*x - 259632,13,x^16 - 19*x^15 + 34*x^14 + 1419*x^13 -
8221*x^12 - 28219*x^11 + 306840*x^10 - 46964*x^9 - 4570200*x^8 + 6126032*x^7 +
30425472*x^6 - 50967168*x^5 - 96196224*x^4 + 114630656*x^3 + 159542272*x^2 +
17356800*x - 14366720[]

Total time: 15.479 seconds, Total memory usage: 5.44MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 19:11:39 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [527..529] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:11:20 on modular  [Seed = 1855706696]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
527,1,2,x^2 - x - 1,3,x^2 - 5,5,x^2,7,x^2 - 2*x - 4,11,x^2 + 8*x + 11,13,x^2 +
2*x - 4[]
527,2,2,x^5 + 2*x^4 - 5*x^3 - 7*x^2 + 7*x + 1,3,x^5 + 3*x^4 - 3*x^3 - 11*x^2 +
2*x + 7,5,x^5 + 2*x^4 - 8*x^3 - 11*x^2 + 18*x + 9,7,x^5 + 4*x^4 + x^3 - 9*x^2 -
7*x - 1,11,x^5 + 2*x^4 - 26*x^3 - x^2 + 118*x - 77,13,x^5 + 15*x^4 + 78*x^3 +
175*x^2 + 165*x + 53[]
527,3,2,x^7 + x^6 - 8*x^5 - 8*x^4 + 15*x^3 + 13*x^2 - 8*x - 5,3,x^7 + 3*x^6 -
7*x^5 - 23*x^4 + 2*x^3 + 33*x^2 + 22*x + 4,5,x^7 + 6*x^6 + 5*x^5 - 29*x^4 -
54*x^3 + 8*x^2 + 60*x + 23,7,x^7 + 10*x^6 + 30*x^5 + 11*x^4 - 80*x^3 - 98*x^2 -
5*x + 19,11,x^7 - 38*x^5 - 25*x^4 + 408*x^3 + 549*x^2 - 898*x - 1412,13,x^7 +
9*x^6 + 10*x^5 - 97*x^4 - 277*x^3 - 123*x^2 + 218*x + 164[]
527,4,2,x^11 + 2*x^10 - 17*x^9 - 34*x^8 + 101*x^7 + 202*x^6 - 238*x^5 - 469*x^4
+ 182*x^3 + 295*x^2 - 83*x - 3,3,x^11 - 7*x^10 + 3*x^9 + 71*x^8 - 105*x^7 -
252*x^6 + 472*x^5 + 388*x^4 - 741*x^3 - 302*x^2 + 330*x + 139,5,x^11 - 6*x^10 -
30*x^9 + 217*x^8 + 276*x^7 - 2917*x^6 - 404*x^5 + 17936*x^4 - 5320*x^3 -
49088*x^2 + 17152*x + 46272,7,x^11 - 8*x^10 - 21*x^9 + 305*x^8 - 237*x^7 -
3483*x^6 + 6828*x^5 + 11052*x^4 - 32712*x^3 + 1504*x^2 + 28576*x - 4928,11,x^11
- 12*x^10 + 411*x^8 - 609*x^7 - 5455*x^6 + 8507*x^5 + 32317*x^4 - 39900*x^3 -
63546*x^2 + 71648*x - 6729,13,x^11 - 17*x^10 + 58*x^9 + 491*x^8 - 3815*x^7 +
4485*x^6 + 24590*x^5 - 57012*x^4 - 30624*x^3 + 98976*x^2 + 43488*x - 15424[]
527,5,2,x^16 - 3*x^15 - 22*x^14 + 70*x^13 + 179*x^12 - 631*x^11 - 642*x^10 +
2789*x^9 + 792*x^8 - 6335*x^7 + 903*x^6 + 6928*x^5 - 3096*x^4 - 2631*x^3 +
2063*x^2 - 344*x - 11,3,x^16 - 3*x^15 - 34*x^14 + 102*x^13 + 444*x^12 -
1341*x^11 - 2785*x^10 + 8642*x^9 + 8401*x^8 - 28364*x^7 - 10183*x^6 + 44605*x^5
+ 2730*x^4 - 29441*x^3 - 966*x^2 + 7148*x + 1008,5,x^16 - 4*x^15 - 57*x^14 +
249*x^13 + 1172*x^12 - 5894*x^11 - 9730*x^10 + 65513*x^9 + 14914*x^8 -
336400*x^7 + 164680*x^6 + 663056*x^5 - 440640*x^4 - 529088*x^3 + 302976*x^2 +
133120*x - 67584,7,x^16 - 8*x^15 - 48*x^14 + 477*x^13 + 722*x^12 - 10702*x^11 -
3811*x^10 + 118555*x^9 + 15646*x^8 - 721168*x^7 - 217504*x^6 + 2353408*x^5 +
1536384*x^4 - 3198336*x^3 - 3539200*x^2 - 278272*x + 456704,11,x^16 + 6*x^15 -
81*x^14 - 519*x^13 + 2237*x^12 + 16810*x^11 - 21684*x^10 - 252558*x^9 -
35799*x^8 + 1779801*x^7 + 1694694*x^6 - 5021831*x^5 - 7678550*x^4 + 2811663*x^3
+ 9030698*x^2 + 3399132*x - 259632,13,x^16 - 19*x^15 + 34*x^14 + 1419*x^13 -
8221*x^12 - 28219*x^11 + 306840*x^10 - 46964*x^9 - 4570200*x^8 + 6126032*x^7 +
30425472*x^6 - 50967168*x^5 - 96196224*x^4 + 114630656*x^3 + 159542272*x^2 +
17356800*x - 14366720[]
528,1,2,x,3,x + 1,5,x,7,x + 2,11,x + 1,13,x[]
528,2,2,x,3,x + 1,5,x + 2,7,x + 4,11,x - 1,13,x - 6[]
528,3,2,x,3,x + 1,5,x - 4,7,x - 2,11,x - 1,13,x[]
528,4,2,x,3,x - 1,5,x - 2,7,x,11,x + 1,13,x - 2[]
528,5,2,x,3,x + 1,5,x - 2,7,x - 2,11,x + 1,13,x + 2[]
528,6,2,x,3,x + 1,5,x + 4,7,x - 2,11,x + 1,13,x - 4[]
528,7,2,x,3,x + 1,5,x,7,x + 2,11,x - 1,13,x + 4[]
528,8,2,x,3,x - 1,5,x + 2,7,x + 4,11,x + 1,13,x + 2[]
528,9,2,x,3,x - 1,5,x - 2,7,x + 2,11,x - 1,13,x - 6[]
528,10,2,x,3,x - 1,5,x - 2,7,x - 4,11,x - 1,13,x + 6[]
529,1,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 6*x + 6,11,x^2 - 6*x +
6,13,x^2 - 2*x + 1[]
529,2,2,x^2 - 3,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 + 6*x + 6,11,x^2 + 6*x +
6,13,x^2 - 2*x + 1[]
529,3,2,x^2 + x - 1,3,x^2 - 5,5,x^2 - 2*x - 4,7,x^2 + 2*x - 4,11,x^2 - 6*x +
4,13,x^2 - 6*x + 9[]
529,4,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 - 2*x - 7,7,x^2 - 4*x + 2,11,x^2 -
2,13,x^2 + 6*x + 9[]
529,5,2,x^2 - 2*x - 1,3,x^2 - 2,5,x^2 + 2*x - 7,7,x^2 + 4*x + 2,11,x^2 -
2,13,x^2 + 6*x + 9[]
529,6,2,x^3 - 6*x - 3,3,x^3 - 9*x - 4,5,x^3,7,x^3,11,x^3,13,x^3 - 39*x + 74[]
529,7,2,x^4 + 2*x^3 - 5*x^2 - 6*x + 9,3,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,5,x^4 -
14*x^2 + 36,7,x^4 - 14*x^2 + 36,11,x^4 - 14*x^2 + 36,13,x^4 + 8*x^3 - 2*x^2 -
72*x + 81[]
529,8,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 4*x^3 - 8*x + 4,5,x^4 - 4*x^2 +
1,7,x^4 - 12*x^2 + 36,11,x^4 - 28*x^2 + 4,13,x^4 + 4*x^3 - 18*x^2 - 44*x + 121[]
529,9,2,x^5 - 2*x^4 - 5*x^3 + 13*x^2 - 7*x + 1,3,x^5 - 2*x^4 - 5*x^3 + 13*x^2 -
7*x + 1,5,x^5 + 7*x^4 + 13*x^3 - 6*x^2 - 35*x - 23,7,x^5 + 8*x^4 + 19*x^3 +
4*x^2 - 32*x - 23,11,x^5 + 13*x^4 + 61*x^3 + 119*x^2 + 70*x - 23,13,x^5 - 4*x^4
- 9*x^3 + 38*x^2 - 2*x - 1[]
529,10,2,x^5 - 2*x^4 - 5*x^3 + 13*x^2 - 7*x + 1,3,x^5 - 2*x^4 - 5*x^3 + 13*x^2 -
7*x + 1,5,x^5 - 7*x^4 + 13*x^3 + 6*x^2 - 35*x + 23,7,x^5 - 8*x^4 + 19*x^3 -
4*x^2 - 32*x + 23,11,x^5 - 13*x^4 + 61*x^3 - 119*x^2 + 70*x + 23,13,x^5 - 4*x^4
- 9*x^3 + 38*x^2 - 2*x - 1[]

Total time: 18.709 seconds, Total memory usage: 5.90MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 19:15:43 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [530..532] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:15:24 on modular  [Seed = 1637144179]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
530,1,2,x + 1,3,x - 1,5,x + 1,7,x - 2,11,x,13,x - 5[]
530,2,2,x + 1,3,x,5,x - 1,7,x + 2,11,x,13,x + 2[]
530,3,2,x + 1,3,x + 3,5,x - 1,7,x + 2,11,x,13,x - 1[]
530,4,2,x - 1,3,x + 1,5,x + 1,7,x + 2,11,x + 4,13,x + 3[]
530,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 10*x - 13,5,x^3 + 3*x^2 + 3*x +
1,7,x^3 - 3*x^2 - 18*x + 47,11,x^3 + x^2 - 16*x - 7,13,x^3 + 7*x^2 - 27[]
530,6,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - 3*x^2 - 2*x + 7,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 5*x^2 - 2*x + 25,11,x^3 + x^2 - 4*x - 3,13,x^3 - 7*x^2 + 12*x - 1[]
530,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - x^3 - 10*x^2 + 9*x + 16,5,x^4 +
4*x^3 + 6*x^2 + 4*x + 1,7,x^4 - 3*x^3 - 12*x^2 + 5*x + 10,11,x^4 - 7*x^3 - 4*x^2
+ 65*x + 24,13,x^4 - x^3 - 22*x^2 + 3*x + 98[]
530,8,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5 - 4*x^4 - 3*x^3 + 23*x^2 -
19*x + 4,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 - x^4 - 16*x^3 + 19*x^2
+ 30*x + 8,11,x^5 + x^4 - 40*x^3 - 11*x^2 + 192*x + 176,13,x^5 - 51*x^3 - 29*x^2
+ 265*x - 82[]
531,1,2,x^2 - 3*x + 1,3,x^2,5,x^2 - 6*x + 9,7,x^2 + 7*x + 11,11,x^2 - 2*x -
19,13,x^2 - 45[]
531,2,2,x^2 - x - 1,3,x^2,5,x^2 - 5,7,x^2 + 7*x + 11,11,x^2 - 5,13,x^2 + 8*x +
11[]
531,3,2,x^2 + x - 1,3,x^2,5,x^2 + 2*x + 1,7,x^2 - x - 1,11,x^2 + 4*x - 1,13,x^2
+ 2*x + 1[]
531,4,2,x^3 - 4*x + 1,3,x^3,5,x^3 - 2*x^2 - 5*x + 2,7,x^3 - 9*x^2 + 23*x -
16,11,x^3 - 2*x^2 - 11*x - 4,13,x^3 - 4*x^2 - 7*x + 26[]
531,5,2,x^5 + 3*x^4 - 3*x^3 - 11*x^2 + x + 5,3,x^5,5,x^5 + 8*x^4 + 16*x^3 -
8*x^2 - 29*x + 8,7,x^5 - 2*x^4 - 13*x^3 - 2*x^2 + 13*x + 4,11,x^5 + 10*x^4 +
12*x^3 - 66*x^2 + 35*x + 4,13,x^5 + 4*x^4 - 30*x^3 - 170*x^2 - 243*x - 86[]
531,6,2,x^5 - 3*x^4 - 3*x^3 + 11*x^2 + x - 5,3,x^5,5,x^5 - 8*x^4 + 16*x^3 +
8*x^2 - 29*x - 8,7,x^5 - 2*x^4 - 13*x^3 - 2*x^2 + 13*x + 4,11,x^5 - 10*x^4 +
12*x^3 + 66*x^2 + 35*x - 4,13,x^5 + 4*x^4 - 30*x^3 - 170*x^2 - 243*x - 86[]
531,7,2,x^5 - 9*x^3 - 2*x^2 + 16*x + 8,3,x^5,5,x^5 + 2*x^4 - 14*x^3 - 23*x^2 +
19*x - 1,7,x^5 - 2*x^4 - 16*x^3 + 43*x^2 + 13*x - 71,11,x^5 - 2*x^4 - 24*x^3 +
24*x^2 + 128*x + 64,13,x^5 - 8*x^4 + 88*x^2 - 48*x - 224[]
532,1,2,x,3,x,5,x + 2,7,x - 1,11,x - 4,13,x - 4[]
532,2,2,x^2,3,x^2 - x - 1,5,x^2 + 4*x - 1,7,x^2 + 2*x + 1,11,x^2 + 3*x +
1,13,x^2 + 2*x - 19[]
532,3,2,x^2,3,x^2 + 3*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - x -
31,13,x^2 - 5[]
532,4,2,x^2,3,x^2 + x - 5,5,x^2 - 6*x + 9,7,x^2 - 2*x + 1,11,x^2 + 3*x -
3,13,x^2 + 2*x + 1[]
532,5,2,x^3,3,x^3 + x^2 - 7*x - 8,5,x^3 - 2*x^2 - 9*x + 14,7,x^3 + 3*x^2 + 3*x +
1,11,x^3 + 3*x^2 - 7*x - 20,13,x^3 - 8*x^2 + 11*x + 16[]

Total time: 18.319 seconds, Total memory usage: 6.44MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 19:18:50 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [533..535] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:18:35 on modular  [Seed = 1954661281]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
533,1,2,x^2 - 2*x - 1,3,x^2 - 2*x - 1,5,x^2 - 8,7,x^2 - 4*x - 4,11,x^2 -
8,13,x^2 + 2*x + 1[]
533,2,2,x^7 + 2*x^6 - 6*x^5 - 12*x^4 + 9*x^3 + 19*x^2 - x - 5,3,x^7 + 8*x^6 +
19*x^5 + 2*x^4 - 45*x^3 - 50*x^2 - 17*x - 1,5,x^7 + 2*x^6 - 17*x^5 - 34*x^4 +
63*x^3 + 150*x^2 + 19*x - 59,7,x^7 + 10*x^6 + 25*x^5 - 45*x^4 - 267*x^3 -
245*x^2 + 245*x + 343,11,x^7 + 2*x^6 - 50*x^5 - 54*x^4 + 548*x^3 - 268*x^2 -
203*x - 25,13,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1[]
533,3,2,x^8 - x^7 - 10*x^6 + 8*x^5 + 31*x^4 - 22*x^3 - 28*x^2 + 22*x - 3,3,x^8 -
4*x^7 - 11*x^6 + 52*x^5 + 31*x^4 - 220*x^3 + 27*x^2 + 299*x - 162,5,x^8 - 4*x^7
- 13*x^6 + 68*x^5 + x^4 - 236*x^3 + 83*x^2 + 237*x - 14,7,x^8 - 6*x^7 - 9*x^6 +
75*x^5 + 49*x^4 - 301*x^3 - 191*x^2 + 389*x + 294,11,x^8 - 2*x^7 - 38*x^6 +
98*x^5 + 378*x^4 - 1246*x^3 - 533*x^2 + 4217*x - 3138,13,x^8 + 8*x^7 + 28*x^6 +
56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1[]
533,4,2,x^11 + 2*x^10 - 14*x^9 - 26*x^8 + 64*x^7 + 103*x^6 - 117*x^5 - 149*x^4 +
65*x^3 + 71*x^2 + 5*x - 1,3,x^11 + 8*x^10 + 7*x^9 - 86*x^8 - 189*x^7 + 214*x^6 +
773*x^5 + 113*x^4 - 724*x^3 - 400*x^2 - 58*x - 2,5,x^11 + 4*x^10 - 23*x^9 -
96*x^8 + 121*x^7 + 664*x^6 + 243*x^5 - 1291*x^4 - 1888*x^3 - 1084*x^2 - 284*x -
28,7,x^11 + 18*x^10 + 111*x^9 + 143*x^8 - 1367*x^7 - 6565*x^6 - 9777*x^5 +
1275*x^4 + 13932*x^3 + 5098*x^2 - 3270*x - 1466,11,x^11 + 10*x^10 - 16*x^9 -
438*x^8 - 814*x^7 + 4636*x^6 + 14709*x^5 - 8983*x^4 - 56906*x^3 - 12200*x^2 +
45646*x - 5402,13,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 +
462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1[]
533,5,2,x^13 - 21*x^11 + 166*x^9 + x^8 - 613*x^7 - 16*x^6 + 1074*x^5 + 72*x^4 -
822*x^3 - 76*x^2 + 215*x + 27,3,x^13 - 10*x^12 + 24*x^11 + 62*x^10 - 330*x^9 +
154*x^8 + 1082*x^7 - 1389*x^6 - 889*x^5 + 2087*x^4 - 332*x^3 - 634*x^2 + 170*x -
2,5,x^13 - 39*x^11 + 12*x^10 + 539*x^9 - 356*x^8 - 3093*x^7 + 3139*x^6 +
6168*x^5 - 8492*x^4 - 2420*x^3 + 7004*x^2 - 2560*x + 96,7,x^13 - 10*x^12 -
3*x^11 + 303*x^10 - 595*x^9 - 2829*x^8 + 8439*x^7 + 8049*x^6 - 35878*x^5 -
1806*x^4 + 47502*x^3 - 6426*x^2 - 15552*x - 1944,11,x^13 - 2*x^12 - 68*x^11 +
122*x^10 + 1732*x^9 - 2470*x^8 - 20989*x^7 + 18027*x^6 + 129028*x^5 - 26852*x^4
- 353854*x^3 - 123922*x^2 + 221632*x + 98352,13,x^13 - 13*x^12 + 78*x^11 -
286*x^10 + 715*x^9 - 1287*x^8 + 1716*x^7 - 1716*x^6 + 1287*x^5 - 715*x^4 +
286*x^3 - 78*x^2 + 13*x - 1[]
534,1,2,x - 1,3,x + 1,5,x + 2,7,x + 2,11,x + 4,13,x[]
534,2,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + 4*x + 4,7,x^2 - 4*x + 2,11,x^2 +
4*x - 4,13,x^2 - 18[]
534,3,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 3*x - 1,7,x^2 + 2*x - 12,11,x^2 -
5*x + 3,13,x^2 + x - 3[]
534,4,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - x - 1,7,x^2 - 2*x - 4,11,x^2 - 3*x
- 9,13,x^2 + x - 11[]
534,5,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 -
3*x^3 - 13*x^2 + 32*x + 12,7,x^4 - 2*x^3 - 22*x^2 + 60*x - 8,11,x^4 - x^3 -
13*x^2 + 8*x + 36,13,x^4 - 13*x^3 + 43*x^2 + 38*x - 262[]
534,6,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,5,x^4 -
x^3 - 13*x^2 + 16*x - 4,7,x^4 - 4*x^3 - 4*x^2 + 16*x + 16,11,x^4 - 3*x^3 -
17*x^2 + 72*x - 64,13,x^4 + x^3 - 33*x^2 + 74*x - 44[]
535,1,2,x^3 + 2*x^2 - x - 1,3,x^3,5,x^3 - 3*x^2 + 3*x - 1,7,x^3 + x^2 - 2*x -
1,11,x^3 + 7*x^2 - 49,13,x^3 + 2*x^2 - 8*x - 8[]
535,2,2,x^8 + 4*x^7 - 4*x^6 - 27*x^5 - 3*x^4 + 49*x^3 + 14*x^2 - 24*x - 8,3,x^8
+ 2*x^7 - 10*x^6 - 17*x^5 + 31*x^4 + 37*x^3 - 36*x^2 - 20*x + 8,5,x^8 + 8*x^7 +
28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,7,x^8 + 3*x^7 - 24*x^6 -
73*x^5 + 166*x^4 + 556*x^3 - 224*x^2 - 1344*x - 736,11,x^8 + 9*x^7 + 6*x^6 -
110*x^5 - 216*x^4 + 136*x^3 + 340*x^2 - 53*x - 1,13,x^8 + 8*x^7 - 2*x^6 - 93*x^5
- x^4 + 211*x^3 + 20*x^2 - 108*x - 8[]
535,3,2,x^9 - 5*x^8 + 31*x^6 - 29*x^5 - 47*x^4 + 59*x^3 + 2*x^2 - 8*x - 1,3,x^9
- 2*x^8 - 20*x^7 + 36*x^6 + 124*x^5 - 168*x^4 - 296*x^3 + 208*x^2 + 192*x -
64,5,x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x +
1,7,x^9 - 3*x^8 - 19*x^7 + 48*x^6 + 66*x^5 - 151*x^4 - 63*x^3 + 111*x^2 - 8*x -
1,11,x^9 - 9*x^8 + 3*x^7 + 188*x^6 - 562*x^5 - 277*x^4 + 3847*x^3 - 7105*x^2 +
5524*x - 1611,13,x^9 - 4*x^8 - 54*x^7 + 168*x^6 + 1048*x^5 - 2184*x^4 - 8760*x^3
+ 7936*x^2 + 27552*x + 6208[]
535,4,2,x^15 - 4*x^14 - 18*x^13 + 85*x^12 + 103*x^11 - 685*x^10 - 108*x^9 +
2595*x^8 - 846*x^7 - 4594*x^6 + 2565*x^5 + 3187*x^4 - 1951*x^3 - 470*x^2 + 136*x
+ 24,3,x^15 - 38*x^13 + 7*x^12 + 565*x^11 - 209*x^10 - 4158*x^9 + 2268*x^8 +
15708*x^7 - 11036*x^6 - 28200*x^5 + 23544*x^4 + 18192*x^3 - 16512*x^2 - 1472*x +
1280,5,x^15 - 15*x^14 + 105*x^13 - 455*x^12 + 1365*x^11 - 3003*x^10 + 5005*x^9 -
6435*x^8 + 6435*x^7 - 5005*x^6 + 3003*x^5 - 1365*x^4 + 455*x^3 - 105*x^2 + 15*x
- 1,7,x^15 + 3*x^14 - 69*x^13 - 202*x^12 + 1846*x^11 + 5081*x^10 - 24969*x^9 -
61451*x^8 + 185062*x^7 + 379539*x^6 - 740046*x^5 - 1147436*x^4 + 1379008*x^3 +
1421664*x^2 - 695328*x - 407552,11,x^15 - 11*x^14 - 43*x^13 + 785*x^12 -
108*x^11 - 20672*x^10 + 28631*x^9 + 247214*x^8 - 473963*x^7 - 1323229*x^6 +
2902537*x^5 + 2521814*x^4 - 6646278*x^3 - 494379*x^2 + 4818017*x -
1525884,13,x^15 + 4*x^14 - 112*x^13 - 365*x^12 + 4707*x^11 + 11137*x^10 -
91822*x^9 - 127346*x^8 + 810968*x^7 + 421400*x^6 - 2458304*x^5 - 562392*x^4 +
1665872*x^3 + 52704*x^2 - 185472*x - 24704[]

Total time: 14.989 seconds, Total memory usage: 5.70MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sun Nov 30 19:27:15 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [536..538] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:26:59 on modular  [Seed = 2624137537]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
536,1,2,x^2,3,x^2 + x - 1,5,x^2 + 2*x + 1,7,x^2 + x - 1,11,x^2 - 2*x - 19,13,x^2
+ 5*x + 5[]
536,2,2,x^3,3,x^3 + 3*x^2 - x - 2,5,x^3 + 2*x^2 - 5*x - 2,7,x^3 + x^2 - 5*x +
2,11,x^3 + 4*x^2 - x - 8,13,x^3 + 5*x^2 - 7*x + 2[]
536,3,2,x^3,3,x^3 - 3*x^2 - 7*x + 20,5,x^3 - 2*x^2 - 9*x + 14,7,x^3 - x^2 - 7*x
+ 8,11,x^3 - 4*x^2 - 5*x + 4,13,x^3 + 5*x^2 + x - 2[]
536,4,2,x^4,3,x^4 + 3*x^3 - 2*x^2 - 7*x - 2,5,x^4 + x^3 - 16*x^2 - 7*x +
58,7,x^4 + 2*x^3 - 28*x^2 - 32*x + 176,11,x^4 + 3*x^3 - 24*x^2 - 109*x -
112,13,x^4 - 11*x^3 + 24*x^2 + 77*x - 242[]
536,5,2,x^5,3,x^5 - 4*x^4 - 2*x^3 + 16*x^2 - x - 15,5,x^5 - x^4 - 15*x^3 +
16*x^2 + 16*x + 3,7,x^5 - 7*x^4 + 7*x^3 + 20*x^2 - 4*x - 8,11,x^5 - 5*x^4 -
13*x^3 + 74*x^2 - 86*x + 25,13,x^5 - 6*x^4 - 24*x^3 + 106*x^2 + 249*x - 125[]
537,1,2,x - 1,3,x + 1,5,x,7,x + 1,11,x - 6,13,x - 7[]
537,2,2,x,3,x - 1,5,x - 1,7,x,11,x,13,x - 3[]
537,3,2,x,3,x - 1,5,x + 3,7,x - 2,11,x - 6,13,x + 1[]
537,4,2,x - 1,3,x - 1,5,x - 4,7,x - 1,11,x - 2,13,x + 1[]
537,5,2,x + 2,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x + 1[]
537,6,2,x^2 - x - 4,3,x^2 - 2*x + 1,5,x^2 - x - 4,7,x^2 - 3*x - 2,11,x^2 - 4*x +
4,13,x^2 + 2*x + 1[]
537,7,2,x^2 - 4*x + 4,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 - 4*x - 4,11,x^2 +
4*x - 4,13,x^2 + 2*x - 31[]
537,8,2,x^6 + 2*x^5 - 6*x^4 - 10*x^3 + 8*x^2 + 8*x - 4,3,x^6 + 6*x^5 + 15*x^4 +
20*x^3 + 15*x^2 + 6*x + 1,5,x^6 - 4*x^5 - 7*x^4 + 28*x^3 + 7*x^2 - 8*x - 1,7,x^6
+ 12*x^5 + 46*x^4 + 34*x^3 - 156*x^2 - 300*x - 116,11,x^6 + 4*x^5 - 22*x^4 -
66*x^3 + 96*x^2 + 92*x + 4,13,x^6 + 10*x^5 + 3*x^4 - 136*x^3 - 69*x^2 + 126*x +
49[]
537,9,2,x^6 + 4*x^5 - 12*x^3 - 4*x^2 + 8*x + 4,3,x^6 - 6*x^5 + 15*x^4 - 20*x^3 +
15*x^2 - 6*x + 1,5,x^6 + 10*x^5 + 31*x^4 + 20*x^3 - 41*x^2 - 30*x + 25,7,x^6 +
10*x^5 + 22*x^4 - 28*x^3 - 72*x^2 - 36*x - 4,11,x^6 + 4*x^5 - 50*x^4 - 184*x^3 +
540*x^2 + 1164*x - 2404,13,x^6 + 6*x^5 - 41*x^4 - 204*x^3 + 463*x^2 + 1350*x +
137[]
537,10,2,x^8 - 2*x^7 - 13*x^6 + 22*x^5 + 54*x^4 - 66*x^3 - 72*x^2 + 32*x +
12,3,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 +
6*x^7 - 15*x^6 - 114*x^5 + 79*x^4 + 646*x^3 - 401*x^2 - 1050*x + 800,7,x^8 -
15*x^7 + 72*x^6 - 42*x^5 - 642*x^4 + 1636*x^3 + 8*x^2 - 3812*x + 3152,11,x^8 +
4*x^7 - 24*x^6 - 74*x^5 + 136*x^4 + 292*x^3 - 20*x^2 - 136*x - 32,13,x^8 + x^7 -
45*x^6 - 55*x^5 + 657*x^4 + 971*x^3 - 3199*x^2 - 5349*x + 842[]
538,1,2,x^2 - 2*x + 1,3,x^2 - x - 3,5,x^2 - x - 3,7,x^2 + 2*x + 1,11,x^2 - 6*x +
9,13,x^2 - 10*x + 25[]
538,2,2,x^2 - 2*x + 1,3,x^2 + x - 1,5,x^2 + 5*x + 5,7,x^2 + 4*x - 1,11,x^2 + 4*x
- 1,13,x^2 + 2*x + 1[]
538,3,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 - 3*x^3 - 3*x^2 + 10*x - 4,5,x^4 -
5*x^3 + 3*x^2 + 6*x - 4,7,x^4 + x^3 - 6*x^2 - x + 1,11,x^4 - 7*x^3 + 12*x^2 +
3*x - 13,13,x^4 - 4*x^3 - 11*x^2 + 30*x + 52[]
538,4,2,x^7 + 7*x^6 + 21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,3,x^7 + 4*x^6
- 6*x^5 - 30*x^4 + 31*x^2 + 2*x - 3,5,x^7 + 6*x^6 - 4*x^5 - 82*x^4 - 102*x^3 +
229*x^2 + 520*x + 233,7,x^7 + 3*x^6 - 23*x^5 - 70*x^4 + 127*x^3 + 392*x^2 -
187*x - 563,11,x^7 + 12*x^6 + 5*x^5 - 370*x^4 - 980*x^3 + 1576*x^2 + 4864*x -
480,13,x^7 - 3*x^6 - 51*x^5 + 88*x^4 + 635*x^3 - 54*x^2 - 607*x - 89[]
538,5,2,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 + 7*x - 1,3,x^7 - x^6 -
16*x^5 + 19*x^4 + 63*x^3 - 87*x^2 - 10*x + 12,5,x^7 - 7*x^6 - 4*x^5 + 109*x^4 -
161*x^3 - 109*x^2 + 130*x - 4,7,x^7 - 6*x^6 - 14*x^5 + 142*x^4 - 258*x^3 +
137*x^2 + 18*x - 19,11,x^7 + 3*x^6 - 33*x^5 - 130*x^4 + 100*x^3 + 856*x^2 +
992*x + 288,13,x^7 + 9*x^6 + 8*x^5 - 71*x^4 - 79*x^3 + 117*x^2 + 54*x + 4[]

Total time: 16.369 seconds, Total memory usage: 5.55MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sun Nov 30 19:32:26 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [539..541] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:32:03 on modular  [Seed = 2908233383]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
539,1,2,x,3,x + 1,5,x + 3,7,x,11,x + 1,13,x - 4[]
539,2,2,x,3,x - 3,5,x - 1,7,x,11,x + 1,13,x - 4[]
539,3,2,x - 1,3,x + 2,5,x - 2,7,x,11,x - 1,13,x + 4[]
539,4,2,x + 2,3,x - 1,5,x + 1,7,x,11,x - 1,13,x + 4[]
539,5,2,x^2 + 2*x + 1,3,x^2 - 2,5,x^2 - 2,7,x^2,11,x^2 + 2*x + 1,13,x^2[]
539,6,2,x^2 - 5,3,x^2 + 2*x - 4,5,x^2 - 4*x + 4,7,x^2,11,x^2 + 2*x + 1,13,x^2 +
2*x - 4[]
539,7,2,x^3 - 5*x + 3,3,x^3 + x^2 - 4*x - 3,5,x^3 + 2*x^2 - 7*x - 5,7,x^3,11,x^3
+ 3*x^2 + 3*x + 1,13,x^3 + 11*x^2 + 36*x + 35[]
539,8,2,x^3 - 3*x - 1,3,x^3 - 3*x^2 + 1,5,x^3 - 6*x^2 + 9*x - 1,7,x^3,11,x^3 -
3*x^2 + 3*x - 1,13,x^3 - 3*x^2 - 6*x - 1[]
539,9,2,x^3 - 5*x + 3,3,x^3 - x^2 - 4*x + 3,5,x^3 - 2*x^2 - 7*x + 5,7,x^3,11,x^3
+ 3*x^2 + 3*x + 1,13,x^3 - 11*x^2 + 36*x - 35[]
539,10,2,x^3 - 3*x - 1,3,x^3 + 3*x^2 - 1,5,x^3 + 6*x^2 + 9*x + 1,7,x^3,11,x^3 -
3*x^2 + 3*x - 1,13,x^3 + 3*x^2 - 6*x + 1[]
539,11,2,x^4 - 2*x^3 - 7*x^2 + 8*x + 16,3,x^4 - 7*x^2 + 8,5,x^4 - 23*x^2 +
128,7,x^4,11,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,13,x^4 - 56*x^2 + 512[]
539,12,2,x^10 - 2*x^9 - 17*x^8 + 36*x^7 + 87*x^6 - 202*x^5 - 119*x^4 + 360*x^3 -
192*x + 64,3,x^10 - 26*x^8 + 245*x^6 - 1038*x^4 + 1884*x^2 - 968,5,x^10 - 34*x^8
+ 365*x^6 - 1214*x^4 + 204*x^2 - 8,7,x^10,11,x^10 - 10*x^9 + 45*x^8 - 120*x^7 +
210*x^6 - 252*x^5 + 210*x^4 - 120*x^3 + 45*x^2 - 10*x + 1,13,x^10 - 72*x^8 +
1696*x^6 - 16672*x^4 + 69120*x^2 - 100352[]
540,1,2,x,3,x,5,x + 1,7,x - 2,11,x,13,x - 2[]
540,2,2,x,3,x,5,x - 1,7,x + 4,11,x + 6,13,x + 4[]
540,3,2,x,3,x,5,x + 1,7,x + 1,11,x + 6,13,x + 1[]
540,4,2,x,3,x,5,x + 1,7,x + 4,11,x - 6,13,x + 4[]
540,5,2,x,3,x,5,x - 1,7,x + 1,11,x - 6,13,x + 1[]
540,6,2,x,3,x,5,x - 1,7,x - 2,11,x,13,x - 2[]
541,1,2,x^20 + 5*x^19 - 15*x^18 - 105*x^17 + 53*x^16 + 888*x^15 + 248*x^14 -
3950*x^13 - 2525*x^12 + 10014*x^11 + 8292*x^10 - 14513*x^9 - 13426*x^8 +
11322*x^7 + 10779*x^6 - 4166*x^5 - 3649*x^4 + 669*x^3 + 389*x^2 - 45*x -
9,3,x^20 + 12*x^19 + 35*x^18 - 120*x^17 - 818*x^16 - 503*x^15 + 5196*x^14 +
9925*x^13 - 10141*x^12 - 40746*x^11 - 9933*x^10 + 61918*x^9 + 46584*x^8 -
29769*x^7 - 31815*x^6 + 7628*x^5 + 8524*x^4 - 1815*x^3 - 808*x^2 + 263*x -
19,5,x^20 + 17*x^19 + 83*x^18 - 160*x^17 - 2704*x^16 - 5758*x^15 + 21317*x^14 +
106677*x^13 + 35612*x^12 - 597190*x^11 - 1068980*x^10 + 739500*x^9 + 3863028*x^8
+ 2706594*x^7 - 3110844*x^6 - 5424167*x^5 - 1630358*x^4 + 1640521*x^3 +
1393701*x^2 + 366210*x + 31369,7,x^20 + 6*x^19 - 63*x^18 - 424*x^17 + 1388*x^16
+ 11650*x^15 - 10625*x^14 - 157713*x^13 - 39378*x^12 + 1086458*x^11 +
1033532*x^10 - 3437110*x^9 - 5033789*x^8 + 3390483*x^7 + 7142396*x^6 -
568725*x^5 - 3050148*x^4 + 134703*x^3 + 337508*x^2 - 2990*x - 7943,11,x^20 +
40*x^19 + 654*x^18 + 5168*x^17 + 12370*x^16 - 120631*x^15 - 1142633*x^14 -
3208037*x^13 + 6005022*x^12 + 67537660*x^11 + 168761948*x^10 - 5915323*x^9 -
844155774*x^8 - 1364248341*x^7 + 615302043*x^6 + 3549597747*x^5 + 1885966284*x^4
- 2836376965*x^3 - 2724916829*x^2 + 461761032*x + 726492771,13,x^20 + 5*x^19 -
127*x^18 - 631*x^17 + 6439*x^16 + 32187*x^15 - 167332*x^14 - 859067*x^13 +
2369765*x^12 + 12999623*x^11 - 17717297*x^10 - 113532837*x^9 + 56650003*x^8 +
559512234*x^7 + 41271202*x^6 - 1422693506*x^5 - 694255401*x^4 + 1382830503*x^3 +
1185975823*x^2 + 192015993*x - 12374199[]
541,2,2,x^24 - 3*x^23 - 31*x^22 + 97*x^21 + 402*x^20 - 1333*x^19 - 2825*x^18 +
10187*x^17 + 11576*x^16 - 47520*x^15 - 27272*x^14 + 139733*x^13 + 31933*x^12 -
258608*x^11 - 4817*x^10 + 293651*x^9 - 26127*x^8 - 196645*x^7 + 21140*x^6 +
74903*x^5 - 4562*x^4 - 14861*x^3 - 379*x^2 + 1179*x + 153,3,x^24 - 12*x^23 +
23*x^22 + 264*x^21 - 1202*x^20 - 1359*x^19 + 16144*x^18 - 11151*x^17 -
101433*x^16 + 169382*x^15 + 316059*x^14 - 879646*x^13 - 352728*x^12 +
2350767*x^11 - 566655*x^10 - 3332320*x^9 + 2073100*x^8 + 2202693*x^7 -
2071804*x^6 - 371069*x^5 + 648245*x^4 - 62600*x^3 - 27760*x^2 + 2960*x -
16,5,x^24 - 13*x^23 + 16*x^22 + 471*x^21 - 1896*x^20 - 5343*x^19 + 39712*x^18 +
8885*x^17 - 408527*x^16 + 324485*x^15 + 2485859*x^14 - 3477513*x^13 -
9557728*x^12 + 17929032*x^11 + 23513024*x^10 - 55616625*x^9 - 35612272*x^8 +
108441058*x^7 + 28373219*x^6 - 129873224*x^5 - 2688364*x^4 + 86826119*x^3 -
13479964*x^2 - 24511980*x + 7776873,7,x^24 - 2*x^23 - 87*x^22 + 192*x^21 +
3132*x^20 - 7646*x^19 - 60269*x^18 + 164371*x^17 + 664490*x^16 - 2077806*x^15 -
4115052*x^14 + 15762462*x^13 + 12202559*x^12 - 70260609*x^11 - 2852624*x^10 +
173225463*x^9 - 69692264*x^8 - 212783853*x^7 + 138052360*x^6 + 115329438*x^5 -
88029127*x^4 - 24541960*x^3 + 17114400*x^2 + 2046176*x - 11152,11,x^24 - 38*x^23
+ 593*x^22 - 4588*x^21 + 13589*x^20 + 51937*x^19 - 565855*x^18 + 1360874*x^17 +
3383657*x^16 - 24858652*x^15 + 29524911*x^14 + 119539590*x^13 - 389706424*x^12 +
50644662*x^11 + 1409318191*x^10 - 1892090669*x^9 - 1290184109*x^8 +
4815555739*x^7 - 2466416816*x^6 - 3172675484*x^5 + 4274432912*x^4 -
1163442301*x^3 - 719976526*x^2 + 498835026*x - 82710567,13,x^24 + 3*x^23 -
155*x^22 - 429*x^21 + 10213*x^20 + 26473*x^19 - 373202*x^18 - 929109*x^17 +
8265861*x^16 + 20477029*x^15 - 113584445*x^14 - 292969719*x^13 + 943671573*x^12
+ 2693354440*x^11 - 4261879806*x^10 - 15062333404*x^9 + 6721329171*x^8 +
45156864567*x^7 + 14102878627*x^6 - 53248950673*x^5 - 40969305993*x^4 +
8026474040*x^3 + 11935366248*x^2 + 819040384*x - 350893376[]

Total time: 22.529 seconds, Total memory usage: 6.78MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sun Nov 30 19:40:54 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [542..544] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:40:38 on modular  [Seed = 3040871613]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
542,1,2,x - 1,3,x - 2,5,x - 2,7,x,11,x + 4,13,x[]
542,2,2,x - 1,3,x + 1,5,x,7,x + 5,11,x,13,x + 1[]
542,3,2,x^2 - 2*x + 1,3,x^2 + 2*x - 1,5,x^2 + 4*x + 2,7,x^2 + 2*x - 1,11,x^2 +
8*x + 14,13,x^2 + 6*x + 1[]
542,4,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 + x^2 - 3*x - 1,5,x^3 - 4*x - 2,7,x^3 +
5*x^2 + 5*x - 1,11,x^3 - 4*x^2 - 10*x + 38,13,x^3 + 7*x^2 + 7*x - 19[]
542,5,2,x^3 + 3*x^2 + 3*x + 1,3,x^3 - x^2 - 5*x - 1,5,x^3 + 2*x^2 - 4*x -
6,7,x^3 - x^2 - 19*x + 37,11,x^3 + 10*x^2 + 26*x + 6,13,x^3 - 15*x^2 + 75*x -
125[]
542,6,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 - 3*x^2 - x + 5,5,x^3 - 4*x^2 - 4*x +
20,7,x^3 - 5*x^2 + 3*x + 5,11,x^3 - 4*x^2 + 4,13,x^3 + 5*x^2 - 5*x + 1[]
542,7,2,x^4 - 4*x^3 + 6*x^2 - 4*x + 1,3,x^4 + 4*x^3 + 2*x^2 - 4*x + 1,5,x^4 +
4*x^3 - 2*x^2 - 8*x + 4,7,x^4 - 4*x^3 - 8*x^2 + 8*x + 7,11,x^4 - 8*x^3 + 10*x^2
+ 40*x - 68,13,x^4 - 12*x^3 + 16*x^2 + 240*x - 721[]
542,8,2,x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15*x^2 + 6*x + 1,3,x^6 - 16*x^4 + 2*x^3
+ 69*x^2 - 8*x - 82,5,x^6 - 2*x^5 - 32*x^4 + 80*x^3 + 232*x^2 - 768*x +
416,7,x^6 - 10*x^5 + 20*x^4 + 74*x^3 - 285*x^2 + 224*x - 32,11,x^6 - 2*x^5 -
44*x^4 + 104*x^3 + 312*x^2 - 640*x + 256,13,x^6 - 26*x^4 + 6*x^3 + 171*x^2 -
108*x - 162[]
543,1,2,x^3 + 2*x^2 - x - 1,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 + x^2 - 2*x - 1,7,x^3
+ 7*x^2 + 14*x + 7,11,x^3 + 2*x^2 - x - 1,13,x^3 + 9*x^2 + 20*x - 1[]
543,2,2,x^5 + x^4 - 6*x^3 - 8*x^2 + 1,3,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x -
1,5,x^5 - 3*x^4 - 14*x^3 + 43*x^2 - 12*x - 16,7,x^5 - 9*x^4 - 2*x^3 + 211*x^2 -
562*x + 284,11,x^5 + 4*x^4 - 13*x^3 - 27*x^2 + 86*x - 52,13,x^5 - 9*x^4 + 23*x^3
- 8*x^2 - 18*x + 7[]
543,3,2,x^7 + 4*x^6 - 3*x^5 - 23*x^4 - 5*x^3 + 32*x^2 + 15*x - 1,3,x^7 + 7*x^6 +
21*x^5 + 35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1,5,x^7 + 3*x^6 - 11*x^5 - 30*x^4 +
17*x^3 + 28*x^2 - 6*x - 7,7,x^7 + x^6 - 19*x^5 + 43*x^3 - 26*x^2 + 1,11,x^7 +
4*x^6 - 27*x^5 - 111*x^4 + 136*x^3 + 556*x^2 - 272*x - 400,13,x^7 + 11*x^6 +
21*x^5 - 84*x^4 - 123*x^3 + 322*x^2 - 130*x + 7[]
543,4,2,x^8 - 3*x^7 - 6*x^6 + 21*x^5 + 5*x^4 - 35*x^3 + 10*x^2 + 4*x - 1,3,x^8 +
8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,5,x^8 - 5*x^7 -
14*x^6 + 97*x^5 - 30*x^4 - 336*x^3 + 192*x^2 + 320*x - 128,7,x^8 + 3*x^7 -
26*x^6 - 57*x^5 + 216*x^4 + 268*x^3 - 576*x^2 - 272*x + 448,11,x^8 - 4*x^7 -
23*x^6 + 57*x^5 + 172*x^4 - 68*x^3 - 208*x^2 + 16*x + 64,13,x^8 - 13*x^7 +
24*x^6 + 289*x^5 - 1077*x^4 - 1095*x^3 + 6318*x^2 + 1067*x - 6298[]
543,5,2,x^8 - 3*x^7 - 12*x^6 + 43*x^5 + 24*x^4 - 169*x^3 + 84*x^2 + 113*x -
73,3,x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1,5,x^8 +
2*x^7 - 25*x^6 - 30*x^5 + 193*x^4 + 40*x^3 - 524*x^2 + 304*x + 64,7,x^8 + 2*x^7
- 19*x^6 - 2*x^5 + 87*x^4 - 58*x^3 - 92*x^2 + 112*x - 32,11,x^8 + 2*x^7 - 56*x^6
- 104*x^5 + 864*x^4 + 1824*x^3 - 3648*x^2 - 10240*x - 5120,13,x^8 - 8*x^7 -
40*x^6 + 430*x^5 - 84*x^4 - 4996*x^3 + 6205*x^2 + 7300*x + 500[]
544,1,2,x,3,x,5,x,7,x + 2,11,x + 4,13,x - 2[]
544,2,2,x,3,x - 2,5,x - 2,7,x - 2,11,x + 2,13,x - 2[]
544,3,2,x,3,x + 2,5,x - 2,7,x + 2,11,x - 2,13,x - 2[]
544,4,2,x,3,x,5,x,7,x - 2,11,x - 4,13,x - 2[]
544,5,2,x,3,x - 2,5,x - 4,7,x + 4,11,x - 2,13,x - 2[]
544,6,2,x,3,x + 2,5,x - 4,7,x - 4,11,x + 2,13,x - 2[]
544,7,2,x^2,3,x^2 - 2,5,x^2 + 4*x + 4,7,x^2 - 18,11,x^2 - 2,13,x^2 + 8*x + 16[]
544,8,2,x^2,3,x^2 - 10,5,x^2 + 4*x + 4,7,x^2 - 10,11,x^2 - 10,13,x^2 + 8*x +
16[]
544,9,2,x^3,3,x^3 - 2*x^2 - 4*x + 4,5,x^3 + 2*x^2 - 12*x - 8,7,x^3 - 2*x^2 - 8*x
- 4,11,x^3 - 10*x^2 + 28*x - 20,13,x^3 + 6*x^2 - 4*x - 40[]
544,10,2,x^3,3,x^3 + 2*x^2 - 4*x - 4,5,x^3 + 2*x^2 - 12*x - 8,7,x^3 + 2*x^2 -
8*x + 4,11,x^3 + 10*x^2 + 28*x + 20,13,x^3 + 6*x^2 - 4*x - 40[]

Total time: 16.039 seconds, Total memory usage: 5.78MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 19:45:46 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [545..547] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:45:26 on modular  [Seed = 3341973487]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
545,1,2,x - 1,3,x,5,x - 1,7,x + 4,11,x - 4,13,x + 6[]
545,2,2,x^2 - 2*x - 1,3,x^2 + 4*x + 2,5,x^2 + 2*x + 1,7,x^2 - 4*x + 2,11,x^2 -
18,13,x^2 - 4*x + 4[]
545,3,2,x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x - 1,3,x^5 - x^4 - 4*x^3 + 3*x^2 + 3*x -
1,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 + 8*x^4 + 19*x^3 + 15*x^2 + x
- 1,11,x^5 + 4*x^4 - 9*x^3 - 27*x^2 - 13*x + 1,13,x^5 - 33*x^3 - 22*x^2 + 220*x
+ 253[]
545,4,2,x^5 + 3*x^4 - 2*x^3 - 11*x^2 - 7*x - 1,3,x^5 + 7*x^4 + 12*x^3 - 11*x^2 -
39*x - 17,5,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,7,x^5 + 8*x^4 + 17*x^3 -
11*x^2 - 69*x - 53,11,x^5 + 8*x^4 + 9*x^3 - 43*x^2 - 73*x + 1,13,x^5 - 7*x^3 +
2*x^2 + 8*x + 1[]
545,5,2,x^11 + 3*x^10 - 17*x^9 - 52*x^8 + 98*x^7 + 305*x^6 - 228*x^5 - 681*x^4 +
257*x^3 + 460*x^2 - 215*x - 3,3,x^11 - x^10 - 22*x^9 + 21*x^8 + 171*x^7 -
159*x^6 - 558*x^5 + 522*x^4 + 672*x^3 - 616*x^2 - 100*x + 36,5,x^11 + 11*x^10 +
55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 + 330*x^4 + 165*x^3 + 55*x^2 +
11*x + 1,7,x^11 - 8*x^10 - 23*x^9 + 271*x^8 + 131*x^7 - 3211*x^6 - 694*x^5 +
16258*x^4 + 9132*x^3 - 27752*x^2 - 29036*x - 6668,11,x^11 - 12*x^10 + 11*x^9 +
325*x^8 - 975*x^7 - 1889*x^6 + 8558*x^5 + 2550*x^4 - 24700*x^3 + 176*x^2 +
21892*x + 5556,13,x^11 - 6*x^10 - 69*x^9 + 472*x^8 + 1224*x^7 - 11855*x^6 +
1988*x^5 + 101740*x^4 - 142056*x^3 - 128800*x^2 + 186464*x + 113328[]
545,6,2,x^13 - 3*x^12 - 18*x^11 + 57*x^10 + 113*x^9 - 391*x^8 - 300*x^7 +
1206*x^6 + 323*x^5 - 1685*x^4 - 114*x^3 + 921*x^2 - 5*x - 89,3,x^13 - 9*x^12 +
12*x^11 + 109*x^10 - 339*x^9 - 261*x^8 + 1992*x^7 - 988*x^6 - 4096*x^5 +
4120*x^4 + 2588*x^3 - 3680*x^2 - 180*x + 652,5,x^13 - 13*x^12 + 78*x^11 -
286*x^10 + 715*x^9 - 1287*x^8 + 1716*x^7 - 1716*x^6 + 1287*x^5 - 715*x^4 +
286*x^3 - 78*x^2 + 13*x - 1,7,x^13 - 16*x^12 + 73*x^11 + 101*x^10 - 1649*x^9 +
2759*x^8 + 9104*x^7 - 29636*x^6 - 6940*x^5 + 95220*x^4 - 47024*x^3 - 101440*x^2
+ 64948*x + 24556,11,x^13 - 73*x^11 + 61*x^10 + 2007*x^9 - 3051*x^8 - 24732*x^7
+ 51576*x^6 + 125860*x^5 - 335844*x^4 - 181096*x^3 + 781432*x^2 - 143596*x -
349292,13,x^13 - 6*x^12 - 75*x^11 + 544*x^10 + 1308*x^9 - 15931*x^8 + 12832*x^7
+ 155056*x^6 - 411384*x^5 - 3464*x^4 + 1262416*x^3 - 1774384*x^2 + 908576*x -
143536[]
546,1,2,x + 1,3,x + 1,5,x + 1,7,x + 1,11,x + 1,13,x - 1[]
546,2,2,x + 1,3,x - 1,5,x - 1,7,x + 1,11,x - 3,13,x + 1[]
546,3,2,x + 1,3,x - 1,5,x + 2,7,x + 1,11,x + 4,13,x - 1[]
546,4,2,x + 1,3,x - 1,5,x - 3,7,x - 1,11,x - 3,13,x - 1[]
546,5,2,x - 1,3,x + 1,5,x - 3,7,x + 1,11,x - 1,13,x + 1[]
546,6,2,x - 1,3,x - 1,5,x + 1,7,x - 1,11,x - 5,13,x + 1[]
546,7,2,x - 1,3,x - 1,5,x - 2,7,x - 1,11,x + 4,13,x + 1[]
546,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + x - 14,7,x^2 - 2*x + 1,11,x^2 -
3*x - 12,13,x^2 + 2*x + 1[]
546,9,2,x^2 - 2*x + 1,3,x^2 + 2*x + 1,5,x^2 + x - 10,7,x^2 - 2*x + 1,11,x^2 -
5*x - 4,13,x^2 - 2*x + 1[]
546,10,2,x^2 - 2*x + 1,3,x^2 - 2*x + 1,5,x^2 - 3*x - 2,7,x^2 + 2*x + 1,11,x^2 -
x - 4,13,x^2 - 2*x + 1[]
547,1,2,x^2 + 2*x - 1,3,x^2 - 2,5,x^2 - 2,7,x^2 - 4*x + 4,11,x^2 + 10*x +
23,13,x^2 - 6*x + 9[]
547,2,2,x^18 + 4*x^17 - 18*x^16 - 84*x^15 + 116*x^14 + 708*x^13 - 282*x^12 -
3104*x^11 - 137*x^10 + 7703*x^9 + 2068*x^8 - 11068*x^7 - 4274*x^6 + 9021*x^5 +
4048*x^4 - 3834*x^3 - 1851*x^2 + 654*x + 328,3,x^18 + 10*x^17 + 16*x^16 -
141*x^15 - 499*x^14 + 485*x^13 + 3908*x^12 + 1561*x^11 - 12985*x^10 - 13361*x^9
+ 17477*x^8 + 27279*x^7 - 4923*x^6 - 17035*x^5 - 529*x^4 + 4092*x^3 + 221*x^2 -
266*x - 32,5,x^18 + 27*x^17 + 304*x^16 + 1771*x^15 + 4872*x^14 - 1378*x^13 -
53562*x^12 - 157710*x^11 - 138777*x^10 + 238435*x^9 + 649756*x^8 + 308466*x^7 -
551465*x^6 - 657632*x^5 + 22692*x^4 + 316340*x^3 + 88161*x^2 - 42046*x -
15872,7,x^18 + 11*x^17 - 17*x^16 - 591*x^15 - 1324*x^14 + 9436*x^13 + 41987*x^12
- 23119*x^11 - 382155*x^10 - 455177*x^9 + 916701*x^8 + 2110064*x^7 - 191995*x^6
- 3024596*x^5 - 1344002*x^4 + 1335870*x^3 + 1038609*x^2 + 62202*x -
58576,11,x^18 - 2*x^17 - 113*x^16 + 224*x^15 + 4921*x^14 - 9574*x^13 -
104309*x^12 + 191844*x^11 + 1134032*x^10 - 1787123*x^9 - 6381183*x^8 +
6865320*x^7 + 18625653*x^6 - 7534045*x^5 - 23371203*x^4 - 5528150*x^3 +
3523832*x^2 + 843423*x - 82432,13,x^18 + 25*x^17 + 185*x^16 - 448*x^15 -
13499*x^14 - 57203*x^13 + 128151*x^12 + 1756201*x^11 + 3932642*x^10 -
10003709*x^9 - 62952777*x^8 - 74607411*x^7 + 173378296*x^6 + 573367312*x^5 +
388950788*x^4 - 562304121*x^3 - 1130971990*x^2 - 716121924*x - 160401143[]
547,3,2,x^25 - 4*x^24 - 30*x^23 + 134*x^22 + 365*x^21 - 1926*x^20 - 2226*x^19 +
15560*x^18 + 6033*x^17 - 77601*x^16 + 4782*x^15 + 246402*x^14 - 87059*x^13 -
493902*x^12 + 275826*x^11 + 594258*x^10 - 427359*x^9 - 378617*x^8 + 334926*x^7 +
87006*x^6 - 111411*x^5 + 8810*x^4 + 6600*x^3 - 872*x^2 - 68*x + 8,3,x^25 -
8*x^24 - 20*x^23 + 311*x^22 - 159*x^21 - 4979*x^20 + 8554*x^19 + 41509*x^18 -
110927*x^17 - 181277*x^16 + 746037*x^15 + 285827*x^14 - 2917461*x^13 +
845121*x^12 + 6693937*x^11 - 4939122*x^10 - 8518495*x^9 + 9727960*x^8 +
5007908*x^7 - 9161144*x^6 - 323960*x^5 + 4025440*x^4 - 733752*x^3 - 682336*x^2 +
165984*x + 25088,5,x^25 - 29*x^24 + 340*x^23 - 1865*x^22 + 2290*x^21 +
29052*x^20 - 157882*x^19 + 151052*x^18 + 1248513*x^17 - 4381041*x^16 +
564172*x^15 + 24220956*x^14 - 42611521*x^13 - 31283226*x^12 + 174636898*x^11 -
123240086*x^10 - 225721819*x^9 + 401447188*x^8 - 46423448*x^7 - 329851888*x^6 +
207596896*x^5 + 74345104*x^4 - 101463976*x^3 + 10062688*x^2 + 14644416*x -
3804416,7,x^25 - 5*x^24 - 85*x^23 + 465*x^22 + 2784*x^21 - 17422*x^20 -
43107*x^19 + 340033*x^18 + 289119*x^17 - 3774099*x^16 + 59601*x^15 +
24772864*x^14 - 13059041*x^13 - 96710450*x^12 + 83645960*x^11 + 217712200*x^10 -
246472963*x^9 - 258864260*x^8 + 371321974*x^7 + 128241888*x^6 - 273367336*x^5 -
31328*x^4 + 88279072*x^3 - 15330560*x^2 - 9703552*x + 2553344,11,x^25 - 10*x^24
- 86*x^23 + 1174*x^22 + 1669*x^21 - 54292*x^20 + 51648*x^19 + 1293656*x^18 -
2890661*x^17 - 17268413*x^16 + 56033375*x^15 + 130103461*x^14 - 581944349*x^13 -
510635922*x^12 + 3569100663*x^11 + 607783568*x^10 - 13299156853*x^9 +
2729170202*x^8 + 29712735620*x^7 - 12132769546*x^6 - 37413264447*x^5 +
19408199907*x^4 + 22917476944*x^3 - 13010797205*x^2 - 4446362004*x +
2284779388,13,x^25 - 19*x^24 + 32*x^23 + 1521*x^22 - 9375*x^21 - 29718*x^20 +
394046*x^19 - 344627*x^18 - 6307669*x^17 + 16538325*x^16 + 40622837*x^15 -
191250128*x^14 - 31072558*x^13 + 969686277*x^12 - 786046477*x^11 -
2107130475*x^10 + 3278287707*x^9 + 1043197692*x^8 - 4333912697*x^7 +
1663175229*x^6 + 1272531297*x^5 - 926066215*x^4 + 26976803*x^3 + 80134296*x^2 -
8499211*x - 1439326[]

Total time: 19.819 seconds, Total memory usage: 7.13MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Sun Nov 30 19:57:06 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [548..550] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 19:56:48 on modular  [Seed = 3961078322]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
548,1,2,x^4,3,x^4 + 3*x^3 - 2*x^2 - 4*x - 1,5,x^4 + 4*x^3 + 2*x^2 - 5*x -
3,7,x^4 + x^3 - 8*x^2 - 10*x - 3,11,x^4 + x^3 - 20*x^2 + 14*x + 27,13,x^4 +
14*x^3 + 60*x^2 + 61*x - 69[]
548,2,2,x^8,3,x^8 - 3*x^7 - 14*x^6 + 42*x^5 + 55*x^4 - 170*x^3 - 46*x^2 + 198*x
- 54,5,x^8 - 2*x^7 - 28*x^6 + 61*x^5 + 213*x^4 - 484*x^3 - 312*x^2 + 624*x +
144,7,x^8 + x^7 - 32*x^6 - 30*x^5 + 233*x^4 + 120*x^3 - 472*x^2 + 112*x +
32,11,x^8 - 3*x^7 - 48*x^6 + 214*x^5 + 339*x^4 - 3340*x^3 + 6784*x^2 - 5584*x +
1632,13,x^8 - 20*x^7 + 118*x^6 + 95*x^5 - 3497*x^4 + 12820*x^3 - 16232*x^2 +
3056*x + 4016[]
549,1,2,x - 1,3,x,5,x,7,x + 2,11,x + 4,13,x + 2[]
549,2,2,x + 1,3,x,5,x,7,x + 2,11,x - 4,13,x + 2[]
549,3,2,x - 1,3,x,5,x - 3,7,x - 1,11,x - 5,13,x - 1[]
549,4,2,x^2 - 3,3,x^2,5,x^2 - 3,7,x^2 + 2*x + 1,11,x^2 - 27,13,x^2 - 10*x + 25[]
549,5,2,x^2 - 2*x - 1,3,x^2,5,x^2 - 2*x + 1,7,x^2 + 2*x - 1,11,x^2 - 2*x -
1,13,x^2 + 6*x + 9[]
549,6,2,x^3 + x^2 - 3*x - 1,3,x^3,5,x^3 - x^2 - 9*x + 13,7,x^3 + 3*x^2 - x -
1,11,x^3 + 13*x^2 + 53*x + 67,13,x^3 + 9*x^2 + 11*x - 37[]
549,7,2,x^3 + x^2 - 3*x - 1,3,x^3,5,x^3 + 6*x^2 + 12*x + 8,7,x^3 - 16*x -
16,11,x^3 + 2*x^2 - 4*x - 4,13,x^3 - 6*x^2 - 4*x + 40[]
549,8,2,x^6 - 13*x^4 + 41*x^2 - 1,3,x^6,5,x^6 - 19*x^4 + 80*x^2 - 64,7,x^6 -
6*x^5 - 23*x^4 + 184*x^3 - 8*x^2 - 1408*x + 1936,11,x^6 - 15*x^4 + 56*x^2 -
4,13,x^6 + 6*x^5 - 23*x^4 - 80*x^3 + 304*x^2 - 256*x + 64[]
549,9,2,x^6 - 11*x^4 - 2*x^3 + 31*x^2 + 10*x - 17,3,x^6,5,x^6 + 2*x^5 - 23*x^4 -
28*x^3 + 144*x^2 + 80*x - 144,7,x^6 - 2*x^5 - 25*x^4 + 60*x^3 + 128*x^2 - 432*x
+ 288,11,x^6 - 8*x^5 - 5*x^4 + 110*x^3 - 68*x^2 - 8*x + 4,13,x^6 - 6*x^5 -
23*x^4 + 116*x^3 + 168*x^2 - 464*x - 608[]
550,1,2,x + 1,3,x + 1,5,x,7,x - 1,11,x + 1,13,x + 2[]
550,2,2,x + 1,3,x - 1,5,x,7,x + 3,11,x - 1,13,x - 6[]
550,3,2,x + 1,3,x + 2,5,x,7,x,11,x - 1,13,x + 3[]
550,4,2,x + 1,3,x + 2,5,x,7,x + 4,11,x + 1,13,x - 5[]
550,5,2,x + 1,3,x - 3,5,x,7,x - 1,11,x + 1,13,x[]
550,6,2,x + 1,3,x - 1,5,x,7,x + 3,11,x - 1,13,x + 4[]
550,7,2,x + 1,3,x + 2,5,x,7,x,11,x - 1,13,x - 2[]
550,8,2,x - 1,3,x - 2,5,x,7,x - 4,11,x + 1,13,x + 5[]
550,9,2,x - 1,3,x + 1,5,x,7,x + 5,11,x - 1,13,x + 2[]
550,10,2,x - 1,3,x + 3,5,x,7,x + 1,11,x + 1,13,x[]
550,11,2,x - 1,3,x + 1,5,x,7,x - 3,11,x - 1,13,x - 4[]
550,12,2,x - 1,3,x - 2,5,x,7,x,11,x - 1,13,x + 2[]
550,13,2,x - 1,3,x - 2,5,x,7,x,11,x - 1,13,x - 3[]
550,14,2,x^2 - 2*x + 1,3,x^2 - x - 8,5,x^2,7,x^2 + x - 8,11,x^2 + 2*x + 1,13,x^2
+ 4*x + 4[]

Total time: 18.119 seconds, Total memory usage: 6.34MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 20:33:09 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [551..553] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 20:32:51 on modular  [Seed = 2574007511]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
551,1,2,x - 1,3,x - 1,5,x + 1,7,x + 4,11,x - 1,13,x + 1[]
551,2,2,x + 1,3,x - 1,5,x + 1,7,x - 2,11,x + 3,13,x + 5[]
551,3,2,x - 2,3,x + 2,5,x + 1,7,x + 1,11,x + 3,13,x + 2[]
551,4,2,x + 2,3,x + 2,5,x + 1,7,x + 1,11,x - 1,13,x - 2[]
551,5,2,x^2 + 2*x + 1,3,x^2 - 5,5,x^2 + 2*x + 1,7,x^2 + 2*x - 4,11,x^2 -
5,13,x^2 - 2*x + 1[]
551,6,2,x^3 - 4*x + 2,3,x^3,5,x^3 - x^2 - 9*x + 13,7,x^3 + 3*x^2 + 3*x +
1,11,x^3 + 7*x^2 + 13*x + 5,13,x^3 + 4*x^2 + 2*x - 2[]
551,7,2,x^16 - 3*x^15 - 22*x^14 + 68*x^13 + 190*x^12 - 608*x^11 - 832*x^10 +
2760*x^9 + 1972*x^8 - 6728*x^7 - 2502*x^6 + 8420*x^5 + 1642*x^4 - 4511*x^3 -
577*x^2 + 572*x - 18,3,x^16 - 4*x^15 - 28*x^14 + 120*x^13 + 284*x^12 - 1372*x^11
- 1215*x^10 + 7450*x^9 + 1666*x^8 - 19442*x^7 + 1155*x^6 + 21898*x^5 - 1672*x^4
- 8702*x^3 + 5*x^2 + 704*x - 44,5,x^16 + 2*x^15 - 51*x^14 - 86*x^13 + 1000*x^12
+ 1272*x^11 - 9667*x^10 - 7454*x^9 + 48303*x^8 + 11318*x^7 - 114963*x^6 +
30334*x^5 + 93501*x^4 - 67948*x^3 + 12083*x^2 + 290*x - 15,7,x^16 - 4*x^15 -
66*x^14 + 266*x^13 + 1682*x^12 - 6726*x^11 - 21539*x^10 + 82902*x^9 + 150434*x^8
- 518552*x^7 - 592907*x^6 + 1516972*x^5 + 1351768*x^4 - 1568050*x^3 -
1469107*x^2 + 71670*x + 181540,11,x^16 - 4*x^15 - 104*x^14 + 404*x^13 +
3867*x^12 - 14080*x^11 - 62900*x^10 + 198392*x^9 + 453696*x^8 - 974432*x^7 -
1614912*x^6 + 1469568*x^5 + 1840384*x^4 - 896512*x^3 - 576512*x^2 + 133120*x +
61440,13,x^16 - 8*x^15 - 89*x^14 + 894*x^13 + 1978*x^12 - 36384*x^11 +
29448*x^10 + 632752*x^9 - 1640672*x^8 - 3621440*x^7 + 18889472*x^6 -
11678720*x^5 - 52017152*x^4 + 102978560*x^3 - 61104128*x^2 + 188416*x +
7135232[]
551,8,2,x^18 - 2*x^17 - 29*x^16 + 56*x^15 + 342*x^14 - 632*x^13 - 2112*x^12 +
3692*x^11 + 7332*x^10 - 11948*x^9 - 14282*x^8 + 21322*x^7 + 14618*x^6 -
19599*x^5 - 6476*x^4 + 7481*x^3 + 560*x^2 - 346*x + 6,3,x^18 + 2*x^17 - 42*x^16
- 74*x^15 + 738*x^14 + 1102*x^13 - 7037*x^12 - 8474*x^11 + 39398*x^10 +
36022*x^9 - 130265*x^8 - 85036*x^7 + 240754*x^6 + 109972*x^5 - 215593*x^4 -
80360*x^3 + 66816*x^2 + 26928*x + 1472,5,x^18 - 7*x^17 - 47*x^16 + 417*x^15 +
656*x^14 - 9996*x^13 + 1989*x^12 + 121685*x^11 - 144781*x^10 - 764253*x^9 +
1543373*x^8 + 2012045*x^7 - 7000435*x^6 + 940819*x^5 + 12069681*x^4 -
11086865*x^3 - 951023*x^2 + 4806227*x - 1538766,7,x^18 - 11*x^17 - 34*x^16 +
732*x^15 - 556*x^14 - 18180*x^13 + 36623*x^12 + 215027*x^11 - 555132*x^10 -
1334394*x^9 + 3662293*x^8 + 4526337*x^7 - 10650664*x^6 - 7964510*x^5 +
10172147*x^4 + 3566067*x^3 - 2623386*x^2 - 553488*x + 86272,11,x^18 - 5*x^17 -
142*x^16 + 732*x^15 + 8121*x^14 - 43647*x^13 - 238272*x^12 + 1358396*x^11 +
3768136*x^10 - 23468128*x^9 - 30660192*x^8 + 220323264*x^7 + 110432384*x^6 -
1008092928*x^5 - 169786880*x^4 + 1619770368*x^3 + 674871296*x^2 - 84307968*x -
45400064,13,x^18 - 10*x^17 - 143*x^16 + 1646*x^15 + 7412*x^14 - 108898*x^13 -
152348*x^12 + 3748776*x^11 + 22496*x^10 - 72958208*x^9 + 48721024*x^8 +
816188032*x^7 - 764462080*x^6 - 5085597696*x^5 + 4716821504*x^4 +
15931901952*x^3 - 12106178560*x^2 - 17603731456*x + 13163282432[]
552,1,2,x,3,x + 1,5,x + 2,7,x - 2,11,x + 2,13,x + 2[]
552,2,2,x,3,x + 1,5,x,7,x + 2,11,x,13,x - 2[]
552,3,2,x,3,x + 1,5,x - 4,7,x - 2,11,x,13,x - 2[]
552,4,2,x,3,x + 1,5,x - 2,7,x + 4,11,x + 4,13,x + 2[]
552,5,2,x,3,x - 1,5,x + 2,7,x + 4,11,x,13,x + 2[]
552,6,2,x^2,3,x^2 - 2*x + 1,5,x^2 - 2*x - 4,7,x^2 - 4*x + 4,11,x^2 - 2*x -
4,13,x^2 - 20[]
552,7,2,x^3,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 16*x + 16,7,x^3 - 2*x^2 - 12*x +
8,11,x^3 - 4*x^2 - 16*x + 32,13,x^3 - 6*x^2 + 12*x - 8[]
553,1,2,x^7 + 6*x^6 + 7*x^5 - 17*x^4 - 35*x^3 - 3*x^2 + 15*x + 3,3,x^7 + 3*x^6 -
5*x^5 - 16*x^4 + 5*x^3 + 23*x^2 + 3*x - 5,5,x^7 + 4*x^6 - 9*x^5 - 57*x^4 -
49*x^3 + 78*x^2 + 126*x + 45,7,x^7 - 7*x^6 + 21*x^5 - 35*x^4 + 35*x^3 - 21*x^2 +
7*x - 1,11,x^7 + 13*x^6 + 40*x^5 - 92*x^4 - 614*x^3 - 810*x^2 + 375,13,x^7 + x^6
- 49*x^5 - 87*x^4 + 533*x^3 + 845*x^2 - 1282*x - 125[]
553,2,2,x^8 - 3*x^7 - 7*x^6 + 24*x^5 + 6*x^4 - 40*x^3 + 6*x^2 + 8*x + 1,3,x^8 -
3*x^7 - 7*x^6 + 26*x^5 + 3*x^4 - 55*x^3 + 31*x^2 + 9*x - 4,5,x^8 - 4*x^7 - 9*x^6
+ 49*x^5 - 11*x^4 - 96*x^3 + 14*x^2 + 63*x + 18,7,x^8 + 8*x^7 + 28*x^6 + 56*x^5
+ 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,11,x^8 - 3*x^7 - 36*x^6 + 136*x^5 + 214*x^4
- 1430*x^3 + 1936*x^2 - 849*x + 32,13,x^8 - 3*x^7 - 45*x^6 + 155*x^5 + 483*x^4 -
1925*x^3 - 778*x^2 + 6281*x - 3566[]
553,3,2,x^11 + 5*x^10 - 4*x^9 - 49*x^8 - 24*x^7 + 154*x^6 + 125*x^5 - 183*x^4 -
154*x^3 + 67*x^2 + 32*x - 11,3,x^11 + 5*x^10 - 11*x^9 - 80*x^8 + 3*x^7 + 391*x^6
+ 215*x^5 - 577*x^4 - 324*x^3 + 256*x^2 + 88*x - 16,5,x^11 + 10*x^10 + 18*x^9 -
107*x^8 - 365*x^7 + 257*x^6 + 1820*x^5 + 360*x^4 - 3191*x^3 - 1265*x^2 + 1640*x
+ 709,7,x^11 + 11*x^10 + 55*x^9 + 165*x^8 + 330*x^7 + 462*x^6 + 462*x^5 +
330*x^4 + 165*x^3 + 55*x^2 + 11*x + 1,11,x^11 + 5*x^10 - 67*x^9 - 335*x^8 +
1343*x^7 + 6855*x^6 - 8554*x^5 - 49991*x^4 + 5762*x^3 + 111885*x^2 + 41180*x -
14797,13,x^11 + 11*x^10 - 22*x^9 - 596*x^8 - 999*x^7 + 8945*x^6 + 25960*x^5 -
40773*x^4 - 165481*x^3 + 35172*x^2 + 309446*x + 54547[]
553,4,2,x^13 - 7*x^12 + 3*x^11 + 78*x^10 - 144*x^9 - 249*x^8 + 769*x^7 + 79*x^6
- 1451*x^5 + 654*x^4 + 878*x^3 - 686*x^2 + 56*x + 27,3,x^13 - x^12 - 29*x^11 +
26*x^10 + 321*x^9 - 231*x^8 - 1741*x^7 + 857*x^6 + 4836*x^5 - 1136*x^4 -
6360*x^3 - 176*x^2 + 2944*x + 768,5,x^13 - 4*x^12 - 30*x^11 + 119*x^10 + 299*x^9
- 1121*x^8 - 1472*x^7 + 4586*x^6 + 3617*x^5 - 8619*x^4 - 3396*x^3 + 7075*x^2 +
400*x - 1500,7,x^13 - 13*x^12 + 78*x^11 - 286*x^10 + 715*x^9 - 1287*x^8 +
1716*x^7 - 1716*x^6 + 1287*x^5 - 715*x^4 + 286*x^3 - 78*x^2 + 13*x - 1,11,x^13 -
15*x^12 + 53*x^11 + 225*x^10 - 1725*x^9 + 859*x^8 + 14506*x^7 - 24231*x^6 -
42950*x^5 + 112769*x^4 + 20848*x^3 - 166973*x^2 + 58620*x + 27200,13,x^13 + x^12
- 80*x^11 + 14*x^10 + 2299*x^9 - 2341*x^8 - 27032*x^7 + 37029*x^6 + 134289*x^5 -
173902*x^4 - 286484*x^3 + 193213*x^2 + 281180*x + 61284[]

Total time: 17.569 seconds, Total memory usage: 6.01MB

************** MAGMA *****************
Host genoa.ucc.usyd.edu.au. (129.78.228.114)
Time: Sun Nov 30 20:48:32 2003

Input: !ls

Output: Magma V2.10-6     Sun Nov 30 2003 20:48:28 on modular  [Seed = 3860022279]
-------------------------------------

>> !ls;
^

Total time: 3.029 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host genoa.ucc.usyd.edu.au. (129.78.228.114)
Time: Sun Nov 30 20:49:49 2003

Input: !ls

Output: Magma V2.10-6     Sun Nov 30 2003 20:49:46 on modular  [Seed = 4026880455]
-------------------------------------

>> !ls;
^

Total time: 2.999 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host genoa.ucc.usyd.edu.au. (129.78.228.114)
Time: Sun Nov 30 20:50:03 2003

Input: %ls

Output: Magma V2.10-6     Sun Nov 30 2003 20:50:00 on modular  [Seed = 16097604]
-------------------------------------

Total time: 3.079 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host genoa.ucc.usyd.edu.au. (129.78.228.114)
Time: Sun Nov 30 20:50:18 2003

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 20:52:01 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [554..556] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 20:51:44 on modular  [Seed = 617711000]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
554,1,2,x^3 - 3*x^2 + 3*x - 1,3,x^3 + 2*x^2 - x - 1,5,x^3 + 7*x^2 + 14*x +
7,7,x^3 + 6*x^2 + 5*x + 1,11,x^3 + x^2 - 2*x - 1,13,x^3 + 6*x^2 - 9*x - 41[]
554,2,2,x^4 + 4*x^3 + 6*x^2 + 4*x + 1,3,x^4 + 2*x^3 - 5*x^2 - 7*x - 2,5,x^4 -
x^3 - 8*x^2 - 5*x + 2,7,x^4 + 6*x^3 + 9*x^2 - x - 4,11,x^4 + 8*x^3 - 5*x^2 -
151*x - 257,13,x^4 + 3*x^3 - 9*x^2 - 38*x - 31[]
554,3,2,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1,3,x^8
- 3*x^7 - 13*x^6 + 37*x^5 + 54*x^4 - 146*x^3 - 60*x^2 + 182*x - 49,5,x^8 + 2*x^7
- 25*x^6 - 32*x^5 + 201*x^4 + 168*x^3 - 620*x^2 - 285*x + 609,7,x^8 - 8*x^7 -
9*x^6 + 207*x^5 - 430*x^4 - 204*x^3 + 1080*x^2 - 768*x + 160,11,x^8 - 5*x^7 -
20*x^6 + 121*x^5 - 10*x^4 - 604*x^3 + 848*x^2 - 240*x - 96,13,x^8 - 4*x^7 -
47*x^6 + 137*x^5 + 856*x^4 - 1500*x^3 - 6960*x^2 + 5088*x + 20320[]
554,4,2,x^9 - 9*x^8 + 36*x^7 - 84*x^6 + 126*x^5 - 126*x^4 + 84*x^3 - 36*x^2 +
9*x - 1,3,x^9 + x^8 - 17*x^7 - 9*x^6 + 94*x^5 + 12*x^4 - 194*x^3 + 46*x^2 +
119*x - 54,5,x^9 - 8*x^8 + 3*x^7 + 112*x^6 - 197*x^5 - 434*x^4 + 1014*x^3 +
519*x^2 - 1447*x - 66,7,x^9 - 8*x^8 - 5*x^7 + 169*x^6 - 294*x^5 - 620*x^4 +
2392*x^3 - 2752*x^2 + 1376*x - 256,11,x^9 - 67*x^7 - 87*x^6 + 1409*x^5 +
3326*x^4 - 8052*x^3 - 31744*x^2 - 26384*x - 1056,13,x^9 - 7*x^8 - 49*x^7 +
434*x^6 + 283*x^5 - 7876*x^4 + 11764*x^3 + 31536*x^2 - 92832*x + 62048[]
555,1,2,x,3,x - 1,5,x + 1,7,x + 2,11,x - 4,13,x - 5[]
555,2,2,x,3,x - 1,5,x - 1,7,x - 2,11,x,13,x + 1[]
555,3,2,x^2 - x - 1,3,x^2 + 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 5,11,x^2 - x -
1,13,x^2 + 4*x - 1[]
555,4,2,x^2 + x - 3,3,x^2 + 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 6*x + 9,11,x^2 - 3*x
- 1,13,x^2 + 10*x + 25[]
555,5,2,x^2 - x - 3,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 - 2*x + 1,11,x^2 - x -
3,13,x^2 - 13[]
555,6,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 2*x + 1,7,x^2 + 2*x + 1,11,x^2 + 9*x
+ 19,13,x^2 + 4*x - 1[]
555,7,2,x^2 + 3*x + 1,3,x^2 - 2*x + 1,5,x^2 - 2*x + 1,7,x^2 + 4*x - 1,11,x^2 +
3*x - 9,13,x^2 + 10*x + 25[]
555,8,2,x^3 - x^2 - 5*x + 4,3,x^3 + 3*x^2 + 3*x + 1,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 - 4*x^2 - 7*x + 14,11,x^3 - x^2 - 7*x - 4,13,x^3 - 15*x^2 + 75*x - 125[]
555,9,2,x^3 - 2*x^2 - 4*x + 7,3,x^3 - 3*x^2 + 3*x - 1,5,x^3 - 3*x^2 + 3*x -
1,7,x^3 + 4*x^2 - x - 8,11,x^3 + x^2 - 15*x - 28,13,x^3 - 4*x^2 - 7*x + 26[]
555,10,2,x^5 + 3*x^4 - 4*x^3 - 13*x^2 + x + 4,3,x^5 + 5*x^4 + 10*x^3 + 10*x^2 +
5*x + 1,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 - 2*x^4 - 25*x^3 +
62*x^2 + 96*x - 256,11,x^5 + x^4 - 31*x^3 - 48*x^2 + 80*x + 128,13,x^5 - 7*x^4 +
3*x^3 + 39*x^2 - 40*x - 4[]
556,1,2,x,3,x,5,x + 1,7,x + 1,11,x - 1,13,x + 3[]
556,2,2,x^3,3,x^3 + 2*x^2 - 3*x - 3,5,x^3 - 9*x + 1,7,x^3 + 4*x^2 - x - 1,11,x^3
+ 13*x^2 + 52*x + 63,13,x^3 - x^2 - 12*x - 9[]
556,3,2,x^7,3,x^7 - 4*x^6 - 9*x^5 + 43*x^4 + 14*x^3 - 120*x^2 + 24*x + 64,5,x^7
+ x^6 - 24*x^5 - 2*x^4 + 161*x^3 - 117*x^2 - 91*x + 49,7,x^7 - x^6 - 22*x^5 +
18*x^4 + 125*x^3 - 85*x^2 - 209*x + 121,11,x^7 - 14*x^6 + 64*x^5 - 104*x^4 +
48*x^3 + 12*x^2 - 10*x + 1,13,x^7 + 2*x^6 - 54*x^5 - 132*x^4 + 588*x^3 + 846*x^2
- 2466*x + 919[]

Total time: 17.279 seconds, Total memory usage: 6.07MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 20:56:33 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [557..559] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: Magma V2.10-6     Sun Nov 30 2003 20:56:17 on modular  [Seed = 1136059278]
-------------------------------------

11,1,2,$.1 + 2,3,$.1 + 1,5,$.1 - 1,7,$.1 + 2,11,$.1 - 1,13,$.1 - 4[]
557,1,2,x - 1,3,x + 1,5,x,7,x - 2,11,x + 3,13,x - 2[]
557,2,2,x - 2,3,x - 2,5,x,7,x - 5,11,x + 6,13,x + 4[]
557,3,2,x^18 + 6*x^17 - 6*x^16 - 98*x^15 - 83*x^14 + 588*x^13 + 978*x^12 -
1507*x^11 - 3913*x^10 + 1062*x^9 + 7268*x^8 + 2007*x^7 - 6225*x^6 - 3695*x^5 +
2078*x^4 + 1980*x^3 - 23*x^2 - 339*x - 72,3,x^18 + 15*x^17 + 75*x^16 + 49*x^15 -
814*x^14 - 2394*x^13 + 1044*x^12 + 13596*x^11 + 12477*x^10 - 25556*x^9 -
45888*x^8 + 6698*x^7 + 47848*x^6 + 15237*x^5 - 10287*x^4 - 2442*x^3 + 395*x^2 +
93*x + 4,5,x^18 + 6*x^17 - 32*x^16 - 254*x^15 + 188*x^14 + 3821*x^13 + 3078*x^12
- 23586*x^11 - 38270*x^10 + 49953*x^9 + 115450*x^8 - 32043*x^7 - 118597*x^6 +
6367*x^5 + 32117*x^4 - 219*x^3 - 1942*x^2 - 25*x + 28,7,x^18 + 23*x^17 +
195*x^16 + 518*x^15 - 2765*x^14 - 25160*x^13 - 65832*x^12 + 26918*x^11 +
542548*x^10 + 1102830*x^9 + 79979*x^8 - 2707932*x^7 - 3217980*x^6 + 804502*x^5 +
3679394*x^4 + 1446746*x^3 - 1010698*x^2 - 715740*x - 86551,11,x^18 + 3*x^17 -
117*x^16 - 397*x^15 + 5485*x^14 + 20912*x^13 - 130583*x^12 - 568746*x^11 +
1616882*x^10 + 8545534*x^9 - 8748519*x^8 - 69281842*x^7 - 1470968*x^6 +
266228143*x^5 + 148974278*x^4 - 337958309*x^3 - 118352665*x^2 + 206218677*x -
44939592,13,x^18 + 26*x^17 + 217*x^16 - 6*x^15 - 10471*x^14 - 52386*x^13 +
44764*x^12 + 1116943*x^11 + 2635070*x^10 - 4804436*x^9 - 29573582*x^8 -
26419680*x^7 + 68269706*x^6 + 126084225*x^5 - 33806500*x^4 - 151090139*x^3 -
1952582*x^2 + 58539389*x - 10679518[]
557,4,2,x^26 - x^25 - 40*x^24 + 36*x^23 + 701*x^22 - 557*x^21 - 7078*x^20 +
4855*x^19 + 45533*x^18 - 26248*x^17 - 194780*x^16 + 91281*x^15 + 561051*x^14 -
204613*x^13 - 1077249*x^12 + 286983*x^11 + 1332859*x^10 - 233167*x^9 -
994145*x^8 + 90493*x^7 + 396290*x^6 - 6446*x^5 - 68301*x^4 - 2616*x^3 + 3093*x^2
+ 320*x + 1,3,x^26 - 16*x^25 + 73*x^24 + 144*x^23 - 2140*x^22 + 3536*x^21 +
19587*x^20 - 71418*x^19 - 52175*x^18 + 543571*x^17 - 309381*x^16 - 2168193*x^15
+ 2929364*x^14 + 4627520*x^13 - 10350762*x^12 - 4071610*x^11 + 19645056*x^10 -
2652133*x^9 - 20674454*x^8 + 9142187*x^7 + 11093092*x^6 - 7524689*x^5 -
2244755*x^4 + 2413207*x^3 - 114917*x^2 - 214756*x + 37327,5,x^26 - 4*x^25 -
78*x^24 + 330*x^23 + 2574*x^22 - 11831*x^21 - 46244*x^20 + 241510*x^19 +
476450*x^18 - 3087203*x^17 - 2525590*x^16 + 25559573*x^15 + 1236433*x^14 -
136506775*x^13 + 70273939*x^12 + 449954679*x^11 - 442035918*x^10 - 811357321*x^9
+ 1215128520*x^8 + 520294416*x^7 - 1490157376*x^6 + 316025488*x^5 +
533790848*x^4 - 242004160*x^3 - 36429056*x^2 + 34909184*x - 4845568,7,x^26 -
14*x^25 - x^24 + 839*x^23 - 2570*x^22 - 19872*x^21 + 98016*x^20 + 231198*x^19 -
1767490*x^18 - 1167484*x^17 + 18924615*x^16 - 1978915*x^15 - 130476091*x^14 +
60221791*x^13 + 599025825*x^12 - 339579585*x^11 - 1840646835*x^10 +
879823953*x^9 + 3680192806*x^8 - 878697236*x^7 - 4373680492*x^6 - 319188000*x^5
+ 2453382528*x^4 + 798349056*x^3 - 415843776*x^2 - 245728000*x -
32370944,11,x^26 - 10*x^25 - 85*x^24 + 1104*x^23 + 1895*x^22 - 48219*x^21 +
29383*x^20 + 1064958*x^19 - 2045082*x^18 - 12448150*x^17 + 38032434*x^16 +
69320330*x^15 - 344799591*x^14 - 57739069*x^13 + 1598735561*x^12 -
1153437848*x^11 - 3364156911*x^10 + 4652056450*x^9 + 1926712089*x^8 -
5389461202*x^7 + 482086769*x^6 + 2377027167*x^5 - 518768014*x^4 - 396989189*x^3
+ 91402908*x^2 + 14339718*x - 3048543,13,x^26 - 30*x^25 + 287*x^24 + 58*x^23 -
18219*x^22 + 86356*x^21 + 323848*x^20 - 3489483*x^19 + 1494832*x^18 +
63108978*x^17 - 139381884*x^16 - 603007232*x^15 + 2327856456*x^14 +
2708706105*x^13 - 20251437668*x^12 + 1287018421*x^11 + 102966116646*x^10 -
76820813555*x^9 - 303743144182*x^8 + 373689287684*x^7 + 471854852632*x^6 -
812789181216*x^5 - 280070965376*x^4 + 795666009856*x^3 - 44401380864*x^2 -
263816327168*x + 48157855744[]
558,1,2,x + 1,3,x,5,x + 1,7,x,11,x + 3,13,x + 1[]
558,2,2,x + 1,3,x,5,x - 3,7,x + 4,11,x - 3,13,x - 5[]
558,3,2,x + 1,3,x,5,x - 2,7,x,11,x,13,x - 2[]
558,4,2,x + 1,3,x,5,x + 1,7,x + 2,11,x - 3,13,x + 1[]
558,5,2,x - 1,3,x,5,x - 1,7,x,11,x - 3,13,x + 1[]
558,6,2,x - 1,3,x,5,x + 3,7,x + 4,11,x + 3,13,x - 5[]
558,7,2,x - 1,3,x,5,x + 3,7,x + 2,11,x + 5,13,x + 7[]
558,8,2,x - 1,3,x,5,x - 1,7,x - 2,11,x + 3,13,x - 3[]
558,9,2,x^2 + 2*x + 1,3,x^2,5,x^2 + 3*x - 2,7,x^2 - 2*x - 16,11,x^2 - x -
4,13,x^2 - 3*x - 2[]
558,10,2,x^2 - 2*x + 1,3,x^2,5,x^2 - 12,7,x^2 - 4*x + 4,11,x^2 - 6*x + 6,13,x^2
+ 2*x - 26[]
559,1,2,x^3 + 3*x^2 - 3,3,x^3 - 3*x - 1,5,x^3 + 3*x^2 - 3,7,x^3 + 3*x^2 - 6*x -
17,11,x^3 + 3*x^2 - 18*x - 57,13,x^3 - 3*x^2 + 3*x - 1[]
559,2,2,x^4 + x^3 - 5*x^2 - 3*x + 1,3,x^4 - x^3 - 5*x^2 + 3*x + 1,5,x^4 + 5*x^3
+ x^2 - 23*x - 25,7,x^4 - 2*x^3 - 10*x^2 - 7*x - 1,11,x^4 + 11*x^3 + 37*x^2 +
47*x + 19,13,x^4 - 4*x^3 + 6*x^2 - 4*x + 1[]
559,3,2,x^7 + 2*x^6 - 6*x^5 - 9*x^4 + 11*x^3 + 10*x^2 - 5*x - 1,3,x^7 + 3*x^6 -
4*x^5 - 13*x^4 + 5*x^3 + 12*x^2 - 1,5,x^7 - 12*x^5 + 5*x^4 + 13*x^3 - 4*x^2 -
3*x + 1,7,x^7 + x^6 - 26*x^5 - 6*x^4 + 122*x^3 - 97*x^2 - 23*x + 27,11,x^7 +
8*x^6 + 10*x^5 - 47*x^4 - 103*x^3 - 38*x^2 + 17*x + 3,13,x^7 + 7*x^6 + 21*x^5 +
35*x^4 + 35*x^3 + 21*x^2 + 7*x + 1[]
559,4,2,x^14 - 7*x^13 + 3*x^12 + 78*x^11 - 145*x^10 - 243*x^9 + 758*x^8 + 83*x^7
- 1422*x^6 + 532*x^5 + 1004*x^4 - 525*x^3 - 224*x^2 + 82*x + 23,3,x^14 - x^13 -
32*x^12 + 35*x^11 + 389*x^10 - 460*x^9 - 2236*x^8 + 2831*x^7 + 6128*x^6 -
8232*x^5 - 6928*x^4 + 10048*x^3 + 1408*x^2 - 3072*x + 512,5,x^14 - 12*x^13 +
30*x^12 + 163*x^11 - 845*x^10 - 158*x^9 + 6609*x^8 - 6773*x^7 - 20072*x^6 +
36040*x^5 + 15142*x^4 - 58784*x^3 + 20516*x^2 + 15364*x - 7444,7,x^14 - x^13 -
50*x^12 + 68*x^11 + 890*x^10 - 1715*x^9 - 6445*x^8 + 18137*x^7 + 9558*x^6 -
70048*x^5 + 63234*x^4 + 15892*x^3 - 50380*x^2 + 24164*x - 3268,11,x^14 - 10*x^13
- 40*x^12 + 571*x^11 + 511*x^10 - 12470*x^9 - 4325*x^8 + 129449*x^7 + 70816*x^6
- 616632*x^5 - 605584*x^4 + 837216*x^3 + 1101504*x^2 + 81024*x - 104704,13,x^14
- 14*x^13 + 91*x^12 - 364*x^11 + 1001*x^10 - 2002*x^9 + 3003*x^8 - 3432*x^7 +
3003*x^6 - 2002*x^5 + 1001*x^4 - 364*x^3 + 91*x^2 - 14*x + 1[]
559,5,2,x^15 - 2*x^14 - 22*x^13 + 43*x^12 + 187*x^11 - 354*x^10 - 769*x^9 +
1395*x^8 + 1553*x^7 - 2684*x^6 - 1328*x^5 + 2265*x^4 + 241*x^3 - 606*x^2 + 33*x
+ 13,3,x^15 - x^14 - 40*x^13 + 37*x^12 + 629*x^11 - 504*x^10 - 4938*x^9 +
3055*x^8 + 20332*x^7 - 7704*x^6 - 41872*x^5 + 5056*x^4 + 34944*x^3 + 2304*x^2 -
6144*x - 1024,5,x^15 + 2*x^14 - 46*x^13 - 73*x^12 + 819*x^11 + 922*x^10 -
7211*x^9 - 4481*x^8 + 32674*x^7 + 3564*x^6 - 69062*x^5 + 23068*x^4 + 43608*x^3 -
25756*x^2 + 2716*x - 68,7,x^15 - x^14 - 78*x^13 + 96*x^12 + 2364*x^11 -
3329*x^10 - 35253*x^9 + 53543*x^8 + 269506*x^7 - 419404*x^6 - 985046*x^5 +
1486276*x^4 + 1324860*x^3 - 1759896*x^2 - 278100*x + 344412,11,x^15 - 16*x^14 +
30*x^13 + 781*x^12 - 4579*x^11 - 3330*x^10 + 85817*x^9 - 155409*x^8 - 400264*x^7
+ 1487880*x^6 - 434288*x^5 - 3298656*x^4 + 4052928*x^3 - 796032*x^2 - 571648*x +
14848,13,x^15 + 15*x^14 + 105*x^13 + 455*x^12 + 1365*x^11 + 3003*x^10 + 5005*x^9
+ 6435*x^8 + 6435*x^7 + 5005*x^6 + 3003*x^5 + 1365*x^4 + 455*x^3 + 105*x^2 +
15*x + 1[]

Total time: 15.189 seconds, Total memory usage: 5.68MB

************** MAGMA *****************
Time: Sun Nov 30 21:00:22 2003

Input: MinimumDistance(DoubleCirculantQRCode(43));

Output: Magma V2.10-6     Sun Nov 30 2003 21:00:19 on modular  [Seed = 2674524192]
-------------------------------------

>> MinimumDistance(DoubleCirculantQRCode(43));;
^
User error: Identifier 'DoubleCirculantQRCode' has not been declared or assigned

Total time: 2.999 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Sun Nov 30 21:01:06 2003

Input: %

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Time: Sun Nov 30 21:01:18 2003

Input: MinimumDistance(DoublyCirculantQRCode(43));

Output: Magma V2.10-6     Sun Nov 30 2003 21:01:03 on modular  [Seed = 2723626353]
-------------------------------------

15

Total time: 14.709 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Sun Nov 30 21:04:37 2003

Input: MinimumDistance(DoublyCirculantQRCode(59));

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Sun Nov 30 2003 21:04:14 on modular  [Seed = 3275119953]
-------------------------------------

Errors: /home/mfd/gomagma: line 2: 13263 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 21:08:23 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [560..562] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Sun Nov 30 21:09:56 2003

Input: EllipticCurve([1,2,3,4,5]);

Output: Magma V2.10-6     Sun Nov 30 2003 21:09:52 on modular  [Seed = 1588315045]
-------------------------------------

Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational
Field

Total time: 3.059 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 21:10:14 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;
CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
for N in [560..562] do
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for; end for;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Sun Nov 30 21:10:38 2003

Input: EllipticCurve([1,2,3,4,5]); %

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 21:10:57 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Sun Nov 30 21:11:43 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host 3(NXDOMAIN) (62.231.244.23)
Time: Sun Nov 30 23:06:29 2003

Input: 1+1;

Output: Magma V2.10-6     Sun Nov 30 2003 23:06:26 on modular  [Seed = 736012896]
-------------------------------------

2

Total time: 2.959 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (62.231.244.22)
Time: Sun Nov 30 23:09:28 2003

Input: S:=CuspForms(4992);
Newforms(S);

Output: ** WARNING: Computation used more memory than allowed. **

Magma V2.10-6     Sun Nov 30 2003 23:09:17 on modular  [Seed = 634430657]
-------------------------------------

Current total memory usage: 78.6MB, failed memory request: 36.8MB
System Error: User memory limit has been reached

Total time: 10.689 seconds, Total memory usage: 82.41MB

************** MAGMA *****************
Host 130-127-119-141.generic.clemson.edu. (130.127.119.141)
Time: Sun Nov 30 23:21:28 2003

Input:
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

................................................................................

Output: Magma V2.10-6     Sun Nov 30 2003 23:21:24 on modular  [Seed = 2005043642]
-------------------------------------

>> +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
^
User error: yacc stack overflow

>> ...........................................................................
^

Total time: 2.989 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Mon Dec  1 01:50:43 2003

Input: // Allan
printf "%on", 1;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Mon Dec  1 01:50:52 2003

Input: // Allan
printf "%on", 1;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Mon Dec  1 02:11:47 2003

P := PolynomialRing(IntegerRing(), 2);
ExactQuotient(P!1, P!2);

Output: WARNING: MAGMA command contains unsafe command 'read', so it will not be executed.

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Mon Dec  1 02:12:13 2003

P := PolynomialRing(IntegerRing(), 2);
ExactQuotient(P!1, P!2);

Output: Magma V2.10-6     Mon Dec  1 2003 02:12:10 on modular  [Seed = 3040895864]
-------------------------------------

Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
to [email protected]
Version date: Wed Apr 23 11:13:24 EST 2003
Initial seed: 3040895864
Time to this point: 2.96
Internal error in dpoly_exact_div() at dpoly/exact_div.c, line 937

Total time: 2.949 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Mon Dec  1 02:46:47 2003

Input: cos Pi
3x+9

Output: Magma V2.10-6     Mon Dec  1 2003 02:46:44 on modular  [Seed = 251379948]
-------------------------------------

>> cos Pi
^

>> 3x+9
^

Total time: 3.039 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Mon Dec  1 02:47:11 2003

Input: cos Pi
3x+9
hhhh

Output: Magma V2.10-6     Mon Dec  1 2003 02:47:08 on modular  [Seed = 518770916]
-------------------------------------

>> cos Pi
^

>> 3x+9
^

>> hhhh;
^
User error: Identifier 'hhhh' has not been declared or assigned

Total time: 3.009 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Mon Dec  1 06:13:28 2003

Input: > 2+2

Output: Magma V2.10-6     Mon Dec  1 2003 06:13:24 on modular  [Seed = 4077383333]
-------------------------------------

4

Total time: 3.089 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host h24-87-78-5.vc.shawcable.net. (24.87.78.5)
Time: Mon Dec  1 09:46:37 2003

Input: CP:=CharacteristicPolynomial;
DH:=DualHeckeOperator;
N:=11;
A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
for i in [1..#A] do C2:=CP(DH(A[i],2)); C3:=CP(DH(A[i],3));C5:=CP(DH(A[i],5));
C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11)); C13:=CP(DH(A[i],13));
B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
printf "%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o,%o",B[1],B[2],B[3],B[4],B[5],B[6],B[7],B[8],B[9],B[10],B[11],B[12],B[13],B[14]; print [];
end for;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Mon Dec  1 16:44:27 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(3*a-4)/(5*(a-4)),2*(a-3)/(5*(a-4)),2/(4-a),(a+2)*(3*a-4)/(5*(3-a)*(a-4)),2*(4*a-

7)/(5*(a-4)),(a+2)/((a-3)*(a-4)),2*(a-1)*(a+2)/(5*(a-4)),2*(1-a)*(a-3)/(5*(a-4)),(a+2)/(4-a

)];
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,0);

Output: Magma V2.10-6     Mon Dec  1 2003 16:44:24 on modular  [Seed = 3894174119]
-------------------------------------

{
<0, 1>,
<1, 1>,
<(1/5*a - 8/5)/(a - 4), 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-2*a + 6)/(a + 2)         -2/(a - 1))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                     1 (-a^2 + 3*a)/(a^2 - 4)   (-3*a + 4)/(a^2 - 4))

Total time: 3.259 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host rescomp-03-43192.Stanford.EDU. (128.12.179.51)
Time: Mon Dec  1 16:45:36 2003

Input: F<a>:=FieldOfFractions(PolynomialRing(Rationals()));
space:=MatrixAlgebra(F,3);
M:=space![(3*a-4)/(5*(a-4)),2*(a-3)/(5*(a-4)),2/(4-a),(a+2)*(3*a-4)/(5*(3-a)*(a-4)),2*(4*a-

7)/(5*(a-4)),(a+2)/((a-3)*(a-4)),2*(a-1)*(a+2)/(5*(a-4)),2*(1-a)*(a-3)/(5*(a-4)),(a+2)/(4-a

)];
Eigenvalues(M);
Eigenspace(M,1);
Eigenspace(M,(1/5*a - 8/5)/(a - 4));
Eigenspace(M,0);

Output: Magma V2.10-6     Mon Dec  1 2003 16:45:32 on modular  [Seed = 3677311696]
-------------------------------------

{
<0, 1>,
<1, 1>,
<(1/5*a - 8/5)/(a - 4), 1>
}
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-2*a + 6)/(a + 2)         -2/(a - 1))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                 1 (-a + 3)/(a - 1/2)     -5/2/(a - 1/2))
Vector space of degree 3, dimension 1 over Univariate rational function field
over Rational Field
Echelonized basis:
(                     1 (-a^2 + 3*a)/(a^2 - 4)   (-3*a + 4)/(a^2 - 4))

Total time: 3.189 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 19:31:20 2003

Input: >l:=Lattice("Kappa",13);
>G:=AutomorphismGroup(L:Stabilizer:=2);
>#G;

Output: Magma V2.10-6     Mon Dec  1 2003 19:31:13 on modular  [Seed = 1169270625]
-------------------------------------

>>  G:=AutomorphismGroup(L:Stabilizer:=2);
^
User error: Identifier 'L' has not been declared or assigned

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 3.539 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 19:31:20 2003

Input: >l:=Lattice("Kappa",13);
>G:=AutomorphismGroup(L:Stabilizer:=2);
>#G;

Output: Magma V2.10-6     Mon Dec  1 2003 19:31:16 on modular  [Seed = 1102422880]
-------------------------------------

>>  G:=AutomorphismGroup(L:Stabilizer:=2);
^
User error: Identifier 'L' has not been declared or assigned

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 3.379 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 19:31:39 2003

Input: >L:=Lattice("Kappa",13);
>G:=AutomorphismGroup(L:Stabilizer:=2);
>#G;

Output: Magma V2.10-6     Mon Dec  1 2003 19:31:36 on modular  [Seed = 918737963]
-------------------------------------

48

Total time: 3.459 seconds, Total memory usage: 1.99MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 19:47:02 2003

Input: >L:=Lattice("E",8);
>G:=AutomorphismGroup(L);
>#G;FactoredOrder(G);
>M:=MatrixRing(Ratinals(),8);
>B:=BasisMatrix(L);
>A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
>A;

Output: Magma V2.10-6     Mon Dec  1 2003 19:46:59 on modular  [Seed = 468698477]
-------------------------------------

696729600
[ <2, 14>, <3, 5>, <5, 2>, <7, 1> ]

>>  M:=MatrixRing(Ratinals(),8);
^
User error: Identifier 'Ratinals' has not been declared or assigned

>>  A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
^
User error: Identifier 'M' has not been declared or assigned

>>  A;;
^
User error: Identifier 'A' has not been declared or assigned

Total time: 3.129 seconds, Total memory usage: 1.99MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 19:48:02 2003

Input: >L:=Lattice("E",8);
>G:=AutomorphismGroup(L);
>#G;FactoredOrder(G);
>M:=MatrixRing(Rationals(),8);
>B:=BasisMatrix(L);
>A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
>A;

Output: Magma V2.10-6     Mon Dec  1 2003 19:47:58 on modular  [Seed = 49732681]
-------------------------------------

696729600
[ <2, 14>, <3, 5>, <5, 2>, <7, 1> ]
MatrixGroup(8, Rational Field)
Generators:
[ 1/2    0    0 -1/2    0  1/2    0  1/2]
[   0  1/2  1/2    0  1/2    0 -1/2    0]
[   0  1/2 -1/2    0 -1/2    0 -1/2    0]
[   0  1/2  1/2    0 -1/2    0  1/2    0]
[-1/2    0    0 -1/2    0 -1/2    0  1/2]
[   0  1/2 -1/2    0  1/2    0  1/2    0]
[-1/2    0    0  1/2    0  1/2    0  1/2]
[ 1/2    0    0  1/2    0 -1/2    0  1/2]

[ 1/2    0  1/2 -1/2    0    0 -1/2    0]
[   0  1/2    0    0  1/2  1/2    0  1/2]
[   0 -1/2    0    0  1/2 -1/2    0  1/2]
[   0  1/2    0    0  1/2 -1/2    0 -1/2]
[-1/2    0 -1/2 -1/2    0    0 -1/2    0]
[ 1/2    0 -1/2  1/2    0    0 -1/2    0]
[   0  1/2    0    0 -1/2 -1/2    0  1/2]
[ 1/2    0 -1/2 -1/2    0    0  1/2    0]

Total time: 3.279 seconds, Total memory usage: 1.89MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 19:51:13 2003

Input: >L:=Lattice("E",8);
>G:=AutomorphismGroup(L);
>#G;FactoredOrder(G);
>M:=MatrixRing(Rationals(),8);
>B:=BasisMatrix(L);
>A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
>A;

Output: Magma V2.10-6     Mon Dec  1 2003 19:51:10 on modular  [Seed = 3843111790]
-------------------------------------

696729600
[ <2, 14>, <3, 5>, <5, 2>, <7, 1> ]
MatrixGroup(8, Rational Field)
Generators:
[ 1/2    0    0 -1/2    0  1/2    0  1/2]
[   0  1/2  1/2    0  1/2    0 -1/2    0]
[   0  1/2 -1/2    0 -1/2    0 -1/2    0]
[   0  1/2  1/2    0 -1/2    0  1/2    0]
[-1/2    0    0 -1/2    0 -1/2    0  1/2]
[   0  1/2 -1/2    0  1/2    0  1/2    0]
[-1/2    0    0  1/2    0  1/2    0  1/2]
[ 1/2    0    0  1/2    0 -1/2    0  1/2]

[ 1/2    0  1/2 -1/2    0    0 -1/2    0]
[   0  1/2    0    0  1/2  1/2    0  1/2]
[   0 -1/2    0    0  1/2 -1/2    0  1/2]
[   0  1/2    0    0  1/2 -1/2    0 -1/2]
[-1/2    0 -1/2 -1/2    0    0 -1/2    0]
[ 1/2    0 -1/2  1/2    0    0 -1/2    0]
[   0  1/2    0    0 -1/2 -1/2    0  1/2]
[ 1/2    0 -1/2 -1/2    0    0  1/2    0]

Total time: 3.279 seconds, Total memory usage: 1.99MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 20:23:59 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>G:=AutomorphismGroup(L);
>#G;FactoredOrder(G);
>M:=MatrixRing(Rationals(),8);
>B:=BasisMatrix(L);
>A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
>A;

Output: Magma V2.10-6     Mon Dec  1 2003 20:23:55 on modular  [Seed = 2557234758]
-------------------------------------

288
[ <2, 5>, <3, 2> ]

>>  A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
^
Runtime error in '!': Arguments 1 and 2 have incompatible degrees

>>  A;;
^
User error: Identifier 'A' has not been declared or assigned

Total time: 3.179 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 20:24:52 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>G:=AutomorphismGroup(L);
>#G;FactoredOrder(G);
>M:=MatrixRing(Rationals(),6);
>B:=BasisMatrix(L);
>A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
>A;

Output: Magma V2.10-6     Mon Dec  1 2003 20:24:49 on modular  [Seed = 2155107860]
-------------------------------------

288
[ <2, 5>, <3, 2> ]

>>  A:=MatrixGroup<8,Rationals()|[B^-1*M!G.i*B:i in[1..Ngens(G)]]>;
^
Runtime error in '*': Arguments 1 and 2 have incompatible coefficient rings

>>  A;;
^
User error: Identifier 'A' has not been declared or assigned

Total time: 3.019 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 20:28:09 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>G:=AutomorphismGroup(L);
>#G;FactoredOrder(G);
>M:=MatrixRing(Rationals(),6);
>B:=BasisMatrix(L);
>A:=MatrixGroup<8,Rationals()|[B^-1*g*B:g in Generators(G)]>;
>A;

Output: Magma V2.10-6     Mon Dec  1 2003 20:28:06 on modular  [Seed = 1887741346]
-------------------------------------

288
[ <2, 5>, <3, 2> ]

>>  A:=MatrixGroup<8,Rationals()|[B^-1*g*B:g in Generators(G)]>;
^
Runtime error in MatrixGroup< ... >: Can not build a generator from the
arguments given

>>  A;;
^
User error: Identifier 'A' has not been declared or assigned

Total time: 3.109 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Mon Dec  1 20:29:16 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>G:=AutomorphismGroup(L);
>#G;FactoredOrder(G);
>M:=MatrixRing(Rationals(),6);
>B:=BasisMatrix(L);
>A:=MatrixGroup<8,Rationals()|G,[B^-1*g*B:g in Generators(G)]>;
>A;

Output: Magma V2.10-6     Mon Dec  1 2003 20:29:13 on modular  [Seed = 2039327972]
-------------------------------------

288
[ <2, 5>, <3, 2> ]

>>  A:=MatrixGroup<8,Rationals()|G,[B^-1*g*B:g in Generators(G)]>;
^
Runtime error in MatrixGroup< ... >: Argument is not a subgroup

>>  A;;
^
User error: Identifier 'A' has not been declared or assigned

Total time: 3.229 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (162.33.91.63)
Time: Mon Dec  1 21:25:12 2003

Input: 2^6;

Output: Magma V2.10-6     Mon Dec  1 2003 21:25:09 on modular  [Seed = 2205631730]
-------------------------------------

64

Total time: 3.029 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:45:51 2003

P := PolynomialRing(IntegerRing(), 2);
ExactQuotient(P!1, P!2);

Output: Magma V2.10-6     Tue Dec  2 2003 00:45:48 on modular  [Seed = 2106483969]
-------------------------------------

Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
to [email protected]
Version date: Wed Apr 23 11:13:24 EST 2003
Initial seed: 2106483969
Time to this point: 3.1
Internal error in dpoly_exact_div() at dpoly/exact_div.c, line 937

Total time: 3.089 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:47:11 2003

Input: // Allan
time Factorization(2^512 + 1);

Output: Magma V2.10-6     Tue Dec  2 2003 00:47:06 on modular  [Seed = 1755017282]
-------------------------------------

[ <2424833, 1>, <7455602825647884208337395736200454918783366342657, 1>,
<741640062627530801524787141901937474059940781097519023905821316144415759504705\
008092818711693940737, 1> ]
Time: 1.830

Total time: 5.069 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:48:46 2003

Input: // Allan
time Factorization(2^512 - 1);

Output: Magma V2.10-6     Tue Dec  2 2003 00:48:42 on modular  [Seed = 1352878234]
-------------------------------------

[ <3, 1>, <5, 1>, <17, 1>, <257, 1>, <641, 1>, <65537, 1>, <274177, 1>,
<6700417, 1>, <67280421310721, 1>, <1238926361552897, 1>, <59649589127497217,
1>, <5704689200685129054721, 1>, <934616397153579777691635581996068965840512375\
41638188580280321, 1> ]
Time: 0.510

Total time: 3.669 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:49:22 2003

Input: // Allan
time Factorization(2^1024 - 1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Tue Dec  2 2003 00:48:58 on modular  [Seed = 1487618274]
-------------------------------------

Errors: /home/mfd/gomagma: line 2: 20264 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:49:47 2003

Input: // Allan
SetVerbose("Factorization", 1);
time Factorization(2^768 - 1);

Output: Magma V2.10-6     Tue Dec  2 2003 00:49:42 on modular  [Seed = 1102207431]
-------------------------------------

Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 18446744073709551617

Trial Division
Number: 18446744073709551617
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 18446744073709551617
(20 digits)
Factor: 274177 (6 digits)
Cofactor: 67280421310721 (14 digits)
Time: 0.020

Total time: 0.020

[ <3, 2>, <5, 1>, <7, 1>, <13, 1>, <17, 1>, <97, 1>, <193, 1>, <241, 1>, <257,
1>, <641, 1>, <673, 1>, <769, 1>, <65537, 1>, <274177, 1>, <6700417, 1>,
<22253377, 1>, <67280421310721, 1>, <59649589127497217, 1>,
<18446744069414584321, 1>, <5704689200685129054721, 1>,
<349621839326921795694385454593, 1>, <442499826945303593556473164314770689, 1>,
<331192380488114152600457428497953408512758882817, 1> ]
Time: 0.500

Total time: 3.679 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:50:15 2003

Input: // Allan
SetVerbose("Cunningham", 1);
time Factorization(2^768 - 1);

Output: Magma V2.10-6     Tue Dec  2 2003 00:50:12 on modular  [Seed = 834807381]
-------------------------------------

Cunningham Factorization: a = 2, e = 768, c = -1
Trial Division
Found prime <3, 2>
Found prime <5, 1>
Found prime <7, 1>
Found prime <13, 1>
Found prime <17, 1>
Found prime <97, 1>
Found prime <193, 1>
Found prime <241, 1>
Found prime <257, 1>
Found prime <641, 1>
Found prime <673, 1>
Found prime <769, 1>
Database lookup
Found prime <59649589127497217, 1>
Found prime <349621839326921795694385454593, 1>
Aurifeuillian factors
Algebraic factors
Found prime <65537, 1>
Found prime <6700417, 1>
Found prime <22253377, 1>
Found composite 18446744073709551617
Found prime <18446744069414584321, 1>
Found prime <5704689200685129054721, 1>
Found prime <442499826945303593556473164314770689, 1>
Primality testing 331192380488114152600457428497953408512758882817
Found prime <331192380488114152600457428497953408512758882817, 1>
Factoring 18446744073709551617
[ <3, 2>, <5, 1>, <7, 1>, <13, 1>, <17, 1>, <97, 1>, <193, 1>, <241, 1>, <257,
1>, <641, 1>, <673, 1>, <769, 1>, <65537, 1>, <274177, 1>, <6700417, 1>,
<22253377, 1>, <67280421310721, 1>, <59649589127497217, 1>,
<18446744069414584321, 1>, <5704689200685129054721, 1>,
<349621839326921795694385454593, 1>, <442499826945303593556473164314770689, 1>,
<331192380488114152600457428497953408512758882817, 1> ]
Time: 0.520

Total time: 3.559 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:50:39 2003

Input: // Allan
SetVerbose("Cunningham", 1);
SetVerbose("Factorization", 1);
time Factorization(2^800 - 1);

Output: Magma V2.10-6     Tue Dec  2 2003 00:50:35 on modular  [Seed = 969551458]
-------------------------------------

Cunningham Factorization: a = 2, e = 800, c = -1
Trial Division
Found prime <3, 1>
Found prime <5, 3>
Found prime <11, 1>
Found prime <17, 1>
Found prime <31, 1>
Found prime <41, 1>
Found prime <101, 1>
Found prime <251, 1>
Found prime <257, 1>
Found prime <401, 1>
Found prime <601, 1>
Found prime <1601, 1>
Found prime <1801, 1>
Found prime <4051, 1>
Found prime <8101, 1>
Database lookup
Found prime <3399426377632056001, 1>
Found prime <4850484222084371979240001, 1>
Aurifeuillian factors
Found prime <268501, 1>
Algebraic factors
Found prime <65537, 1>
Found prime <61681, 1>
Found prime <4278255361, 1>
Found composite 18446462603027742721
Found composite 3014774729910783238001
Primality testing 912867980842956708437164975496064226186955201
Found composite 912867980842956708437164975496064226186955201
Primality testing 129541188208935646963818844716591986208974410651257601
Found prime <129541188208935646963818844716591986208974410651257601, 1>
Factoring 18446462603027742721
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 18446462603027742721

Trial Division
Number: 18446462603027742721
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 18446462603027742721
(20 digits)
Factor: 414721 (6 digits)
Cofactor: 44479210368001 (14 digits)
Time: 0.009

Total time: 0.009

Factoring 3014774729910783238001
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 3014774729910783238001

Trial Division
Number: 3014774729910783238001
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 3014774729910783238001
(22 digits)
Factor: 340801 (6 digits)
Cofactor: 8846144025137201 (16 digits)
Time: 0.000

Pollard Rho
Trials: 8191
Number: 8846144025137201
(16 digits)
Factor: 2787601 (7 digits)
Cofactor: 3173389601 (10 digits)
Time: 0.010

Total time: 0.010

Factoring 912867980842956708437164975496064226186955201
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 912867980842956708437164975496064226186955201

Trial Division
Number: 912867980842956708437164975496064226186955201
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 912867980842956708437164975496064226186955201
(45 digits)
Factor: 25601 (5 digits)
Cofactor: 35657512630090883498190108804189845169601 (41 digits)
Time: 0.009

Pollard Rho
Trials: 8191
Number: 35657512630090883498190108804189845169601
(41 digits)
No factor found
Time: 0.050

1 composite number remaining

ECM
x: 35657512630090883498190108804189845169601
(41 digits)
Initial smoothness: 500, steps: 6, step size: 100
Step 1/6; smoothness: 500, digits: 41, elapsed time: 0.000
Factor: 82471201 (8 digits)
Cofactor: 432363203127002885506543172618401 (33 digits)
Time: 0.049

Total time: 0.199

[ <3, 1>, <5, 3>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <257,
1>, <401, 1>, <601, 1>, <1601, 1>, <1801, 1>, <4051, 1>, <8101, 1>, <25601, 1>,
<61681, 1>, <65537, 1>, <268501, 1>, <340801, 1>, <414721, 1>, <2787601, 1>,
<82471201, 1>, <3173389601, 1>, <4278255361, 1>, <44479210368001, 1>,
<3399426377632056001, 1>, <4850484222084371979240001, 1>,
<432363203127002885506543172618401, 1>, <12954118820893564696381884471659198620\
8974410651257601, 1> ]
Time: 0.590

Total time: 3.759 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:51:00 2003

Input: // Allan
SetVerbose("Cunningham", 1);
SetVerbose("Factorization", 1);
time Factorization(2^900 - 1);

Output: Magma V2.10-6     Tue Dec  2 2003 00:50:56 on modular  [Seed = 567424529]
-------------------------------------

Cunningham Factorization: a = 2, e = 900, c = -1
Trial Division
Found prime <3, 3>
Found prime <5, 3>
Found prime <7, 1>
Found prime <11, 1>
Found prime <13, 1>
Found prime <19, 1>
Found prime <31, 1>
Found prime <37, 1>
Found prime <41, 1>
Found prime <61, 1>
Found prime <73, 1>
Found prime <101, 1>
Found prime <109, 1>
Found prime <151, 1>
Found prime <181, 1>
Found prime <251, 1>
Found prime <331, 1>
Found prime <601, 1>
Found prime <631, 1>
Found prime <1201, 1>
Found prime <1321, 1>
Found prime <1801, 1>
Found prime <4051, 1>
Found prime <8101, 1>
Database lookup
Found prime <1348206751, 1>
Found prime <4714696801, 1>
Found prime <307116398490301, 1>
Found prime <413150254353901, 1>
Aurifeuillian factors
Found prime <268501, 1>
Found prime <54001, 1>
Found prime <29247661, 1>
Found composite 852100728601
Found prime <1182468601, 1>
Found prime <3192261504216112476901, 1>
Found composite 4362038237992319774101
Algebraic factors
Found prime <23311, 1>
Found prime <18837001, 1>
Found composite 1065184428001
Found prime <1133836730401, 1>
Found composite 985892875836627780943321951
Found prime <281941472953710177758647201, 1>
Factoring 852100728601
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 852100728601

Trial Division
Number: 852100728601
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 852100728601
(12 digits)
Factor: 63901 (5 digits)
Cofactor: 13334701 (8 digits)
Time: 0.000

Total time: 0.000

Factoring 4362038237992319774101
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 4362038237992319774101

Trial Division
Number: 4362038237992319774101
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 4362038237992319774101
(22 digits)
Factor: 695701 (6 digits)
Cofactor: 6269989892198401 (16 digits)
Time: 0.010

Total time: 0.050

Factoring 1065184428001
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 1065184428001

Trial Division
Number: 1065184428001
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 1065184428001
(13 digits)
Factor: 100801 (6 digits)
Cofactor: 10567201 (8 digits)
Time: 0.000

Total time: 0.000

Factoring 985892875836627780943321951
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 985892875836627780943321951

Trial Division
Number: 985892875836627780943321951
Minimum: 2
Maximum: 10000
No factors found
Time: 0.009

Pollard Rho
Trials: 8191
Number: 985892875836627780943321951
(27 digits)
Factor: 71125212601 (11 digits)
Cofactor: 13861369826299351 (17 digits)
Time: 0.000

Pollard Rho
Trials: 8191
Number: 71125212601
(11 digits)
Factor: 115201 (6 digits)
Cofactor: 617401 (6 digits)
Time: 0.010

Total time: 0.049

[ <3, 3>, <5, 3>, <7, 1>, <11, 1>, <13, 1>, <19, 1>, <31, 1>, <37, 1>, <41, 1>,
<61, 1>, <73, 1>, <101, 1>, <109, 1>, <151, 1>, <181, 1>, <251, 1>, <331, 1>,
<601, 1>, <631, 1>, <1201, 1>, <1321, 1>, <1801, 1>, <4051, 1>, <8101, 1>,
<23311, 1>, <54001, 1>, <63901, 1>, <100801, 1>, <115201, 1>, <268501, 1>,
<617401, 1>, <695701, 1>, <10567201, 1>, <13334701, 1>, <18837001, 1>,
<29247661, 1>, <1182468601, 1>, <1348206751, 1>, <4714696801, 1>,
<1133836730401, 1>, <307116398490301, 1>, <413150254353901, 1>,
<6269989892198401, 1>, <13861369826299351, 1>, <3192261504216112476901, 1>,
<281941472953710177758647201, 1> ]
Time: 0.280

Total time: 3.439 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:51:20 2003

Input: // Allan
SetVerbose("Cunningham", 1);
SetVerbose("Factorization", 1);
time Factorization(2^1000 - 1);

Output: Magma V2.10-6     Tue Dec  2 2003 00:51:15 on modular  [Seed = 702168586]
-------------------------------------

Cunningham Factorization: a = 2, e = 1000, c = -1
Trial Division
Found prime <3, 1>
Found prime <5, 4>
Found prime <11, 1>
Found prime <17, 1>
Found prime <31, 1>
Found prime <41, 1>
Found prime <101, 1>
Found prime <251, 1>
Found prime <401, 1>
Found prime <601, 1>
Found prime <1801, 1>
Found prime <4001, 1>
Found prime <4051, 1>
Found prime <7001, 1>
Found prime <8101, 1>
Database lookup
Found prime <269089806001, 1>
Found prime <1481124532001, 1>
Aurifeuillian factors
Found prime <268501, 1>
Found composite 253468230599467758697053367501
Found composite 181111287389941648853409001
Algebraic factors
Found prime <61681, 1>
Found composite 3014774729910783238001
Found prime <4710883168879506001, 1>
Found composite 1267650562449298664439414784001
Primality testing 4357507456648357759435539669451839600394175931174635840276981\
76425409152335529484786678327261647827656001
Found composite 435750745664835775943553966945183960039417593117463584027698176\
425409152335529484786678327261647827656001
Factoring 253468230599467758697053367501
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 253468230599467758697053367501

Trial Division
Number: 253468230599467758697053367501
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 253468230599467758697053367501
(30 digits)
Factor: 28001 (5 digits)
Cofactor: 9052113517355371547339501 (25 digits)
Time: 0.000

Pollard Rho
Trials: 8191
Number: 9052113517355371547339501
(25 digits)
Factor: 96001 (5 digits)
Cofactor: 94291866932171243501 (20 digits)
Time: 0.000

Total time: 0.039

Factoring 181111287389941648853409001
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 181111287389941648853409001

Trial Division
Number: 181111287389941648853409001
Minimum: 2
Maximum: 10000
No factors found
Time: 0.009

Pollard Rho
Trials: 8191
Number: 181111287389941648853409001
(27 digits)
Factor: 3775501 (7 digits)
Cofactor: 47970133603445383501 (20 digits)
Time: 0.030

Total time: 0.069

Factoring 3014774729910783238001
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 3014774729910783238001

Trial Division
Number: 3014774729910783238001
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 3014774729910783238001
(22 digits)
Factor: 340801 (6 digits)
Cofactor: 8846144025137201 (16 digits)
Time: 0.000

Pollard Rho
Trials: 8191
Number: 8846144025137201
(16 digits)
Factor: 2787601 (7 digits)
Cofactor: 3173389601 (10 digits)
Time: 0.010

Total time: 0.010

Factoring 1267650562449298664439414784001
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 1267650562449298664439414784001

Trial Division
Number: 1267650562449298664439414784001
Minimum: 2
Maximum: 10000
No factors found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 1267650562449298664439414784001
(31 digits)
Factor: 229668251 (9 digits)
Cofactor: 5519485418336288303251 (22 digits)
Time: 0.039

Total time: 0.079

Factoring 435750745664835775943553966945183960039417593117463584027698176425409\
152335529484786678327261647827656001
Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 4357507456648357759435539669451839600394175931174635840276981764254\
09152335529484786678327261647827656001

Trial Division
Number: 4357507456648357759435539669451839600394175931174635840276981764254\
09152335529484786678327261647827656001
Minimum: 2
Maximum: 10000
No factors found
Time: 0.009

Pollard Rho
Trials: 8191
Number: 4357507456648357759435539669451839600394175931174635840276981764254\
09152335529484786678327261647827656001
(105 digits)
Factor: 1074001 (7 digits)
Cofactor: 40572657349931310673225999505138632090604905686071389507802895567\
6399884483840783003626930758582001 (99 digits)
Time: 0.010

Pollard Rho
Trials: 8191
Number: 4057265734993131067322599950513863209060490568607138950780289556763\
99884483840783003626930758582001
(99 digits)
Factor: 2020001 (7 digits)
Cofactor: 20085463992310553644887304266254636552459580805193358571507091119\
0835986954383083475516562001 (93 digits)
Time: 0.059

Pollard Rho
Trials: 8191
Number: 2008546399231055364488730426625463655245958080519335857150709111908\
35986954383083475516562001
(93 digits)
No factor found
Time: 0.099

1 composite number remaining

ECM
x: 200854639923105536448873042662546365524595808051933585715070911190835986\
954383083475516562001
(93 digits)
Initial smoothness: 500, steps: 2000, step size: 7
Step 1/2000; smoothness: 500, digits: 93, elapsed time: 0.000
Factor: 22624001 (8 digits)
Cofactor: 88779451487429450011460414390251470340986905035910131773363566944\
16517527310181938001 (85 digits)
Time: 0.569

Total time: 1.439

[ <3, 1>, <5, 4>, <11, 1>, <17, 1>, <31, 1>, <41, 1>, <101, 1>, <251, 1>, <401,
1>, <601, 1>, <1801, 1>, <4001, 1>, <4051, 1>, <7001, 1>, <8101, 1>, <28001, 1>,
<61681, 1>, <96001, 1>, <268501, 1>, <340801, 1>, <1074001, 1>, <2020001, 1>,
<2787601, 1>, <3775501, 1>, <22624001, 1>, <229668251, 1>, <3173389601, 1>,
<269089806001, 1>, <1481124532001, 1>, <4710883168879506001, 1>,
<47970133603445383501, 1>, <94291866932171243501, 1>, <5519485418336288303251,
1>, <88779451487429450011460414390251470340986905035910131773363566944165175273\
10181938001, 1> ]
Time: 1.740

Total time: 4.850 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:52:09 2003

Input: // Allan
SetVerbose("Cunningham", 1);
SetVerbose("Factorization", 1);
time Factorization(2^1020 - 1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Tue Dec  2 2003 00:51:46 on modular  [Seed = 316736784]
-------------------------------------

Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 1123558209288947442330815744243140458511235611838941607958938007235\
829223784381019579427983265047100132000711749196208485367436055090103890580\
296441496713277361049333905409282976888872507788088246581768450531286055238\
441764640393009211956940880170232270940691778664363999670287115498226905220\
9770601514008575

Trial Division
Number: 1123558209288947442330815744243140458511235611838941607958938007235\
829223784381019579427983265047100132000711749196208485367436055090103890580\
296441496713277361049333905409282976888872507788088246581768450531286055238\
441764640393009211956940880170232270940691778664363999670287115498226905220\
9770601514008575
Minimum: 2
Maximum: 10000
Factors found:
<3, 2>
<5, 2>
<7, 1>
<11, 1>
<13, 1>
<31, 1>
<41, 1>
<61, 1>
<103, 1>
<137, 1>
<151, 1>
<307, 1>
<331, 1>
<409, 1>
<953, 1>
<1021, 1>
<1321, 1>
<2143, 1>
<2857, 1>
<3061, 1>
<4421, 1>
<6529, 1>
Time: 0.009

Pollard Rho
Trials: 8191
Number: 1044948278467622800909065101703579308989613169559014911305410475219\
298089905968556479519157552551238986426114626404414391694574968986333572485\
611465254333992032293789721185161402252721828716586103197643087620402928477\
8612010747889805683965422600249102265687
(257 digits)
Factor: 51001 (5 digits)
Cofactor: 20488780189949663749908141050245667908268723545793512113594056493\
388327481931110301357211771387840218553089441901225748351886727103122165692\
547429761266131880400262538404838363997818117854877082864995648862187073360\
8725554611632905348600329848439228687 (252 digits)
Time: 0.000

Pollard Rho
Trials: 8191
Number: 2048878018994966374990814105024566790826872354579351211359405649338\
832748193111030135721177138784021855308944190122574835188672710312216569254\
742976126613188040026253840483836399781811785487708286499564886218707336087\
25554611632905348600329848439228687
(252 digits)
Factor: 11119 (5 digits)
Cofactor: 18426819129372842656631118850837006842583616823269639458219315130\
306976780224040202677589505700009190172757839644955255285445388167211229150\
595763792846597608058514739099593815988684340187855996820753349098108708841\
507829356204056601187186783743073 (248 digits)
Time: 0.009

Pollard Rho
Trials: 8191
Number: 1842681912937284265663111885083700684258361682326963945821931513030\
697678022404020267758950570000919017275783964495525528544538816721122915059\
576379284659760805851473909959381598868434018785599682075334909810870884150\
7829356204056601187186783743073
(248 digits)
Factor: 13669 (5 digits)
Cofactor: 13480736798136544485061905663060214238483880915406861846674456895\
388819065201580366286918944838692801355445050585233195760805756212752380679\
344329353168920629203683326578091898448082771371611673729426694782433761680\
81632113263885917125406890317 (244 digits)
Time: 0.020

Pollard Rho
Trials: 8191
Number: 1348073679813654448506190566306021423848388091540686184667445689538\
881906520158036628691894483869280135544505058523319576080575621275238067934\
432935316892062920368332657809189844808277137161167372942669478243376168081\
632113263885917125406890317
(244 digits)
Factor: 42224050401187 (14 digits)
Cofactor: 31926678445224607850309617780953195990463213540972998416900116726\
320065873311294608464928030296719486759193026819145646274765003102286274489\
005894316061210138362369807695498982330546854527598997386058668316342397336\
427338283622991 (230 digits)
Time: 0.020

Pollard Rho
Trials: 8191
Number: 42224050401187
(14 digits)
Factor: 26317 (5 digits)
Cofactor: 1604440111 (10 digits)
Time: 0.000

Pollard Rho
Trials: 8191
Number: 1604440111
(10 digits)
Factor: 12241 (5 digits)
Cofactor: 131071 (6 digits)
Time: 0.009

Pollard Rho
Trials: 8191
Number: 3192667844522460785030961778095319599046321354097299841690011672632\
006587331129460846492803029671948675919302681914564627476500310228627448900\
589431606121013836236980769549898233054685452759899738605866831634239733642\
7338283622991
(230 digits)
Factor: 2565117370522181 (16 digits)
Cofactor: 12446478594749562360659035480275859729700120829737494476483531092\
027737944850904962950969228296177115731069633024074829851789816687978225425\
630616109032074968145372571686409884423637759183463565512356450267823259011
(215 digits)
Time: 0.049

Pollard Rho
Trials: 8191
Number: 2565117370522181
(16 digits)
Factor: 106591 (6 digits)
Cofactor: 24065046491 (11 digits)
Time: 0.000

Pollard Rho
Trials: 8191
Number: 24065046491
(11 digits)
No factor found
Time: 0.000

Pollard Rho
Trials: 8191
Number: 1244647859474956236065903548027585972970012082973749447648353109202\
773794485090496295096922829617711573106963302407482985178981668797822542563\
0616109032074968145372571686409884423637759183463565512356450267823259011
(215 digits)
Factor: 949111 (6 digits)
Cofactor: 13113828197913165436560144683051676494846357095995615345816802346\
646217296871393296412083758692267938872344365436787509418592574196251255570\
350165690875013531763273812743093151826959922689193956778876707010901 (209
digits)
Time: 0.169

Pollard Rho
Trials: 8191
Number: 1311382819791316543656014468305167649484635709599561534581680234664\
621729687139329641208375869226793887234436543678750941859257419625125557035\
0165690875013531763273812743093151826959922689193956778876707010901
(209 digits)
Factor: 23650061 (8 digits)
Cofactor: 55449447669133561374578038860245123658862262959895178899609613466\
308680120830949638616508256330788909476150465052870305148864411792642968533\
3588175137265545816701014544659870087732962832070241035694441 (201 digits)
Time: 0.309

Pollard Rho
Trials: 8191
Number: 5544944766913356137457803886024512365886226295989517889960961346630\
868012083094963861650825633078890947615046505287030514886441179264296853335\
88175137265545816701014544659870087732962832070241035694441
(201 digits)
No factor found
Time: 0.290

2 composite numbers remaining

ECM
x: 24065046491
(11 digits)
Initial smoothness: 500, steps: 2, step size: 100
Step 1/2; smoothness: 500, digits: 11, elapsed time: 0.000
Factor: 43691 (5 digits)
Cofactor: 550801 (6 digits)
Time: 0.000

ECM
x: 554494476691335613745780388602451236588622629598951788996096134663086801\
208309496386165082563307889094761504650528703051488644117926429685333588175\
137265545816701014544659870087732962832070241035694441
(201 digits)
Initial smoothness: 500, steps: 2000, step size: 23
Step 1/2000; smoothness: 500, digits: 201, elapsed time: 0.000
Factor: 15571321 (8 digits)
Cofactor: 35609983038133734045157786458994149346007485787426242705811288243\
501421697511052298399415345898263165646736371983385549080174001802829039702\
770765250890759095949599558358592060861950173146532721 (194 digits)
Time: 0.289

ECM
x: 356099830381337340451577864589941493460074857874262427058112882435014216\
975110522983994153458982631656467363719833855490801740018028290397027707652\
50890759095949599558358592060861950173146532721
(194 digits)
Initial smoothness: 500, steps: 2000, step size: 22
Step 1/2000; smoothness: 500, digits: 194, elapsed time: 0.000
Factor: 611787251461 (12 digits)
Cofactor: 58206481016225927036648290820789410790816834809883414616064031228\
882053478745057478646190108728449991062204933237010319552919621871841023408\
073689099756654492562777901508038205697661 (182 digits)
Time: 0.739

ECM
x: 582064810162259270366482908207894107908168348098834146160640312288820534\
787450574786461901087284499910622049332370103195529196218718410234080736890\
99756654492562777901508038205697661
(182 digits)
Initial smoothness: 500, steps: 2000, step size: 20
Step 1/2000; smoothness: 500, digits: 182, elapsed time: 0.000
Factor: 1326700741 (10 digits)
Cofactor: 43873105077451620294714443685374719174003110630570918341006663558\
411364058132426624344660789428510608680066255602558919165418346496454563605\
368250186088238939607841751788121 (173 digits)
Time: 1.699

ECM
x: 438731050774516202947144436853747191740031106305709183410066635584113640\
581324266243446607894285106086800662556025589191654183464964545636053682501\
86088238939607841751788121
(173 digits)
Initial smoothness: 500, steps: 2000, step size: 19
Step 1/2000; smoothness: 500, digits: 173, elapsed time: 0.000
Step 2/2000; smoothness: 519, digits: 173, elapsed time: 1.559
Step 3/2000; smoothness: 538, digits: 173, elapsed time: 3.159
Step 4/2000; smoothness: 557, digits: 173, elapsed time: 4.799
Step 5/2000; smoothness: 576, digits: 173, elapsed time: 6.459
Step 6/2000; smoothness: 595, digits: 173, elapsed time: 8.169
Factor: 2949879781 (10 digits)
Cofactor: 14872845110514563133891470164076737056018728185103255345512218878\
594145683977087683338597990623845904003660905665415969426388751703659534186\
748693873666792300919141 (164 digits)
Time: 9.929

ECM
x: 148728451105145631338914701640767370560187281851032553455122188785941456\
839770876833385979906238459040036609056654159694263887517036595341867486938\
73666792300919141
(164 digits)
Initial smoothness: 595, steps: 2000, step size: 17
Step 1/2000; smoothness: 595, digits: 164, elapsed time: 0.000
Step 2/2000; smoo
** WARNING: Output too long, hence truncated.
Errors: /home/mfd/gomagma: line 2: 20322 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host www-cache1.usyd.edu.au. (129.78.64.101)
Time: Tue Dec  2 00:52:46 2003

Input: // Allan
SetVerbose("Cunningham", 1);
SetVerbose("Factorization", 1);
time Factorization(2^1024 - 1);

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Tue Dec  2 2003 00:52:23 on modular  [Seed = 451481085]
-------------------------------------

Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 1797693134862315907729305190789024733617976978942306572734300811577\
326758055009631327084773224075360211201138798713933576587897688144166224928\
474306394741243777678934248654852763022196012460941194530829520850057688381\
506823424628814739131105408272371633505106845862982399472459384797163048353\
56329624224137215

Trial Division
Number: 1797693134862315907729305190789024733617976978942306572734300811577\
326758055009631327084773224075360211201138798713933576587897688144166224928\
474306394741243777678934248654852763022196012460941194530829520850057688381\
506823424628814739131105408272371633505106845862982399472459384797163048353\
56329624224137215
Minimum: 2
Maximum: 10000
Factors found:
<3, 1>
<5, 1>
<17, 1>
<257, 1>
<641, 1>
Time: 0.010

Pollard Rho
Trials: 8191
Number: 4279413246241015912182555964222056460566264394910881891086293129089\
365516431620910018749489171689492023831066199073897768571337029882964313595\
691638721925378568784526658248858847791961238896749374923641261704622444263\
225086938048287160821176780701959364356059982150949337244164429404023426415\
898082689
(301 digits)
Factor: 65537 (5 digits)
Cofactor: 65297667672322747641523963016647946359556653415793855243393703237\
703366288228342921078924716903268261040802389475775482072284923476554683821\
287084222987402208962639831823990400045653008817870048597336485675337938023\
761006560233887531635887769972717081409830477167873862661460921760288438995\
008897 (296 digits)
Time: 0.029

Pollard Rho
Trials: 8191
Number: 6529766767232274764152396301664794635955665341579385524339370323770\
336628822834292107892471690326826104080238947577548207228492347655468382128\
708422298740220896263983182399040004565300881787004859733648567533793802376\
100656023388753163588776997271708140983047716787386266146092176028843899500\
8897
(296 digits)
Factor: 274177 (6 digits)
Cofactor: 23815880862480349424468122058614670945978930915355356300270884588\
314616575507188028565096531402440124824767354473852833050286830578989004847\
703156801258822661624658462170054526836916666539450810460883475154859064773\
398573388808648257014953030331762723134993262442828487678200914650130550336\
1 (291 digits)
Time: 0.130

Pollard Rho
Trials: 8191
Number: 2381588086248034942446812205861467094597893091535535630027088458831\
461657550718802856509653140244012482476735447385283305028683057898900484770\
315680125882266162465846217005452683691666653945081046088347515485906477339\
85733888086482570149530303317627231349932624428284876782009146501305503361
(291 digits)
Factor: 2424833 (7 digits)
Cofactor: 98216581770704825546617528129214139472610818622789100528864810848\
065069122315590511037653031785859582184700366886514795246876096535262448373\
571115211888087392511807873655853936485179253744281814297658746622382097131\
631635617003926691095646711883922410883525844636840919264134538956417 (284
digits)
Time: 0.270

Pollard Rho
Trials: 8191
Number: 9821658177070482554661752812921413947261081862278910052886481084806\
506912231559051103765303178585958218470036688651479524687609653526244837357\
111521188808739251180787365585393648517925374428181429765874662238209713163\
1635617003926691095646711883922410883525844636840919264134538956417
(284 digits)
No factor found
Time: 0.500

1 composite number remaining

ECM
x: 982165817707048255466175281292141394726108186227891005288648108480650691\
223155905110376530317858595821847003668865147952468760965352624483735711152\
118880873925118078736558539364851792537442818142976587466223820971316316356\
17003926691095646711883922410883525844636840919264134538956417
(284 digits)
Initial smoothness: 500, steps: 2000, step size: 35
Step 1/2000; smoothness: 500, digits: 284, elapsed time: 0.000
Factor: 6700417 (7 digits)
Cofactor: 14658278995278178290488118594591073879821333302507754447053789465\
351942889870226063696879318374641396525723752251018823939894501571359282321\
319869377068335805444916021444016683810153793971969478063478548666804185042\
756538229934633425217512090946566819779056414643572320836768001 (278 digits)
Time: 3.710

ECM
x: 146582789952781782904881185945910738798213333025077544470537894653519428\
898702260636968793183746413965257237522510188239398945015713592823213198693\
770683358054449160214440166838101537939719694780634785486668041850427565382\
29934633425217512090946566819779056414643572320836768001
(278 digits)
Initial smoothness: 500, steps: 2000, step size: 34
Step 1/2000; smoothness: 500, digits: 278, elapsed time: 0.000
Step 2/2000; smoothness: 534, digits: 278, elapsed time: 3.479
Step 3/2000; smoothness: 568, digits: 278, elapsed time: 7.099
Step 4/2000; smoothness: 602, digits: 278, elapsed time: 10.869
Step 5/2000; smoothness: 636, digits: 278, elapsed time: 14.829

Errors: /home/mfd/gomagma: line 2: 20330 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host 168ext7.cab.uniroma3.it. (193.204.163.2)
Time: Tue Dec  2 04:24:23 2003

Input: d=prodeuler(p=2,436270000,1-(2*p)/(p^3-1))

Output: Magma V2.10-6     Tue Dec  2 2003 04:24:20 on modular  [Seed = 3342115567]
-------------------------------------

>> d=prodeuler(p=2,436270000,1-(2*p)/(p^3-1));
^
User error: Identifier 'p' has not been declared or assigned

Total time: 3.179 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host isgpc002.rhul.ac.uk. (134.219.148.41)
Time: Tue Dec  2 09:20:33 2003

Input: F := GF( 103); g:= F.1; R<x> := PolynomialRing(F);
p := x^4  + g*x + 1;
l := Factorization(p);
print "Steven Galbraith tests!  l = ", l;

Output: Magma V2.10-6     Tue Dec  2 2003 09:19:55 on modular  [Seed = 1003002834]
-------------------------------------

Steven Galbraith tests!  l =  [
<x + 10, 1>,
<x^3 + 93*x^2 + 100*x + 31, 1>
]

Total time: 3.809 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host maximum.byu.edu. (128.187.91.72)
Time: Tue Dec  2 14:48:23 2003

Input: GaloisGroup(x^5+5*x+1);

Output: Magma V2.10-6     Tue Dec  2 2003 14:48:20 on modular  [Seed = 15979482]
-------------------------------------

>> GaloisGroup(x^5+5*x+1);;
^
User error: Identifier 'x' has not been declared or assigned

Total time: 3.039 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host px1wh.vc.shawcable.net. (24.69.255.202)
Time: Tue Dec  2 23:41:12 2003

Input: printf "%o",5;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host pclecacheux.institut.math.jussieu.fr. (134.157.51.81)
Time: Wed Dec  3 05:21:27 2003

Input: vecsort([6,8,1,2])

Output: Magma V2.10-6     Wed Dec  3 2003 05:21:22 on modular  [Seed = 3192666317]
-------------------------------------

>> vecsort([6,8,1,2]);
^
User error: Identifier 'vecsort' has not been declared or assigned

Total time: 3.059 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host ub084068.mat.ub.es. (161.116.84.68)
Time: Wed Dec  3 09:38:01 2003

Input: A:=NewSubspace(ModularForms(6400,4));
pp:=HeckePolynomial(A,7);
print pp;

Output: ** WARNING: Computation time exceeded 20 seconds, so computation was terminated after 20 seconds. **

Magma V2.10-6     Wed Dec  3 2003 09:37:37 on modular  [Seed = 3125309633]
-------------------------------------

Errors: /home/mfd/gomagma: line 2: 30192 Alarm clock             /usr/local/bin/magma

************** MAGMA *****************
Host ub084068.mat.ub.es. (161.116.84.68)
Time: Wed Dec  3 09:38:28 2003

Input: A:=NewSubspace(ModularForms(64,4));
pp:=HeckePolynomial(A,7);
print pp;

Output: Magma V2.10-6     Wed Dec  3 2003 09:38:23 on modular  [Seed = 3007412646]
-------------------------------------

Computing Hecke polynomial on Eisenstein series not yet implemented. (Returning
1.)
$.1^5 - 832*$.1^3 + 147456*$.1 Total time: 4.519 seconds, Total memory usage: 2.99MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:34:53 2003 Input: P4<[z]> := PolynomialRing(Rationals(), 4); Output: Magma V2.10-6 Wed Dec 3 2003 10:34:50 on modular [Seed = 834669795] ------------------------------------- Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:35:41 2003 Input: Output: Magma V2.10-6 Wed Dec 3 2003 10:35:37 on modular [Seed = 3224501570] ------------------------------------- Total time: 3.039 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:35:52 2003 Input: Output: Magma V2.10-6 Wed Dec 3 2003 10:35:49 on modular [Seed = 3626624325] ------------------------------------- Total time: 3.059 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:36:01 2003 Input: Output: Magma V2.10-6 Wed Dec 3 2003 10:35:58 on modular [Seed = 3491884358] ------------------------------------- Total time: 2.989 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:36:05 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; Output: Magma V2.10-6 Wed Dec 3 2003 10:36:02 on modular [Seed = 3894007106] ------------------------------------- Total time: 2.959 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:37:02 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; > D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; > Q2mat := func<Q | Matrix([[(i eq j select 1 else 1/2) > *MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>; > M1 := Q2mat(D1);> M2 := Q2mat(D2); > M1; [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] > M2; [ 1 0 1 -1] [ 0 1 1 0] [ 1 1 -1 -1] [-1 0 -1 0] > P1<x> := PolynomialRing(Rationals()); Output: Magma V2.10-6 Wed Dec 3 2003 10:36:59 on modular [Seed = 2239019478] ------------------------------------- >> M1 := Q2mat(D1);> M2 := Q2mat(D2); ^ User error: bad syntax [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] >> [ 1 1 0 0] ^ User error: bad syntax >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 2 0] ^ User error: bad syntax >> [ 0 -1 0 3] ^ User error: bad syntax >> M2; ^ User error: Identifier 'M2' has not been declared or assigned >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 1 0] ^ User error: bad syntax >> [ 1 1 -1 -1] ^ User error: bad syntax >> [-1 0 -1 0] ^ User error: bad syntax Total time: 3.299 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:37:46 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; > D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; > Q2mat := func<Q | Matrix([[(i eq j select 1 else 1/2) > *MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>; > M1 := Q2mat(D1);> M2 := Q2mat(D2); > M1; [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] > M2; [ 1 0 1 -1] [ 0 1 1 0] [ 1 1 -1 -1] [-1 0 -1 0] > P1<x> := PolynomialRing(Rationals()); Output: Magma V2.10-6 Wed Dec 3 2003 10:37:42 on modular [Seed = 2506402203] ------------------------------------- >> M1 := Q2mat(D1);> M2 := Q2mat(D2); ^ User error: bad syntax [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] >> [ 1 1 0 0] ^ User error: bad syntax >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 2 0] ^ User error: bad syntax >> [ 0 -1 0 3] ^ User error: bad syntax >> M2; ^ User error: Identifier 'M2' has not been declared or assigned >> [ 1 0 1 -1] ^ User error: bad syntax >> [ 0 1 1 0] ^ User error: bad syntax >> [ 1 1 -1 -1] ^ User error: bad syntax >> [-1 0 -1 0] ^ User error: bad syntax Total time: 3.279 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:38:46 2003 Input: Q:=Rationals(); Output: Magma V2.10-6 Wed Dec 3 2003 10:38:43 on modular [Seed = 2773784942] ------------------------------------- Total time: 3.139 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134) Time: Wed Dec 3 10:38:55 2003 Input: Q:=Rationals(); Q Output: Magma V2.10-6 Wed Dec 3 2003 10:38:52 on modular [Seed = 3175907705] ------------------------------------- Rational Field Total time: 3.009 seconds, Total memory usage: 1.80MB ************** MAGMA ***************** Host graduate02.graduate.iu-bremen.de. (212.201.46.235) Time: Wed Dec 3 10:40:30 2003 Input: > P4<[z]> := PolynomialRing(Rationals(), 4); > D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2; > D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4]; > Q2mat := func<Q | Matrix([[(i eq j select 1 else 1/2) > *MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>; > M1 := Q2mat(D1);> M2 := Q2mat(D2); > M1; [ 1 1 0 0] [ 1 0 1 -1] [ 0 1 2 0] [ 0 -1 0 3] > M2; [ 1 0 1 -1] [ 0 1 1 0] [ 1 1 -1 -1] [-1 0 -1 0] > P1<x> := PolynomialRing(Rationals()); > Determinant(x*ChangeRing(M1,P1) + ChangeRing(M2,P1)); -11*x^4 + 11*x^3 - 12*x + 3 > Reduce($1);
3*x^4 - 18*x^2 + 13*x - 9

[ 0 -1]
[ 1 -1]
> Determinant(ChangeRing(M1,P1) + x*ChangeRing(M2,P1));
3*x^4 - 12*x^3 + 11*x - 11
> g := 27*Evaluate($1, x/3); g; x^4 - 12*x^3 + 99*x - 297 > K<lambda> := NumberField(g); > Mlambda := ChangeRing(M1, K) + lambda/3*ChangeRing(M2, K); Mlambda; [ 1/3*(lambda + 3) 1 1/3*lambda -1/3*lambda] [ 1 1/3*lambda 1/3*(lambda + 3) -1] [ 1/3*lambda 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ -1/3*lambda -1 -1/3*lambda 3] > Determinant(Mlambda); 0 > Kernel(Mlambda); Vector space of degree 4, dimension 1 over K Echelonized basis: (1 1/1947*(17*lambda^3 - 110*lambda^2 - 990*lambda + 561) 1/5841*(-65*lambda^3 + 726*lambda^2 + 693*lambda - 6039) 1/531*(lambda^3 - 3*lambda^2 - 27*lambda - 144)) > node := Eltseq(Basis($1)[1]);
> node := Eltseq(1947*Basis($1)[1]); > node; [ 1947, 17*lambda^3 - 110*lambda^2 - 990*lambda + 561, 1/3*(-65*lambda^3 + 726*lambda^2 + 693*lambda - 6039), 1/3*(11*lambda^3 - 33*lambda^2 - 297*lambda - 1584) ] > T := Matrix([node, [0,1,0,0], [0,0,1,0], [0,0,0,1]]); > T*Mlambda*Transpose(T); [ 0 0 0 0] [ 0 1/3*lambda 1/3*(lambda + 3) -1] [ 0 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ 0 -1 -1/3*lambda 3] > Rlambda := Submatrix($1, 2,2, 3,3); Rlambda;
[     1/3*lambda  1/3*(lambda + 3)              -1]
[ 1/3*(lambda + 3) 1/3*(-lambda + 6)     -1/3*lambda]
[             -1     -1/3*lambda               3]
> Determinant($1); 1/27*(-lambda^3 - 12*lambda^2 + 27*lambda - 135) > Norm($1);
421201/27
> Factorisation(Numerator($1)); [ <11, 2>, <59, 2> ] > Rlambda *:= 3; > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > Determinant($1);
-lambda^3 - 12*lambda^2 + 27*lambda - 135
> Norm($1); 8290499283 > Factorisation(Integers()!($1));
[ <3, 9>, <11, 2>, <59, 2> ]
> OK := Integers(K);
> [K | b : b in Basis(OK)];
[
1,
lambda,
1/3*lambda^2,
1/9*lambda^3
]
> Decomposition(OK, 3);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Basis:
[1 0 0 2]
[0 1 0 0]
[0 0 1 0]
[0 0 0 3], 3>
]
> p31 := $1[1,1]; p32 :=$1[2,1];
> Decomposition(OK, 11);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 3>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> p111 := $1[1,1]; p112 :=$1[1,2];
> Decomposition(OK, 59);
[
<Prime Ideal of OK
Two element generators:
[59, 0, 0, 0]
[50, 1, 0, 0], 1>,
<Prime Ideal of OK
Two element generators:
[59, 0, 0, 0]
[55, 1, 0, 0], 1>,
<Prime Ideal of OK
Two element generators:
[59, 0, 0, 0]
[36, 1, 3, 0], 1>
]
> p591 := $1[1,1]; p592 :=$1[2,1]; p593 := $1[3,1]; > RlO := ChangeRing(Rlambda, OK); > RlO; [[0, 1, 0, 0] [3, 1, 0, 0] [-3, 0, 0, 0]] [[3, 1, 0, 0] [6, -1, 0, 0] [0, -1, 0, 0]] [[-3, 0, 0, 0] [0, -1, 0, 0] [9, 0, 0, 0]] > p31; Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] > p32; Prime Ideal of OK Basis: [1 0 0 2] [0 1 0 0] [0 0 1 0] [0 0 0 3] > p111; Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0] > p112; 3 > Decomposition(OK, 11); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 3>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > p111 :=$1[1,1]; p112 := $1[2,1]; > pl := [p31, p32, p111, p112, p591, p592,p593]; > det := Determinant(RlO); > [Valuation(det, p) : p in pl]; [ 3, 6, 0, 2, 2, 0, 0 ] > pl1 := [pl[i] : i in [1..#pl] |$1[i] ne 0]; #pl1;
4
> pl1[4];
Prime Ideal of OK
Two element generators:
[59, 0, 0, 0]
[50, 1, 0, 0]
> F4, m4 := ResidueClassField(pl1[4]);
> RlO4 := Matrix(3, [m4(c) : c in Eltseq(RlO)]);
> RlO4;
[ 9 12 56]
[12 56 50]
[56 50  9]
> Kernel($1); Vector space of degree 3, dimension 1 over GF(59) Echelonized basis: ( 1 45 6) > T1 := Matrix([Eltseq(Basis($1)[1]), [0,1,0], [0,0,1]]);
> T1*RlO4*Transpose(T1);
[ 0  0  0]
[ 0 56 50]
[ 0 50  9]
> PF<u> := PolynomialRing(F4);
> Factorisation($1[2,2]*u^2 + 2*$1[2,3]*u + $1[3,3]); [ <u + 25, 1>, <u + 40, 1> ] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 54 2] [ 0 2 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 39 39] [ 0 39 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]); > T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,0,1]])*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 54 2] [ 0 2 9] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,1,-40]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 54 24] [ 0 24 13] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,1,40]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 39 34] [ 0 34 48] > T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]); > T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,1,-40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 5 7] [ 0 7 30] > T2 := Matrix(F4, [[1,0,0], [0,1,25], [0,1,40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 5 52] [ 0 52 30] > T2 := Matrix(F4, [[1,0,0], [0,1,1], [0,25,40]])^-1*T1; > T2*RlO4*Transpose(T2); [ 0 0 0] [ 0 0 28] [ 0 28 0] > T2l := Matrix(3, [c @@ m4 : c in Eltseq(T2)]); > T2l; [[1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]] [[0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]] [[0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]] > T2b := Matrix(OK, [[1,0,0,0]] cat [[0] cat Eltseq(T2l[i]) : i in [1..3]]); > T2b; [[1, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0]] [[0, 0, 0, 0] [1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]] [[0, 0, 0, 0] [0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]] [[0, 0, 0, 0] [0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]] > Rnew1 := T2l*RlO*Transpose(T2l); > Rnew1; [[12708, -2474, 0, 0] [14271, -4575, 0, 0] [5118, -1080, 0, 0]] [[14271, -4575, 0, 0] [37809, -6384, 0, 0] [6516, -1914, 0, 0]] [[5118, -1080, 0, 0] [6516, -1914, 0, 0] [2088, -468, 0, 0]] > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > P1; Univariate Polynomial Ring in x over Rational Field > P1K<U> := PolynomialRing(K); > P3K<[Z]> := PolynomialRing(K, 3); > Rpol := &+[Rlambda[i,j]*Z[i]*Z[j] : i,j in [1..3]]; > rand := func< | K!OK![Random(-5,5) : i in [1..4]]>; > rand(); 1/9*(2*lambda^3 - 9*lambda^2 + 45*lambda - 18) > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>; > try(); false > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>; > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>; > try(); false 1/9*(-4*lambda^3 - 15*lambda^2 + 27*lambda - 18) 1/3*(-lambda^3 - 2*lambda^2 + 6*lambda + 12) > repeat flag, r1, r2 := try(); until flag; [Interrupted] > rand := func< | K!OK![Random(-15,15) : i in [1..4]]>; > try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>; > repeat flag, r1, r2 := try(); until flag; [Interrupted] > Rpol; lambda*Z[1]^2 + (2*lambda + 6)*Z[1]*Z[2] - 6*Z[1]*Z[3] + (-lambda + 6)*Z[2]^2 - 2*lambda*Z[2]*Z[3] + 9*Z[3]^2 > Rpol/lambda; Z[1]^2 + 1/99*(2*lambda^3 - 24*lambda^2 + 396)*Z[1]*Z[2] + 1/99*(-2*lambda^3 + 24*lambda^2 - 198)*Z[1]*Z[3] + 1/99*(2*lambda^3 - 24*lambda^2 + 99)*Z[2]^2 - 2*Z[2]*Z[3] + 1/33*(lambda^3 - 12*lambda^2 + 99)*Z[3]^2 > Rpol1 := Evaluate($1, [Z[1]-1/2*MonomialCoefficient($1,Z[1]*Z[2])*Z[2] > -1/2*MonomialCoefficient($1, Z[1]*Z[3])*Z[3], Z[2], Z[3]]);
> Rpol1;
Z[1]^2 + 1/99*(-lambda^3 + 9*lambda^2 + 36*lambda - 297)*Z[2]^2 +
1/99*(4*lambda^3 - 42*lambda^2 - 72*lambda + 198)*Z[2]*Z[3] +
1/99*(2*lambda^3 - 27*lambda^2 + 36*lambda + 198)*Z[3]^2
> Rpol1 := lambda*Rpol1; Rpol1;
lambda*Z[1]^2 + 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99)*Z[2]^2 +
1/33*(2*lambda^3 - 24*lambda^2 - 66*lambda + 396)*Z[2]*Z[3] +
1/33*(-lambda^3 + 12*lambda^2 + 198)*Z[3]^2
> Rpol1 := lambda*Rpol1; Rpol1;
lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + (-2*lambda^2 + 6*lambda +
18)*Z[2]*Z[3] + (9*lambda - 9)*Z[3]^2
> Rpol2 := Evaluate($1, [Z[1], Z[2] - 1/(2*MonomialCoefficient($1,Z[2]^2))*
> MonomialCoefficient($1, Z[2]*Z[3])*Z[3], Z[3]]); > Rpol2; lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + 1/33*(4*lambda^3 - 33*lambda^2 + 198*lambda + 99)*Z[3]^2 > lambda*Rpol2; lambda^3*Z[1]^2 + (-2*lambda^3 - 9*lambda)*Z[2]^2 + 1/11*(5*lambda^3 + 66*lambda^2 - 99*lambda + 396)*Z[3]^2 > lambda^2*Rpol2; (12*lambda^3 - 99*lambda + 297)*Z[1]^2 + (-24*lambda^3 - 9*lambda^2 + 198*lambda - 594)*Z[2]^2 + 1/11*(126*lambda^3 - 99*lambda^2 - 99*lambda + 1485)*Z[3]^2 > (2*lambda^2+9)*Rpol2; (24*lambda^3 + 9*lambda^2 - 198*lambda + 594)*Z[1]^2 + (-48*lambda^3 - 36*lambda^2 + 396*lambda - 1269)*Z[2]^2 + (24*lambda^3 - 27*lambda^2 + 36*lambda + 297)*Z[3]^2 > Rpol3 :=$1;
> ideal<OK | ChangeUniverse(Coefficients(Rpol3), OK)>;
Ideal of OK
Basis:
[  27   18    0  783]
[   0   27    0   54]
[   0    0   27  513]
[   0    0    0 3267]
> Norm($1); 64304361 > Factorisation($1);
[ <3, 12>, <11, 2> ]
> ChangeUniverse(Coefficients(Rpol3), OK);
[
[594, -198, 27, 216],
[-1269, 396, -108, -432],
[297, 36, -81, 216]
]
> GCD(&cat[ChangeUniverse(Eltseq(c), Integers()) : c in $1]); 9 > Rpol3 := 1/9*Rpol3; > ideal<OK | ChangeUniverse(Coefficients(Rpol3), OK)>; Ideal of OK Basis: [ 3 2 0 87] [ 0 3 0 6] [ 0 0 3 57] [ 0 0 0 363] > Norm($1);
9801
> Factorisation($1); [ <3, 4>, <11, 2> ] > ideal<OK | ChangeUniverse(Coefficients(Rpol3), OK)>; Ideal of OK Basis: [ 3 2 0 87] [ 0 3 0 6] [ 0 0 3 57] [ 0 0 0 363] > flag, gen := IsPrincipal($1); flag;
true
> gen;
[-48, 4, 12, -3]
> Rpol3 := 1/gen*Rpol3;
> Rpol3;
1/9*(5*lambda^3 - 60*lambda^2 + 198*lambda - 297)*Z[1]^2 + 1/9*(-13*lambda^3 +
165*lambda^2 - 549*lambda + 837)*Z[2]^2 + 1/9*(-10*lambda^3 + 171*lambda^2 -
603*lambda + 990)*Z[3]^2
> [Norm(c) : c in Coefficients(Rpol3)];
[ -3993, -131769, 38291 ]
> [Factorisation(Integers()!n) : n in $1]; [ [ <3, 1>, <11, 3> ], [ <3, 2>, <11, 4> ], [ <11, 1>, <59, 2> ] ] > > > a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]); > ideal<OK | a,b>; Ideal of OK Two element generators: [-33, 22, -20, 5] [93, -61, 55, -13] > flag, gen := IsPrincipal($1); flag;
true
> a := a/gen; b := b/gen; c := c*gen;
> ideal<OK | b,c>;
Ideal of OK
Two element generators:
[77724, -48384, 41973, -8147]
[-66, -3, 13, -1]
> flag, gen := IsPrincipal($1); flag; true > b := b/gen; c := c/gen; a := a*gen; > ideal<OK | a,c>; Ideal of OK Two element generators: [-33, 22, -20, 5] [110, -67, 57, -10] > flag, gen := IsPrincipal($1); flag;
true
> a := a/gen; b := b*gen; c := c/gen;
> ideal<OK | a,b>;
Ideal of OK
Two element generators:
[126225, -78574, 68161, -13228]
[-17468, 10844, -9385, 1795]
> Norm($1); 121 > a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]); > ideal<OK | a,b,c>; Ideal of OK Basis: [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] > Factorisation(ideal<OK | a>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 2>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > flag, gen := IsPrincipal($1[2,1]); flag;
true
> a := a/gen^2;
> IsIntegral(a);
true
> Factorisation(ideal<OK | b>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 2>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 4>
]
> flag, rt := IsSquare(b); flag;
false
> Factorisation(ideal<OK | b>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 2>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 4>
]
> flag, gen := IsPrincipal($1[1,1]*$1[2,1]^2); flag;
true
> b := b/gen^2; IsIntegral(b);
true
> IsUnit(b);
true
> b;
1/9*(-35203866485*lambda^3 + 544192313463*lambda^2 - 1881986216391*lambda +
3023310688146)
> U, mU := UnitGroup(OK);
> U;
Abelian Group isomorphic to Z/2 + Z + Z
Defined on 3 generators
Relations:
2*U.1 = 0
> (OK!b) @@ mU;
U.1 - U.2 + U.3
> Factorisation(ideal<OK | c>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>,
<Prime Ideal of OK
Two element generators:
[59, 0, 0, 0]
[50, 1, 0, 0], 2>
]
> flag, gen := IsPrincipal($1[2,1]); flag; true > c := c/gen^2; > IsIntegral(c); true > ideal<OK | a,c>; Ideal of OK Two element generators: [-435353142, 271003776, -235089137, 45623834] [97396574, -60628572, 52593801, -10206898] > flag, gen := IsPrincipal($1); flag;
true
> a := a*b; c := c*b; b := b/b;
> a;
1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 +
4741581890375719065612*lambda - 7617098936772540178011)
> c;
1/3*(-6614209165540654351*lambda^3 + 102244501724191609815*lambda^2 -
353593276101607037424*lambda + 568028778098368129917)
> Factorisation(ideal<OK | a>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> Norm(a);
33
> Norm(c);
-11
> b;
1
> L := ext<K | PolynomialRing(K)![-c,0,1]>;
> NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true);

Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
to [email protected]
Version date: Wed Aug 29 16:18:10 EST 2001
Initial seed: 2725307260
Time to this point: 202.77
Segmentation fault
> DefiningPolynomial(K);
x^4 - 12*x^3 + 99*x - 297
> lambda;
lambda
> MinimalPolynomial(lambda);
x^4 - 12*x^3 + 99*x - 297
> OL := Integers(L);
> NormEquation(OL, -OK!a : Integral := false, All := false, Solutions := 1, Exact := true);

Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
to [email protected]
Version date: Wed Aug 29 16:18:10 EST 2001
Initial seed: 2725307260
Time to this point: 202.98
Segmentation fault
> SUnitGroup;
Intrinsic 'SUnitGroup'

Signatures:

(<RngOrdFracIdl> I) -> GrpAb, Map
(<SeqEnum[RngOrdIdl]> S) -> GrpAb, Map

The group of s-units of the prime ideals given in the sequence S or the
factorization of I

(<SetEnum[PlcFunElt]> S) -> GrpAb, Map

The group of S-units as an Abelian group and the map into the function
field

> Labs := AbsoluteField(L);
> OLabs := Integers(Labs);
> ClassGroup(OLabs : Bound := 300);
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to Set of ideals of OLabs
> ideal<OK | a,c>;
Ideal of OK
Two element generators:
88694600599454463649]
-19842627496621963053]
> I := ideal<OLabs | $1>; > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z + Z + Z + Z
Defined on 5 generators
Relations:
2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU :=$1;
> [Norm(L!mSU(SU.i)) : i in [1..5]];
[
1,
1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620),
1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda +
58003196403),
1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda +
58003196403),
1
]
> a;
1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 +
4741581890375719065612*lambda - 7617098936772540178011)
> norms := $2; > Factorisation(ideal<OK | a>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > p31 :=$1[1,1]; p111 := $1[2,1]; > Factorisation(ideal<OK | norms[2]>); [] > Factorisation(ideal<OK | norms[3]>); [] > Factorisation(ideal<OK | norms[4]>); [] > I; Principal Ideal of OLabs Generator: [1, 0, 0, 0, 0, 0, 0, 0] > ideal<OK | a,c>; Ideal of OK Two element generators: 88694600599454463649] -19842627496621963053] > flag, gen := IsPrincipal($1); flag;
true
> I := ideal<OLabs | OLabs!Labs!L!K!gen>;
> I;
Principal Ideal of OLabs
Generator:
[1, 0, 0, 0, 0, 0, 0, 0]
> Norm($3); 1 > Factorisation(ideal<OK | c>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1> ] > I := ideal<OLabs | OLabs!Labs!L!(a*c)>; > I; Principal Ideal of OLabs Generator: 97187721532932707077425300749268443936597, 0, 0, 0, 0] > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies)
Defined on 8 generators
Relations:
2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU :=$1;
> [Norm(L!mSU(SU.i)) : i in [1..8]];
[
1,
1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620),
1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda +
58003196403),
1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda +
58003196403),
1,
1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66),
1/3*(4*lambda^3 - 8*lambda^2 - 33*lambda + 147),
1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399)
]
> norms := $1; > Factorisation(ideal<OK | norms[2]>); [] > Factorisation(ideal<OK | norms[3]>); [] > Factorisation(ideal<OK | norms[4]>); [] > Factorisation(ideal<OK | norms[5]>); [] > Factorisation(ideal<OK | norms[6]>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1> ] > Factorisation(ideal<OK | norms[7]>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 2> ] > Factorisation(ideal<OK | norms[8]>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 2> ] > Rlambda; [ lambda lambda + 3 -3] [ lambda + 3 -lambda + 6 -lambda] [ -3 -lambda 9] > Tr1 := Matrix([[1, -(lambda+3)/lambda, 3/lambda], [0,1,0], [0,0,1]]); Tr1; [1 1/99*(-lambda^3 + 12*lambda^2 - 198) 1/99*(lambda^3 - 12*lambda^2 + 99)] [0 1 0] [0 0 1] > Tr1*Rlambda*Transpose(Tr1); [1/11*(2*lambda^3 - 19*lambda^2 - 82*lambda + 132) 1/33*(-2*lambda^3 + 24*lambda^2 + 66*lambda - 297) 1/11*(lambda^3 - 12*lambda^2 + 11*lambda + 99)] [1/33*(-2*lambda^3 + 24*lambda^2 + 66*lambda - 297) -lambda + 6 -lambda] [1/11*(lambda^3 - 12*lambda^2 + 11*lambda + 99) -lambda 9] > Transpose(Tr1)*Rlambda*Tr1; [lambda 0 0] [0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 1/33*(lambda^3 - 12*lambda^2 - 33*lambda + 198)] [0 1/33*(lambda^3 - 12*lambda^2 - 33*lambda + 198) 1/33*(-lambda^3 + 12*lambda^2 + 198)] > Tr2 := Matrix([[1,0,0], [0,1,-$1[2,3]/$1[2,2]], [0,0,1]]); Tr2; [1 0 0] [0 1 1/3267*(26*lambda^3 - 297*lambda^2 - 297*lambda + 2277)] [0 0 1] > Transpose(Tr2)*$2*Tr2;
[lambda 0 0]
[0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 0]
[0 0 1/99*(lambda^3 - 99*lambda + 693)]
> a,b,c := Explode([$1[i,i] : i in [1..3]]); > IsIntegral(b); false > IsIntegral(c); false > Denominator(b); 33 > Denominator(c); 99 > Factorisation(ideal<OK | c>); [ <Prime Ideal of OK Basis: [1 0 0 2] [0 1 0 0] [0 0 1 0] [0 0 0 3], 2>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], -1>, <Prime Ideal of OK Two element generators: [59, 0, 0, 0] [50, 1, 0, 0], 2> ] > flag, gen := IsPrincipal($1[1,1]*$1[3,1]); flag; true > c := c/gen; > flag, gen := IsPrincipal($2[2,1]); flag;
true
> flag, gen := IsPrincipal($3[1,1]*$3[3,1]); flag;
true
> c := c/gen;
> Factorisation(ideal<OK | c>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], -1>
]
> flag, gen := IsPrincipal($1[1,1]); flag; true > c := c*gen^2; > c; 1/9*(-25211*lambda^3 + 524037*lambda^2 - 1578888*lambda - 12770478) > Factorisation(ideal<OK | b>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 2>, <Prime Ideal of OK Basis: [1 0 0 2] [0 1 0 0] [0 0 1 0] [0 0 0 3], 2>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], -1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 3> ] > flag, gen := IsPrincipal($1[1,1]*$1[2,1]*$1[4,1]); flag;
true
> b := b/gen^2;
> Factorisation(ideal<OK | b>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], -1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> flag, gen := IsPrincipal($1[1,1]); flag; true > b := b*gen^2; > Factorisation(ideal<OK | a>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Basis: [1 0 0 2] [0 1 0 0] [0 0 1 0] [0 0 0 3], 2>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1> ] > flag, gen := IsPrincipal($1[2,1]); flag;
true
> a := a/gen^2;
> Factorisation(ideal<OK | a>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>
]
> Factorisation(ideal<OK | b>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> Factorisation(ideal<OK | c>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> flag, gen := IsPrincipal($1[1,1]); flag; true > c := c/gen; b := b/gen; a := a*gen; > c; 1/9*(-12910*lambda^3 + 73386*lambda^2 + 747855*lambda + 1174653) > IsUnit(c); true > a := a/c; b := b/c; c := c/c; > a; 1/9*(11768733070573612150898*lambda^3 - 6565975199446345850085*lambda^2 - 75128433793103508474861*lambda + 305478792168156995505975) > b; 1/3*(-lambda^3 + 9*lambda^2 + 24*lambda - 66) > L := ext<K | PolynomialRing(K)![-b,0,1]>; > NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to [email protected] Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 289.15 Segmentation fault > Factorisation(ideal<OK | a>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > Labs := AbsoluteField(L); > OLabs := Integers(Labs); > OL := Integers(L); > ClassGroup(OLabs : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OLabs > I := ideal<OLabs | OLabs!Labs!L!(a*b)>; > I; Principal Ideal of OLabs Generator: 81061059655244371456034, -435877053076387089543350, 0, 0, 0, 0] > SUnitGroup(I); Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies)
Defined on 8 generators
Relations:
2*$.1 = 0 to Field of Fractions of OLabs > SU, mSU :=$1;
> [Norm(L!mSU(SU.i)) : i in [1..8]];
[
1,
1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620),
1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666),
1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666),
1,
124*lambda^3 - 1075*lambda^2 - 4228*lambda + 3364,
1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66),
1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399)
]
> norms := $1; > Factorisation(ideal<OK | norms[2]>); [] > Factorisation(ideal<OK | norms[3]>); [] > Factorisation(ideal<OK | norms[4]>); [] > Factorisation(ideal<OK | norms[5]>); [] > Factorisation(ideal<OK | norms[6]>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 2> ] > Factorisation(ideal<OK | norms[7]>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1> ] > Factorisation(ideal<OK | norms[8]>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 2> ] > ClassGroup(OK : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OK > ideal<OK | a,b>; Ideal of OK Two element generators: 11768733070573612150898] [-22, 8, 9, -3] > Factorisation($1);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>
]
> flag, gen := IsPrincipal($2); flag; true > a := a/gen; b := b/gen; c := c*gen; > ideal<OK | a,b>; Ideal of OK Two element generators: [-1, 0, 0, 0] 317757210900264194558] > Norm($1);
1
> $2 eq ideal<OK | 1>; true > ideal<OK | a,c>; Ideal of OK Two element generators: 317757210900264194558] [22, -8, -9, 3] >$1 eq ideal<OK | 1>;
true
> ideal<OK | b,c>;
Ideal of OK
Two element generators:
[-1, 0, 0, 0]
[22, -8, -9, 3]
> $1 eq ideal<OK | 1>; true > c; 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66) > b; -1 > a; 1/9*(317757210900264194558*lambda^3 - 177282073464141075450*lambda^2 - 2028476957468286393567*lambda + 8247964555766062942857) > Factorisation(ideal<OK | a>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > Factorisation(ideal<OK | c>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1> ] > p3 :=$2[1,1]; p11a := $2[2,1]; p11b :=$1[1,1];
> F3, mF3 := ResidueClassField(p3);
> IsSquare(mF3(c));
true 1
> F11a, mF11a := ResidueClassField(p11a);
> IsSquare(mF11a(c));
true 9
> F11b, mF11b := ResidueClassField(p11b);
> IsSquare(mF11b(a));
true 1
> Conjugates(a);

Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134)
Time: Wed Dec  3 10:41:10 2003

Input: > Q:=Rationals(); R<x>:=PolynomialRing(Q)
P<x>:=

Output: Magma V2.10-6     Wed Dec  3 2003 10:41:07 on modular  [Seed = 1220113180]
-------------------------------------

>> P<x>:=;
^

Total time: 3.039 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Wed Dec  3 10:41:34 2003

Input:  P4<[z]> := PolynomialRing(Rationals(), 4);
D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2;
D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4];
Q2mat := func<Q | Matrix([[(i eq j select 1 else 1/2)
*MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>;
M1 := Q2mat(D1);> M2 := Q2mat(D2);
M1;
[ 1  1  0  0]
[ 1  0  1 -1]
[ 0  1  2  0]
[ 0 -1  0  3]
> M2;
[ 1  0  1 -1]
[ 0  1  1  0]
[ 1  1 -1 -1]
[-1  0 -1  0]
> P1<x> := PolynomialRing(Rationals());
> Determinant(x*ChangeRing(M1,P1) + ChangeRing(M2,P1));
-11*x^4 + 11*x^3 - 12*x + 3
> Reduce($1); 3*x^4 - 18*x^2 + 13*x - 9 [ 0 -1] [ 1 -1] > Determinant(ChangeRing(M1,P1) + x*ChangeRing(M2,P1)); 3*x^4 - 12*x^3 + 11*x - 11 > g := 27*Evaluate($1, x/3); g;
x^4 - 12*x^3 + 99*x - 297
> K<lambda> := NumberField(g);
> Mlambda := ChangeRing(M1, K) + lambda/3*ChangeRing(M2, K); Mlambda;
[ 1/3*(lambda + 3)               1      1/3*lambda     -1/3*lambda]
[              1      1/3*lambda  1/3*(lambda + 3)              -1]
[     1/3*lambda  1/3*(lambda + 3) 1/3*(-lambda + 6)     -1/3*lambda]
[    -1/3*lambda              -1     -1/3*lambda               3]
> Determinant(Mlambda);
0
> Kernel(Mlambda);
Vector space of degree 4, dimension 1 over K
Echelonized basis:
(1 1/1947*(17*lambda^3 - 110*lambda^2 - 990*lambda + 561) 1/5841*(-65*lambda^3 +
726*lambda^2 + 693*lambda - 6039) 1/531*(lambda^3 - 3*lambda^2 - 27*lambda -
144))
> node := Eltseq(Basis($1)[1]); > node := Eltseq(1947*Basis($1)[1]);
> node;
[
1947,
17*lambda^3 - 110*lambda^2 - 990*lambda + 561,
1/3*(-65*lambda^3 + 726*lambda^2 + 693*lambda - 6039),
1/3*(11*lambda^3 - 33*lambda^2 - 297*lambda - 1584)
]
> T := Matrix([node, [0,1,0,0], [0,0,1,0], [0,0,0,1]]);
> T*Mlambda*Transpose(T);
[              0               0               0               0]
[              0      1/3*lambda  1/3*(lambda + 3)              -1]
[              0  1/3*(lambda + 3) 1/3*(-lambda + 6)     -1/3*lambda]
[              0              -1     -1/3*lambda               3]
> Rlambda := Submatrix($1, 2,2, 3,3); Rlambda; [ 1/3*lambda 1/3*(lambda + 3) -1] [ 1/3*(lambda + 3) 1/3*(-lambda + 6) -1/3*lambda] [ -1 -1/3*lambda 3] > Determinant($1);
1/27*(-lambda^3 - 12*lambda^2 + 27*lambda - 135)
> Norm($1); 421201/27 > Factorisation(Numerator($1));
[ <11, 2>, <59, 2> ]
> Rlambda *:= 3;
> Rlambda;
[     lambda  lambda + 3          -3]
[ lambda + 3 -lambda + 6     -lambda]
[         -3     -lambda           9]
> Determinant($1); -lambda^3 - 12*lambda^2 + 27*lambda - 135 > Norm($1);
8290499283
> Factorisation(Integers()!($1)); [ <3, 9>, <11, 2>, <59, 2> ] > OK := Integers(K); > [K | b : b in Basis(OK)]; [ 1, lambda, 1/3*lambda^2, 1/9*lambda^3 ] > Decomposition(OK, 3); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Basis: [1 0 0 2] [0 1 0 0] [0 0 1 0] [0 0 0 3], 3> ] > p31 :=$1[1,1]; p32 := $1[2,1]; > Decomposition(OK, 11); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 3>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > p111 :=$1[1,1]; p112 := $1[1,2]; > Decomposition(OK, 59); [ <Prime Ideal of OK Two element generators: [59, 0, 0, 0] [50, 1, 0, 0], 1>, <Prime Ideal of OK Two element generators: [59, 0, 0, 0] [55, 1, 0, 0], 1>, <Prime Ideal of OK Two element generators: [59, 0, 0, 0] [36, 1, 3, 0], 1> ] > p591 :=$1[1,1]; p592 := $1[2,1]; p593 :=$1[3,1];
> RlO := ChangeRing(Rlambda, OK);
> RlO;
[[0, 1, 0, 0] [3, 1, 0, 0] [-3, 0, 0, 0]]
[[3, 1, 0, 0] [6, -1, 0, 0] [0, -1, 0, 0]]
[[-3, 0, 0, 0] [0, -1, 0, 0] [9, 0, 0, 0]]
> p31;
Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
> p32;
Prime Ideal of OK
Basis:
[1 0 0 2]
[0 1 0 0]
[0 0 1 0]
[0 0 0 3]
> p111;
Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0]
> p112;
3
> Decomposition(OK, 11);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 3>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> p111 := $1[1,1]; p112 :=$1[2,1];
> pl := [p31, p32, p111, p112, p591, p592,p593];
> det := Determinant(RlO);
> [Valuation(det, p) : p in pl];
[ 3, 6, 0, 2, 2, 0, 0 ]
> pl1 := [pl[i] : i in [1..#pl] | $1[i] ne 0]; #pl1; 4 > pl1[4]; Prime Ideal of OK Two element generators: [59, 0, 0, 0] [50, 1, 0, 0] > F4, m4 := ResidueClassField(pl1[4]); > RlO4 := Matrix(3, [m4(c) : c in Eltseq(RlO)]); > RlO4; [ 9 12 56] [12 56 50] [56 50 9] > Kernel($1);
Vector space of degree 3, dimension 1 over GF(59)
Echelonized basis:
( 1 45  6)
> T1 := Matrix([Eltseq(Basis($1)[1]), [0,1,0], [0,0,1]]); > T1*RlO4*Transpose(T1); [ 0 0 0] [ 0 56 50] [ 0 50 9] > PF<u> := PolynomialRing(F4); > Factorisation($1[2,2]*u^2 + 2*$1[2,3]*u +$1[3,3]);
[
<u + 25, 1>,
<u + 40, 1>
]
> T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,0,1]]);
> T1*RlO4*Transpose(T1);
[ 0  0  0]
[ 0 54  2]
[ 0  2  9]
> T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,0,1]]);
> T1*RlO4*Transpose(T1);
[ 0  0  0]
[ 0 39 39]
[ 0 39  9]
> T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]);
> T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,0,1]])*T1;
> T2*RlO4*Transpose(T2);
[ 0  0  0]
[ 0 54  2]
[ 0  2  9]
> T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,-25], [0,1,-40]]);
> T1*RlO4*Transpose(T1);
[ 0  0  0]
[ 0 54 24]
[ 0 24 13]
> T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,25], [0,1,40]]);
> T1*RlO4*Transpose(T1);
[ 0  0  0]
[ 0 39 34]
[ 0 34 48]
> T1 := Matrix([Eltseq(Basis(Kernel(RlO4))[1]), [0,1,0], [0,0,1]]);
> T2 := Matrix(F4, [[1,0,0], [0,1,-25], [0,1,-40]])^-1*T1;
> T2*RlO4*Transpose(T2);
[ 0  0  0]
[ 0  5  7]
[ 0  7 30]
> T2 := Matrix(F4, [[1,0,0], [0,1,25], [0,1,40]])^-1*T1;
> T2*RlO4*Transpose(T2);
[ 0  0  0]
[ 0  5 52]
[ 0 52 30]
> T2 := Matrix(F4, [[1,0,0], [0,1,1], [0,25,40]])^-1*T1;
> T2*RlO4*Transpose(T2);
[ 0  0  0]
[ 0  0 28]
[ 0 28  0]
> T2l := Matrix(3, [c @@ m4 : c in Eltseq(T2)]);
> T2l;
[[1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]]
[[0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]]
[[0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]]
> T2b := Matrix(OK, [[1,0,0,0]] cat [[0] cat Eltseq(T2l[i]) : i in [1..3]]);
> T2b;
[[1, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0] [0, 0, 0, 0]]
[[0, 0, 0, 0] [1, 0, 0, 0] [45, 0, 0, 0] [6, 0, 0, 0]]
[[0, 0, 0, 0] [0, 0, 0, 0] [42, 0, 0, 0] [55, 0, 0, 0]]
[[0, 0, 0, 0] [0, 0, 0, 0] [18, 0, 0, 0] [4, 0, 0, 0]]
> Rnew1 := T2l*RlO*Transpose(T2l);
> Rnew1;
[[12708, -2474, 0, 0] [14271, -4575, 0, 0] [5118, -1080, 0, 0]]
[[14271, -4575, 0, 0] [37809, -6384, 0, 0] [6516, -1914, 0, 0]]
[[5118, -1080, 0, 0] [6516, -1914, 0, 0] [2088, -468, 0, 0]]
> Rlambda;
[     lambda  lambda + 3          -3]
[ lambda + 3 -lambda + 6     -lambda]
[         -3     -lambda           9]
> P1;
Univariate Polynomial Ring in x over Rational Field
> P1K<U> := PolynomialRing(K);
> P3K<[Z]> := PolynomialRing(K, 3);
> Rpol := &+[Rlambda[i,j]*Z[i]*Z[j] : i,j in [1..3]];
> rand := func< | K!OK![Random(-5,5) : i in [1..4]]>;
> rand();
1/9*(2*lambda^3 - 9*lambda^2 + 45*lambda - 18)
> try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>;
> try();
false
> try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, rand(), rand()])))>;
> try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>;
> try();
false 1/9*(-4*lambda^3 - 15*lambda^2 + 27*lambda - 18)
1/3*(-lambda^3 - 2*lambda^2 + 6*lambda + 12)
> repeat flag, r1, r2 := try(); until flag;

[Interrupted]
> rand := func< | K!OK![Random(-15,15) : i in [1..4]]>;
> try := func< | IsSquare(Discriminant(Evaluate(Rpol, [U, r1, r2]))), r1, r2 where r1 := rand() where r2 := rand()>;
> repeat flag, r1, r2 := try(); until flag;

[Interrupted]
> Rpol;
lambda*Z[1]^2 + (2*lambda + 6)*Z[1]*Z[2] - 6*Z[1]*Z[3] + (-lambda + 6)*Z[2]^2 -
2*lambda*Z[2]*Z[3] + 9*Z[3]^2
> Rpol/lambda;
Z[1]^2 + 1/99*(2*lambda^3 - 24*lambda^2 + 396)*Z[1]*Z[2] + 1/99*(-2*lambda^3 +
24*lambda^2 - 198)*Z[1]*Z[3] + 1/99*(2*lambda^3 - 24*lambda^2 + 99)*Z[2]^2 -
2*Z[2]*Z[3] + 1/33*(lambda^3 - 12*lambda^2 + 99)*Z[3]^2
> Rpol1 := Evaluate($1, [Z[1]-1/2*MonomialCoefficient($1,Z[1]*Z[2])*Z[2]
> -1/2*MonomialCoefficient($1, Z[1]*Z[3])*Z[3], Z[2], Z[3]]); > Rpol1; Z[1]^2 + 1/99*(-lambda^3 + 9*lambda^2 + 36*lambda - 297)*Z[2]^2 + 1/99*(4*lambda^3 - 42*lambda^2 - 72*lambda + 198)*Z[2]*Z[3] + 1/99*(2*lambda^3 - 27*lambda^2 + 36*lambda + 198)*Z[3]^2 > Rpol1 := lambda*Rpol1; Rpol1; lambda*Z[1]^2 + 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99)*Z[2]^2 + 1/33*(2*lambda^3 - 24*lambda^2 - 66*lambda + 396)*Z[2]*Z[3] + 1/33*(-lambda^3 + 12*lambda^2 + 198)*Z[3]^2 > Rpol1 := lambda*Rpol1; Rpol1; lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + (-2*lambda^2 + 6*lambda + 18)*Z[2]*Z[3] + (9*lambda - 9)*Z[3]^2 > Rpol2 := Evaluate($1, [Z[1], Z[2] - 1/(2*MonomialCoefficient($1,Z[2]^2))* > MonomialCoefficient($1, Z[2]*Z[3])*Z[3], Z[3]]);
> Rpol2;
lambda^2*Z[1]^2 + (-2*lambda^2 - 9)*Z[2]^2 + 1/33*(4*lambda^3 - 33*lambda^2 +
198*lambda + 99)*Z[3]^2
> lambda*Rpol2;
lambda^3*Z[1]^2 + (-2*lambda^3 - 9*lambda)*Z[2]^2 + 1/11*(5*lambda^3 +
66*lambda^2 - 99*lambda + 396)*Z[3]^2
> lambda^2*Rpol2;
(12*lambda^3 - 99*lambda + 297)*Z[1]^2 + (-24*lambda^3 - 9*lambda^2 + 198*lambda
- 594)*Z[2]^2 + 1/11*(126*lambda^3 - 99*lambda^2 - 99*lambda + 1485)*Z[3]^2
> (2*lambda^2+9)*Rpol2;
(24*lambda^3 + 9*lambda^2 - 198*lambda + 594)*Z[1]^2 + (-48*lambda^3 -
36*lambda^2 + 396*lambda - 1269)*Z[2]^2 + (24*lambda^3 - 27*lambda^2 +
36*lambda + 297)*Z[3]^2
> Rpol3 := $1; > ideal<OK | ChangeUniverse(Coefficients(Rpol3), OK)>; Ideal of OK Basis: [ 27 18 0 783] [ 0 27 0 54] [ 0 0 27 513] [ 0 0 0 3267] > Norm($1);
64304361
> Factorisation($1); [ <3, 12>, <11, 2> ] > ChangeUniverse(Coefficients(Rpol3), OK); [ [594, -198, 27, 216], [-1269, 396, -108, -432], [297, 36, -81, 216] ] > GCD(&cat[ChangeUniverse(Eltseq(c), Integers()) : c in$1]);
9
> Rpol3 := 1/9*Rpol3;
> ideal<OK | ChangeUniverse(Coefficients(Rpol3), OK)>;
Ideal of OK
Basis:
[  3   2   0  87]
[  0   3   0   6]
[  0   0   3  57]
[  0   0   0 363]
> Norm($1); 9801 > Factorisation($1);
[ <3, 4>, <11, 2> ]
> ideal<OK | ChangeUniverse(Coefficients(Rpol3), OK)>;
Ideal of OK
Basis:
[  3   2   0  87]
[  0   3   0   6]
[  0   0   3  57]
[  0   0   0 363]
> flag, gen := IsPrincipal($1); flag; true > gen; [-48, 4, 12, -3] > Rpol3 := 1/gen*Rpol3; > Rpol3; 1/9*(5*lambda^3 - 60*lambda^2 + 198*lambda - 297)*Z[1]^2 + 1/9*(-13*lambda^3 + 165*lambda^2 - 549*lambda + 837)*Z[2]^2 + 1/9*(-10*lambda^3 + 171*lambda^2 - 603*lambda + 990)*Z[3]^2 > [Norm(c) : c in Coefficients(Rpol3)]; [ -3993, -131769, 38291 ] > [Factorisation(Integers()!n) : n in$1];
[
[ <3, 1>, <11, 3> ],
[ <3, 2>, <11, 4> ],
[ <11, 1>, <59, 2> ]
]
>
>
> a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]);
> ideal<OK | a,b>;
Ideal of OK
Two element generators:
[-33, 22, -20, 5]
[93, -61, 55, -13]
> flag, gen := IsPrincipal($1); flag; true > a := a/gen; b := b/gen; c := c*gen; > ideal<OK | b,c>; Ideal of OK Two element generators: [77724, -48384, 41973, -8147] [-66, -3, 13, -1] > flag, gen := IsPrincipal($1); flag;
true
> b := b/gen; c := c/gen; a := a*gen;
> ideal<OK | a,c>;
Ideal of OK
Two element generators:
[-33, 22, -20, 5]
[110, -67, 57, -10]
> flag, gen := IsPrincipal($1); flag; true > a := a/gen; b := b*gen; c := c/gen; > ideal<OK | a,b>; Ideal of OK Two element generators: [126225, -78574, 68161, -13228] [-17468, 10844, -9385, 1795] > Norm($1);
121
> a,b,c := Explode([MonomialCoefficient(Rpol3, Z[i]^2) : i in [1..3]]);
> ideal<OK | a,b,c>;
Ideal of OK
Basis:
[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]
> Factorisation(ideal<OK | a>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 2>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> flag, gen := IsPrincipal($1[2,1]); flag; true > a := a/gen^2; > IsIntegral(a); true > Factorisation(ideal<OK | b>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 2>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 4> ] > flag, rt := IsSquare(b); flag; false > Factorisation(ideal<OK | b>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 2>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 4> ] > flag, gen := IsPrincipal($1[1,1]*$1[2,1]^2); flag; true > b := b/gen^2; IsIntegral(b); true > IsUnit(b); true > b; 1/9*(-35203866485*lambda^3 + 544192313463*lambda^2 - 1881986216391*lambda + 3023310688146) > U, mU := UnitGroup(OK); > U; Abelian Group isomorphic to Z/2 + Z + Z Defined on 3 generators Relations: 2*U.1 = 0 > (OK!b) @@ mU; U.1 - U.2 + U.3 > Factorisation(ideal<OK | c>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1>, <Prime Ideal of OK Two element generators: [59, 0, 0, 0] [50, 1, 0, 0], 2> ] > flag, gen := IsPrincipal($1[2,1]); flag;
true
> c := c/gen^2;
> IsIntegral(c);
true
> ideal<OK | a,c>;
Ideal of OK
Two element generators:
[-435353142, 271003776, -235089137, 45623834]
[97396574, -60628572, 52593801, -10206898]
> flag, gen := IsPrincipal($1); flag; true > a := a*b; c := c*b; b := b/b; > a; 1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 + 4741581890375719065612*lambda - 7617098936772540178011) > c; 1/3*(-6614209165540654351*lambda^3 + 102244501724191609815*lambda^2 - 353593276101607037424*lambda + 568028778098368129917) > Factorisation(ideal<OK | a>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > Norm(a); 33 > Norm(c); -11 > b; 1 > L := ext<K | PolynomialRing(K)![-c,0,1]>; > NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to [email protected] Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 202.77 Segmentation fault > DefiningPolynomial(K); x^4 - 12*x^3 + 99*x - 297 > lambda; lambda > MinimalPolynomial(lambda); x^4 - 12*x^3 + 99*x - 297 > OL := Integers(L); > NormEquation(OL, -OK!a : Integral := false, All := false, Solutions := 1, Exact := true); Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to [email protected] Version date: Wed Aug 29 16:18:10 EST 2001 Initial seed: 2725307260 Time to this point: 202.98 Segmentation fault > SUnitGroup; Intrinsic 'SUnitGroup' Signatures: (<RngOrdFracIdl> I) -> GrpAb, Map (<SeqEnum[RngOrdIdl]> S) -> GrpAb, Map The group of s-units of the prime ideals given in the sequence S or the factorization of I (<SetEnum[PlcFunElt]> S) -> GrpAb, Map The group of S-units as an Abelian group and the map into the function field > Labs := AbsoluteField(L); > OLabs := Integers(Labs); > ClassGroup(OLabs : Bound := 300); Abelian Group of order 1 Mapping from: Abelian Group of order 1 to Set of ideals of OLabs > ideal<OK | a,c>; Ideal of OK Two element generators: 88694600599454463649] -19842627496621963053] > I := ideal<OLabs |$1>;
> SUnitGroup(I);
Abelian Group isomorphic to Z/2 + Z + Z + Z + Z
Defined on 5 generators
Relations:
2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z + Z + Z + Z Defined on 5 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs
> SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..5]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1 ] > a; 1/9*(88694600599454463649*lambda^3 - 1371068712366028393233*lambda^2 + 4741581890375719065612*lambda - 7617098936772540178011) > norms :=$2;
> Factorisation(ideal<OK | a>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> p31 := $1[1,1]; p111 :=$1[2,1];
> Factorisation(ideal<OK | norms[2]>);
[]
> Factorisation(ideal<OK | norms[3]>);
[]
> Factorisation(ideal<OK | norms[4]>);
[]
> I;
Principal Ideal of OLabs
Generator:
[1, 0, 0, 0, 0, 0, 0, 0]
> ideal<OK | a,c>;
Ideal of OK
Two element generators:
88694600599454463649]
-19842627496621963053]
> flag, gen := IsPrincipal($1); flag; true > I := ideal<OLabs | OLabs!Labs!L!K!gen>; > I; Principal Ideal of OLabs Generator: [1, 0, 0, 0, 0, 0, 0, 0] > Norm($3);
1
> Factorisation(ideal<OK | c>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>
]
> I := ideal<OLabs | OLabs!Labs!L!(a*c)>;
> I;
Principal Ideal of OLabs
Generator:
97187721532932707077425300749268443936597, 0, 0, 0, 0]
> SUnitGroup(I);
Abelian Group isomorphic to Z/2 + Z (7 copies)
Defined on 8 generators
Relations:
2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs
> SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..8]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1/3*(-675397597*lambda^3 + 10440506075*lambda^2 - 36106516113*lambda + 58003196403), 1, 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66), 1/3*(4*lambda^3 - 8*lambda^2 - 33*lambda + 147), 1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399) ] > norms :=$1;
> Factorisation(ideal<OK | norms[2]>);
[]
> Factorisation(ideal<OK | norms[3]>);
[]
> Factorisation(ideal<OK | norms[4]>);
[]
> Factorisation(ideal<OK | norms[5]>);
[]
> Factorisation(ideal<OK | norms[6]>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>
]
> Factorisation(ideal<OK | norms[7]>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 2>
]
> Factorisation(ideal<OK | norms[8]>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 2>
]
> Rlambda;
[     lambda  lambda + 3          -3]
[ lambda + 3 -lambda + 6     -lambda]
[         -3     -lambda           9]
> Tr1 := Matrix([[1, -(lambda+3)/lambda, 3/lambda], [0,1,0], [0,0,1]]); Tr1;
[1 1/99*(-lambda^3 + 12*lambda^2 - 198) 1/99*(lambda^3 - 12*lambda^2 + 99)]
[0 1 0]
[0 0 1]
> Tr1*Rlambda*Transpose(Tr1);
[1/11*(2*lambda^3 - 19*lambda^2 - 82*lambda + 132) 1/33*(-2*lambda^3 +
24*lambda^2 + 66*lambda - 297) 1/11*(lambda^3 - 12*lambda^2 + 11*lambda +
99)]
[1/33*(-2*lambda^3 + 24*lambda^2 + 66*lambda - 297) -lambda + 6 -lambda]
[1/11*(lambda^3 - 12*lambda^2 + 11*lambda + 99) -lambda 9]
> Transpose(Tr1)*Rlambda*Tr1;
[lambda 0 0]
[0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 1/33*(lambda^3 - 12*lambda^2
- 33*lambda + 198)]
[0 1/33*(lambda^3 - 12*lambda^2 - 33*lambda + 198) 1/33*(-lambda^3 + 12*lambda^2
+ 198)]
> Tr2 := Matrix([[1,0,0], [0,1,-$1[2,3]/$1[2,2]], [0,0,1]]); Tr2;
[1 0 0]
[0 1 1/3267*(26*lambda^3 - 297*lambda^2 - 297*lambda + 2277)]
[0 0 1]
> Transpose(Tr2)*$2*Tr2; [lambda 0 0] [0 1/33*(-lambda^3 + 12*lambda^2 - 66*lambda - 99) 0] [0 0 1/99*(lambda^3 - 99*lambda + 693)] > a,b,c := Explode([$1[i,i] : i in [1..3]]);
> IsIntegral(b);
false
> IsIntegral(c);
false
> Denominator(b);
33
> Denominator(c);
99
> Factorisation(ideal<OK | c>);
[
<Prime Ideal of OK
Basis:
[1 0 0 2]
[0 1 0 0]
[0 0 1 0]
[0 0 0 3], 2>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], -1>,
<Prime Ideal of OK
Two element generators:
[59, 0, 0, 0]
[50, 1, 0, 0], 2>
]
> flag, gen := IsPrincipal($1[1,1]*$1[3,1]); flag;
true
> c := c/gen;
> flag, gen := IsPrincipal($2[2,1]); flag; true > flag, gen := IsPrincipal($3[1,1]*$3[3,1]); flag; true > c := c/gen; > Factorisation(ideal<OK | c>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], -1> ] > flag, gen := IsPrincipal($1[1,1]); flag;
true
> c := c*gen^2;
> c;
1/9*(-25211*lambda^3 + 524037*lambda^2 - 1578888*lambda - 12770478)
> Factorisation(ideal<OK | b>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 2>,
<Prime Ideal of OK
Basis:
[1 0 0 2]
[0 1 0 0]
[0 0 1 0]
[0 0 0 3], 2>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], -1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 3>
]
> flag, gen := IsPrincipal($1[1,1]*$1[2,1]*$1[4,1]); flag; true > b := b/gen^2; > Factorisation(ideal<OK | b>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], -1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > flag, gen := IsPrincipal($1[1,1]); flag;
true
> b := b*gen^2;
> Factorisation(ideal<OK | a>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Basis:
[1 0 0 2]
[0 1 0 0]
[0 0 1 0]
[0 0 0 3], 2>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>
]
> flag, gen := IsPrincipal($1[2,1]); flag; true > a := a/gen^2; > Factorisation(ideal<OK | a>); [ <Prime Ideal of OK Basis: [3 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1> ] > Factorisation(ideal<OK | b>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1>, <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > Factorisation(ideal<OK | c>); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [10, 1, 0, 0], 1> ] > flag, gen := IsPrincipal($1[1,1]); flag;
true
> c := c/gen; b := b/gen; a := a*gen;
> c;
1/9*(-12910*lambda^3 + 73386*lambda^2 + 747855*lambda + 1174653)
> IsUnit(c);
true
> a := a/c; b := b/c; c := c/c;
> a;
1/9*(11768733070573612150898*lambda^3 - 6565975199446345850085*lambda^2 -
75128433793103508474861*lambda + 305478792168156995505975)
> b;
1/3*(-lambda^3 + 9*lambda^2 + 24*lambda - 66)
> L := ext<K | PolynomialRing(K)![-b,0,1]>;
> NormEquation(L, -a : Integral := false, All := false, Solutions := 1, Exact := true);

Magma: Internal error
Please mail this entire run [**WITH THE FOLLOWING LINES**]
to [email protected]
Version date: Wed Aug 29 16:18:10 EST 2001
Initial seed: 2725307260
Time to this point: 289.15
Segmentation fault
> Factorisation(ideal<OK | a>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> Labs := AbsoluteField(L);
> OLabs := Integers(Labs);
> OL := Integers(L);
> ClassGroup(OLabs : Bound := 300);
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to Set of ideals of OLabs
> I := ideal<OLabs | OLabs!Labs!L!(a*b)>;
> I;
Principal Ideal of OLabs
Generator:
81061059655244371456034, -435877053076387089543350, 0, 0, 0, 0]
> SUnitGroup(I);
Abelian Group isomorphic to Z/2 + Z (7 copies)
Defined on 8 generators
Relations:
2*$.1 = 0 Mapping from: Abelian Group isomorphic to Z/2 + Z (7 copies) Defined on 8 generators Relations: 2*$.1 = 0 to Field of Fractions of OLabs
> SU, mSU := $1; > [Norm(L!mSU(SU.i)) : i in [1..8]]; [ 1, 1/3*(377420*lambda^3 - 210569*lambda^2 - 2409348*lambda + 9796620), 1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666), 1/3*(-11795*lambda^3 + 673408*lambda^2 - 4157784*lambda - 22920666), 1, 124*lambda^3 - 1075*lambda^2 - 4228*lambda + 3364, 1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66), 1/9*(-44*lambda^3 + 513*lambda^2 + 450*lambda - 6399) ] > norms :=$1;
> Factorisation(ideal<OK | norms[2]>);
[]
> Factorisation(ideal<OK | norms[3]>);
[]
> Factorisation(ideal<OK | norms[4]>);
[]
> Factorisation(ideal<OK | norms[5]>);
[]
> Factorisation(ideal<OK | norms[6]>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 2>
]
> Factorisation(ideal<OK | norms[7]>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>
]
> Factorisation(ideal<OK | norms[8]>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 2>
]
> ClassGroup(OK : Bound := 300);
Abelian Group of order 1
Mapping from: Abelian Group of order 1 to Set of ideals of OK
> ideal<OK | a,b>;
Ideal of OK
Two element generators:
11768733070573612150898]
[-22, 8, 9, -3]
> Factorisation($1); [ <Prime Ideal of OK Two element generators: [11, 0, 0, 0] [0, 1, 0, 0], 1> ] > flag, gen := IsPrincipal($2); flag;
true
> a := a/gen; b := b/gen; c := c*gen;
> ideal<OK | a,b>;
Ideal of OK
Two element generators:
[-1, 0, 0, 0]
317757210900264194558]
> Norm($1); 1 >$2 eq ideal<OK | 1>;
true
> ideal<OK | a,c>;
Ideal of OK
Two element generators:
317757210900264194558]
[22, -8, -9, 3]
> $1 eq ideal<OK | 1>; true > ideal<OK | b,c>; Ideal of OK Two element generators: [-1, 0, 0, 0] [22, -8, -9, 3] >$1 eq ideal<OK | 1>;
true
> c;
1/3*(lambda^3 - 9*lambda^2 - 24*lambda + 66)
> b;
-1
> a;
1/9*(317757210900264194558*lambda^3 - 177282073464141075450*lambda^2 -
2028476957468286393567*lambda + 8247964555766062942857)
> Factorisation(ideal<OK | a>);
[
<Prime Ideal of OK
Basis:
[3 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1], 1>,
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[10, 1, 0, 0], 1>
]
> Factorisation(ideal<OK | c>);
[
<Prime Ideal of OK
Two element generators:
[11, 0, 0, 0]
[0, 1, 0, 0], 1>
]
> p3 := $2[1,1]; p11a :=$2[2,1]; p11b := \$1[1,1];
> F3, mF3 := ResidueClassField(p3);
> IsSquare(mF3(c));
true 1
> F11a, mF11a := ResidueClassField(p11a);
> IsSquare(mF11a(c));
true 9
> F11b, mF11b := ResidueClassField(p11b);
> IsSquare(mF11b(a));
true 1
> Conjugates(a);

Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134)
Time: Wed Dec  3 10:41:40 2003

Input: > Q:=Rationals(); R<x>:=PolynomialRing(Q)
P:=x^2

Output: Magma V2.10-6     Wed Dec  3 2003 10:41:37 on modular  [Seed = 1872647193]
-------------------------------------

>> P:=x^2;
^

Total time: 3.079 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Wed Dec  3 10:41:56 2003

Input:  P4<[z]> := PolynomialRing(Rationals(), 4);
D1 := z[1]^2+2*z[1]*z[2]+2*z[2]*z[3]-2*z[2]*z[4]+2*z[3]^2+3*z[4]^2;
D2 := z[1]^2+2*z[1]*z[3]-2*z[1]*z[4]+z[2]^2+2*z[2]*z[3]-z[3]^2-2*z[3]*z[4];
Q2mat := func<Q | Matrix([[(i eq j select 1 else 1/2)
*MonomialCoefficient(Q, z[i]*z[j]) : j in [1..4]] : i in [1..4]])>;
M1 := Q2mat(D1);> M2 := Q2mat(D2);
M1;

Output: Magma V2.10-6     Wed Dec  3 2003 10:41:53 on modular  [Seed = 2005290097]
-------------------------------------

>>  M1 := Q2mat(D1);> M2 := Q2mat(D2);
^
[ 1  1  0  0]
[ 1  0  1 -1]
[ 0  1  2  0]
[ 0 -1  0  3]

Total time: 3.039 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134)
Time: Wed Dec  3 10:42:03 2003

Input: > Q:=Rationals(); R<x>:=PolynomialRing(Q);
P:=x^2

Output: Magma V2.10-6     Wed Dec  3 2003 10:42:00 on modular  [Seed = 2140030064]
-------------------------------------

Total time: 2.949 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134)
Time: Wed Dec  3 10:42:16 2003

Input: > Q:=Rationals(); R<x>:=PolynomialRing(Q);
P:=x^2; P

Output: Magma V2.10-6     Wed Dec  3 2003 10:42:13 on modular  [Seed = 133577749]
-------------------------------------

x^2

Total time: 3.059 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host facultypc-134.faculty.iu-bremen.de. (212.201.48.134)
Time: Wed Dec  3 10:42:31 2003

Input: > Q:=Rationals(); R<x>:=PolynomialRing(Q);
> P:=x^2; P

Output: Magma V2.10-6     Wed Dec  3 2003 10:42:27 on modular  [Seed = 251606314]
-------------------------------------

x^2

Total time: 3.099 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Wed Dec  3 10:56:38 2003

Input: > SetVerbose("Factorization", true);
> SetVerbose("MPQS", true);
> n := 279227912220351686582028455516412641158896790659830288566001946957408;
> time Factorization(n);

Output: Magma V2.10-6     Wed Dec  3 2003 10:56:24 on modular  [Seed = 719000261]
-------------------------------------

Integer main factorization (primality of factors will be proved)
Seed: 1
Number: 2792279122203516865820284555164126411588967906598302885660019469574\
08

Trial Division
Number: 2792279122203516865820284555164126411588967906598302885660019469574\
08
Minimum: 2
Maximum: 10000
Factors found:
<2, 5>
<3, 2>
<61, 1>
Time: 0.000

Pollard Rho
Trials: 8191
Number: 15894120686495428425661911174659189501303323694207097482126704631
(65 digits)
Factor: 1234577 (7 digits)
Cofactor: 12874142873628318384079657384399020475274789417109744861703 (59
digits)
Time: 0.039

Pollard Rho
Trials: 8191
Number: 12874142873628318384079657384399020475274789417109744861703
(59 digits)
No factor found
Time: 0.069

1 composite number remaining

ECM
x: 12874142873628318384079657384399020475274789417109744861703
(59 digits)
Initial smoothness: 500, steps: 14, step size: 285
Step 1/14; smoothness: 500, digits: 59, elapsed time: 0.000
Step 2/14; smoothness: 785, digits: 59, elapsed time: 0.330
Factor: 51030885799 (11 digits)
Cofactor: 252281391397689588517339571105707909275219700897 (48 digits)
Time: 0.780

ECM
x: 252281391397689588517339571105707909275219700897
(48 digits)
Initial smoothness: 785, steps: 10, step size: 100
Step 1/10; smoothness: 785, digits: 48, elapsed time: 0.000
Step 2/10; smoothness: 885, digits: 48, elapsed time: 0.359
Step 3/10; smoothness: 985, digits: 48, elapsed time: 0.709
Step 4/10; smoothness: 1085, digits: 48, elapsed time: 1.089
Step 5/10; smoothness: 1185, digits: 48, elapsed time: 1.489
Step 6/10; smoothness: 1285, digits: 48, elapsed time: 1.909
Step 7/10; smoothness: 1385, digits: 48, elapsed time: 2.359
Step 8/10; smoothness: 1485, digits: 48, elapsed time: 2.839
Step 9/10; smoothness: 1585, digits: 48, elapsed time: 3.339
Step 10/10; smoothness: 1685, digits: 48, elapsed time: 3.869
No factor found
Time: 4.409

MPQS
MPQS: 252281391397689588517339571105707909275219700897 (48d)
1042 factor base elements created in 0.010 seconds
master completed initialization for /tmp/mqs30829:
multiplier=1
sievelength=62464, sievesize=124928
one large prime will be used
initialized global data in -0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
cycles: 8 total
100 fulls, 8 cycles, rate 0.018, need 966 more fulls+cycles
another 894 fulls and 3872 partials and double partials should suffice
533 relations: 100 fulls, 433 partials, 0 double partials
initialized global data in -0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
cycles: 35 new, 43 total
200 fulls, 43 cycles, rate 0.094, need 831 more fulls+cycles
another 602 fulls and 2433 partials and double partials should suffice
1007 relations: 200 fulls, 807 partials, 0 double partials
initialized global data in -0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
cycles: 47 new, 90 total
302 fulls, 90 cycles, rate 0.118, need 682 more fulls+cycles
another 463 fulls and 1852 partials and double partials should suffice
1508 relations: 302 fulls, 1206 partials, 0 double partials
initialized global data in 0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
cycles: 57 new, 147 total
402 fulls, 147 cycles, rate 0.148, need 525 more fulls+cycles
another 330 fulls and 1310 partials and double partials should suffice
1993 relations: 402 fulls, 1591 partials, 0 double partials
initialized global data in -0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
cycles: 104 new, 251 total
503 fulls, 251 cycles, rate 0.223, need 320 more fulls+cycles
another 167 fulls and 684 partials and double partials should suffice
2560 relations: 503 fulls, 2057 partials, 0 double partials
initialized global data in -0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
cycles: 78 new, 329 total
603 fulls, 329 cycles, rate 0.222, need 142 more fulls+cycles
another 75 fulls and 300 partials and double partials should suffice
3012 relations: 603 fulls, 2409 partials, 0 double partials
initialized global data in -0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
cycles: 76 new, 405 total
663 fulls, 405 cycles, rate 0.256, need 6 more fulls+cycles
another 2 fulls and 11 partials and double partials should suffice
3369 relations: 663 fulls, 2706 partials, 0 double partials
initialized global data in -0.000 seconds

interrupt sieving: collect, count, try to factor if appropriate
no need to count cycles
sent termination signal to slaves, start factoring attempt
used partials: 405 combined relations formed
collecting from /tmp/mqs30829/f777mas: accepted 405
Lanczos call with seed 12
first scan: 1074 rows, 1028 columns>16, weight 9326
second scan complete, matrix read into memory
Removed 59 singletons
Removed 3 singletons
all 62 singletons removed
Got 947 by 1012 matrix with 8779 nonzeros in 0.040 seconds
average of 9 nonzero entries per column
Lanczos iteration 0, sum = 32, 915 to go
Lanczos iterations done at i=31, sum=946, after 0.030 seconds
Lanczos complete in 0.030 seconds, 17 dependencies
factoring attempt
dependency 1 produced 21905534578936053246671913391051 (32d)
dependency 2 produced 6756504442031587 (16d)
dependency 3 produced 11516787708996547 (17d)
dependency 4 failed to produce a factor
dependency 5 produced 11516787708996547 (17d)
dependency 6 failed to produce a factor
dependency 7 produced 6756504442031587 (16d)
dependency 8 produced 3242140187559673 (16d)
dependency 9 produced 37339040262931001600391513449131 (32d)
dependency 10 produced 3242140187559673 (16d)
dependency 11 produced 37339040262931001600391513449131 (32d)
dependency 12 produced 6756504442031587 (16d)
dependency 13 failed to produce a factor
dependency 14 produced 77813227313769953941525847930089 (32d)
dependency 15 failed to produce a factor
dependency 16 produced 77813227313769953941525847930089 (32d)
dependency 17 produced 37339040262931001600391513449131 (32d)
done at 1065: 3803(1074,2729,0)(3398(669,2729,0)), 4.69(2.98,1.71), 0.001s/r

MPQS time: 5.439
Factor 1: 6756504442031587 (16 digits)
Factor 2: 3242140187559673 (16 digits)
Factor 3: 11516787708996547 (17 digits)
Total MPQS Time: 5.559

Total time: 10.859

[ <2, 5>, <3, 2>, <61, 1>, <1234577, 1>, <51030885799, 1>, <3242140187559673,
1>, <6756504442031587, 1>, <11516787708996547, 1> ]
Time: 10.860

Total time: 13.839 seconds, Total memory usage: 2.99MB

************** MAGMA *****************
Time: Wed Dec  3 11:02:48 2003

Input: > SetVerbose("Factorization", true);
> SetVerbose("MPQS", true);
> n := 279227912220351686582028455516412641158896790659830288566001946957408;
> time Factorization(n);
> b := 10^20;
> for n in [b .. b + 100] do
>     s, x, y := NormEquation(1, n);
>     if s then
>         printf "%o = %o^2 + %o^2n", n, x, y;
>     end if;
> end for;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Time: Wed Dec  3 11:03:46 2003

Input: > d := func< m | DivisorSigma(1, m) - m >;
> for m := 2 to 10000 do
>     n := d(m);
>     if d(n) eq m then
>         print m, n;
>     end if;
> end for;

Output: Magma V2.10-6     Wed Dec  3 2003 11:03:42 on modular  [Seed = 3643338688]
-------------------------------------

6 6
28 28
220 284
284 220
496 496
1184 1210
1210 1184
2620 2924
2924 2620
5020 5564
5564 5020
6232 6368
6368 6232
8128 8128

Total time: 3.599 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Time: Wed Dec  3 11:04:33 2003

Input: > d := func< m | DivisorSigma(1, m) - m >;
> for m := 2 to 10000 do
>     n := d(m);
>     if d(n) eq m then
>         print m, n;
>     end if;
> end for;
> k<w> := GF(2, 100);
> P<x> := PolynomialRing(k);
> time Factorization(x^100 + x + 1);

Output: Magma V2.10-6     Wed Dec  3 2003 11:04:29 on modular  [Seed = 3775977259]
-------------------------------------

6 6
28 28
220 284
284 220
496 496
1184 1210
1210 1184
2620 2924
2924 2620
5020 5564
5564 5020
6232 6368
6368 6232
8128 8128
[
<x^7 + (w^95 + w^90 + w^70 + w^60 + w^55 + w^50 + w^40 + w^35 + w^30 + w^25
+ w^15 + w^5)*x^5 + (w^95 + w^90 + w^70 + w^60 + w^55 + w^50 + w^40 +
w^35 + w^30 + w^25 + w^15 + w^5 + 1)*x^2 + w^95 + w^90 + w^70 + w^60 +
w^55 + w^50 + w^40 + w^35 + w^30 + w^25 + w^15 + w^5 + 1, 1>,
<x^7 + (w^95 + w^90 + w^70 + w^60 + w^55 + w^50 + w^40 + w^35 + w^30 + w^25
+ w^15 + w^5 + 1)*x^5 + (w^95 + w^90 + w^70 + w^60 + w^55 + w^50 + w^40
+ w^35 + w^30 + w^25 + w^15 + w^5)*x^2 + w^95 + w^90 + w^70 + w^60 +
w^55 + w^50 + w^40 + w^35 + w^30 + w^25 + w^15 + w^5, 1>,
<x^17 + x^15 + x^13 + x^11 + x^6 + x^5 + x^4 + x^2 + 1, 1>,
<x^69 + x^65 + x^64 + x^63 + x^62 + x^61 + x^59 + x^58 + x^53 + x^50 + x^48
+ x^45 + x^44 + x^43 + x^41 + x^39 + x^34 + x^33 + x^28 + x^25 + x^24 +
x^23 + x^20 + x^19 + x^18 + x^15 + x^13 + x^10 + x^9 + x^8 + x^6 + x^5 +
x^4 + x^3 + x^2 + x + 1, 1>
]
Time: 0.120

Total time: 3.669 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host dsl3-63-249-104-22.cruzio.com. (63.249.104.22)
Time: Wed Dec  3 19:46:32 2003

Input: 3+2

Output: Magma V2.10-6     Wed Dec  3 2003 19:46:29 on modular  [Seed = 1036812697]
-------------------------------------

5

Total time: 3.019 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Wed Dec  3 20:30:15 2003

Input: printf "%o",1;

Output: An error occured in the MAGMA system call.

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Wed Dec  3 20:30:30 2003

Input: printf "%o",1;

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Wed Dec  3 20:36:30 2003

Input: 1+1

Output: Magma V2.10-6     Wed Dec  3 2003 20:36:27 on modular  [Seed = 1771624882]
-------------------------------------

2

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Wed Dec  3 20:36:39 2003

Input: printf "%o",2;

Output: Magma V2.10-6     Wed Dec  3 2003 20:36:36 on modular  [Seed = 1904263573]
-------------------------------------

2
Total time: 2.929 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host h00096bd05fc4.ne.client2.attbi.com. (65.96.162.217)
Time: Wed Dec  3 20:36:46 2003

Input: %s

Output: WARNING: MAGMA command contains unsafe command '%', so it will not be executed.

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:06:07 2003

Input:
P<x,y>:=PolynomialRing(IntegerRing(),2);
f0:=2*(x^2+y^2)+x-y-16;
f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192;
f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905;
I:=ideal<P|f0,f1,f2>;
B:=GroebnerBasis(I:Al:="Direct");
B;
Factorization(2749936217096833768575);
Bn:=GroebnerBasis(ChangeRing(I,GF(11)));
Bn;

Output: Magma V2.10-6     Thu Dec  4 2003 02:06:04 on modular  [Seed = 1904251543]
-------------------------------------

[
x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167,
x*y + 317*x + 18988427413535611858*y + 7168823795450084621,
495*x + 18988427413535611680*y + 17880669574151734350,
y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949,
495*y^2 + 1107757839383877825*y + 7099394057680662045,
18988427413535612175
]
[ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <35159, 1>, <2430902559671, 1> ]
[
x^2 + 6*x + y^2 + 5*y + 3,
x*y + 9*x + 2*y + 7,
y^3 + 3*y^2 + 7*y + 10
]

Total time: 2.979 seconds, Total memory usage: 1.93MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:09:02 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
f0:=2*(x^2+y^2)+x-y-16;
f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192;
f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905;
I:=ideal<P|f0,f1,f2>;
B:=GroebnerBasis(I:Al:="Direct");
B;
Factorization(18988427413535612175);
Bn:=GroebnerBasis(ChangeRing(I,GF(11)));
Bn;

Output: Magma V2.10-6     Thu Dec  4 2003 02:08:59 on modular  [Seed = 1636860880]
-------------------------------------

[
x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167,
x*y + 317*x + 18988427413535611858*y + 7168823795450084621,
495*x + 18988427413535611680*y + 17880669574151734350,
y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949,
495*y^2 + 1107757839383877825*y + 7099394057680662045,
18988427413535612175
]
[ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1>
]
[
x^2 + 6*x + y^2 + 5*y + 3,
x*y + 9*x + 2*y + 7,
y^3 + 3*y^2 + 7*y + 10
]

Total time: 2.959 seconds, Total memory usage: 1.93MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:11:10 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
f0:=2*(x^2+y^2)+x-y-16;
f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192;
f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905;
I:=ideal<P|f0,f1,f2>;
B:=GroebnerBasis(I:Al:="Direct");
B;
Factorization(18988427413535612175);
Bn:=GroebnerBasis(ChangeRing(I,GF(11)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(13)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(19)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(47)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(1693)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(390357049)));
Bn;

Output: Magma V2.10-6     Thu Dec  4 2003 02:11:07 on modular  [Seed = 1470543462]
-------------------------------------

[
x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167,
x*y + 317*x + 18988427413535611858*y + 7168823795450084621,
495*x + 18988427413535611680*y + 17880669574151734350,
y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949,
495*y^2 + 1107757839383877825*y + 7099394057680662045,
18988427413535612175
]
[ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1>
]
[
x^2 + 6*x + y^2 + 5*y + 3,
x*y + 9*x + 2*y + 7,
y^3 + 3*y^2 + 7*y + 10
]
[
x + 12*y,
y^2 + 9
]
[
x + 18*y + 2,
y^2 + 17*y + 7
]
[
x + 46*y + 12,
y^2 + 35*y + 18
]
[
x + 1692*y + 1205,
y^2 + 488*y + 680
]
[
x + 390357048*y + 86547272,
y^2 + 303809777*y + 387394951
]

Total time: 2.939 seconds, Total memory usage: 2.03MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:13:23 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
f0:=2*(x^2+y^2)+x-y-16;
f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192;
f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905;
I:=ideal<P|f0,f1,f2>;
B:=GroebnerBasis(I:Al:="Direct");
B;
Factorization(18988427413535612175);
Bn:=GroebnerBasis(ChangeRing(I,GF(11)));
Bn;
Factorization( y^3 + 3*y^2 + 7*y + 10)
Bn:=GroebnerBasis(ChangeRing(I,GF(13)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(19)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(47)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(1693)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(390357049)));
Bn;

Output: Magma V2.10-6     Thu Dec  4 2003 02:13:20 on modular  [Seed = 1085383146]
-------------------------------------

[
x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167,
x*y + 317*x + 18988427413535611858*y + 7168823795450084621,
495*x + 18988427413535611680*y + 17880669574151734350,
y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949,
495*y^2 + 1107757839383877825*y + 7099394057680662045,
18988427413535612175
]
[ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1>
]
[
x^2 + 6*x + y^2 + 5*y + 3,
x*y + 9*x + 2*y + 7,
y^3 + 3*y^2 + 7*y + 10
]

>> Bn:=GroebnerBasis(ChangeRing(I,GF(13)));
^
[
x^2 + 6*x + y^2 + 5*y + 3,
x*y + 9*x + 2*y + 7,
y^3 + 3*y^2 + 7*y + 10
]
[
x + 18*y + 2,
y^2 + 17*y + 7
]
[
x + 46*y + 12,
y^2 + 35*y + 18
]
[
x + 1692*y + 1205,
y^2 + 488*y + 680
]
[
x + 390357048*y + 86547272,
y^2 + 303809777*y + 387394951
]

Total time: 2.909 seconds, Total memory usage: 1.93MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:13:49 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
f0:=2*(x^2+y^2)+x-y-16;
f1:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192;
f2:=640*(x^6+y^6)+1472*(x^5-y^5)+1080*(x^4+y^4)-280*(x^3-y^3)-300*(x^2+y^2) +73*(x-y)-81905;
I:=ideal<P|f0,f1,f2>;
B:=GroebnerBasis(I:Al:="Direct");
B;
Factorization(18988427413535612175);
Bn:=GroebnerBasis(ChangeRing(I,GF(11)));
Bn;
Factorization( y^3 + 3*y^2 + 7*y + 10);
Bn:=GroebnerBasis(ChangeRing(I,GF(13)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(19)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(47)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(1693)));
Bn;
Bn:=GroebnerBasis(ChangeRing(I,GF(390357049)));
Bn;

Output: Magma V2.10-6     Thu Dec  4 2003 02:13:44 on modular  [Seed = 3108526123]
-------------------------------------

[
x^2 + 248*x + y^2 + 18988427413535611927*y + 8940334787075867167,
x*y + 317*x + 18988427413535611858*y + 7168823795450084621,
495*x + 18988427413535611680*y + 17880669574151734350,
y^3 + 69*y^2 + 1771510991625782546*y + 1184572834778843949,
495*y^2 + 1107757839383877825*y + 7099394057680662045,
18988427413535612175
]
[ <3, 2>, <5, 2>, <11, 1>, <13, 1>, <19, 1>, <47, 1>, <1693, 1>, <390357049, 1>
]
[
x^2 + 6*x + y^2 + 5*y + 3,
x*y + 9*x + 2*y + 7,
y^3 + 3*y^2 + 7*y + 10
]
[
<y + 2, 1>,
<y^2 + y + 5, 1>
]
[
x + 12*y,
y^2 + 9
]
[
x + 18*y + 2,
y^2 + 17*y + 7
]
[
x + 46*y + 12,
y^2 + 35*y + 18
]
[
x + 1692*y + 1205,
y^2 + 488*y + 680
]
[
x + 390357048*y + 86547272,
y^2 + 303809777*y + 387394951
]

Total time: 2.989 seconds, Total memory usage: 2.03MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:20:53 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(9*x^2-4)*(9*x^2-1)*3*x-6*(4*x^2-4)*(4*x^2-1)*2*x+15*(x^2-4)*(x^2-1)*x;

Output: Magma V2.10-6     Thu Dec  4 2003 02:20:50 on modular  [Seed = 2523351550]
-------------------------------------

Total time: 2.939 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:21:04 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(9*x^2-4)*(9*x^2-1)*3*x-6*(4*x^2-4)*(4*x^2-1)*2*x+15*(x^2-4)*(x^2-1)*x;
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:21:01 on modular  [Seed = 2390708713]
-------------------------------------

66*x^5 + 30*x^3 + 24*x

Total time: 2.979 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:22:02 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(9*x^2-4)*(9*x^2-1)*3*x-6*(4*x^2-4)*(4*x^2-1)*2*x+15*(x^2-4)*(x^2-1)*x;
c/120;

Output: Magma V2.10-6     Thu Dec  4 2003 02:21:59 on modular  [Seed = 4195034455]
-------------------------------------

>> c/120;;
^
Runtime error in '/': Coefficient ring of argument 1 is not a field

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:25:10 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(16*x^2-9)*(16*x^2-4)*(16*x^2-1)*4*x-8*(9*x^2-9)*(9*x^2-4)*(9*x^2-1)*3*x+28*(4*x^2-9)*(4*x^2-4)*(4*x^2-1)*2*x-56*(x^2-9)*(x^2-4)*(x^2-1)*x;
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:25:07 on modular  [Seed = 4093979293]
-------------------------------------

2416*x^7 + 1120*x^5 + 784*x^3 + 720*x

Total time: 2.989 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:25:29 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(16*x^2-9)*(16*x^2-4)*(16*x^2-1)*4*x-8*(9*x^2-9)*(9*x^2-4)*(9*x^2-1)*3*x+28*(4*x^2-9)*(4*x^2-4)*(4*x^2-1)*2*x-56*(x^2-9)*(x^2-4)*(x^2-1)*x;
c/16;

Output: Magma V2.10-6     Thu Dec  4 2003 02:25:26 on modular  [Seed = 3961336496]
-------------------------------------

>> c/16;;
^
Runtime error in '/': Coefficient ring of argument 1 is not a field

Total time: 2.989 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:25:54 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(16*x^2-9)*(16*x^2-4)*(16*x^2-1)*4*x-8*(9*x^2-9)*(9*x^2-4)*(9*x^2-1)*3*x+28*(4*x^2-9)*(4*x^2-4)*(4*x^2-1)*2*x-56*(x^2-9)*(x^2-4)*(x^2-1)*x;
Factorization(c);

Output: Magma V2.10-6     Thu Dec  4 2003 02:25:51 on modular  [Seed = 3826596513]
-------------------------------------

[
<2, 4>,
<x, 1>,
<151*x^6 + 70*x^4 + 49*x^2 + 45, 1>
]

Total time: 2.929 seconds, Total memory usage: 1.89MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:27:39 2003

Input: P<x,y>:=PolynomialRing(GF(11),2);
c:=y^3 + 3*y^2 + 7*y + 10;
Factorization(c);

Output: Magma V2.10-6     Thu Dec  4 2003 02:27:36 on modular  [Seed = 3491827202]
-------------------------------------

[
<y + 2, 1>,
<y + 3, 1>,
<y + 9, 1>
]

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:28:43 2003

Input: P<x,y>:=PolynomialRing(GF(19),2);
c:=y^2 + 17*y + 7;
Factorization(c);

Output: Magma V2.10-6     Thu Dec  4 2003 02:28:39 on modular  [Seed = 3460240339]
-------------------------------------

[
<y^2 + 17*y + 7, 1>
]

Total time: 3.019 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:29:40 2003

Input: P<x,y>:=PolynomialRing(GF(47),2);
c:=y^2 + 35*y + 18;
Factorization(c);

Output: Magma V2.10-6     Thu Dec  4 2003 02:29:37 on modular  [Seed = 1003152995]
-------------------------------------

[
<y + 15, 1>,
<y + 20, 1>
]

Total time: 2.959 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:30:29 2003

Input: P<x,y>:=PolynomialRing(GF(1693),2);
c:=y^2 + 488*y + 680;
Factorization(c);

Output: Magma V2.10-6     Thu Dec  4 2003 02:30:26 on modular  [Seed = 685372803]
-------------------------------------

[
<y + 636, 1>,
<y + 1545, 1>
]

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:31:23 2003

Input: P<x,y>:=PolynomialRing(GF(390357049),2);
c:=y^2 +303809777*y + 387394951 ;
Factorization(c);

Output: Magma V2.10-6     Thu Dec  4 2003 02:31:20 on modular  [Seed = 601030354]
-------------------------------------

[
<y + 311735453, 1>,
<y + 382431373, 1>
]

Total time: 2.919 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:34:26 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(8*x+7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1);
Factorization(c);

Output: Magma V2.10-6     Thu Dec  4 2003 02:34:23 on modular  [Seed = 268358473]
-------------------------------------

[
<8*x - 5, 1>,
<8*x - 3, 1>,
<8*x - 1, 1>,
<8*x + 1, 1>,
<8*x + 3, 1>,
<8*x + 5, 1>,
<8*x + 7, 1>
]

Total time: 2.929 seconds, Total memory usage: 1.89MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:34:44 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(8*x+7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:34:41 on modular  [Seed = 133618607]
-------------------------------------

2097152*x^7 + 1835008*x^6 - 1146880*x^5 - 1003520*x^4 + 132608*x^3 + 116032*x^2
- 1800*x - 1575

Total time: 2.979 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:38:09 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(8*x+7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1)-8*(6*x+7)*(36*x^2-25)*(36*x^2-9)*(36*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:38:06 on modular  [Seed = 1838986762]
-------------------------------------

-142336*x^7 - 777728*x^6 + 1030400*x^5 + 1536640*x^4 - 314944*x^3 - 406112*x^2 +
9000*x + 11025

Total time: 2.919 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:40:08 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(8*x-7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1)-8*(6*x-7)*(36*x^2-25)*(36*x^2-9)*(36*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:40:05 on modular  [Seed = 1571587761]
-------------------------------------

-142336*x^7 + 777728*x^6 + 1030400*x^5 - 1536640*x^4 - 314944*x^3 + 406112*x^2 +
9000*x - 11025

Total time: 2.959 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:40:56 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
c:=(8*x-7)*(64*x^2-25)*(64*x^2-9)*(64*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:40:53 on modular  [Seed = 1420136040]
-------------------------------------

2097152*x^7 - 1835008*x^6 - 1146880*x^5 + 1003520*x^4 + 132608*x^3 - 116032*x^2
- 1800*x + 1575

Total time: 2.929 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:44:48 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=x^6+y^6+(11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y))/40+(144*(x^5-y^5)-40*(x^3-y^3)+x-y)*18/1280+(144*(x^4+y^4)-20*(x^2+y^2)+1)*15/1280-128;
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:44:45 on modular  [Seed = 1321178266]
-------------------------------------

x^6 + 23/10*x^5 + 27/16*x^4 - 7/16*x^3 - 15/64*x^2 + 73/640*x + y^6 - 23/10*y^5
+ 27/16*y^4 + 7/16*y^3 - 15/64*y^2 - 73/640*y - 32765/256

Total time: 2.929 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:46:11 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=x^6+y^6+(11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y))/40+(144*(x^5-y^5)-40*(x^3-y^3)+x-y)*18/1280+(144*(x^4+y^4)-40*(x^2+y^2)+2)*15/1280-128;
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:46:09 on modular  [Seed = 3125502914]
-------------------------------------

x^6 + 23/10*x^5 + 27/16*x^4 - 7/16*x^3 - 15/32*x^2 + 73/640*x + y^6 - 23/10*y^5
+ 27/16*y^4 + 7/16*y^3 - 15/32*y^2 - 73/640*y - 16381/128

Total time: 2.899 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:46:34 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=x^6+y^6+(11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y))/40+(144*(x^5-y^5)-40*(x^3-y^3)+x-y)*18/1280+(144*(x^4+y^4)-40*(x^2+y^2)+2)*15/1280-128;
640*c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:46:31 on modular  [Seed = 2990762972]
-------------------------------------

640*x^6 + 1472*x^5 + 1080*x^4 - 280*x^3 - 300*x^2 + 73*x + 640*y^6 - 1472*y^5 +
1080*y^4 + 280*y^3 - 300*y^2 - 73*y - 81905

Total time: 2.919 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:58:21 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=(6*x+5)*(36*x^2-9)*(36*x^2-1);
640*c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:58:18 on modular  [Seed = 2373737390]
-------------------------------------

4976640*x^5 + 4147200*x^4 - 1382400*x^3 - 1152000*x^2 + 34560*x + 28800

Total time: 2.869 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 02:58:44 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=(6*x+5)*(36*x^2-9)*(36*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 02:58:41 on modular  [Seed = 2222281356]
-------------------------------------

7776*x^5 + 6480*x^4 - 2160*x^3 - 1800*x^2 + 54*x + 45

Total time: 2.929 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:04:57 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>A:=AutomorphismGroup(L);
>#A;

Output: Magma V2.10-6     Thu Dec  4 2003 03:04:54 on modular  [Seed = 3626569031]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]
288

Total time: 2.909 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:05:24 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>A:=AutomorphismGroup(L);
>#A;

Output: Magma V2.10-6     Thu Dec  4 2003 03:05:21 on modular  [Seed = 3609592367]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]
288

Total time: 2.989 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:06:55 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>G:=AutomorphismGroup(L);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:06:52 on modular  [Seed = 3460242155]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]
288

Total time: 2.909 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:09:13 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>F:=latticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]);
>G:=AutomorphismGroup(L,[F]);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:09:10 on modular  [Seed = 952757414]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>  F:=latticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]);
^
User error: Identifier 'latticeWithGram' has not been declared or assigned

>>  G:=AutomorphismGroup(L,[F]);
^
User error: Identifier 'F' has not been declared or assigned

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.889 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:09:32 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>F:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]);
>G:=AutomorphismGroup(L,[F]);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:09:29 on modular  [Seed = 834725296]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>  G:=AutomorphismGroup(L,[F]);
^
Runtime error in 'AutomorphismGroup': Universe of argument 2 is not a matrix
structure

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:09:59 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>F:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]);
>G:=AutomorphismGroup(L,F);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:09:56 on modular  [Seed = 702086597]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>  G:=AutomorphismGroup(L,F);
^
Runtime error in 'AutomorphismGroup': Bad argument types
Argument types given: Lat, Lat

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.909 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 03:10:54 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=(6*x+5)*(36*x^2-9)*(36*x^2-1)-6*(4*x+5)*(16*x^2-9)*(16*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 03:10:51 on modular  [Seed = 417975083]
-------------------------------------

1632*x^5 - 1200*x^4 + 1680*x^3 + 3000*x^2 - 162*x - 225

Total time: 2.999 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:11:32 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>F:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]);
>F;
>G:=AutomorphismGroup(L,F);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:11:29 on modular  [Seed = 283231001]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]
Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 3 2]
[2 2 2 2 2 3]

>>  G:=AutomorphismGroup(L,F);
^
Runtime error in 'AutomorphismGroup': Bad argument types
Argument types given: Lat, Lat

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.869 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 03:11:53 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=(6*x-5)*(36*x^2-9)*(36*x^2-1)-6*(4*x-5)*(16*x^2-9)*(16*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 03:11:50 on modular  [Seed = 150592374]
-------------------------------------

1632*x^5 + 1200*x^4 + 1680*x^3 - 3000*x^2 - 162*x + 225

Total time: 2.909 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:12:35 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
>F:=Gram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]);
>F;
>G:=AutomorphismGroup(L,F);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:12:32 on modular  [Seed = 32559689]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>  F:=Gram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,3,2,2,2,2,2,3]);
^
User error: Identifier 'Gram' has not been declared or assigned

>>  F;
^
User error: Identifier 'F' has not been declared or assigned

>>  G:=AutomorphismGroup(L,F);
^
User error: Identifier 'F' has not been declared or assigned

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.949 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 03:12:56 2003

Input: P<x,y>:=PolynomialRing(RationalField(),2);
c:=(6*x-5)*(36*x^2-9)*(36*x^2-1);
c;

Output: Magma V2.10-6     Thu Dec  4 2003 03:12:53 on modular  [Seed = 2038999748]
-------------------------------------

7776*x^5 - 6480*x^4 - 2160*x^3 + 1800*x^2 + 54*x - 45

Total time: 2.979 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:27:06 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
> Q := RationalField();
> A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0,  >0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>;
>G:=AutomorphismGroup(L,A);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:27:03 on modular  [Seed = 1537903540]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>   A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0,  >0,1,0,0,0,0,0,0,1,0,0,0,0,0,0
^

>>  G:=AutomorphismGroup(L,A);
^
User error: Identifier 'A' has not been declared or assigned

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.929 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:27:30 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
> Q := RationalField();
> A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0,  0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>;
>G:=AutomorphismGroup(L,A);
>#G;

Output: Magma V2.10-6     Thu Dec  4 2003 03:27:27 on modular  [Seed = 1403159428]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>  G:=AutomorphismGroup(L,A);
^
Runtime error in 'AutomorphismGroup': Bad argument types
Argument types given: Lat, AlgMat

>>  #G;;
^
User error: Identifier 'G' has not been declared or assigned

Total time: 2.969 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:30:49 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
> Q := RationalField();
> A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0,  0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>;
>G:=AutomorphismGroup(L,A);
>#G;
>AlgMatElt?;

Output: Magma V2.10-6     Thu Dec  4 2003 03:30:46 on modular  [Seed = 1152748490]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>  G:=AutomorphismGroup(L,A);
^
Runtime error in 'AutomorphismGroup': Bad argument types
Argument types given: Lat, AlgMat

>>  #G;
^
User error: Identifier 'G' has not been declared or assigned

>>  AlgMatElt?;
^

Total time: 2.919 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (202.196.32.3)
Time: Thu Dec  4 03:31:27 2003

Input: >L:=LatticeWithGram(6,[4,1,4,2,2,4,2,2,1,4,2,2,1,1,4,2,2,2,2,2,4]);
>L;
> Q := RationalField();
> A := MatrixAlgebra< Q, 6 | [ 1,0,0,0,0,0,  0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1]>;
>G:=AutomorphismGroup(L,A);
>#G;
>?AlgMatElt

Output: Magma V2.10-6     Thu Dec  4 2003 03:31:24 on modular  [Seed = 3175903833]
-------------------------------------

Standard Lattice of rank 6 and degree 6
Inner Product Matrix:
[4 1 2 2 2 2]
[1 4 2 2 2 2]
[2 2 4 1 1 2]
[2 2 1 4 1 2]
[2 2 1 1 4 2]
[2 2 2 2 2 4]

>>  G:=AutomorphismGroup(L,A);
^
Runtime error in 'AutomorphismGroup': Bad argument types
Argument types given: Lat, AlgMat

>>  #G;
^
User error: Identifier 'G' has not been declared or assigned
No references for word "AlgMatElt"

Total time: 2.989 seconds, Total memory usage: 1.80MB

************** MAGMA *****************
Host 3(NXDOMAIN) (193.226.4.152)
Time: Thu Dec  4 03:59:42 2003

Input: P<x,y>:=PolynomialRing(IntegerRing(),2);
f1:=2*(x^2+y^2)+x-y-16;
f2:=6*(x^4+y^4)+2*(x^3-y^3)+x-y-192;
f3:=40*(x^6+y^6)+11*(x^5-y^5)+5*(x^3-y^3)+4*(x-y)-5120;
f4:=630*(x^8+y^8)+151*(x^7-y^7)+71*(x^5-y^5)+49*(x^3-y^3)+45*(x-y)-1024*315;
I:=ideal<P|f1,f2,f3,f4>;
B:=GroebnerBasis(I:Al:="Direct");
B;

Output: Magma V2.10-6     Thu Dec  4 2003 03:59:39 on modular  [Seed = 2390705869]
---------