Sharedwww / people / yeung / CharpolyProgram.txtOpen in CoCalc
Author: William A. Stein
1for N in [361..367] do
2A:=SortDecomposition(NewformDecomposition(NewSubspace(CuspidalSubspace(ModularSymbols(N,2,+1)))));
3for i in [1..#A] do C2:=CP(DH(A[i],2));
4C3:=CP(DH(A[i],3)); C5:=CP(DH(A[i],5));
5C7:=CP(DH(A[i],7)); C11:=CP(DH(A[i],11));
6C13:=CP(DH(A[i],13));
7B:=[N,i,2,C2,3,C3,5,C5,7,C7,11,C11,13,C13];
8printf
9"%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];
10print [];
11end for; end for;
12OUTPUT:
13Magma V2.10-6     Sat Nov 29 2003 04:18:24 on modular
14[Seed = 3609234643]
15   -------------------------------------
16
17361,1,2,$.1,3,$.1,5,$.1 + 1,7,$.1 - 3,11,$.1 + 185,13,$.1[]
19361,2,2,$.1,3,$.1 - 2,5,$.1 - 3,7,$.1 + 1,11,$.1 - 203,13,$.1 - 4[]
21361,3,2,$.1^2 - 5,3,$.1^2 - 4*$.1 + 4,5,$.1^2 - $.1 - 221,7,$.1^2 + 2*$.1 - 234,11,$.1^2 - 6*$.1 + 4,13,$.1^2 - 3*$.1 - 9[] 24361,4,2,$.1^2 - 5,3,$.1^2 + 4*$.1 + 4,5,$.1^2 -$.1 -
251,7,$.1^2 + 2*$.1 -
264,11,$.1^2 - 6*$.1 + 4,13,$.1^2 + 3*$.1 - 9[]
27361,5,2,$.1^2 -$.1 - 1,3,$.1^2 - 3*$.1 + 1,5,$.1^2 - 282*$.1 - 4,7,$.1^2 - 6*$.1
29+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 + 2*$.1 + 1[]
30361,6,2,$.1^2 +$.1 - 1,3,$.1^2 + 3*$.1 + 1,5,$.1^2 - 312*$.1 - 4,7,$.1^2 - 6*$.1
32+ 9,11,$.1^2 +$.1 - 1,13,$.1^2 - 2*$.1 + 1[]
33361,7,2,$.1^3 + 3*$.1^2 - 3,3,$.1^3 + 3*$.1^2 -
341,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 35- 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 +
3637[]
37361,8,2,$.1^3 - 3*$.1^2 + 3,3,$.1^3 - 3*$.1^2 +
381,5,$.1^3 + 3*$.1^2 - 3,7,$.1^3 39- 3*$.1 + 1,11,$.1^3 - 9*$.1 - 9,13,$.1^3 - 21*$.1 -
4037[]
41361,9,2,$.1^4 - 5*$.1^2 + 5,3,$.1^4 - 5*$.1^2 +
425,5,$.1^4 + 4*$.1^3 - 4*$.1^2 - 4316*$.1 + 16,7,$.1^4 + 8*$.1^3 + 14*$.1^2 - 8*$.1 +
441,11,$.1^4 + 10*$.1^3 +
4535*$.1^2 + 50*$.1 + 25,13,$.1^4 - 10*$.1^2 + 5[]
46362,1,2,x + 1,3,x + 1,5,x - 2,7,x + 4,11,x + 1,13,x -
474[]
48362,2,2,x - 1,3,x + 1,5,x + 2,7,x + 4,11,x + 1,13,x +
494[]
50362,3,2,x^2 + 2*x + 1,3,x^2 + 2*x - 4,5,x^2 + x -
511,7,x^2 + 3*x + 1,11,x^2 + 2*x
52- 4,13,x^2 + 7*x + 11[]
53362,4,2,x^2 - 2*x + 1,3,x^2 - 2*x - 1,5,x^2 - 4*x +
542,7,x^2 - 8,11,x^2 + 10*x +
5523,13,x^2 - 8*x + 14[]
56362,5,2,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,3,x^5
57- 4*x^4 - 2*x^3 + 17*x^2 -
58x - 17,5,x^5 - 18*x^3 + 8*x^2 + 56*x - 48,7,x^5 -
595*x^4 - 9*x^3 + 61*x^2 -
60136,11,x^5 - 4*x^4 - 4*x^3 + 13*x^2 + 5*x - 9,13,x^5 -
6110*x^4 + 22*x^3 + 20*x^2
62- 48*x + 16[]
63362,6,2,x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1,3,x^5
64- 13*x^3 + 3*x^2 + 38*x -
6528,5,x^5 + x^4 - 17*x^3 - 16*x^2 + 68*x + 72,7,x^5 -
666*x^4 - 3*x^3 + 51*x^2 -
676*x - 109,11,x^5 - 4*x^4 - 23*x^3 + 139*x^2 - 214*x +
6884,13,x^5 + 5*x^4 - 31*x^3
69- 90*x^2 + 328*x + 8[]
70363,1,2,x + 1,3,x + 1,5,x + 2,7,x + 4,11,x,13,x - 2[]
71363,2,2,x - 2,3,x + 1,5,x - 4,7,x + 1,11,x,13,x - 2[]
72363,3,2,x + 2,3,x + 1,5,x - 4,7,x - 1,11,x,13,x + 2[]
73363,4,2,x^2 - 3,3,x^2 + 2*x + 1,5,x^2 + 6*x + 9,7,x^2
74- 12,11,x^2,13,x^2 - 3[]
75363,5,2,x^2 + 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x -
761,7,x^2 + 2*x +
771,11,x^2,13,x^2 + 4*x - 1[]
78363,6,2,x^2 - 3*x + 1,3,x^2 + 2*x + 1,5,x^2 - x -
791,7,x^2 - 2*x +
801,11,x^2,13,x^2 - 4*x - 1[]
81363,7,2,x^2 - 5,3,x^2 - 2*x + 1,5,x^2 - 4*x + 4,7,x^2
82- 20,11,x^2,13,x^2[]
83363,8,2,x^2 - x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x +
841,7,x^2 - 6*x +
859,11,x^2,13,x^2 - 8*x + 11[]
86363,9,2,x^2 + x - 1,3,x^2 - 2*x + 1,5,x^2 + 3*x +
871,7,x^2 + 6*x +
889,11,x^2,13,x^2 + 8*x + 11[]
89363,10,2,x^4 - 7*x^2 + 4,3,x^4 - 4*x^3 + 6*x^2 - 4*x +
901,5,x^4 - 2*x^3 - 15*x^2
91+ 16*x + 64,7,x^4 - 7*x^2 + 4,11,x^4,13,x^4 - 51*x^2 +
92576[]
93364,1,2,x,3,x + 2,5,x - 1,7,x + 1,11,x + 4,13,x - 1[]
94364,2,2,x,3,x,5,x + 3,7,x - 1,11,x + 2,13,x + 1[]
95364,3,2,x^2,3,x^2 - 6,5,x^2 + 2*x - 5,7,x^2 + 2*x +
961,11,x^2 - 8*x + 10,13,x^2 +
972*x + 1[]
98364,4,2,x^2,3,x^2 - 2*x - 2,5,x^2 - 3,7,x^2 - 2*x +
991,11,x^2 - 6*x + 6,13,x^2 -
1002*x + 1[]
101365,1,2,x^2 - 3,3,x^2 - 4*x + 4,5,x^2 - 2*x + 1,7,x^2
102- 6*x + 6,11,x^2 + 6*x +
1036,13,x^2 - 12[]
104365,2,2,x^3 + x^2 - 2*x - 1,3,x^3 + 4*x^2 + 3*x -
1051,5,x^3 - 3*x^2 + 3*x -
1061,7,x^3 + x^2 - 16*x - 29,11,x^3 + 9*x^2 + 27*x +
10727,13,x^3 + x^2 - 16*x + 13[]
108365,3,2,x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1,3,x^5 +
1096*x^4 + 7*x^3 - 9*x^2 - 8*x
110+ 4,5,x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1,7,x^5 +
1115*x^4 + 2*x^3 - 15*x^2 -
11216*x - 2,11,x^5 - 3*x^4 - 31*x^3 + 49*x^2 + 174*x -
113278,13,x^5 + 9*x^4 + 24*x^3
114+ 9*x^2 - 28*x - 4[]
115365,4,2,x^7 + x^6 - 12*x^5 - 9*x^4 + 39*x^3 + 19*x^2 -
11616*x - 3,3,x^7 - 2*x^6 -
11714*x^5 + 17*x^4 + 64*x^3 - 31*x^2 - 77*x + 17,5,x^7 -
1187*x^6 + 21*x^5 - 35*x^4 +
11935*x^3 - 21*x^2 + 7*x - 1,7,x^7 + 3*x^6 - 22*x^5 -
12053*x^4 + 148*x^3 + 196*x^2 -
121352*x + 48,11,x^7 - 15*x^6 + 78*x^5 - 150*x^4 + 28*x^3
122+ 112*x^2 - 11*x -
1233,13,x^7 - 5*x^6 - 37*x^5 + 170*x^4 + 227*x^3 -
1241084*x^2 + 736*x - 27[]
125365,5,2,x^8 - 2*x^7 - 11*x^6 + 19*x^5 + 36*x^4 -
12646*x^3 - 41*x^2 + 25*x +
1273,3,x^8 - 8*x^7 + 14*x^6 + 35*x^5 - 124*x^4 + 47*x^3 +
128163*x^2 - 163*x +
12932,5,x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 +
13028*x^2 + 8*x + 1,7,x^8 -
1317*x^7 - 12*x^6 + 171*x^5 - 166*x^4 - 980*x^3 +
1321736*x^2 + 496*x - 1312,11,x^8 +
1337*x^7 - 32*x^6 - 230*x^5 + 396*x^4 + 2344*x^3 -
1342867*x^2 - 7633*x + 9702,13,x^8
135- 11*x^7 + 17*x^6 + 200*x^5 - 889*x^4 + 1046*x^3 +
136244*x^2 - 643*x - 74[]
137366,1,2,x + 1,3,x + 1,5,x + 2,7,x - 4,11,x + 4,13,x +
1382[]
139366,2,2,x + 1,3,x - 1,5,x - 1,7,x + 2,11,x - 6,13,x[]
140366,3,2,x + 1,3,x - 1,5,x + 3,7,x + 1,11,x + 3,13,x +
1411[]
142366,4,2,x - 1,3,x + 1,5,x + 1,7,x - 2,11,x - 2,13,x -
1434[]
144366,5,2,x - 1,3,x + 1,5,x + 3,7,x + 3,11,x + 1,13,x +
1455[]
146366,6,2,x - 1,3,x - 1,5,x - 1,7,x - 1,11,x + 1,13,x +
1475[]
148366,7,2,x - 1,3,x - 1,5,x - 1,7,x + 2,11,x - 2,13,x -
1494[]
150366,8,2,x^2 + 2*x + 1,3,x^2 + 2*x + 1,5,x^2 - 17,7,x^2
151+ 3*x - 2,11,x^2 - 3*x -
1522,13,x^2 - 7*x + 8[]
153367,1,2,x^11 + 8*x^10 + 16*x^9 - 26*x^8 - 121*x^7 -
15461*x^6 + 197*x^5 + 212*x^4 -
15566*x^3 - 132*x^2 - 12*x + 13,3,x^11 + 6*x^10 + 3*x^9 -
15641*x^8 - 64*x^7 + 64*x^6
157+ 158*x^5 - 9*x^4 - 118*x^3 - 14*x^2 + 24*x - 1,5,x^11
158+ 8*x^10 + 7*x^9 - 85*x^8
159- 191*x^7 + 190*x^6 + 791*x^5 + 247*x^4 - 815*x^3 -
160687*x^2 - 128*x + 5,7,x^11 +
1617*x^10 - 13*x^9 - 186*x^8 - 277*x^7 + 859*x^6 +
1622780*x^5 + 1778*x^4 - 1871*x^3 -
1632671*x^2 - 799*x + 25,11,x^11 + 10*x^10 - 12*x^9 -
164313*x^8 - 120*x^7 + 3196*x^6
165+ 661*x^5 - 11246*x^4 + 2768*x^3 + 5371*x^2 - 892*x -
166743,13,x^11 + 5*x^10 -
16748*x^9 - 277*x^8 + 569*x^7 + 4656*x^6 + 745*x^5 -
16822685*x^4 - 14329*x^3 +
16925989*x^2 - 1682*x - 2621[]
170367,2,2,x^19 - 9*x^18 + 11*x^17 + 123*x^16 - 372*x^15
171- 469*x^14 + 2884*x^13 -
172550*x^12 - 10042*x^11 + 8029*x^10 + 17059*x^9 -
17320350*x^8 - 12836*x^7 +
17420779*x^6 + 2682*x^5 - 7739*x^4 + 63*x^3 + 899*x^2 -
17527*x - 29,3,x^19 - 4*x^18 -
17635*x^17 + 149*x^16 + 486*x^15 - 2260*x^14 - 3442*x^13
177+ 18203*x^12 + 13108*x^11
178- 84580*x^10 - 25304*x^9 + 229397*x^8 + 19212*x^7 -
179348172*x^6 - 3000*x^5 +
180262144*x^4 + 15968*x^3 - 68672*x^2 - 21504*x -
1811792,5,x^19 - 6*x^18 - 43*x^17 +
182309*x^16 + 595*x^15 - 6046*x^14 - 2461*x^13 +
18358707*x^12 - 5347*x^11 -
184322649*x^10 + 48332*x^9 + 1052323*x^8 + 41520*x^7 -
1851950148*x^6 - 697328*x^5 +
1861640832*x^4 + 1181408*x^3 - 153984*x^2 - 315520*x -
18768864,7,x^19 - x^18 -
18868*x^17 + 93*x^16 + 1821*x^15 - 3162*x^14 - 24162*x^13
189+ 51825*x^12 +
190161877*x^11 - 438685*x^10 - 465321*x^9 + 1870316*x^8 +
19163387*x^7 - 3600393*x^6 +
1921757269*x^5 + 2308835*x^4 - 1465397*x^3 - 561533*x^2 +
193257949*x + 75177,11,x^19
194- 4*x^18 - 120*x^17 + 545*x^16 + 5632*x^15 -
19529392*x^14 - 128435*x^13 +
196812306*x^12 + 1363286*x^11 - 12382021*x^10 -
1972606314*x^9 + 102742747*x^8 -
19871962574*x^7 - 413796744*x^6 + 565237368*x^5 +
199539820496*x^4 - 1225061216*x^3 +
200173670080*x^2 + 608625792*x - 263379712,13,x^19 -
2015*x^18 - 99*x^17 + 398*x^16 +
2024006*x^15 - 11816*x^14 - 82529*x^13 + 167855*x^12 +
203890309*x^11 - 1326823*x^10 -
2044991303*x^9 + 6366113*x^8 + 13486540*x^7 -
20517861951*x^6 - 12151477*x^5 +
20622331038*x^4 - 6313452*x^3 - 683605*x^2 + 175252*x -
2072548[]
208
209Total time: 21.159 seconds, Total memory usage: 6.39MB
210