Open in CoCalc
1\\ charpoly_s10new.gp
2\\ This is a table of characteristic polynomials of the
3\\ Hecke operators T_p acting on the space S_10^{new}(Gamma_0(N))
4\\ of weight 10 cuspidal newforms for Gamma_0(N).
5\\ The cases in which S_k = S_k^{new} are omitted, since
6\\ they appear in other tables.
7\\ William Stein ([email protected]), September, 1998.
8
9{
10T=matrix(20,97,m,n,0);
11T[4,2]=x ;
12T[4,3]=x -228;
13T[4,5]=x + 666;
14T[4,7]=x + 6328;
15T[4,11]=x + 30420;
16T[4,13]=x + 32338;
17T[4,17]=x -590994;
18T[4,19]=x -34676;
19T[4,23]=x -1048536;
20T[4,29]=x -4409406;
21T[4,31]=x + 7401184;
22T[4,37]=x -10234502;
23T[4,41]=x -18352746;
24T[4,43]=x + 252340;
25T[4,47]=x + 49517136;
26T[4,53]=x + 66396906;
27T[4,59]=x + 61523748;
28T[4,61]=x -35638622;
29T[4,67]=x -181742372;
30T[4,71]=x -90904968;
31T[4,73]=x + 262978678;
32T[4,79]=x + 116502832;
33T[4,83]=x + 9563724;
34T[4,89]=x -611826714;
35T[4,97]=x + 259312798;
36
37T[6,2]=x + 16;
38T[6,3]=x -81;
39T[6,5]=x -2694;
40T[6,7]=x + 3544;
41T[6,11]=x -29580;
42T[6,13]=x + 44818;
43T[6,17]=x + 101934;
44T[6,19]=x + 895084;
45T[6,23]=x + 1113000;
46T[6,29]=x + 2357346;
47T[6,31]=x -175808;
48T[6,37]=x + 2919418;
49T[6,41]=x -26218794;
50T[6,43]=x + 18762964;
51T[6,47]=x + 20966160;
52T[6,53]=x -57251574;
53T[6,59]=x -33587580;
54T[6,61]=x -82260830;
55T[6,67]=x + 188455804;
56T[6,71]=x -80924040;
57T[6,73]=x + 236140918;
58T[6,79]=x -526909808;
59T[6,83]=x -18346452;
60T[6,89]=x -690643098;
61T[6,97]=x + 438251038;
62
63T[8,2]=(x )^2;
64T[8,3]=(x + 60)*(x -68);
65T[8,5]=(x -1510)*(x + 2074);
66T[8,7]=(x -10248)*(x + 4344);
67T[8,11]=(x -3916)*(x -93644);
68T[8,13]=(x + 12242)*(x + 176594);
69T[8,17]=(x + 319598)*(x -148370);
70T[8,19]=(x + 553516)*(x -499796);
71T[8,23]=(x + 1889768)*(x + 712936);
72T[8,29]=(x + 920898)*(x -2075838);
73T[8,31]=(x + 6420448)*(x -1379360);
74T[8,37]=(x -5064966)*(x + 18197754);
75T[8,41]=(x + 24100758)*(x -9033834);
76T[8,43]=(x -25785196)*(x -19594732);
77T[8,47]=(x + 60790224)*(x + 18484176);
78T[8,53]=(x -10255766)*(x -29496214);
79T[8,59]=(x -51819388)*(x -121666556);
80T[8,61]=(x + 45948962)*(x -33426910);
81T[8,67]=(x -144856196)*(x -50535428);
82T[8,71]=(x -267044680)*(x -68397128);
83T[8,73]=(x -168216202)*(x + 176213366);
84T[8,79]=(x + 269685680)*(x -235398736);
85T[8,83]=(x + 64639852)*(x + 227032556);
86T[8,89]=(x + 78782694)*(x -72141594);
87T[8,97]=(x -228776546)*(x + 24113566);
88
89T[9,2]=(x + 18)*(x -36)*(x );
90T[9,3]=(x )^3;
91T[9,5]=(x -1314)*(x -1530)*(x );
92T[9,7]=(x -9128)*(x + 12580)*(x + 4480);
93T[9,11]=(x + 21132)*(x + 1476)*(x );
94T[9,13]=(x -31214)*(x -118370)*(x + 151522);
95T[9,17]=(x + 108162)*(x -279342)*(x );
96T[9,19]=(x -593084)*(x -144020)*(x + 976696);
97T[9,23]=(x -969480)*(x -1763496)*(x );
98T[9,29]=(x -6642522)*(x + 4692510)*(x );
99T[9,31]=(x -7070600)*(x -1691228)*(x + 369088);
100T[9,37]=(x + 15384490)*(x + 7472410)*(x -9347078);
101T[9,41]=(x -7226838)*(x -4350150)*(x );
102T[9,43]=(x + 4358716)*(x + 16577080)*(x + 23147476);
103T[9,47]=(x + 28309248)*(x + 22971888)*(x );
104T[9,53]=(x + 78477174)*(x + 16111710)*(x );
105T[9,59]=(x -20310660)*(x -86075964)*(x );
106T[9,61]=(x -32213918)*(x + 117903058)*(x + 179339938);
107T[9,67]=(x -274528388)*(x -112542320)*(x -99531452);
108T[9,71]=(x -44170488)*(x -36342648)*(x );
109T[9,73]=(x -296368310)*(x + 247089526)*(x + 23560630);
110T[9,79]=(x + 401754760)*(x + 616732324)*(x -191874800);
111T[9,83]=(x -276159276)*(x -744528708)*(x );
112T[9,89]=(x + 769871034)*(x -678997350)*(x );
113T[9,97]=(x + 567657502)*(x -1288928270)*(x -907130882);
114
115T[10,2]=(x -16)*(x + 16)^2;
116T[10,3]=(x -174)*(x + 204)*(x -46);
117T[10,5]=(x -625)*(x + 625)^2;
118T[10,7]=(x -4658)*(x -5432)*(x + 10318);
119T[10,11]=(x -73932)*(x + 5568)*(x -28992);
120T[10,13]=(x + 164446)*(x -45986)*(x + 114514);
121T[10,17]=(x + 381318)*(x -41682)*(x + 594822);
122T[10,19]=(x -610460)*(x + 295780)*(x -1057460);
123T[10,23]=(x -2544534)*(x -1599336)*(x + 1447914);
124T[10,29]=(x -5385510)*(x + 3722970)*(x -2184510);
125T[10,31]=(x -2335772)*(x + 9619648)*(x -3053852);
126T[10,37]=(x -12889442)*(x -10840418)*(x -4799942);
127T[10,41]=(x -21593862)*(x + 33786618)*(x -9531882);
128T[10,43]=(x + 13464484)*(x + 36886234)*(x -10832294);
129T[10,47]=(x + 44163798)*(x -11441952)*(x -5172138);
130T[10,53]=(x -29746266)*(x -98179674)*(x -53615766);
131T[10,59]=(x + 65575380)*(x -81862620)*(x -16162860);
132T[10,61]=(x + 104691298)*(x + 43928158)*(x -40183202);
133T[10,67]=(x -140571092)*(x + 115706158)*(x + 81557422);
134T[10,71]=(x + 231681708)*(x -161307732)*(x -97098792);
135T[10,73]=(x + 247147966)*(x -358691906)*(x -171848906);
136T[10,79]=(x + 486017080)*(x + 117380080)*(x + 583345720);
137T[10,83]=(x -251168886)*(x -323637636)*(x + 14571786);
138T[10,89]=(x + 894379110)*(x -470133690)*(x + 526039110);
139T[10,97]=(x + 1075981438)*(x -232678562)*(x + 117838462);
140
141T[12,2]=x ;
142T[12,3]=x + 81;
143T[12,5]=x -990;
144T[12,7]=x -8576;
145T[12,11]=x -70596;
146T[12,13]=x + 2530;
147T[12,17]=x + 200574;
148T[12,19]=x + 695620;
149T[12,23]=x -2472696;
150T[12,29]=x -5474214;
151T[12,31]=x -3732104;
152T[12,37]=x + 21898522;
153T[12,41]=x + 23818950;
154T[12,43]=x -10612676;
155T[12,47]=x -2398464;
156T[12,53]=x + 8994978;
157T[12,59]=x + 143417916;
158T[12,61]=x + 19804258;
159T[12,67]=x + 165625156;
160T[12,71]=x + 194801400;
161T[12,73]=x -148729418;
162T[12,79]=x + 30134152;
163T[12,83]=x -302054076;
164T[12,89]=x -909502650;
165T[12,97]=x + 872463358;
166
167T[14,2]=(x -16)*(x + 16)^3;
168T[14,3]=(x + 6)*(x -170)*(x^2 + 14*x -57576);
169T[14,5]=(x -544)*(x -560)*(x^2 + 2730*x + 846720);
170T[14,7]=(x -2401)^2*(x + 2401)^2;
171T[14,11]=(x -48824)*(x + 54152)*(x^2 -44940*x -2036361600);
172T[14,13]=(x + 15876)*(x + 113172)*(x^2 -100282*x + 2397429256);
173T[14,17]=(x + 21418)*(x -6262)*(x^2 + 870408*x + 183575251116);
174T[14,19]=(x + 716410)*(x -257078)*(x^2 -508774*x -352577596856);
175T[14,23]=(x + 2470000)*(x + 266000)*(x^2 -79800*x -115915968000);
176T[14,29]=(x -5556826)*(x -1574714)*(x^2 -2006328*x -31904129519604);
177T[14,31]=(x -5799348)*(x + 4637484)*(x^2 -2188732*x -2367849772544);
178T[14,37]=(x + 11946238)*(x + 3894430)*(x^2 + 20723576*x + 60225113026444);
179T[14,41]=(x -21909126)*(x + 6360858)*(x^2 -19016592*x -527816477266884);
180T[14,43]=(x + 18701296)*(x -27520592)*(x^2 -4193716*x -271341247682336);
181T[14,47]=(x -52927836)*(x -56539068)*(x^2 + 74542524*x + 1296550084878144);
182T[14,53]=(x -16221222)*(x + 59894682)*(x^2 + 3239748*x -494746212296124);
183T[14,59]=(x + 140509618)*(x -165629662)*(x^2 + 133642362*x + 1575046316366136);
184T[14,61]=(x -51419016)*(x + 202963560)*(x^2 -227801686*x + 11243934945943024);
185T[14,67]=(x -93546508)*(x -153734572)*(x^2 -332930272*x + 21401918313456496);
186T[14,71]=(x -279655936)*(x + 95633536)*(x^2 + 167985720*x -85127259938918400);
187T[14,73]=(x -306496402)*(x + 404022830)*(x^2 + 44684276*x -83678371011966956);
188T[14,79]=(x + 130689816)*(x -496474152)*(x^2 -269642776*x + 6880003984764544);
189T[14,83]=(x -420134014)*(x + 371486962)*(x^2 + 183105762*x -76697718543013464);
190T[14,89]=(x + 165482550)*(x + 469542390)*(x^2 -791657748*x + 50565747709419876);
191T[14,97]=(x + 872501690)*(x -758016742)*(x^2 + 4169480*x -451110491471642900);
192
193T[15,2]=(x -22)*(x + 4)*(x^2 -31*x -302)*(x^2 -19*x -1092);
194T[15,3]=(x -81)^3*(x + 81)^3;
195T[15,5]=(x -625)^3*(x + 625)^3;
196T[15,7]=(x + 7680)*(x + 5988)*(x^2 -14112*x + 22579200)*(x^2 + 11872*x + 31528560);
197T[15,11]=(x + 86404)*(x + 14648)*(x^2 + 21512*x -2924934128)*(x^2 -35488*x -4189882368);
198T[15,13]=(x -37906)*(x + 149978)*(x^2 -143676*x + 2896150388)*(x^2 -24284*x -15338329532);
199T[15,17]=(x + 207622)*(x + 441098)*(x^2 + 156956*x -24505657916)*(x^2 -385156*x + 31364196084);
200T[15,19]=(x -441820)*(x -716284)*(x^2 + 95896*x -15492203120)*(x^2 + 403296*x + 39554119280);
201T[15,23]=(x -2264136)*(x -1369920)*(x^2 -223704*x -4977578430720)*(x^2 + 735264*x -239117414400);
202T[15,29]=(x + 1049350)*(x + 3194402)*(x^2 + 74572*x -180861933660)*(x^2 + 2678212*x -13616383922300);
203T[15,31]=(x + 7910568)*(x + 2349000)*(x^2 -10782432*x + 16415447040000)*(x^2 + 5027128*x -463313088000);
204T[15,37]=(x + 20992558)*(x -18735710)*(x^2 -5373628*x -28861754638220)*(x^2 -21968332*x + 99286893737380);
205T[15,41]=(x -13285562)*(x + 29282630)*(x^2 -14211332*x -210775232832060)*(x^2 -26060372*x + 38475315093220);
206T[15,43]=(x + 23130764)*(x + 1516724)*(x^2 -27748920*x + 165047750825744)*(x^2 + 7191160*x -254550637865456);
207T[15,47]=(x -615752)*(x + 13873688)*(x^2 -95966440*x + 2082398270597376)*(x^2 + 31580240*x -1856218340076224);
208T[15,53]=(x -4747430)*(x + 57635174)*(x^2 + 64305596*x + 11555844938820)*(x^2 -3131116*x -14677210114460);
209T[15,59]=(x + 32042120)*(x -60616076)*(x^2 -187863136*x + 5745641782978560)*(x^2 + 35494664*x -9937984740980720);
210T[15,61]=(x + 126745682)*(x -110664022)*(x^2 -341497340*x + 28665513361108996)*(x^2 -154080060*x -85608279866044);
211T[15,67]=(x + 118568268)*(x + 111182652)*(x^2 + 288195816*x + 20192770248606864)*(x^2 -33592376*x -65232884349014256);
212T[15,71]=(x + 175551608)*(x -276679712)*(x^2 + 228270976*x -45919384536416256)*(x^2 -210286064*x -147594805309376);
213T[15,73]=(x + 264023294)*(x + 61233350)*(x^2 + 33122316*x -49372065464527900)*(x^2 + 232663084*x + 12793033974476260);
214T[15,79]=(x -234431160)*(x -448202760)*(x^2 + 932406760*x + 213523438937692800)*(x^2 + 24755040*x -196612497485568000);
215T[15,83]=(x -118910388)*(x -851015796)*(x^2 -207040152*x -1097200204595568)*(x^2 + 372082152*x + 6028318254901392);
216T[15,89]=(x -189894930)*(x + 316534326)*(x^2 -224518164*x -89786907488203740)*(x^2 + 427639116*x + 1315495255181220);
217T[15,97]=(x -242912258)*(x + 1014149278)*(x^2 -387134596*x -2255431146557740796)*(x^2 -1771658884*x + 686586583127112964);
218
219T[16,2]=(x )^4;
220T[16,3]=(x + 228)*(x + 68)*(x -60)*(x -156);
221T[16,5]=(x + 666)*(x -1510)*(x + 2074)*(x -870);
222T[16,7]=(x -952)*(x -4344)*(x -6328)*(x + 10248);
223T[16,11]=(x -56148)*(x -30420)*(x + 93644)*(x + 3916);
224T[16,13]=(x + 12242)*(x + 176594)*(x -178094)*(x + 32338);
225T[16,17]=(x -590994)*(x + 319598)*(x -148370)*(x + 247662);
226T[16,19]=(x -553516)*(x + 499796)*(x + 34676)*(x + 315380);
227T[16,23]=(x -1889768)*(x -712936)*(x + 1048536)*(x + 204504);
228T[16,29]=(x -4409406)*(x -2075838)*(x + 920898)*(x + 3840450);
229T[16,31]=(x -1309408)*(x + 1379360)*(x -6420448)*(x -7401184);
230T[16,37]=(x -5064966)*(x + 18197754)*(x -4307078)*(x -10234502);
231T[16,41]=(x + 24100758)*(x -9033834)*(x -1512042)*(x -18352746);
232T[16,43]=(x + 25785196)*(x -252340)*(x + 19594732)*(x + 33670604);
233T[16,47]=(x -18484176)*(x -10581072)*(x -60790224)*(x -49517136);
234T[16,53]=(x -29496214)*(x + 66396906)*(x -10255766)*(x -16616214);
235T[16,59]=(x + 121666556)*(x -61523748)*(x + 112235100)*(x + 51819388);
236T[16,61]=(x + 33197218)*(x -33426910)*(x + 45948962)*(x -35638622);
237T[16,67]=(x + 50535428)*(x -121372252)*(x + 181742372)*(x + 144856196);
238T[16,71]=(x + 267044680)*(x -387172728)*(x + 90904968)*(x + 68397128);
239T[16,73]=(x -255240074)*(x -168216202)*(x + 262978678)*(x + 176213366);
240T[16,79]=(x + 492101840)*(x -116502832)*(x -269685680)*(x + 235398736);
241T[16,83]=(x -227032556)*(x -64639852)*(x -457420236)*(x -9563724);
242T[16,89]=(x + 78782694)*(x + 31809510)*(x -72141594)*(x -611826714);
243T[16,97]=(x + 673532062)*(x -228776546)*(x + 24113566)*(x + 259312798);
244
245T[18,2]=(x + 16)^2*(x -16)^2;
246T[18,3]=(x )^4;
247T[18,5]=(x -384)*(x + 384)*(x + 2694)*(x + 870);
248T[18,7]=(x + 952)*(x + 3544)*(x -5852)^2;
249T[18,11]=(x + 29580)*(x -56148)*(x + 90624)*(x -90624);
250T[18,13]=(x + 44818)*(x -178094)*(x + 102814)^2;
251T[18,17]=(x -458496)*(x -247662)*(x + 458496)*(x -101934);
252T[18,19]=(x + 895084)*(x -315380)*(x + 128824)^2;
253T[18,23]=(x + 1274880)*(x -1274880)*(x + 204504)*(x -1113000);
254T[18,29]=(x -3840450)*(x -4884864)*(x -2357346)*(x + 4884864);
255T[18,31]=(x -175808)*(x + 1309408)*(x + 7727524)^2;
256T[18,37]=(x + 2919418)*(x -4307078)*(x -3121238)^2;
257T[18,41]=(x + 1512042)*(x + 25186560)*(x + 26218794)*(x -25186560);
258T[18,43]=(x + 18762964)*(x -33670604)*(x -10223048)^2;
259T[18,47]=(x -19430400)*(x + 19430400)*(x -20966160)*(x -10581072);
260T[18,53]=(x + 16616214)*(x + 57251574)*(x -59935104)*(x + 59935104);
261T[18,59]=(x + 75334656)*(x + 33587580)*(x -75334656)*(x + 112235100);
262T[18,61]=(x + 33197218)*(x -82260830)*(x -207606062)^2;
263T[18,67]=(x + 121372252)*(x + 188455804)*(x + 178167184)^2;
264T[18,71]=(x -4902912)*(x + 80924040)*(x -387172728)*(x + 4902912);
265T[18,73]=(x -255240074)*(x + 236140918)*(x + 42043210)^2;
266T[18,79]=(x -526909808)*(x -492101840)*(x + 364859044)^2;
267T[18,83]=(x + 18346452)*(x + 317941248)*(x -457420236)*(x -317941248);
268T[18,89]=(x -788009472)*(x + 690643098)*(x + 788009472)*(x -31809510);
269T[18,97]=(x + 438251038)*(x + 673532062)*(x -631569422)^2;
270
271T[20,2]=(x )^3;
272T[20,3]=(x + 48)*(x^2 + 260*x -3324);
273T[20,5]=(x -625)*(x + 625)^2;
274T[20,7]=(x + 532)*(x^2 + 380*x -96250364);
275T[20,11]=(x + 33180)*(x^2 -102720*x + 2619648000);
276T[20,13]=(x + 99682)*(x^2 -179140*x + 1589611396);
277T[20,17]=(x + 443454)*(x^2 -316020*x + 22517952804);
278T[20,19]=(x + 357244)*(x^2 -137272*x -533765233904);
279T[20,23]=(x + 142956)*(x^2 + 665460*x -715854707676);
280T[20,29]=(x -1527966)*(x^2 + 6893748*x + 11181707706276);
281T[20,31]=(x -7323416)*(x^2 -291832*x -13914308520944);
282T[20,37]=(x + 2666842)*(x^2 -11261380*x -41043496652924);
283T[20,41]=(x + 7939014)*(x^2 -29773452*x + 116248533661476);
284T[20,43]=(x + 21174520)*(x^2 + 11708180*x -166415379974300);
285T[20,47]=(x -16059636)*(x^2 -62493300*x + 939697938528804);
286T[20,53]=(x + 87822234)*(x^2 -9417780*x -891341422077276);
287T[20,59]=(x -120625212)*(x^2 + 92930856*x -669513681826416);
288T[20,61]=(x -93576542)*(x^2 -195673924*x -954028889496956);
289T[20,67]=(x -193621688)*(x^2 + 219767420*x + 11239877195400196);
290T[20,71]=(x -417763488)*(x^2 -311207016*x -15291364811604336);
291T[20,73]=(x + 450372742)*(x^2 + 99224060*x -82340726355330044);
292T[20,79]=(x + 91425472)*(x^2 -542261776*x + 73412804192378944);
293T[20,83]=(x + 652637376)*(x^2 + 1256915700*x + 394206281091180324);
294T[20,89]=(x + 170059206)*(x^2 + 462291852*x -541109639379720924);
295T[20,97]=(x + 10947022)*(x^2 -1671716740*x + 528228461547839236);
296
297}
298