Sharedwww / Tables / ap_s4g1new_1-18.gpOpen in CoCalc
Author: William A. Stein
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\\ ap_s4g1new_1-18.gp
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\\ This is a table of eigenforms for the action of
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\\ the Hecke operators on S_4^{new}(Gamma_1(N)).
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\\ William Stein ([email protected]), October, 1998.
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\\ 1<=N<=18
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\\ E=matrix(18,?,i,j,0);
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\\ E[N,ith eigenform]=[[a_2,...,a_37], f(x)]
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\\ where the a_i are defined over Q[x]/f(x).
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E[5,1]=[[-4,2,-5,6,32,-38,26,100,-78,-50,-108,266], x-1];
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E[6,1]=[[-2,-3,6,-16,12,38,-126,20,168,30,-88,254], x-1];
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E[7,1]=[[-1,-2,16,-7,-8,28,54,-110,48,-110,12,-246], x-1];
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E[7,2]=[[x,-7/2*x-7,7/2*x,-7*x+7,5/2*x+5,-14,21/2*x+21,49/2*x,-159/2*x,58,-147/2*x-147,219/2*x], x^2+2*x+4];
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E[8,1]=[[x,-2*x-2,4*x+4,-8,6*x+6,-20*x-20,-14,14*x+14,-152,60*x+60,224,-92*x-92], x^2+2*x+8];
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E[8,2]=[[0,-4,-2,24,-44,22,50,44,-56,198,-160,-162], x-1];
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E[9,1]=[[x,1/15*x^3-x-21/5,11/30*x^3+3/2*x^2+11/2*x-33/5,1/30*x^3+1/6*x^2+7/2*x+2/5,-3/2*x^3-15/2*x^2-61/2*x-18,47/30*x^3+17/6*x^2+47/2*x-141/5,3/5*x^3+126/5,-9/5*x^3+172/5,83/30*x^3+15/2*x^2+83/2*x-249/5,9/10*x^3+9/2*x^2+29/2*x+54/5,11/30*x^3+17/6*x^2+11/2*x-33/5,18/5*x^3-854/5], x^4+3*x^3+15*x^2-18*x+36];
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E[9,2]=[[0,0,0,20,0,-70,0,56,0,0,308,110], x-1];
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E[10,1]=[[2,-8,5,-4,12,-58,66,-100,132,-90,152,-34], x-1];
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E[10,2]=[[x,-x,-5*x-5,13*x,-28,-6*x,-32*x,60,29*x,-90,-128,118*x], x^2+4];
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E[11,1]=[[x,-4*x+3,8*x-7,-4*x+14,-11,-20*x+60,12*x-74,60*x-24,-36*x-13,-56*x+128,28*x-45,-8*x+35], x^2-2*x-2];
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E[11,2]=[[x,7854087/12530039192*x^7+63504545/12530039192*x^6+342370821/12530039192*x^5+1179915221/12530039192*x^4+5096697189/12530039192*x^3+2947570539/6265019596*x^2+4281924019/3132509798*x-205898730/142386809,65460729/12530039192*x^7+552230989/12530039192*x^6+2509843013/12530039192*x^5+5878264773/12530039192*x^4+21543781805/12530039192*x^3+5211422753/3132509798*x^2+6669105885/1566254899*x-1399167409/142386809,-10173253/6265019596*x^7-37051976/1566254899*x^6-201930930/1566254899*x^5-529078358/1566254899*x^4-603116818/1566254899*x^3-2838994915/6265019596*x^2+400805026/142386809*x-303971228/142386809,6016831/569547236*x^7+57253073/569547236*x^6+263180693/569547236*x^5+682305897/569547236*x^4+2133410989/569547236*x^3+2176655341/284773618*x^2+1930592910/142386809*x+3161658885/142386809,-21623609/1566254899*x^7-401141199/3132509798*x^6-1038443811/1566254899*x^5-3322525037/1566254899*x^4-11961152037/1566254899*x^3-21755041026/1566254899*x^2-10567604221/284773618*x-3488673848/142386809,378184173/12530039192*x^7+2730907593/12530039192*x^6+13692824873/12530039192*x^5+38221603545/12530039192*x^4+143610027793/12530039192*x^3+3113283403/3132509798*x^2+8034381127/142386809*x-13343797313/142386809,-978553121/12530039192*x^7-7676985551/12530039192*x^6-36552942523/12530039192*x^5-95837033915/12530039192*x^4-363715206051/12530039192*x^3-160933988393/6265019596*x^2-40774218403/284773618*x+19925610694/142386809,-51358737/3132509798*x^7-383089893/3132509798*x^6-1726983121/3132509798*x^5-2111518113/3132509798*x^4-6171702045/3132509798*x^3+10209617226/1566254899*x^2-938140242/142386809*x+14979419012/142386809,-5689259/152805356*x^7-10424776/38201339*x^6-49879011/38201339*x^5-142739653/38201339*x^4-615593069/38201339*x^3-958581961/152805356*x^2-299236207/3472849*x+130696082/3472849,-626181/142386809*x^7+109505815/3132509798*x^6+556362471/1566254899*x^5+3543097935/1566254899*x^4+8651819127/1566254899*x^3+22520131014/1566254899*x^2-116109162533/3132509798*x+3160421352/142386809,508530705/6265019596*x^7+932882740/1566254899*x^6+4449186759/1566254899*x^5+12760701325/1566254899*x^4+56009613659/1566254899*x^3+20055929257/569547236*x^2+303926392967/1566254899*x-12142686470/142386809], x^8+7*x^7+31*x^6+71*x^5+319*x^4+78*x^3+1664*x^2-2816*x+1936];
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E[12,1]=[[x,1/8*x^3-1/2*x^2-1/2*x-1,-1/4*x^3-3*x,x^2+2,-5/4*x^3+5*x,-10,-x^3-12*x,-9*x^2-18,7/2*x^3-14*x,17/4*x^3+51*x,29*x^2+58,-130], x^4+4*x^2+64];
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E[12,2]=[[0,3,-18,8,36,-10,18,-100,72,-234,-16,-226], x-1];
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E[13,1]=[[-5,-7,-7,-13,-26,13,77,-126,-96,-82,196,-131], x-1];
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E[13,2]=[[x,-3*x+4,x-2,11*x-10,12*x+34,-13,-17*x+18,-32*x-26,-12*x+104,96*x-70,-34*x-26,5*x+102], x^2-x-4];
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E[13,3]=[[x,-1,-3*x,-5*x,16*x,-13*x+26,-45,2*x,162,-144,88*x,-101*x], x^2+9];
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E[13,4]=[[x,7/2*x+14,-8*x-24,13/2*x+39,13/2*x,-26*x-91,27/2*x+27,-51/2*x-153,-57/2*x-114,69/2*x+138,42*x+126,23/2*x], x^2+6*x+12];
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E[13,5]=[[x,1/2*x,17,-5*x-20,-8*x,-13/4*x-52,13/4*x+13,-15/2*x-30,39/2*x,197/4*x,-74,-227/4*x], x^2+4*x+16];
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E[13,6]=[[x,2*x-4,-2*x+3,8*x-24,8*x,13*x+26,-117*x+117,66*x-198,-78*x+156,-141*x+282,180*x-270,-83*x], x^2-3*x+3];
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E[13,7]=[[x,25/46*x^3-5/2*x^2+19/2*x-10/23,-5/23*x^3-410/23,27/46*x^3-5/2*x^2+27/2*x-135/23,145/46*x^3-29/2*x^2+115/2*x-58/23,118/23*x^3-25*x^2+120*x-145/23,343/46*x^3-75/2*x^2+343/2*x-1715/23,-405/46*x^3+83/2*x^2-405/2*x+2025/23,-775/46*x^3+155/2*x^2-709/2*x+310/23,665/46*x^3-133/2*x^2+545/2*x-266/23,-100/23*x^3-6360/23,-75/46*x^3+15/2*x^2+13/2*x+30/23], x^4-5*x^3+23*x^2-10*x+4];
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E[14,1]=[[2,-2,-12,7,48,56,-114,2,-120,-54,236,146], x-1];
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E[14,2]=[[-2,8,-14,-7,-28,18,74,80,-112,190,72,-346], x-1];
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E[14,3]=[[x,-1/2*x+1,-7/2*x,-9*x-1,35/2*x-35,66,59/2*x-59,-137/2*x,7/2*x,106,75/2*x-75,-11/2*x], x^2-2*x+4];
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E[14,4]=[[x,5/2*x+5,-9/2*x,-7*x-21,57/2*x+57,-70,-51/2*x-51,5/2*x,69/2*x,114,-23/2*x-23,-253/2*x], x^2+2*x+4];
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E[15,1]=[[1,3,5,-24,52,22,-14,-20,-168,230,-288,-34], x-1];
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E[15,2]=[[3,-3,-5,20,-24,74,54,-124,-120,-78,200,-70], x-1];
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E[15,3]=[[x,1/8*x^3+17/8*x,-1/4*x^3-x^2-21/4*x-11,-1/2*x^3-29/2*x,2*x^2+4,2*x^3+40*x,-3/2*x^3-31/2*x,-8*x^2-128,-3/2*x^3-67/2*x,14*x^2+334,4*x^2+76,-3*x^3+3*x], x^4+25*x^2+64];
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E[15,4]=[[x,13/2720*x^7+7/1360*x^6+1/34*x^4+2557/2720*x^3+1063/1360*x^2+79/34,-31/2720*x^7-1/68*x^5-5679/2720*x^3-249/68*x,19/680*x^6-2/17*x^4+3371/680*x^2-243/17,27/1360*x^7+1/34*x^5+6043/1360*x^3+419/34*x,1/40*x^6+1/17*x^4+209/40*x^2+249/17,7/34*x^5+587/34*x,-33/340*x^6-6177/340*x^2,89/1360*x^7+16041/1360*x^3,-137/1360*x^7+11/34*x^5-26633/1360*x^3+1889/34*x,30/17*x^4+4444/17,7/40*x^6+3/17*x^4+1863/40*x^2-2143/17], x^8+209*x^4+1600];
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E[16,1]=[[x,31/32768*x^9-19/16384*x^8-43/16384*x^7+11/1024*x^6-283/4096*x^5-5/32*x^4+133/512*x^3-13/128*x^2-9/8*x+41/4,23/32768*x^9+53/16384*x^8+125/16384*x^7+7/1024*x^6-83/4096*x^5-7/32*x^4-211/512*x^3-213/128*x^2-13/8*x+25/4,-5/2048*x^9-1/1024*x^8-19/1024*x^7-7/256*x^6+49/256*x^5+37/64*x^4+13/32*x^3+2*x^2-1/2*x-38,-55/32768*x^9-85/16384*x^8-413/16384*x^7+65/1024*x^6+1043/4096*x^5+7/64*x^4+499/512*x^3+421/128*x^2-91/8*x-137/4,81/32768*x^9+323/16384*x^8+123/16384*x^7-87/1024*x^6-437/4096*x^5-11/16*x^4-1397/512*x^3+445/128*x^2+213/8*x+23/4,-5/512*x^9-3/128*x^8+3/256*x^7+15/128*x^6+47/64*x^5+55/32*x^4+3*x^3-25/4*x^2-26*x-74,143/32768*x^9+125/16384*x^8+37/16384*x^7-173/1024*x^6-2123/4096*x^5-27/16*x^4-1451/512*x^3+771/128*x^2+127/8*x+313/4,7/2048*x^9+3/1024*x^8+81/1024*x^7+41/256*x^6-27/256*x^5+5/64*x^4+9/32*x^3-27/2*x^2-69/2*x+34,321/32768*x^9-173/16384*x^8-1461/16384*x^7+113/1024*x^6-2405/4096*x^5-39/32*x^4+1755/512*x^3-179/128*x^2+29/8*x+167/4,5/128*x^8+1/64*x^7-21/64*x^6+3/16*x^5-13/16*x^4-25/4*x^3+1/2*x^2+44*x+8,343/32768*x^9-459/16384*x^8-1603/16384*x^7+31/1024*x^6-915/4096*x^5-25/8*x^4+5229/512*x^3+1739/128*x^2-101/8*x+441/4], x^10+2*x^9-2*x^8+8*x^7-40*x^6-352*x^5-320*x^4+512*x^3-1024*x^2+8192*x+32768];
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E[16,2]=[[0,4,-2,-24,44,22,50,-44,56,198,160,-162], x-1];
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E[17,1]=[[-3,-8,6,-28,-24,-58,17,116,-60,30,-172,-58], x-1];
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E[17,2]=[[-1/18*x^2-5/9*x+11/3,x,-1/9*x^2+8/9*x+4/3,1/3*x^2-5/3*x-6,-10/9*x^2-19/9*x+136/3,-11/9*x^2+16/9*x+194/3,-17,-2*x^2-6*x+128,41/9*x^2+23/9*x-506/3,1/9*x^2+136/9*x-532/3,-47/9*x^2+25/9*x+950/3,53/9*x^2-172/9*x-392/3], x^3-4*x^2-62*x+204];
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E[17,3]=[[1/6*x^2+17/3,x,-1/6*x^3-23/3*x,1/6*x^3+20/3*x,7*x,-7/3*x^2-154/3,1/6*x^3+7/3*x^2-1/3*x+343/3,-28,-7/6*x^3-182/3*x,7/6*x^3+161/3*x,-1/6*x^3-44/3*x,-7/6*x^3-245/3*x], x^4+74*x^2+1072];
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E[17,4]=[[-7612499/15890298752*x^7+94276/372428877*x^6+50505/124142959*x^5+345159855/3972574688*x^4-185528256/124142959*x^3+8049443725/1489715508*x^2-19111193147/1986287344*x-347757255/124142959,x,150795/15890298752*x^7-130979/496571836*x^6-5065183/1489715508*x^5-63963119/3972574688*x^4+13132215/248285918*x^3-49626505/496571836*x^2-27831291079/5958862032*x-3002496/124142959,1623081/496571836*x^7+847973/372428877*x^6+1817085/496571836*x^5-222467795/372428877*x^4+2318031077/248285918*x^3-10098529939/372428877*x^2+5220365850/124142959*x+11198803648/372428877,-42688015/11917724064*x^7-342748/372428877*x^6-183615/124142959*x^5+1949347799/2979431016*x^4-3943059161/372428877*x^3+12691664837/372428877*x^2-26889944985/496571836*x-14366373560/372428877,-393050/372428877*x^7-421125/248285918*x^6+2403253/744857754*x^5+74897024/372428877*x^4-1026454766/372428877*x^3+637751205/124142959*x^2+1331787104/372428877*x-19909455796/372428877,60055889/11917724064*x^7+383704/372428877*x^6+20201377/1489715508*x^5-817122523/993143672*x^4+11337521009/744857754*x^3-18255468809/372428877*x^2+143988357733/1489715508*x+10754633261/124142959,-64357687/11917724064*x^7+7576757/1489715508*x^6+4152652/372428877*x^5+983162385/993143672*x^4-6410886464/372428877*x^3+24848881388/372428877*x^2-165024850463/1489715508*x-4003837860/124142959,-91818881/11917724064*x^7+237895/372428877*x^6+509775/496571836*x^5+4074693853/2979431016*x^4-17547903293/744857754*x^3+29184850786/372428877*x^2-62751687795/496571836*x-33450166504/372428877,-143492055/15890298752*x^7+2626775/1489715508*x^6-106620325/1489715508*x^5+16262593249/11917724064*x^4-6927020265/248285918*x^3+165431284007/1489715508*x^2-1780415659165/5958862032*x+8571258752/372428877,-85015035/3972574688*x^7+10077359/496571836*x^6+106225069/1489715508*x^5+4107968879/993143672*x^4-16776367875/248285918*x^3+32543101609/124142959*x^2-635285521073/1489715508*x+6770975232/124142959,266460375/15890298752*x^7-19568599/1489715508*x^6-27015857/1489715508*x^5-36780599777/11917724064*x^4+13083626985/248285918*x^3-306260646439/1489715508*x^2+2388255991645/5958862032*x-15916566400/372428877], x^8-180*x^5+3008*x^4-10080*x^3+16200*x^2+11520*x+4096];
45
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46
E[18,1]=[[1/3*x-1,x,3/2*x+9/2,-31/6*x+31/2,-5/2*x+15/2,37/6*x+37/2,-42,-28,-65/2*x-195/2,37/2*x-111/2,205/6*x+205/2,-166], x^2+27];
47
E[18,2]=[[-1/351*x^3-8/117*x^2+8/117*x+1/13,x,1/234*x^3+4/39*x^2-121/39*x+153/26,89/702*x^3+5/117*x^2+346/117*x-167/26,-19/78*x^3+2/13*x^2-80/13*x+327/26,-29/702*x^3-116/117*x^2+467/117*x-803/26,1/9*x^3-1/3*x^2+1/3*x-3,-5/9*x^3+5/3*x^2-5/3*x+89,-11/234*x^3-44/39*x^2+161/39*x-903/26,25/26*x^3+27/13*x^2+246/13*x-1221/26,-101/702*x^3-404/117*x^2+1457/117*x-2759/26,14/9*x^3-14/3*x^2+14/3*x+68], x^4-3*x^3+30*x^2-81*x+729];
48
E[18,3]=[[2,0,-6,-16,-12,38,126,20,-168,-30,-88,254], x-1];
49