Sharedwww / Tables / ap_s3g1new_1-19.gpOpen in CoCalc
\\ ap_s3g1new_1-19.gp
\\ This is a table of eigenforms for the action of 
\\ the Hecke operators on S_3^{new}(Gamma_1(N)).
\\ William Stein ([email protected]), October, 1998.
\\ 1<=N<=20
\\ E=matrix(20,?,i,j,0);
\\ E[N,ith eigenform]=[[a_2,...,a_37],  f(x)]
\\ where the a_i are defined over Q[x]/f(x).
\\ If p|N, a_p is replaced by the W(p) eigenvalue.

E[7,1]=[[-3,0,0,0,-6,0,0,0,18,-54,0,-38],	x-1];
E[8,1]=[[0,-2,0,0,14,0,2,-34,0,0,0,0],	x-1];
E[9,1]=[[x,0,2*x+6,-2*x-4,x,-4*x-4,18*x+27,11,-16*x-48,-26*x,32*x+32,-34],	x^2+3*x+3];
E[10,1]=[[0,x,0,x+4,-8,-3/2*x,7/2*x+14,-10*x-20,x,20*x+40,52,-3/2*x-6],	x^2+4*x+8];
E[11,1]=[[x,-3/11*x^3-14/11*x^2-5*x-45/11,-28/11*x^3-116/11*x^2-28*x-156/11,50/11*x^3+226/11*x^2+58*x+420/11,0,8/11*x^3+30/11*x^2+10*x+10/11,26/11*x^3+169/11*x^2+39*x+390/11,-8/11*x^3-52/11*x^2-13*x-65/11,-2/11*x^3-2/11*x^2-30/11,-146/11*x^3-652/11*x^2-166*x-1200/11,-48/11*x^3-158/11*x^2-44*x-302/11,-180/11*x^3-774/11*x^2-180*x-720/11],	x^4+5*x^3+15*x^2+15*x+5];
E[11,2]=[[0,-5,-1,0,0,0,0,0,35,0,-37,-25],	x-1];
E[12,1]=[[0,0,0,2,0,-22,0,26,0,0,-46,26],	x-1];
E[12,2]=[[0,0,-2,x,-x,2,10,-3*x,4*x,-26,-x,26],	x^2+48];
E[13,1]=[[x,-x^3-x^2-5*x-2,-5*x^3-7*x^2-23*x-13,2*x^3+4*x^2+14*x+12,-34*x^3-54*x^2-146*x-68,0,19*x^3+21*x^2+76*x+19,-13*x^3-20*x^2-56*x-23,21*x^3+39*x^2+99*x+60,16*x^3+21*x^2+70*x+27,-26*x^3-43*x^2-113*x-61,67*x^3+115*x^2+292*x+134],	x^4+2*x^3+5*x^2+4*x+1];
E[13,2]=[[x,1/7*x^3+2/7*x^2-3/7*x-27/7,2/7*x^3+11/7*x^2+29/7*x+9/7,11/21*x^3+50/21*x^2+100/21*x-50/7,-6/7*x^3-19/7*x^2-38/7*x+57/7,0,16/7*x^3+67/7*x^2+176/7*x-96/7,4/21*x^3+22/21*x^2+86/21*x+6/7,5/7*x^3+38/7*x^2+55/7*x-30/7,5/7*x^3+10/7*x^2-15/7*x-30/7,8/21*x^3+44/21*x^2-38/21*x+12/7,-65/21*x^3-263/21*x^2-526/21*x+263/7],	x^4+4*x^3+8*x^2-12*x+9];
E[14,1]=[[0,x,4/7*x^3+23/7*x^2+32/7*x-66/7,0,-2/7*x^3-22/7*x^2-51/7*x+54/7,38/21*x^3+88/7*x^2+176/7*x-132/7,-2/7*x^3-15/7*x^2-16/7*x-9/7,-1/3*x^3-2*x^2-3*x+6,19/7*x^3+132/7*x^2+285/7*x-114/7,2/7*x^3+8/7*x^2-12/7*x+30/7,-44/21*x^3-110/7*x^2-325/7*x-66/7,10/21*x^3-3/7*x^2+50/7*x-20/7],	x^4+6*x^3+9*x^2-18*x+9];
E[15,1]=[[1,0,0,0,0,0,-14,-22,34,0,2,0],	x-1];
E[15,2]=[[-1,0,0,0,0,0,14,-22,-34,0,2,0],	x-1];
E[15,3]=[[x,0,0,-6,-2*x,16,-2*x,-2,-6*x,14*x,-18,-16],	x^2+5];
E[15,4]=[[x,0,0,6/5*x^3+27/5*x^2+64/5*x+3/5,-3/5*x^3-6/5*x^2+3/5*x+56/5,2*x^3+10*x^2+20*x-10,-32/5*x^3-144/5*x^2-318/5*x-16/5,18/5*x^3+66/5*x^2+162/5*x-36/5,-22/5*x^3-104/5*x^2-208/5*x+104/5,71/5*x^3+302/5*x^2+639/5*x-142/5,-6/5*x^3-12/5*x^2+6/5*x+52/5,-4/5*x^3-18/5*x^2-126/5*x-2/5],	x^4+4*x^3+8*x^2-4*x+1];
E[16,1]=[[0,x,53/352*x^5+63/176*x^4+9/22*x^3-54/11*x^2+2341/88*x-9/44,-1/88*x^5-17/176*x^4-2/11*x^3+2/11*x^2-1/22*x-425/44,-35/176*x^5-61/176*x^4-2/11*x^3+79/11*x^2-1751/44*x+499/44,81/352*x^5+83/176*x^4+15/22*x^3-79/11*x^2+3953/88*x-565/44,-5/176*x^5-13/88*x^4-5/11*x^3+5/11*x^2-5/44*x-149/22,23/44*x^5+105/88*x^4+15/11*x^3-180/11*x^2+1068/11*x-15/22,1/44*x^5+23/176*x^4+4/11*x^3-4/11*x^2+1/11*x+751/44,-63/352*x^5-67/176*x^4-19/22*x^3+59/11*x^2-3055/88*x+437/44,15/88*x^5+17/44*x^4+8/11*x^3-30/11*x^2+807/22*x-59/11,-239/352*x^5-287/176*x^4-41/22*x^3+246/11*x^2-11503/88*x+41/44],	x^6+2*x^5+2*x^4-32*x^3+196*x^2-56*x+8];
E[16,2]=[[0,0,-6,0,0,10,-30,0,0,42,0,-70],	x-1];
E[17,1]=[[x,29324/37927*x^7+6819/37927*x^6+123684/37927*x^5+29248/2231*x^4+374111/37927*x^3-79196/37927*x^2+32225/2231*x-107109/37927,-15/97*x^7+34/97*x^6-53/97*x^5-94/97*x^4+397/97*x^3+604/97*x^2-518/97*x+59/97,96691/37927*x^7+7762/37927*x^6+384619/37927*x^5+92682/2231*x^4+898580/37927*x^3-777545/37927*x^2+108608/2231*x-600689/37927,64054/37927*x^7+36673/37927*x^6+263501/37927*x^5+68210/2231*x^4+1143047/37927*x^3-164342/37927*x^2+56536/2231*x+281315/37927,106042/37927*x^7-14714/37927*x^6+420123/37927*x^5+97317/2231*x^4+628237/37927*x^3-976588/37927*x^2+145796/2231*x-699569/37927,0,-126231/37927*x^7-37643/37927*x^6-535004/37927*x^5-130581/2231*x^4-1772383/37927*x^3+94987/37927*x^2-213288/2231*x-54335/37927,710780/37927*x^7+113591/37927*x^6+2848821/37927*x^5+696942/2231*x^4+7554013/37927*x^3-4612918/37927*x^2+815512/2231*x-3099571/37927,-703266/37927*x^7-107097/37927*x^6-2849535/37927*x^5-688281/2231*x^4-7470135/37927*x^3+4198662/37927*x^2-822513/2231*x+3717963/37927,-114366/37927*x^7-59299/37927*x^6-472129/37927*x^5-116667/2231*x^4-1941201/37927*x^3+752996/37927*x^2-51868/2231*x+570236/37927,195663/37927*x^7+101385/37927*x^6+845592/37927*x^5+211639/2231*x^4+3430901/37927*x^3+390301/37927*x^2+252559/2231*x-872486/37927],	x^8+4*x^6+16*x^5+8*x^4-8*x^3+20*x^2-8*x+1];
E[17,2]=[[x,22439534/21892069583*x^7+239238237/21892069583*x^6+1257644857/21892069583*x^5+3084953944/21892069583*x^4+4499411978/21892069583*x^3-4459221110/21892069583*x^2-16388067342/21892069583*x-1057840936/706195793,-126674912/21892069583*x^7-1286719724/21892069583*x^6-5471494094/21892069583*x^5-10774347192/21892069583*x^4-3245758000/21892069583*x^3+24881595350/21892069583*x^2+13369744260/21892069583*x-1280002988/706195793,-136937775/21892069583*x^7-582317381/21892069583*x^6+592816175/21892069583*x^5+8594768203/21892069583*x^4+29880519191/21892069583*x^3+58679069841/21892069583*x^2-8000389837/21892069583*x+476735943/706195793,3929160/225691439*x^7+20388910/225691439*x^6+55249164/225691439*x^5+108838891/225691439*x^4+156537358/225691439*x^3+193018350/225691439*x^2+1180332329/225691439*x-64663256/7280369,-619842170/21892069583*x^7-4647589120/21892069583*x^6-18946823062/21892069583*x^5-45759586858/21892069583*x^4-63871800814/21892069583*x^3-1199928496/21892069583*x^2+48676299394/21892069583*x+9673856798/706195793,0,832406749/21892069583*x^7+5284186682/21892069583*x^6+14214721264/21892069583*x^5+13141623978/21892069583*x^4-30750047861/21892069583*x^3-99392345438/21892069583*x^2+120132443730/21892069583*x+889134746/706195793,433532347/21892069583*x^7+4052532733/21892069583*x^6+16058640907/21892069583*x^5+31012994059/21892069583*x^4-2097488773/21892069583*x^3-141083839517/21892069583*x^2-215236638765/21892069583*x-2775673967/706195793,-327218038/21892069583*x^7+377872248/21892069583*x^6+8166950478/21892069583*x^5+34647180572/21892069583*x^4+57273947168/21892069583*x^3+22955180566/21892069583*x^2-183884054344/21892069583*x+14813850594/706195793,84186487/21892069583*x^7+758294473/21892069583*x^6+6099265969/21892069583*x^5+23572574043/21892069583*x^4+49918040447/21892069583*x^3+64186344983/21892069583*x^2+8837516153/21892069583*x-2080108537/706195793,986198446/21892069583*x^7+4376771418/21892069583*x^6+3371423138/21892069583*x^5-21338855302/21892069583*x^4-81862990214/21892069583*x^3-81138252988/21892069583*x^2+454917261204/21892069583*x+1956466102/706195793],	x^8+8*x^7+32*x^6+72*x^5+64*x^4-120*x^3-192*x^2-248*x+961];
E[18,1]=[[0,0,-1/4*x,-4,x,8,-3/4*x,-16,-x,1/4*x,44,-34],	x^2+288];
E[18,2]=[[0,0,2/27*x^3-11/9*x^2+22/3*x-10,-14/81*x^3+86/27*x^2-181/9*x+58/3,x,20/81*x^3-119/27*x^2+220/9*x-40/3,-14/27*x^3+80/9*x^2-160/3*x+40,-2/27*x^3+8/9*x^2-4/3*x-24,-1/27*x^3+4/9*x^2-5/3*x+2,2/9*x^3-11/3*x^2+20*x-3,-7/81*x^3+52/27*x^2-77/9*x+14/3,2/27*x^3-8/9*x^2+4/3*x+46],	x^4-18*x^3+117*x^2-162*x+81];
E[19,1]=[[x,-x,4,-5,-10,x,15,0,35,5*x,-10*x,-6*x],	x^2+13];
E[19,2]=[[x,-67/1114*x^5-83/1114*x^4+489/1114*x^3+313/1114*x^2-4869/1114*x-135/1114,-113/1114*x^5-273/1114*x^4+991/1114*x^3+2573/1114*x^2-6915/1114*x-6363/1114,-53/1114*x^5-170/557*x^4-245/1114*x^3+1084/557*x^2+2583/1114*x-4048/557,43/1114*x^5+222/557*x^4+451/1114*x^3-1468/557*x^2-3609/1114*x+9159/557,328/1671*x^5+274/557*x^4-964/1671*x^3-1852/557*x^2+10036/1671*x+5358/557,-276/557*x^5-583/557*x^4+1898/557*x^3+5762/557*x^2-15061/557*x-13974/557,0,-121/557*x^5-491/1114*x^4+933/557*x^3+4697/1114*x^2-5285/557*x-4503/1114,-641/557*x^5-4157/1114*x^4+2176/557*x^3+27313/1114*x^2-23546/557*x-76581/1114,6221/3342*x^5+2325/557*x^4-36359/3342*x^3-20297/557*x^2+323681/3342*x+36195/557,-4499/3342*x^5-1745/557*x^4+22943/3342*x^3+14043/557*x^2-232559/3342*x-25890/557],	x^6+3*x^5-4*x^4-21*x^3+40*x^2+63*x+27];
E[19,3]=[[x,687532106182/126986230663847*x^11+3993392645975/126986230663847*x^10+11511966621985/126986230663847*x^9+23395972570737/126986230663847*x^8+23670166065275/126986230663847*x^7+22700952718220/126986230663847*x^6+29073300949132/126986230663847*x^5-95616497891/126103506121*x^4-91755560144671/126986230663847*x^3-186298214500061/126986230663847*x^2+916081720534552/126986230663847*x-34266789256809/6683485824413,-1575029289010/126986230663847*x^11-9387727754308/126986230663847*x^10-27541689357157/126986230663847*x^9-2952420916572/6683485824413*x^8-56779457495866/126986230663847*x^7-47463489071911/126986230663847*x^6-45712774579184/126986230663847*x^5+5120537404956/2395966616299*x^4+370803867918775/126986230663847*x^3+645870976687596/126986230663847*x^2-2166254330356600/126986230663847*x+59808627798150/6683485824413,236269581517/126986230663847*x^11-534619517101/126986230663847*x^10-9755324907663/126986230663847*x^9-41047898719754/126986230663847*x^8-113354032575133/126986230663847*x^7-187024691410281/126986230663847*x^6-243486672404398/126986230663847*x^5-6401258999285/2395966616299*x^4+12889463916153/126986230663847*x^3+480929817313005/126986230663847*x^2+1518482569756366/126986230663847*x-75620180219996/6683485824413,-7828309404970/126986230663847*x^11-52702232935704/126986230663847*x^10-179097251867073/126986230663847*x^9-434415333166859/126986230663847*x^8-691639483940962/126986230663847*x^7-50614276443057/6683485824413*x^6-1340798707554744/126986230663847*x^5-2640310194123/2395966616299*x^4+1174368176182293/126986230663847*x^3+3793514670603756/126986230663847*x^2-5604796985424275/126986230663847*x+162940524134610/6683485824413,4002354533461/126986230663847*x^11+27293877944009/126986230663847*x^10+95193038926560/126986230663847*x^9+237367640875345/126986230663847*x^8+398569729031002/126986230663847*x^7+603305217457492/126986230663847*x^6+888328832166555/126986230663847*x^5+7913614226450/2395966616299*x^4-206491669717572/126986230663847*x^3-1740559594872832/126986230663847*x^2+3712795240784467/126986230663847*x-83681972351676/6683485824413,-8654751419672/126986230663847*x^11-60709877922965/126986230663847*x^10-218710203859078/126986230663847*x^9-562334314280730/126986230663847*x^8-974908185946267/126986230663847*x^7-1431639606629037/126986230663847*x^6-1942053047791560/126986230663847*x^5-717479435177/126103506121*x^4+835584416007887/126986230663847*x^3+4742166252213516/126986230663847*x^2-5016561921476043/126986230663847*x+128963483591477/6683485824413,0,342088613310/126986230663847*x^11+236918629180/6683485824413*x^10+24603031941680/126986230663847*x^9+72301996335302/126986230663847*x^8+129600956284110/126986230663847*x^7+130296207131936/126986230663847*x^6-35282373434470/126986230663847*x^5-6724385841240/2395966616299*x^4-1144196406395530/126986230663847*x^3-2737175834201526/126986230663847*x^2-90996361669952/6683485824413*x+26630108976050/6683485824413,-7855220949523/126986230663847*x^11-2579625313770/6683485824413*x^10-151272670824778/126986230663847*x^9-333585601495174/126986230663847*x^8-438174736476872/126986230663847*x^7-524988477842255/126986230663847*x^6-701602266177344/126986230663847*x^5+15201505006494/2395966616299*x^4+1618606268314049/126986230663847*x^3+2972403367413459/126986230663847*x^2-7975879662422376/126986230663847*x+363201922179131/6683485824413,-21335353699640/126986230663847*x^11-145402420526964/126986230663847*x^10-502035892547698/126986230663847*x^9-1231963256000701/126986230663847*x^8-1988642442020542/126986230663847*x^7-2737210276250786/126986230663847*x^6-190446785737347/6683485824413*x^5-126580856674/126103506121*x^4+3989416852208052/126986230663847*x^3+11541969852678953/126986230663847*x^2-14561386004881360/126986230663847*x+467436254854074/6683485824413,11977157229458/126986230663847*x^11+90482379497876/126986230663847*x^10+350265043736055/126986230663847*x^9+959770256359738/126986230663847*x^8+1851318631890042/126986230663847*x^7+2920577432570912/126986230663847*x^6+4096425076684252/126986230663847*x^5+52662206213880/2395966616299*x^4-467976099220750/126986230663847*x^3-6907842408209180/126986230663847*x^2+3403504863833502/126986230663847*x-96495262860239/6683485824413],	x^12+6*x^11+18*x^10+39*x^9+48*x^8+57*x^7+74*x^6-120*x^5-171*x^4-381*x^3+1110*x^2-969*x+361];
E[19,4]=[[0,0,-9,-5,3,0,15,0,-30,0,0,0],	x-1];