Sharedwww / Tables / an_s8g0new_1-20.gpOpen in CoCalc
Author: William A. Stein
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\\ an_s8g0new_1-20.gp
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\\ This is a PARI readable nonnormalized basis for S_k(Gamma_0(N)) for N
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\\ in the range: 1 <= N <= 20.
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\\ The number of a_n computed is sufficient to satisfy Sturm's bound.
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\\ William Stein ([email protected])
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E[2,1] = [x, [1,-8]];
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E[3,1] = [x, [1,6]];
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E[5,1] = [x, [1,-14,-48,68]];
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E[5,2] = [x^2-20*x+24, [1,x,-8*x+90,20*x-152]];
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E[6,1] = [x, [1,8,27,64,-114,216,-1576,512]];
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E[7,1] = [x, [1,-6,-42,-92,-84]];
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E[7,2] = [x^2+3*x-214, [1,x,-2*x+44,-3*x+86,-10*x+150]];
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E[8,1] = [x, [1,0,-84,0,-82,0,-456,0]];
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E[8,2] = [x, [1,0,44,0,430,0,-1224,0]];
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E[9,1] = [x, [1,-6,0,-92,-390,0,-64,1320]];
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E[9,2] = [x^2-360, [1,x,0,232,-16*x,0,260,104*x]];
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E[10,1] = [x, [1,8,28,64,125,224,104,512,-1403,1000,-5148,1792]];
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E[11,1] = [x^2+8*x-44, [1,x,-6*x-27,-8*x-84,20*x-155,21*x-264,82*x-286,-148*x-352]];
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E[11,2] = [x^4-558*x^2+140*x+51744, [252,252*x,-x^3-70*x^2+698*x+17220,252*x^2-32256,27*x^3-126*x^2-9774*x+71820,-70*x^3+140*x^2+17360*x+51744,-18*x^3-1260*x^2-540*x+360360,252*x^3-64512*x]];
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E[12,1] = [x, [1,0,-27,0,-378,0,-832,0,729,0,-2484,0,14870,0,10206,0]];
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E[12,2] = [x, [1,0,27,0,270,0,1112,0,729,0,-5724,0,-4570,0,7290,0]];
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E[13,1] = [x, [1,10,-73,-28,-295,-730,1373,-1560,3142]];
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E[13,2] = [x^2+19*x+6, [1,x,-3*x-6,-19*x-134,11*x-72,51*x+18,-9*x-1090,99*x+114,-135*x-2205]];
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E[13,3] = [x^4-15*x^3-270*x^2+3264*x+12880, [4,4*x,-x^3-3*x^2+260*x+1112,4*x^2-512,13*x^3+15*x^2-3220*x-9168,-18*x^3-10*x^2+4376*x+12880,-3*x^3-25*x^2+684*x+8208,4*x^3-1024*x,-67*x^3-129*x^2+16556*x+62108]];
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E[14,1] = [x, [1,-8,-82,64,448,656,-343,-512,4537,-3584,2408,-5248,7116,2744,-36736,4096]];
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E[14,2] = [x, [1,8,-66,64,-400,-528,-343,512,2169,-3200,40,-4224,-4452,-2744,26400,4096]];
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E[14,3] = [x^2-70*x-744, [1,8,x,64,-9*x+378,8*x,343,512,70*x-1443,-72*x+3024,-126*x+2700,64*x,189*x-9814,2744,-252*x-6696,4096]];
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E[15,1] = [x, [1,-13,-27,41,-125,351,1380,1131,729,1625,-3304,-1107,8506,-17940,3375,-19951]];
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E[15,2] = [x, [1,-22,27,356,-125,-594,-420,-5016,729,2750,-2944,9612,-11006,9240,-3375,64784]];
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E[15,3] = [x^2-7*x-138, [1,x,27,7*x+10,125,27*x,-56*x+848,-69*x+966,729,125*x,-464*x+3348,189*x+270,824*x-7378,456*x-7728,3375,-413*x-10802]];
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E[16,1] = [x, [1,0,-12,0,-210,0,-1016,0,-2043,0,-1092,0,1382,0,2520,0]];
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E[16,2] = [x, [1,0,-44,0,430,0,1224,0,-251,0,3164,0,6118,0,-18920,0]];
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E[16,3] = [x, [1,0,84,0,-82,0,456,0,4869,0,2524,0,-10778,0,-6888,0]];
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E[17,1] = [x, [1,-2,18,-124,-10,-36,-902,504,-1863,20,-8634,-2232]];
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E[17,2] = [x^6-15*x^5-514*x^4+5312*x^3+83552*x^2-422208*x-4272768, [214848,214848*x,119*x^5-2237*x^4-39354*x^3+587296*x^2+3088656*x-23079744,214848*x^2-27500544,-234*x^5+2142*x^4+112140*x^3-1021248*x^2-7218144*x+101551104,-452*x^5+21812*x^4-44832*x^3-6854032*x^2+27163008*x+508459392,-459*x^5-14391*x^4+420354*x^3+6574176*x^2-64152144*x-528758208,214848*x^3-55001088*x,3042*x^5-27846*x^4-1457820*x^3+4682304*x^2+138524256*x+486492480,-1368*x^5-8136*x^4+221760*x^3+12333024*x^2+2754432*x-999827712,4959*x^5-30933*x^4-1911690*x^3-9807840*x^2+175429008*x+2536062912,-200*x^5+9176*x^4+584304*x^3-10245376*x^2-77726592*x+1022916096]];
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E[17,3] = [x^3-x^2-304*x+1692, [4,4*x,-x^2-17*x+94,4*x^2-512,8*x^2+24*x-1896,-18*x^2-210*x+1692,-35*x^2-259*x+5114,4*x^2+192*x-6768,110*x^2+1438*x-21344,32*x^2+536*x-13536,-119*x^2-743*x+31794,-100*x^2-1604*x+18424]];
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E[18,1] = [x, [1,-8,0,64,114,0,-1576,-512,0,-912,-7332,0,-3802,12608,0,4096,6606,0,24860,7296,0,58656,-41448,0]];
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E[18,2] = [x, [1,8,0,64,210,0,1016,512,0,1680,-1092,0,1382,8128,0,4096,-14706,0,-39940,13440,0,-8736,-68712,0]];
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E[19,1] = [x^4+9*x^3-234*x^2-396*x+3240, [72,72*x,-x^3-27*x^2-36*x+1908,72*x^2-9216,27*x^3+297*x^2-6084*x-18900,-18*x^3-270*x^2+1512*x+3240,-108*x^3-1044*x^2+21168*x+10296,72*x^3-18432*x,47*x^3+837*x^2-468*x-135252,54*x^3+234*x^2-8208*x-87480,207*x^3+3429*x^2-16308*x-361044,20*x^3+756*x^2+720*x-185904,-837*x^3-5319*x^2+195804*x-136044]];
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E[19,2] = [x^6-15*x^5-450*x^4+4650*x^3+64272*x^2-289800*x-1974784, [35136,35136*x,43*x^5-1235*x^4-4856*x^3+274750*x^2-193916*x-8240000,35136*x^2-4497408,98*x^5-2338*x^4-11680*x^3+378452*x^2-128584*x+2840000,-590*x^5+14494*x^4+74800*x^3-2957612*x^2+4221400*x+84915712,211*x^5-2315*x^4-58760*x^3+204910*x^2+3277444*x+28292800,35136*x^3-8994816*x,675*x^5-25515*x^4+32040*x^3+5570478*x^2-23034780*x-127295424,-868*x^5+32420*x^4-77248*x^3-6427240*x^2+31240400*x+193528832,190*x^5+5506*x^4-316640*x^3-267284*x^2+45140680*x+50802880,140*x^5-32620*x^4+407456*x^3+6973880*x^2-61245040*x-110402560,4955*x^5-173635*x^4+173384*x^3+35089310*x^2-147944380*x-753018880]];
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E[20,1] = [x, [1,0,-6,0,-125,0,-706,0,-2151,0,-3840,0,-4054,0,750,0,858,0,21044,0,4236,0,85338,0]];
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E[20,2] = [x^2+20*x-4416, [1,0,x,0,125,0,-9*x+740,0,-20*x+2229,0,90*x+2700,0,-36*x+6230,0,125*x,0,-468*x-1950,0,-180*x-22036,0,920*x-39744,0,-63*x-21540,0]];
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