Sharedwww / tables / ap_s3g1new_1-15.gpOpen in CoCalc
Author: William A. Stein
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\\ ap_s3g1new_1-15.gp
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\\ This is a table of eigenforms for the action of
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\\ the Hecke operators on S_3^{new}(Gamma_1(N)).
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\\ William Stein ([email protected]), October, 1998.
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\\ 7<=N<=15
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\\ E=matrix(15,?,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[7,1]=[[-3,0,0,-7,-6,0,0,0,18,-54,0,-38], x-1];
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E[8,1]=[[-2,-2,0,0,14,0,2,-34,0,0,0,0], x-1];
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E[9,1]=[[x,-3*x-6,2*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];
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E[10,1]=[[x,-2*x-4,5*x+5,-2*x,-8,3*x+6,-7*x,20*x+20,-2*x-4,-40*x-40,52,3*x], x^2+2*x+2];
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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+420/11,3*x^3+10*x^2+26*x+4,8/11*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];
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E[11,2]=[[0,-5,-1,0,-11,0,0,0,35,0,-37,-25], x-1];
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E[12,1]=[[x,-x-1,-2,4*x+4,-4*x-4,2,10,-12*x-12,16*x+16,-26,-4*x-4,26], x^2+2*x+4];
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E[12,2]=[[0,-3,0,2,0,-22,0,26,0,0,-46,26], x-1];
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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-68,26*x^3+39*x^2+104*x+39,19*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];
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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,-16/21*x^3-109/21*x^2-281/21*x+11/7,16/7*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];
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E[14,1]=[[x,1/2*x^3-1/2*x^2-x-2,-2*x^3+1/2*x^2-2*x-1,5/2*x^3+x^2+4*x+3,-3/2*x^3-9/2*x^2-3*x,-x^3+6*x^2-4*x+6,x^3-5/2*x^2-2*x-10,x^3-1/2*x^2+x+1,15/2*x^2-9*x+15,-3*x^3+12,-15/2*x^3-7/2*x^2+15*x-14,-31/2*x^2-24*x-31], x^4+2*x^2+4];
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E[15,1]=[[1,-3,5,0,0,0,-14,-22,34,0,2,0], x-1];
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E[15,2]=[[-1,3,-5,0,0,0,14,-22,-34,0,2,0], x-1];
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E[15,3]=[[x,-x-2,-x,-6,-2*x,16,-2*x,-2,-6*x,14*x,-18,-16], x^2+5];
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E[15,4]=[[x,3/5*x^3+11/5*x^2+22/5*x-11/5,x^3+4*x^2+6*x-6,6/5*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];
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