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\\ ap_s2g1new_1-20.gp
\\ This is a table of eigenforms for the action of 
\\ the Hecke operators on S_2^{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_97],  f(x)]
\\ where the a_i are defined over Q[x]/f(x).

E[11,1]=[[-2,-1,1,-2,1,4,-2,0,-1,0,7,3,-8,-6,8,-6,5,12,-7,-3,4,-10,-6,15,-7], x-1];
E[13,1]=[[x,-2*x-4,2*x+3,0,0,3*x+2,-3*x-3,-2*x-6,6*x+12,-3*x-6,-4*x-6,-5*x,3*x,8*x+8,4*x+6,-3,4*x+12,x+1,-2*x,2*x+6,-2*x-3,4,-16*x-24,4*x,4*x+12], x^2+3*x+3];
E[14,1]=[[-1,-2,0,1,0,-4,6,2,0,-6,-4,2,6,8,-12,6,-6,8,-4,0,2,8,-6,-6,-10], x-1];
E[15,1]=[[-1,-1,1,0,-4,-2,2,4,0,-2,0,-10,10,4,8,-10,-4,-2,12,-8,10,0,12,-6,2], x-1];
E[16,1]=[[x,-x-2,x,2*x+2,-x,-x-2,-2,3*x+6,-6*x-6,3*x+6,-8,-3*x,0,-5*x,8,5*x,3*x,-9*x-18,-5*x-10,10*x+10,4*x+4,0,-x-2,-4*x-4,-2], x^2+2*x+2];
E[17,1]=[[-1,0,-2,4,0,-2,1,-4,4,6,4,-2,-6,4,0,6,-12,-10,4,-4,-6,12,-4,10,2], x-1];
E[17,2]=[[x,-1/3*x^3-5/3*x^2-13/3*x-11/3,-4/3*x^3-14/3*x^2-25/3*x-5/3,1/3*x^3+5/3*x^2+13/3*x+5/3,1/3*x^3+5/3*x^2+7/3*x-1/3,-x^3-4*x^2-7*x-2,8/3*x^3+25/3*x^2+44/3*x+4/3,-8/3*x^3-28/3*x^2-50/3*x-4/3,-5/3*x^3-13/3*x^2-23/3*x+5/3,3*x^3+11*x^2+20*x+4,-x^3-5*x^2-7*x-5,-5*x-5,-14/3*x^3-55/3*x^2-107/3*x-40/3,-2*x^3-8*x^2-16*x-8,22/3*x^3+80/3*x^2+154/3*x+44/3,2/3*x^3+7/3*x^2+14/3*x+1/3,-2*x^3-10*x^2-20*x-10,5*x^3+20*x^2+40*x+15,-2/3*x^3-4/3*x^2-2/3*x+20/3,5/3*x^3+25/3*x^2+65/3*x+55/3,7/3*x^3+35/3*x^2+70/3*x+14/3,5/3*x^3+13/3*x^2+23/3*x-5/3,4/3*x^3+14/3*x^2+10/3*x+2/3,-19/3*x^3-68/3*x^2-133/3*x-38/3,-10/3*x^3-44/3*x^2-85/3*x-17/3], x^4+4*x^3+8*x^2+4*x+1];
E[18,1]=[[x,-x-2,0,2*x,-3*x,-2*x-2,-3,-1,6*x+6,6*x,4*x+4,-4,-9*x-9,-x,-6*x,12,-3*x-3,8*x,-5*x-5,-12,11,-4*x,12*x,6,5*x], x^2+x+1];
E[19,1]=[[x,-1/9*x^5-1/3*x^4-1/3*x^3+1/3*x^2-x-1,-2/3*x^5-11/3*x^4-10*x^3-14*x^2-15*x-9,2/3*x^5+11/3*x^4+10*x^3+14*x^2+15*x+8,4/3*x^5+20/3*x^4+17*x^3+21*x^2+22*x+9,-19/9*x^5-11*x^4-89/3*x^3-125/3*x^2-46*x-23,1/3*x^5+4/3*x^4+3*x^3+3*x^2+3*x,4/3*x^5+7*x^4+58/3*x^3+27*x^2+30*x+12,-2/3*x^5-10/3*x^4-26/3*x^3-12*x^2-12*x-4,x^5+6*x^4+49/3*x^3+23*x^2+20*x+11,-x^5-6*x^4-17*x^3-24*x^2-22*x-10,-1/3*x^4-7/3*x^3-6*x^2-6*x-3,5/3*x^5+8*x^4+21*x^3+27*x^2+31*x+15,13/9*x^5+8*x^4+22*x^3+101/3*x^2+36*x+20,1/3*x^5+2*x^4+16/3*x^3+6*x^2+2*x-1,5/3*x^5+23/3*x^4+55/3*x^3+21*x^2+24*x+8,-2*x^5-9*x^4-21*x^3-21*x^2-20*x,-10/9*x^5-13/3*x^4-25/3*x^3-17/3*x^2-9*x-3,-22/9*x^5-44/3*x^4-42*x^3-188/3*x^2-62*x-40,-10/3*x^5-58/3*x^4-56*x^3-86*x^2-94*x-54,28/9*x^5+16*x^4+124/3*x^3+164/3*x^2+60*x+28,31/9*x^5+19*x^4+154/3*x^3+215/3*x^2+72*x+31,-2*x^5-11*x^4-30*x^3-42*x^2-36*x-15,-4/3*x^5-20/3*x^4-47/3*x^3-16*x^2-14*x-7,4/9*x^5+7/3*x^4+17/3*x^3+17/3*x^2], x^6+6*x^5+18*x^4+30*x^3+36*x^2+27*x+9];
E[19,2]=[[0,-2,3,-1,3,-4,-3,1,0,6,-4,2,-6,-1,-3,12,-6,-1,-4,6,-7,8,12,12,8], x-1];
E[20,1]=[[x,0,-x-3,0,0,-x-2,-3*x,0,0,-4*x-4,0,7*x,-8,0,0,9*x+18,0,12,0,0,-11*x-22,0,0,16*x+16,-13*x], x^2+2*x+2];
E[20,2]=[[0,-2,-1,2,0,2,-6,-4,6,6,-4,2,6,-10,-6,-6,12,2,2,-12,2,8,6,-6,2], x-1];