sym4wt12

N=500;

aa=vector(N,j,0);

a4=vector(N,j,0);

b=vector(N+1,j,0);

c=vector(N+1,j,0);

k=12;

aa[1]=1;

b[1]=1;

c[1]=1;

{for(i=1,N,

b[i+1]=240*sigma(i,3);

c[i+1]=-504*sigma(i,5););}

{for(i=2,N,

t=0;

r=1;

while(i>(3*r^2+r)/2,

t=t+(-1)^(r+1)*(i-1-75*r^2/2-25*r/2)*aa[i-(3*r^2+r)/2];

r=r+1;);

r=1;

while(i>(3*r^2-r)/2,

t=t+(-1)^(r+1)*(i-1-75*r^2/2+25*r/2)*aa[i-(3*r^2-r)/2];

r=r+1;);

aa[i]=t/(i-1););}

a4[1]=1;

{forprime(p=1,N,

c1=aa[p]^4-3*p^(k-1)*aa[p]^2+p^(2*k-2);

c2=p^(k-1)*(aa[p]^6-5*p^(k-1)*aa[p]^4+7*p^(2*k-2)*aa[p]^2-2*p^(3*k-3));

c3=p^(2*k-2)*c2;

c4=p^(6*k-6)*c1;

c5=p^(10*k-10);

a4[p]=c1*a4[1];

if(p^2<N+1, a4[p^2]=c1*a4[p]-c2*a4[1];);

if(p^3<N+1, a4[p^3]=c1*a4[p^2]-c2*a4[p]+c3*a4[1];);

if(p^4<N+1, a4[p^4]=c1*a4[p^3]-c2*a4[p^2]+c3*a4[p]-c4*a4[1];);

r=5;

while(p^r<N+1, a4[p^r]=c1*a4[p^(r-1)]-c2*a4[p^(r-2)]+c3*a4[p^(r-3)]-c4*a4[p^(r-4)]+c5*a4[p^(r-5)]; r=r+1;););}

{for(n=2,N, b=1;

for(j=1,omega(n), b=b*a4[factor(n)[j,1]^(factor(n)[j,2])];);

a4[n]=b;);}

\p30;

read("computel");

conductor=1;

weight=4*k-3;

sgn=1;

gammaV=[0,1,1-k,2-k,2-2*k];

initLdata("a4[k]");

L(28)/((2*Pi)^6*L(26))