\\ orthogonal modular forms of level 79 * 5^2
N = 79 * 5^2;

Q = [2,1,0,0,0; 1,2,0,0,5; 0,0,2,0,5; 0,0,0,4,5; 0,5,5,5,200];

print("Q(x0, x1, x2, x3, x4)", " = ", qfeval(Q,[x0,x1,x2,x3,x4])/2);

\r omf.gp
print();
print1("Computing V ... "); gettime(); t=getwalltime();
omf = omf_init(Q);
printf("Time: CPU %.2f s, Wall: %.2f s\n", gettime()/1000., (getwalltime()-t)/1000.);

print1("Computing T₂ ... "); gettime(); t=getwalltime();
T2 = omf_tp1(omf, 2);
printf("Time: CPU %.2f s, Wall: %.2f s\n", gettime()/1000., (getwalltime()-t)/1000.);

\\ ambient space
V = matker(0*T2);

\\ F_79
print1("Computing V₁ = ker(T₂+5) ... "); gettime(); t=getwalltime();
V1 = matker(T2+5);
printf("Time: CPU %.2f s, Wall: %.2f s\n", gettime()/1000., (getwalltime()-t)/1000.);

\\ JR(h_79)
print1("Computing V₂ = ker(T₂) ... "); gettime(); t=getwalltime();
V2 = matker(T2);
printf("Time: CPU %.2f s, Wall: %.2f s\n", gettime()/1000., (getwalltime()-t)/1000.);

\\ the intersection mod 5
V1mod5 = V1*Mod(1,5);
V2mod5 = V2*Mod(1,5);
V12mod5 = matintersect(V1mod5, V2mod5);

print();
print("Lemma 2.1.");
print("  (1) The dimension of V is ", #V);
print("  (2) The dimension of V₁ is ", #V1);
print("  (3) The dimension of V₂ is ", #V2);
print("  (4) The dimension of V₁⊗𝔽₅ ∩ V₂⊗𝔽₅ is ", #V12mod5);
print();