D = mfDelta(); V = mfcoefs(D, 8) Ser(V,q) E4 = mfEk(4); E6 = mfEk(6); apply(x->mfcoefs(x,4),[E4,E6]) E43 = mfpow(E4, 3); E62 = mfpow(E6, 2); DP = mflinear([E43, E62], [1, -1]/1728); mfcoefs(DP, 6) mfisequal(D, DP) F = mfetaquo([1,2;11,2]); mfcoefs(F,10) G = mffromell(ellinit("11a1"))[2]; mfisequal(F, G) mf = mfinit([1,12]); L = mfbasis(mf); #L mfcoefs(L[1],6) mfcoefs(L[2],6) mf = mfinit([1,12], 1); L = mfbasis(mf); #L mfdim(mf) mfcoefs(L[1],6) mf = mfinit([35,2], 0); L = mfbasis(mf); #L for (i = 1, 3, print(mfcoefs(L[i], 10))) mf = mfsplit(mf); mffields(mf) L = mfeigenbasis(mf); #L mfcoefs(L[1],10) mfcoefs(L[2],4) lift(mfcoefs(L[2],10)) F=mfembed(L[2]);for(i=1,2,print(mfcoefs(F[i],5))) [mf,F,co] = mffromell(ellinit("35a1")); mfcoefs(F, 10) mfisequal(F, L[1]) apply(x->mfdim([96, 2], x), [0..4]) mf = mfinit([96,2]); L = mfbasis(mf); for (i = 12, 15, print(mfcoefs(L[i], 18))) F = mflinear([L[14],L[12]],[1,-1]); mfcoefs(F, 50) G = mfhecke(F, 24); mfcoefs(G, 12) mftobasis(mf, G) 24*mfcoefs(L[5], 12) mf=mfsplit([96,2]);mffields(mf) L = mfeigenbasis(mf); for(i = 1, 2, print(mfcoefs(L[i], 16))) Fa = mffromell(ellinit("96a1"))[2]; mfcoefs(Fa, 16) Fb = mffromell(ellinit("96b1"))[2]; mfcoefs(Fb, 16) mfisequal(mftwist(Fa, -4), Fb) mf = mfsplit([35,2,5]); mffields(mf) F = mfeigenbasis(mf)[1]; lift(mfcoefs(F, 10)) mf = mfinit([23,1,-23], 0); mfdim(mf) F = mfbasis(mf)[1]; mfcoefs(F, 16) mfgaloistype(mf,F) F1 = mffromqf([2,1;1,12])[2]; V1 = mfcoefs(F1, 16) F2 = mffromqf([4,1;1,6])[2]; V2 = mfcoefs(F2, 16) (V1 - V2)/2 mfisequal(F, mflinear([F1, F2], [1, -1]/2)) G = znstar(23, 1); L = [[G,chi] | chi<-znchargalois(G), zncharisodd(G,chi)]; #L apply(x->mfdim([23,1,x], 0), L) apply(x->charorder(x[1],x[2]), L) mfa = mfinit([23,1,0], 0); #mfa mf = mfa[1]; mfdim(mf) mfparams(mf) wt1exp(lim1,lim2)= { my(mfall,mf,chi,chiz,ord,M,res,V); for(N=lim1,lim2, mfall=mfinit([N,1,0], 0); /* Use wildcard, more efficient */ for(i=1,#mfall, mf=mfsplit(mfall[i]); chi=mfparams(mf)[3]; /* nice format: D or Mod(a,N) */ chiz=znchar(chi); /* necessary to use charorder */ ord=charorder(chiz[1],chiz[2]); M=mfeigenbasis(mf); for(k=1,#M, res=mfgaloistype(mf,M[k]); if(res<0,print([N,chi,k,ord,-res])) ) ) ); } wt1exp(1,230) wt1exp(633,633) mf=mfsplit([96,6]); mffields(mf) mfatkineigenvalues(mf,3) mf=mfsplit([96,3,-3]); mffields(mf) mfatkineigenvalues(mf,3) mfatkineigenvalues(mf,32) mf = mfinit([96,2], 1); L = mfbasis(mf); apply(x->mfconductor(mf,x), L) mf = mfsplit([35,2]); L=mfbasis(mf); for (i=1,#L,print(mfcoefs(L[i],16))) for (i=1,#L,print(mfcuspexpansion(mf,L[i],1/5,16))); C = mfcusps(108) apply(x->mfcuspwidth(108,x), C) NK = [108,3,-4]; apply(x->mfcuspisregular(NK,x), C) [c | c<-C, !mfcuspisregular(NK,c)] E4 = mfEk(4); G = mfderivE2(E4); mfcoefs(G, 6) mfcoefs(mfEk(6), 6)/(-3) F = mfderivE2(E4, 3); (-9)*mfcoefs(F, 6) mfisequal(mfEk(10), mflinear([F],[-9])) E4 = mfEk(4); mfeval(E4,I) 3*gamma(1/4)^8/(2*Pi)^6 mf = mfinit([96,4], 0); mfdim(mf) M = mfmathecke(mf, 7) P = charpoly(M) factor(P) mf = mfsplit(mf); mffields(mf) L = mfeigenbasis(mf); for(i=1,6,print(mfcoefs(L[i],16))) mfmatatkin(mf,3) matdet(%) mfatkineigenvalues(mf,3) LE = mftolfun(mfEk(4), 1); lfun(LE, 2)/Pi^2 lfun(LE, 0) D = mfDelta(); L = mftolfun(D, 3); lfunlambda(L, 3)/lfunlambda(L, 5) lfunlambda(L, 1)/lfunlambda(L, 3) bestappr(%) LIN = lfuninit(L, [6, 6, 50]); ploth(t = 0, 50, lfunhardy(LIN, t)) PP = mfperiodpol(mfDelta(),-1); PP /= polcoeff(PP,1); bestappr(PP) PM = mfperiodpol(mfDelta(),1); PM /= polcoeff(PM,0); bestappr(PP) mfperiodpolbasis(12) E4 = mfEk(4); F = mfbracket(E4, E4, 2); mfcoefs(F, 6)/4800 D = mfDelta(); mftaylor(D, 10)*1728 D3 = mftwist(D, -3); mfcoefs(D3, 10) P = mfparams(D3) mf = mfinit(P, 1); mftobasis(mf, D3) F = mffromell(ellinit("49a1"))[2]; mfisCM(F) mfisequal(F, mftwist(F, -7)) mf = mfsplit([23,1,-23], 1); F = mfeigenbasis(mf)[1]; mfisCM(F) mfisequal(F, mftwist(F, -23)) L = mfsearch([30,4], [[2,2],[3,-1]]); #L [N, F] = L[1]; mfparams(F) mfcoefs(F, 10) L = mfsearch([80,2], [[2,2], [7,-3]]); #L [N, F] = L[1]; mfparams(F) mfcoefs(F, 12) L = mfsearch([30,4], [[2,Mod(2,5)],[3,Mod(-1,5)]]); #L apply(x->x[1], L) F1 = L[1][2]; mfcoefs(F1, 10) F2 = L[2][2]; mfcoefs(F2, 10) F = mflinear([F1, F2], [-1, 1]); mfcoefs(F, 16)/5 mfsturm([26,4])