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 = mffrometaquo([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) mfcoefs(mf,6) mf = mfinit([1,12], 1); L = mfbasis(mf); #L mfcoefs(L[1],6) mf = mfinit([35,2], 0); L = mfbasis(mf); #L for (i = 1, 3, print(mfcoefs(L[i], 10))) mffields(mf) L = mfeigenbasis(mf); #L mfcoefs(L[1],10) mfcoefs(L[2],4) lift(mfcoefs(L[2],9)) mfcoefsembed(F,n)=mfembed(F,mfcoefs(F,n)); [V1,V2]=mfcoefsembed(L[2],5); V1 V2 [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(mf, F, 24); mfcoefs(G, 12) mftobasis(mf, G) 24*mfcoefs(L[5], 12) mf=mfinit([96,2],0);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 = mfinit([35,2,5],0); 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<-chargalois(G), zncharisodd(G,chi)]; #L apply(x->mfdim([23,1,x], 1), L) apply(x->charorder(x[1],x[2]), L) mfa = mfinit([23,1,0], 1); #mfa mf = mfa[1]; mfdim(mf) mfparams(mf) wt1exp(lim1,lim2)= { my(mfall,mf,chi); for(N=lim1,lim2, mfall=mfinit([N,1,0], 0); /* Use wildcard */ for(i=1,#mfall, mf=mfall[i]; chi=mfparams(mf)[3]; /* nice format: D or Mod(a,N) */ [ print([N,chi,-t]) | t<-mfgaloistype(mf), t < 0 ] ) ); } # wt1exp(1,230) wt1exp(633,633) # mf=mfinit([96,6],0); mffields(mf) mfatkineigenvalues(mf,3) mf=mfinit([96,3,-3],0); mffields(mf) mfatkineigenvalues(mf,32) mfatkineigenvalues(mf,3) mf = mfinit([96,2]); L = mfbasis(mf); mfdim([96,2],3) apply(x->mfconductor(mf,x), L) 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])) mfeval(mfinit(E4), E4,I) 3*gamma(1/4)^8/(2*Pi)^6 mf = mfinit([96,4], 0); M = mfheckemat(mf, 7) P = charpoly(M) print(factor(P)) mffields(mf) L = mfeigenbasis(mf); for(i=1,6,print(mfcoefs(L[i],16))) [mfB,M,C] = mfatkininit(mf,3); M [C,matdet(M/C)] mfatkineigenvalues(mf,3) E4 = mfEk(4); mf = mfinit(E4); LE = lfunmf(mf, E4); lfun(LE, 2)/Pi^2 lfun(LE, 0) D = mfDelta(); mf = mfinit(D); L = lfunmf(mf, D); lfunlambda(L, 3)/lfunlambda(L, 5) r = lfunlambda(L, 1)/lfunlambda(L, 3) bestappr(r) LIN = lfuninit(L, [50]); ploth(t = 0, 50, lfunhardy(LIN, t)) PP = mfperiodpol(mf,D,-1); PP /= polcoeff(PP,1); bestappr(PP) PM = mfperiodpol(mf,D,1); PM /= polcoeff(PM,0); bestappr(PM) 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(D3, 1); mftobasis(mf, D3) F = mffromell(ellinit("49a1"))[2]; mfisCM(F) mfisequal(F, mftwist(F, -7)) mf = mfinit([23,1,-23], 1); F = mfeigenbasis(mf)[1]; mfisCM(F) mfisequal(F, mftwist(F, -23)) L = mfeigensearch([[1..30],4], [[2,2],[3,-1]]); #L F = L[1]; mfparams(F) mfcoefs(F, 10) L = mfeigensearch([[1..30],4], [[2,Mod(2,5)],[3,Mod(-1,5)]]); [ mfparams(F)[1] | F <- L ] F1 = L[1]; mfcoefs(F1, 10) F2 = L[2]; mfcoefs(F2, 10) F = mflinear([F1, F2], [-1, 1]); mfcoefs(F, 16)/5 mfsturm([26,4]) W = mfsearch([[1..35],3],[0,1,2,3,4,5,6,7,8],1); #W [ mfparams(F) | F <- W] mfcoefs(W[1],10) mfcoefs(W[2],10) mf = mfinit([32,4],0); F = mfbasis(mf)[1]; mfcoefs(F,10) mfslashexpansion(mf,F,[0,-1;32,0],10,1,&A); A mf = mfinit([12,8],0); F = mfbasis(mf)[1]; mfslashexpansion(mf,F,[1,0;2,1],7,0,&A) A mfslashexpansion(mf,F,[1,0;2,1],7,1,&A) mf = mfinit([12,7,-4],0); F = mfbasis(mf)[1]; mfslashexpansion(mf,F,[1,0;6,1],5,1,&A) A mf = mfinit([12,4],1); F = mfbasis(mf)[1]; mfeval(mf,F,1/Pi+10^(-6)*I) mfeval(mf,F,1/Pi+10^(-7)*I) mfeval(mf,F,1/Pi+10^(-8)*I) \p57 mfeval(mf,F,1/Pi+10^(-8)*I) \p38 T = mfTheta(); mf = mfinit(T); mfeval(mf,T,[0,1/2,1,oo]) mfeval(mf,T,10^(-8)*I) mf = mfinit([35,2],1); F = mfbasis(mf)[1]; FS = mfsymbol(mf,F); mfsymboleval(FS,[0,oo]) mfsymboleval(FS,[1/2,3/5]) mfsymboleval(FS,[I,2*I]) mfsymboleval(FS,[1/2,I]) mf = mfinit([5,4],1); F = mfbasis(mf)[1]; FS = mfsymbol(mf,F); mfsymboleval(FS,[0,oo]) T4 = mfpow(mfTheta(),4); mf = mfinit(T4); TS = mfsymbol(mf,T4); mfsymboleval(TS,[0,oo]) mfsymboleval(TS,[1/2,oo]) mfsymboleval(TS,[1/2,355/226]) # mf = mfinit([96,6],0); F = mfbasis(mf)[1]; FS = mfsymbol(mf,F); mfsymboleval(FS,[0,oo]); mfperiodpol(mf,F); mf = mfinit([96,4],0); [F1,F2] = mfbasis(mf); FS1 = mfsymbol(mf,F1); FS2 = mfsymbol(mf,F2); mfpetersson(FS1) mfpetersson(FS2) mfpetersson(FS1,FS2) # mf12 = mfinit([12,5,-3]); E1 = mfeisenstein(5,1,-3); E2 = mfeisenstein(5,-3,1); cusps = mfcusps(12) [mfcuspval(mf12,E1,c) | c<-cusps] [mfcuspval(mf12,E2,c) | c<-cusps] P(mf) = mfpetersson(mfsymbol(mf,E1),mfsymbol(mf,E2)); mf3 = mfinit([3,5,-3]); mf96 = mfinit([96,5,-3]); # P(mf12) P(mf3); P(mf96); #