/* This code can be loaded, or copied and pasted, into Magma. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. At the *bottom* of the file, there is code to recreate the Hilbert modular form in Magma, by creating the HMF space and cutting out the corresponding Hecke irreducible subspace. From there, you can ask for more eigenvalues or modify as desired. It is commented out, as this computation may be lengthy. */ P := PolynomialRing(Rationals()); g := P![-1, -2, 7, 2, -7, -1, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [29, 29, -9*w^5 + 3*w^4 + 64*w^3 + 26*w^2 - 40*w - 10], [29, 29, w^5 - 7*w^3 - 5*w^2 + 2*w + 2], [29, 29, w^4 - w^3 - 6*w^2 + 2], [29, 29, 5*w^5 - w^4 - 36*w^3 - 19*w^2 + 21*w + 9], [29, 29, -w^5 + w^4 + 7*w^3 - 2*w^2 - 6*w + 1], [29, 29, 2*w^5 - 15*w^3 - 10*w^2 + 11*w + 5], [41, 41, 5*w^5 - w^4 - 36*w^3 - 18*w^2 + 21*w + 5], [41, 41, -5*w^5 + 2*w^4 + 36*w^3 + 11*w^2 - 25*w - 2], [41, 41, 6*w^5 - w^4 - 44*w^3 - 23*w^2 + 30*w + 8], [41, 41, 13*w^5 - 4*w^4 - 93*w^3 - 39*w^2 + 59*w + 16], [41, 41, -4*w^5 + 30*w^3 + 19*w^2 - 19*w - 8], [41, 41, w^5 - 7*w^3 - 6*w^2 + 2*w + 3], [49, 7, -5*w^5 + w^4 + 36*w^3 + 19*w^2 - 22*w - 6], [64, 2, -2], [71, 71, -8*w^5 + w^4 + 58*w^3 + 34*w^2 - 34*w - 16], [71, 71, -6*w^5 + 2*w^4 + 42*w^3 + 18*w^2 - 23*w - 6], [71, 71, -8*w^5 + 2*w^4 + 58*w^3 + 27*w^2 - 38*w - 10], [71, 71, 4*w^5 - 30*w^3 - 19*w^2 + 20*w + 8], [71, 71, -10*w^5 + 3*w^4 + 72*w^3 + 30*w^2 - 48*w - 10], [71, 71, -8*w^5 + 2*w^4 + 58*w^3 + 26*w^2 - 37*w - 8], [125, 5, 4*w^5 - w^4 - 29*w^3 - 13*w^2 + 19*w + 2], [139, 139, -w^5 - w^4 + 8*w^3 + 12*w^2 - 3*w - 5], [139, 139, -11*w^5 + 4*w^4 + 78*w^3 + 29*w^2 - 49*w - 11], [139, 139, -12*w^5 + 3*w^4 + 86*w^3 + 41*w^2 - 52*w - 18], [139, 139, -4*w^5 + w^4 + 28*w^3 + 15*w^2 - 14*w - 7], [139, 139, 8*w^5 - 2*w^4 - 58*w^3 - 27*w^2 + 39*w + 10], [139, 139, 7*w^5 - 2*w^4 - 51*w^3 - 21*w^2 + 35*w + 7], [169, 13, -8*w^5 + 2*w^4 + 57*w^3 + 28*w^2 - 34*w - 13], [169, 13, w^5 - w^4 - 6*w^3 + w^2 + 2*w - 2], [169, 13, -7*w^5 + w^4 + 51*w^3 + 29*w^2 - 32*w - 12], [181, 181, -5*w^5 + 36*w^3 + 26*w^2 - 18*w - 12], [181, 181, -6*w^5 + 44*w^3 + 30*w^2 - 23*w - 13], [181, 181, 9*w^5 - 4*w^4 - 64*w^3 - 19*w^2 + 44*w + 7], [181, 181, 2*w^4 - w^3 - 14*w^2 - 2*w + 8], [181, 181, -12*w^5 + 4*w^4 + 85*w^3 + 35*w^2 - 53*w - 16], [181, 181, -11*w^5 + 3*w^4 + 78*w^3 + 37*w^2 - 45*w - 18], [211, 211, -10*w^5 + 3*w^4 + 71*w^3 + 32*w^2 - 43*w - 15], [211, 211, -7*w^5 + 3*w^4 + 49*w^3 + 16*w^2 - 31*w - 5], [211, 211, 8*w^5 - w^4 - 58*w^3 - 34*w^2 + 35*w + 15], [211, 211, -w^4 + w^3 + 7*w^2 - 2*w - 4], [211, 211, 6*w^5 - 2*w^4 - 42*w^3 - 17*w^2 + 23*w + 6], [211, 211, w^3 - w^2 - 5*w], [239, 239, w^3 - w^2 - 5*w + 1], [239, 239, w^4 - w^3 - 7*w^2 + 2*w + 5], [239, 239, 8*w^5 - w^4 - 58*w^3 - 34*w^2 + 35*w + 14], [239, 239, 7*w^5 - 3*w^4 - 49*w^3 - 16*w^2 + 31*w + 6], [239, 239, 10*w^5 - 3*w^4 - 71*w^3 - 32*w^2 + 43*w + 14], [239, 239, -11*w^5 + 2*w^4 + 80*w^3 + 42*w^2 - 50*w - 18], [251, 251, 6*w^5 - w^4 - 44*w^3 - 23*w^2 + 31*w + 8], [251, 251, 11*w^5 - 2*w^4 - 79*w^3 - 43*w^2 + 47*w + 18], [251, 251, 10*w^5 - w^4 - 73*w^3 - 44*w^2 + 45*w + 18], [251, 251, -11*w^5 + 4*w^4 + 78*w^3 + 29*w^2 - 48*w - 13], [251, 251, 6*w^5 - 2*w^4 - 42*w^3 - 17*w^2 + 23*w + 5], [251, 251, -16*w^5 + 4*w^4 + 115*w^3 + 54*w^2 - 70*w - 22], [281, 281, 8*w^5 - 3*w^4 - 57*w^3 - 20*w^2 + 36*w + 7], [281, 281, 3*w^5 - w^4 - 22*w^3 - 8*w^2 + 18*w + 3], [281, 281, 2*w^5 - 2*w^4 - 13*w^3 + 2*w^2 + 9*w], [281, 281, w^5 + w^4 - 8*w^3 - 11*w^2 + 3*w + 4], [281, 281, w^5 - w^4 - 7*w^3 + 2*w^2 + 8*w - 2], [281, 281, -13*w^5 + 4*w^4 + 93*w^3 + 39*w^2 - 58*w - 15], [349, 349, 7*w^5 - 2*w^4 - 51*w^3 - 21*w^2 + 36*w + 5], [349, 349, 7*w^5 - w^4 - 51*w^3 - 28*w^2 + 32*w + 8], [349, 349, 3*w^5 - w^4 - 21*w^3 - 8*w^2 + 12*w], [349, 349, 10*w^5 - 2*w^4 - 72*w^3 - 38*w^2 + 45*w + 17], [349, 349, 7*w^5 - 2*w^4 - 50*w^3 - 23*w^2 + 33*w + 12], [349, 349, 17*w^5 - 5*w^4 - 122*w^3 - 53*w^2 + 79*w + 21], [379, 379, 2*w^5 - 14*w^3 - 11*w^2 + 7*w + 4], [379, 379, -10*w^5 + 3*w^4 + 71*w^3 + 32*w^2 - 42*w - 15], [379, 379, -15*w^5 + 5*w^4 + 106*w^3 + 44*w^2 - 63*w - 17], [379, 379, 2*w^5 - 3*w^4 - 12*w^3 + 9*w^2 + 8*w - 4], [379, 379, 4*w^5 - 29*w^3 - 20*w^2 + 14*w + 10], [379, 379, 13*w^5 - 2*w^4 - 94*w^3 - 53*w^2 + 55*w + 24], [419, 419, 3*w^5 - 2*w^4 - 20*w^3 - 4*w^2 + 12*w + 4], [419, 419, 3*w^5 - 22*w^3 - 16*w^2 + 15*w + 8], [419, 419, -11*w^5 + 4*w^4 + 77*w^3 + 31*w^2 - 45*w - 14], [419, 419, -19*w^5 + 5*w^4 + 137*w^3 + 62*w^2 - 87*w - 24], [419, 419, -16*w^5 + 5*w^4 + 114*w^3 + 48*w^2 - 72*w - 17], [419, 419, 17*w^5 - 5*w^4 - 121*w^3 - 54*w^2 + 73*w + 23], [421, 421, 4*w^5 - w^4 - 29*w^3 - 13*w^2 + 20*w + 1], [421, 421, 4*w^5 - 2*w^4 - 29*w^3 - 6*w^2 + 22*w + 1], [421, 421, -8*w^5 + 3*w^4 + 57*w^3 + 20*w^2 - 37*w - 10], [421, 421, -6*w^5 + 45*w^3 + 30*w^2 - 31*w - 14], [421, 421, 5*w^5 + w^4 - 38*w^3 - 31*w^2 + 22*w + 14], [421, 421, -6*w^5 + 3*w^4 + 41*w^3 + 12*w^2 - 24*w - 5], [449, 449, -9*w^5 + w^4 + 66*w^3 + 38*w^2 - 43*w - 16], [449, 449, 2*w^5 + w^4 - 16*w^3 - 17*w^2 + 11*w + 9], [449, 449, 10*w^5 - w^4 - 74*w^3 - 43*w^2 + 49*w + 18], [449, 449, 17*w^5 - 6*w^4 - 121*w^3 - 46*w^2 + 78*w + 16], [449, 449, -11*w^5 + 2*w^4 + 79*w^3 + 44*w^2 - 47*w - 21], [449, 449, 6*w^5 - w^4 - 44*w^3 - 22*w^2 + 28*w + 5], [461, 461, -6*w^5 + 3*w^4 + 42*w^3 + 10*w^2 - 28*w - 4], [461, 461, -15*w^5 + 5*w^4 + 107*w^3 + 43*w^2 - 70*w - 16], [461, 461, -10*w^5 + 2*w^4 + 73*w^3 + 36*w^2 - 46*w - 13], [461, 461, -9*w^5 + 2*w^4 + 66*w^3 + 31*w^2 - 46*w - 10], [461, 461, 12*w^5 - 4*w^4 - 85*w^3 - 34*w^2 + 50*w + 13], [461, 461, -18*w^5 + 4*w^4 + 130*w^3 + 64*w^2 - 81*w - 28], [491, 491, 17*w^5 - 5*w^4 - 121*w^3 - 54*w^2 + 73*w + 21], [491, 491, -10*w^5 + 4*w^4 + 70*w^3 + 26*w^2 - 43*w - 11], [491, 491, -6*w^5 + 3*w^4 + 41*w^3 + 12*w^2 - 23*w - 3], [491, 491, 2*w^5 - 16*w^3 - 9*w^2 + 16*w + 3], [491, 491, 20*w^5 - 5*w^4 - 144*w^3 - 68*w^2 + 90*w + 29], [491, 491, -6*w^5 + w^4 + 44*w^3 + 24*w^2 - 31*w - 13], [601, 601, -10*w^5 + 2*w^4 + 73*w^3 + 36*w^2 - 47*w - 12], [601, 601, -7*w^5 + 2*w^4 + 49*w^3 + 24*w^2 - 26*w - 10], [601, 601, -15*w^5 + 3*w^4 + 108*w^3 + 56*w^2 - 64*w - 24], [601, 601, -3*w^5 + 3*w^4 + 20*w^3 - 5*w^2 - 15*w + 3], [601, 601, 9*w^5 - 2*w^4 - 66*w^3 - 31*w^2 + 45*w + 11], [601, 601, 14*w^5 - 2*w^4 - 102*w^3 - 57*w^2 + 63*w + 25], [631, 631, 5*w^5 - 2*w^4 - 35*w^3 - 13*w^2 + 20*w + 9], [631, 631, -10*w^5 + 4*w^4 + 71*w^3 + 24*w^2 - 47*w - 6], [631, 631, -5*w^5 + w^4 + 36*w^3 + 18*w^2 - 20*w - 9], [631, 631, -21*w^5 + 5*w^4 + 151*w^3 + 73*w^2 - 93*w - 31], [631, 631, 8*w^5 - 2*w^4 - 57*w^3 - 27*w^2 + 34*w + 8], [631, 631, -14*w^5 + 3*w^4 + 102*w^3 + 50*w^2 - 68*w - 19], [659, 659, 14*w^5 - 3*w^4 - 102*w^3 - 49*w^2 + 67*w + 19], [659, 659, 7*w^5 - 2*w^4 - 50*w^3 - 22*w^2 + 30*w + 5], [659, 659, -6*w^5 + 2*w^4 + 43*w^3 + 17*w^2 - 29*w - 10], [659, 659, -18*w^5 + 6*w^4 + 128*w^3 + 52*w^2 - 80*w - 21], [659, 659, 14*w^5 - 2*w^4 - 102*w^3 - 57*w^2 + 64*w + 24], [659, 659, -16*w^5 + 5*w^4 + 114*w^3 + 48*w^2 - 72*w - 18], [701, 701, -7*w^5 + 4*w^4 + 49*w^3 + 9*w^2 - 34*w - 4], [701, 701, 15*w^5 - 3*w^4 - 108*w^3 - 57*w^2 + 65*w + 26], [701, 701, -12*w^5 + 2*w^4 + 87*w^3 + 48*w^2 - 55*w - 22], [701, 701, 7*w^5 - 3*w^4 - 49*w^3 - 16*w^2 + 28*w + 5], [701, 701, -8*w^5 + 2*w^4 + 57*w^3 + 27*w^2 - 32*w - 12], [701, 701, -9*w^5 + 3*w^4 + 64*w^3 + 26*w^2 - 38*w - 12], [729, 3, -3], [769, 769, -12*w^5 + w^4 + 88*w^3 + 53*w^2 - 54*w - 21], [769, 769, 14*w^5 - 2*w^4 - 102*w^3 - 57*w^2 + 62*w + 25], [769, 769, -3*w^5 + 23*w^3 + 13*w^2 - 17*w - 1], [769, 769, 9*w^5 - 2*w^4 - 65*w^3 - 32*w^2 + 43*w + 12], [769, 769, -13*w^5 + 4*w^4 + 94*w^3 + 38*w^2 - 63*w - 14], [769, 769, 16*w^5 - 4*w^4 - 116*w^3 - 53*w^2 + 75*w + 21], [811, 811, 20*w^5 - 7*w^4 - 142*w^3 - 55*w^2 + 89*w + 21], [811, 811, 11*w^5 - 2*w^4 - 80*w^3 - 42*w^2 + 53*w + 17], [811, 811, -w^5 + 7*w^3 + 4*w^2 - w + 1], [811, 811, 9*w^5 - 2*w^4 - 64*w^3 - 34*w^2 + 35*w + 16], [811, 811, 5*w^5 - 2*w^4 - 35*w^3 - 13*w^2 + 20*w + 3], [811, 811, -7*w^5 + 52*w^3 + 34*w^2 - 31*w - 15], [839, 839, -14*w^5 + 5*w^4 + 99*w^3 + 38*w^2 - 60*w - 16], [839, 839, -20*w^5 + 6*w^4 + 143*w^3 + 62*w^2 - 90*w - 25], [839, 839, 7*w^5 - w^4 - 50*w^3 - 29*w^2 + 26*w + 12], [839, 839, -19*w^5 + 5*w^4 + 137*w^3 + 62*w^2 - 88*w - 22], [839, 839, -14*w^5 + 3*w^4 + 101*w^3 + 50*w^2 - 62*w - 21], [839, 839, -w^5 - w^4 + 9*w^3 + 11*w^2 - 10*w - 6], [881, 881, -14*w^5 + 3*w^4 + 102*w^3 + 49*w^2 - 67*w - 18], [881, 881, 12*w^5 - 5*w^4 - 84*w^3 - 29*w^2 + 52*w + 13], [881, 881, -3*w^5 + 2*w^4 + 21*w^3 + 2*w^2 - 15*w - 3], [881, 881, -3*w^5 + 21*w^3 + 16*w^2 - 8*w - 8], [881, 881, -17*w^5 + 4*w^4 + 123*w^3 + 58*w^2 - 79*w - 22], [881, 881, 19*w^5 - 5*w^4 - 136*w^3 - 64*w^2 + 83*w + 26], [911, 911, -6*w^5 + 2*w^4 + 44*w^3 + 15*w^2 - 32*w - 2], [911, 911, -15*w^5 + 4*w^4 + 107*w^3 + 51*w^2 - 66*w - 23], [911, 911, 13*w^5 - 4*w^4 - 94*w^3 - 37*w^2 + 63*w + 13], [911, 911, -15*w^5 + 3*w^4 + 109*w^3 + 55*w^2 - 71*w - 20], [911, 911, -7*w^5 + 3*w^4 + 48*w^3 + 17*w^2 - 25*w - 6], [911, 911, 12*w^5 - 4*w^4 - 86*w^3 - 34*w^2 + 55*w + 13]]; primes := [ideal : I in primesArray]; heckePol := x^8 - 4*x^7 - 86*x^6 + 230*x^5 + 1887*x^4 - 3026*x^3 - 13513*x^2 + 5886*x + 23413; K := NumberField(heckePol); heckeEigenvaluesArray := [e, -10420688/36415534529*e^7 + 54924961/36415534529*e^6 + 745145019/36415534529*e^5 - 3441133101/36415534529*e^4 - 7670573816/36415534529*e^3 + 60147393495/36415534529*e^2 - 59252990171/36415534529*e - 309187269012/36415534529, -116674243/72831069058*e^7 + 397327482/36415534529*e^6 + 8735560717/72831069058*e^5 - 26409955399/36415534529*e^4 - 145482436735/72831069058*e^3 + 771151968267/72831069058*e^2 + 502356588707/72831069058*e - 1648571187205/72831069058, 1173411/72831069058*e^7 - 39150819/36415534529*e^6 + 182017883/72831069058*e^5 + 2906501637/36415534529*e^4 - 12162881955/72831069058*e^3 - 83635806791/72831069058*e^2 + 103472393507/72831069058*e + 425949671075/72831069058, -197736327/145662138116*e^7 + 275114391/36415534529*e^6 + 14157578575/145662138116*e^5 - 32853860947/72831069058*e^4 - 180929123019/145662138116*e^3 + 878448301443/145662138116*e^2 - 7987021459/145662138116*e - 2228401389747/145662138116, 24858292/36415534529*e^7 - 577876507/145662138116*e^6 - 1859842344/36415534529*e^5 + 18633993083/72831069058*e^4 + 109504954609/145662138116*e^3 - 292173827359/72831069058*e^2 + 6928538635/145662138116*e + 2212215179403/145662138116, 1340189/72831069058*e^7 - 12874567/36415534529*e^6 + 33295425/36415534529*e^5 + 341839435/36415534529*e^4 - 2959790593/36415534529*e^3 + 25497428116/36415534529*e^2 + 13115236197/36415534529*e - 454974466191/72831069058, -124291177/72831069058*e^7 + 873640349/72831069058*e^6 + 8595282343/72831069058*e^5 - 57007763399/72831069058*e^4 - 54252602000/36415534529*e^3 + 412446500759/36415534529*e^2 + 102227077341/72831069058*e - 2051383296939/72831069058, -257281897/72831069058*e^7 + 679026460/36415534529*e^6 + 39463867847/145662138116*e^5 - 165850731377/145662138116*e^4 - 647029388595/145662138116*e^3 + 573481918432/36415534529*e^2 + 969694812213/72831069058*e - 5212089632975/145662138116, 38329297/72831069058*e^7 + 33878787/36415534529*e^6 - 1821030379/36415534529*e^5 - 4401900911/36415534529*e^4 + 36707120949/36415534529*e^3 + 72474254708/36415534529*e^2 - 148154639533/36415534529*e - 193713383863/72831069058, -40842897/72831069058*e^7 + 18146599/36415534529*e^6 + 3393452025/72831069058*e^5 + 1153559839/36415534529*e^4 - 55331778757/72831069058*e^3 - 112307558857/72831069058*e^2 + 166606413165/72831069058*e + 805386731443/72831069058, 9580833/72831069058*e^7 + 128481685/72831069058*e^6 - 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880973378049/72831069058, -406006772/36415534529*e^7 + 3928826067/72831069058*e^6 + 63050250517/72831069058*e^5 - 115335619056/36415534529*e^4 - 528738784285/36415534529*e^3 + 3014089254657/72831069058*e^2 + 1927694894816/36415534529*e - 6276154057813/72831069058, 328543069/36415534529*e^7 - 1484380873/36415534529*e^6 - 51278176867/72831069058*e^5 + 171352935305/72831069058*e^4 + 855851046625/72831069058*e^3 - 1171851988690/36415534529*e^2 - 1450020435040/36415534529*e + 5456844887669/72831069058, 129358364/36415534529*e^7 - 1032459453/36415534529*e^6 - 18117912907/72831069058*e^5 + 70451712649/36415534529*e^4 + 251411192513/72831069058*e^3 - 2131772613711/72831069058*e^2 - 176582494757/72831069058*e + 3140873263413/36415534529, -319213663/72831069058*e^7 + 2147192827/72831069058*e^6 + 12543050866/36415534529*e^5 - 73285040732/36415534529*e^4 - 483827004535/72831069058*e^3 + 1122691799742/36415534529*e^2 + 2539003058343/72831069058*e - 2411820827360/36415534529, 648271057/72831069058*e^7 - 2034326346/36415534529*e^6 - 23988564245/36415534529*e^5 + 133941024361/36415534529*e^4 + 363581603557/36415534529*e^3 - 2075370285899/36415534529*e^2 - 766970461093/36415534529*e + 11623145274157/72831069058, 337380656/36415534529*e^7 - 1799276135/36415534529*e^6 - 51459698889/72831069058*e^5 + 217730880237/72831069058*e^4 + 836004441715/72831069058*e^3 - 1425391185337/36415534529*e^2 - 1314361375284/36415534529*e + 6164960123167/72831069058, 195617311/36415534529*e^7 - 2798760875/72831069058*e^6 - 29840231947/72831069058*e^5 + 95750751881/36415534529*e^4 + 273868019343/36415534529*e^3 - 2940585831079/72831069058*e^2 - 1393711048184/36415534529*e + 7156816641619/72831069058, -863436605/72831069058*e^7 + 7764470655/145662138116*e^6 + 34221462153/36415534529*e^5 - 113721657295/36415534529*e^4 - 2372621782137/145662138116*e^3 + 1574218141257/36415534529*e^2 + 8716169180823/145662138116*e - 12811539466091/145662138116, -10454789/36415534529*e^7 - 257576458/36415534529*e^6 + 6037085433/145662138116*e^5 + 89469929041/145662138116*e^4 - 178372428633/145662138116*e^3 - 352036655774/36415534529*e^2 + 1104801868391/72831069058*e + 2516842761313/145662138116, 32979729/3310503139*e^7 - 176584844/3310503139*e^6 - 5113751423/6621006278*e^5 + 10824642392/3310503139*e^4 + 89055747955/6621006278*e^3 - 299491741927/6621006278*e^2 - 360192380751/6621006278*e + 358238310849/3310503139, -14072311/3310503139*e^7 + 41712898/3310503139*e^6 + 2191098901/6621006278*e^5 - 3590473665/6621006278*e^4 - 31147235937/6621006278*e^3 + 18036685271/3310503139*e^2 + 13532756636/3310503139*e - 6964152915/6621006278, -62656271/72831069058*e^7 + 1196672583/72831069058*e^6 + 909177553/36415534529*e^5 - 91135643813/72831069058*e^4 + 68277377881/72831069058*e^3 + 1563513951077/72831069058*e^2 - 635145043470/36415534529*e - 5604113443151/72831069058, -149693441/36415534529*e^7 + 853797721/36415534529*e^6 + 22385945013/72831069058*e^5 - 51003677961/36415534529*e^4 - 356365657839/72831069058*e^3 + 1200876338983/72831069058*e^2 + 691619620933/72831069058*e - 428665668291/36415534529, 145965089/36415534529*e^7 - 350837295/36415534529*e^6 - 11412448636/36415534529*e^5 + 18592328641/72831069058*e^4 + 167084593805/36415534529*e^3 + 156538343503/72831069058*e^2 - 449829306769/72831069058*e - 3657503785791/72831069058]; heckeEigenvalues := AssociativeArray(); for i := 1 to #heckeEigenvaluesArray do heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i]; end for; ALEigenvalues := AssociativeArray(); ALEigenvalues[ideal] := 1; // EXAMPLE: // pp := Factorization(2*ZF)[1][1]; // heckeEigenvalues[pp]; print "To reconstruct the Hilbert newform f, type f, iso := Explode(make_newform());"; function make_newform(); M := HilbertCuspForms(F, NN); S := NewSubspace(M); // SetVerbose("ModFrmHil", 1); NFD := NewformDecomposition(S); newforms := [* Eigenform(U) : U in NFD *]; if #newforms eq 0 then; print "No Hilbert newforms at this level"; return 0; end if; print "Testing ", #newforms, " possible newforms"; newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *]; print #newforms, " newforms have the correct Hecke field"; if #newforms eq 0 then; print "No Hilbert newform found with the correct Hecke field"; return 0; end if; autos := Automorphisms(K); xnewforms := [* *]; for f in newforms do; if K eq RationalField() then; Append(~xnewforms, [* f, autos[1] *]); else; flag, iso := IsIsomorphic(K,BaseField(f)); for a in autos do; Append(~xnewforms, [* f, a*iso *]); end for; end if; end for; newforms := xnewforms; for P in primes do; xnewforms := [* *]; for f_iso in newforms do; f, iso := Explode(f_iso); if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then; Append(~xnewforms, f_iso); end if; end for; newforms := xnewforms; if #newforms eq 0 then; print "No Hilbert newform found which matches the Hecke eigenvalues"; return 0; else if #newforms eq 1 then; print "success: unique match"; return newforms[1]; end if; end if; end for; print #newforms, "Hilbert newforms found which match the Hecke eigenvalues"; return newforms[1]; end function;