/*
  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<x> := PolynomialRing(Rationals());
g := P![1, -5, 2, 8, -4, -2, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {59, 59, w^5 - w^4 - 4*w^3 + 3*w^2 + 3*w - 3}>;

primesArray := [
[9, 3, -w^2 + 2],
[19, 19, -w^3 + 4*w],
[19, 19, w^3 - 3*w - 1],
[29, 29, w^5 - w^4 - 6*w^3 + 4*w^2 + 8*w - 3],
[29, 29, w^4 - w^3 - 4*w^2 + 2*w + 2],
[31, 31, -w^4 + 4*w^2 + w - 3],
[41, 41, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 11*w - 4],
[49, 7, -2*w^5 + 3*w^4 + 10*w^3 - 12*w^2 - 11*w + 6],
[59, 59, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 7*w - 5],
[59, 59, w^5 - w^4 - 4*w^3 + 3*w^2 + 3*w - 3],
[59, 59, 2*w^5 - 3*w^4 - 9*w^3 + 11*w^2 + 9*w - 4],
[61, 61, -w^5 + w^4 + 5*w^3 - 3*w^2 - 7*w + 1],
[64, 2, -2],
[71, 71, -2*w^5 + 2*w^4 + 10*w^3 - 8*w^2 - 11*w + 6],
[79, 79, -3*w^5 + 4*w^4 + 13*w^3 - 14*w^2 - 9*w + 5],
[79, 79, -w^4 - w^3 + 5*w^2 + 4*w - 3],
[79, 79, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 8*w + 4],
[81, 3, 3*w^5 - 5*w^4 - 14*w^3 + 19*w^2 + 13*w - 8],
[89, 89, 2*w^5 - 2*w^4 - 9*w^3 + 6*w^2 + 8*w - 1],
[101, 101, -w^4 - w^3 + 5*w^2 + 3*w - 3],
[101, 101, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w + 4],
[109, 109, -2*w^5 + 4*w^4 + 8*w^3 - 14*w^2 - 6*w + 5],
[109, 109, -3*w^5 + 4*w^4 + 13*w^3 - 14*w^2 - 10*w + 7],
[125, 5, w^5 - w^4 - 5*w^3 + 4*w^2 + 5*w],
[131, 131, -w^2 - w + 3],
[131, 131, w^5 - 3*w^4 - 4*w^3 + 11*w^2 + 3*w - 4],
[131, 131, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 6*w - 5],
[131, 131, -2*w^5 + 4*w^4 + 8*w^3 - 15*w^2 - 6*w + 7],
[139, 139, w^4 - 3*w^3 - 3*w^2 + 9*w],
[149, 149, 2*w^5 - 3*w^4 - 9*w^3 + 12*w^2 + 7*w - 5],
[149, 149, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 2*w - 2],
[151, 151, 3*w^5 - 4*w^4 - 13*w^3 + 14*w^2 + 10*w - 5],
[151, 151, -3*w^5 + 4*w^4 + 14*w^3 - 15*w^2 - 12*w + 6],
[151, 151, 4*w^5 - 5*w^4 - 18*w^3 + 18*w^2 + 15*w - 9],
[151, 151, 2*w^5 - 2*w^4 - 9*w^3 + 7*w^2 + 8*w - 5],
[169, 13, -2*w^5 + w^4 + 11*w^3 - 3*w^2 - 13*w + 1],
[179, 179, w^3 - w^2 - 2*w + 3],
[181, 181, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 10*w - 3],
[181, 181, -2*w^4 + w^3 + 8*w^2 - 3*w - 2],
[191, 191, w^5 - w^4 - 6*w^3 + 5*w^2 + 9*w - 4],
[191, 191, -w^3 + 2*w^2 + 3*w - 4],
[191, 191, -2*w^5 + w^4 + 11*w^3 - 3*w^2 - 12*w],
[191, 191, w^4 - 2*w^3 - 4*w^2 + 7*w],
[199, 199, -3*w^5 + 4*w^4 + 15*w^3 - 14*w^2 - 16*w + 6],
[199, 199, -2*w^5 + 3*w^4 + 10*w^3 - 12*w^2 - 12*w + 7],
[211, 211, -2*w^5 + 4*w^4 + 9*w^3 - 15*w^2 - 8*w + 5],
[211, 211, -3*w^5 + 5*w^4 + 13*w^3 - 18*w^2 - 10*w + 8],
[229, 229, -3*w^5 + 4*w^4 + 13*w^3 - 14*w^2 - 10*w + 6],
[229, 229, w^4 - 4*w^2 - 1],
[229, 229, w^5 - w^4 - 3*w^3 + 3*w^2 - 3*w - 2],
[239, 239, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 8*w + 8],
[241, 241, w^5 - 3*w^4 - 4*w^3 + 10*w^2 + 3*w - 2],
[241, 241, w^5 - w^4 - 5*w^3 + 3*w^2 + 4*w + 1],
[251, 251, -3*w^5 + 3*w^4 + 15*w^3 - 10*w^2 - 17*w + 3],
[271, 271, -2*w^5 + 4*w^4 + 9*w^3 - 14*w^2 - 8*w + 2],
[271, 271, -2*w^5 + 3*w^4 + 8*w^3 - 9*w^2 - 4*w],
[271, 271, w^5 - 2*w^4 - 3*w^3 + 7*w^2 - 2*w - 4],
[289, 17, 4*w^5 - 6*w^4 - 17*w^3 + 22*w^2 + 12*w - 9],
[311, 311, -2*w^5 + 3*w^4 + 7*w^3 - 9*w^2 - 3*w + 2],
[331, 331, 3*w^5 - 5*w^4 - 14*w^3 + 19*w^2 + 14*w - 12],
[349, 349, -4*w^5 + 6*w^4 + 18*w^3 - 21*w^2 - 17*w + 7],
[349, 349, -w^4 + w^3 + 5*w^2 - 3*w - 3],
[359, 359, -2*w^5 + 4*w^4 + 9*w^3 - 15*w^2 - 10*w + 9],
[361, 19, 2*w^5 - 3*w^4 - 9*w^3 + 11*w^2 + 6*w - 4],
[361, 19, -3*w^5 + 5*w^4 + 13*w^3 - 18*w^2 - 10*w + 9],
[379, 379, -4*w^5 + 5*w^4 + 18*w^3 - 17*w^2 - 14*w + 7],
[379, 379, 2*w^5 - 4*w^4 - 10*w^3 + 15*w^2 + 11*w - 5],
[389, 389, -5*w^5 + 7*w^4 + 22*w^3 - 25*w^2 - 17*w + 11],
[389, 389, w^5 - 3*w^4 - 3*w^3 + 12*w^2 - 2*w - 5],
[401, 401, -4*w^5 + 6*w^4 + 18*w^3 - 23*w^2 - 15*w + 10],
[401, 401, -w^5 + 3*w^4 + 4*w^3 - 12*w^2 - w + 4],
[401, 401, 4*w^5 - 5*w^4 - 20*w^3 + 19*w^2 + 21*w - 11],
[401, 401, -3*w^5 + 3*w^4 + 16*w^3 - 12*w^2 - 18*w + 6],
[409, 409, -2*w^4 + 2*w^3 + 7*w^2 - 6*w - 2],
[409, 409, -w^5 + 3*w^4 + 5*w^3 - 13*w^2 - 5*w + 9],
[419, 419, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 10*w - 6],
[419, 419, -w^5 + 7*w^3 - w^2 - 10*w + 4],
[419, 419, w^5 - 2*w^4 - 5*w^3 + 10*w^2 + 5*w - 9],
[421, 421, 3*w^5 - 3*w^4 - 16*w^3 + 12*w^2 + 18*w - 7],
[431, 431, 4*w^5 - 7*w^4 - 17*w^3 + 25*w^2 + 13*w - 10],
[431, 431, -2*w^5 + 3*w^4 + 7*w^3 - 10*w^2 - w + 5],
[431, 431, 4*w^5 - 6*w^4 - 19*w^3 + 23*w^2 + 17*w - 10],
[439, 439, -2*w^5 + 4*w^4 + 10*w^3 - 15*w^2 - 11*w + 4],
[461, 461, w^5 - 2*w^4 - 3*w^3 + 6*w^2 + 2],
[461, 461, w^5 - w^4 - 5*w^3 + 5*w^2 + 6*w - 7],
[479, 479, -2*w^5 + w^4 + 9*w^3 - 2*w^2 - 8*w],
[479, 479, 2*w^5 - 2*w^4 - 10*w^3 + 8*w^2 + 12*w - 7],
[491, 491, -3*w^5 + 3*w^4 + 14*w^3 - 12*w^2 - 12*w + 7],
[491, 491, -3*w^5 + 3*w^4 + 15*w^3 - 12*w^2 - 14*w + 8],
[491, 491, -2*w^2 + w + 6],
[499, 499, -3*w^5 + 3*w^4 + 14*w^3 - 10*w^2 - 13*w + 6],
[509, 509, -2*w^5 + 2*w^4 + 8*w^3 - 6*w^2 - 5*w],
[521, 521, 3*w^5 - 4*w^4 - 14*w^3 + 15*w^2 + 15*w - 9],
[521, 521, -3*w^5 + 5*w^4 + 14*w^3 - 19*w^2 - 15*w + 9],
[521, 521, -4*w^5 + 5*w^4 + 18*w^3 - 17*w^2 - 16*w + 6],
[529, 23, w^5 - 3*w^4 - 5*w^3 + 11*w^2 + 7*w - 5],
[541, 541, -3*w^5 + 4*w^4 + 14*w^3 - 15*w^2 - 14*w + 10],
[569, 569, -w^5 - w^4 + 6*w^3 + 4*w^2 - 6*w - 1],
[571, 571, -2*w^4 + w^3 + 9*w^2 - 3*w - 4],
[599, 599, -3*w^5 + 3*w^4 + 14*w^3 - 11*w^2 - 11*w + 4],
[601, 601, w^4 - 2*w^2 - w - 2],
[619, 619, 2*w^5 - 3*w^4 - 9*w^3 + 11*w^2 + 10*w - 5],
[619, 619, w^5 - 3*w^4 - 4*w^3 + 12*w^2 + 3*w - 3],
[619, 619, -3*w^5 + 5*w^4 + 13*w^3 - 20*w^2 - 10*w + 10],
[619, 619, w^5 - 2*w^4 - 5*w^3 + 10*w^2 + 5*w - 8],
[619, 619, -4*w^5 + 6*w^4 + 19*w^3 - 23*w^2 - 17*w + 11],
[619, 619, -4*w^5 + 6*w^4 + 17*w^3 - 22*w^2 - 13*w + 10],
[631, 631, w^5 - 3*w^4 - 5*w^3 + 13*w^2 + 5*w - 6],
[641, 641, -w^3 + w^2 + 3*w - 5],
[641, 641, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + 3*w + 4],
[659, 659, -w^5 + 3*w^4 + 5*w^3 - 12*w^2 - 5*w + 5],
[661, 661, -2*w^5 + 3*w^4 + 8*w^3 - 12*w^2 - 3*w + 8],
[661, 661, 2*w^5 - 3*w^4 - 8*w^3 + 10*w^2 + 6*w - 1],
[691, 691, -w^3 - w^2 + 5*w + 1],
[691, 691, -3*w^5 + 4*w^4 + 13*w^3 - 13*w^2 - 10*w + 6],
[691, 691, 3*w^5 - 4*w^4 - 15*w^3 + 15*w^2 + 14*w - 6],
[701, 701, 3*w^5 - 6*w^4 - 13*w^3 + 23*w^2 + 10*w - 10],
[701, 701, -3*w^5 + 6*w^4 + 13*w^3 - 23*w^2 - 11*w + 9],
[709, 709, 3*w^5 - 6*w^4 - 13*w^3 + 22*w^2 + 11*w - 10],
[709, 709, -w^5 + 5*w^3 - 4*w - 2],
[709, 709, -w^5 + w^4 + 7*w^3 - 6*w^2 - 11*w + 5],
[719, 719, -2*w^5 + 3*w^4 + 9*w^3 - 12*w^2 - 7*w + 4],
[751, 751, w^4 + w^3 - 5*w^2 - 6*w + 4],
[769, 769, 4*w^5 - 5*w^4 - 19*w^3 + 18*w^2 + 18*w - 10],
[769, 769, 4*w^5 - 6*w^4 - 17*w^3 + 22*w^2 + 13*w - 11],
[809, 809, w^5 - w^4 - 4*w^3 + 5*w^2 + w - 7],
[809, 809, 2*w^5 - 5*w^4 - 9*w^3 + 19*w^2 + 10*w - 7],
[809, 809, -w^5 + 5*w^3 + w^2 - 7*w],
[809, 809, -3*w^5 + 4*w^4 + 15*w^3 - 16*w^2 - 15*w + 11],
[811, 811, -2*w^5 + 4*w^4 + 8*w^3 - 13*w^2 - 6*w + 5],
[811, 811, -w^5 + 3*w^4 + 3*w^3 - 9*w^2 - w],
[811, 811, 2*w^5 - 4*w^4 - 9*w^3 + 16*w^2 + 10*w - 9],
[811, 811, 2*w^5 - 4*w^4 - 10*w^3 + 16*w^2 + 10*w - 7],
[821, 821, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 5*w - 2],
[829, 829, 3*w^5 - 5*w^4 - 13*w^3 + 19*w^2 + 12*w - 9],
[839, 839, 2*w^5 - 4*w^4 - 7*w^3 + 14*w^2 + w - 6],
[839, 839, 4*w^5 - 5*w^4 - 18*w^3 + 19*w^2 + 14*w - 10],
[841, 29, -2*w^5 + 4*w^4 + 10*w^3 - 15*w^2 - 10*w + 5],
[841, 29, -w^5 + 3*w^4 + 6*w^3 - 12*w^2 - 10*w + 6],
[859, 859, 3*w^5 - 3*w^4 - 15*w^3 + 10*w^2 + 14*w - 2],
[881, 881, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 10*w - 4],
[911, 911, -4*w^5 + 5*w^4 + 19*w^3 - 20*w^2 - 17*w + 11],
[919, 919, 2*w^5 - 3*w^4 - 10*w^3 + 13*w^2 + 9*w - 10],
[929, 929, -w^5 + w^4 + 5*w^3 - 2*w^2 - 8*w - 1],
[941, 941, -5*w^5 + 7*w^4 + 23*w^3 - 26*w^2 - 20*w + 11],
[961, 31, -3*w^5 + 4*w^4 + 16*w^3 - 16*w^2 - 20*w + 8],
[971, 971, w^5 - 5*w^3 + 5*w - 4],
[991, 991, 3*w^5 - 5*w^4 - 12*w^3 + 18*w^2 + 8*w - 6],
[991, 991, 3*w^5 - 5*w^4 - 14*w^3 + 18*w^2 + 12*w - 7]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^7 - 6*x^6 - 27*x^5 + 222*x^4 - 110*x^3 - 1492*x^2 + 2825*x - 1408;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 1317/17894*e^6 - 4091/17894*e^5 - 45855/17894*e^4 + 79159/8947*e^3 + 126274/8947*e^2 - 1167801/17894*e + 444564/8947, 141/8947*e^6 - 10/8947*e^5 - 5643/8947*e^4 + 890/8947*e^3 + 58424/8947*e^2 + 1760/8947*e - 119557/8947, -205/17894*e^6 - 310/8947*e^5 + 4007/8947*e^4 + 9696/8947*e^3 - 90717/17894*e^2 - 150343/17894*e + 167784/8947, -758/8947*e^6 + 3163/8947*e^5 + 25006/8947*e^4 - 120461/8947*e^3 - 97005/8947*e^2 + 883779/8947*e - 739428/8947, -703/17894*e^6 + 1992/8947*e^5 + 23947/17894*e^4 - 148795/17894*e^3 - 87287/17894*e^2 + 553055/8947*e - 468193/8947, 277/8947*e^6 - 908/8947*e^5 - 9563/8947*e^4 + 36077/8947*e^3 + 47642/8947*e^2 - 287542/8947*e + 245662/8947, -72/8947*e^6 + 1528/8947*e^5 + 1549/8947*e^4 - 55469/8947*e^3 + 34128/8947*e^2 + 402097/8947*e - 384396/8947, -836/8947*e^6 + 1836/8947*e^5 + 30412/8947*e^4 - 73934/8947*e^3 - 212132/8947*e^2 + 553670/8947*e - 198528/8947, -1, -831/17894*e^6 + 1362/8947*e^5 + 28689/17894*e^4 - 108231/17894*e^3 - 151873/17894*e^2 + 422366/8947*e - 305864/8947, 72/8947*e^6 - 1528/8947*e^5 - 1549/8947*e^4 + 55469/8947*e^3 - 34128/8947*e^2 - 402097/8947*e + 402290/8947, -419/17894*e^6 - 1049/17894*e^5 + 8670/8947*e^4 + 39679/17894*e^3 - 97531/8947*e^2 - 167151/8947*e + 269045/8947, -341/8947*e^6 + 278/8947*e^5 + 11934/8947*e^4 - 15795/8947*e^3 - 79935/8947*e^2 + 138959/8947*e - 65439/8947, 1453/8947*e^6 - 4989/8947*e^5 - 49775/8947*e^4 + 193505/8947*e^3 + 250713/8947*e^2 - 1439209/8947*e + 1129089/8947, -2347/17894*e^6 + 4525/8947*e^5 + 78701/17894*e^4 - 349153/17894*e^3 - 345883/17894*e^2 + 1306145/8947*e - 1081080/8947, -1040/8947*e^6 + 3183/8947*e^5 + 36292/8947*e^4 - 122241/8947*e^3 - 204906/8947*e^2 + 871312/8947*e - 598731/8947, 763/8947*e^6 - 2275/8947*e^5 - 26729/8947*e^4 + 86164/8947*e^3 + 157264/8947*e^2 - 610611/8947*e + 379910/8947, -477/17894*e^6 + 588/8947*e^5 + 7927/8947*e^4 - 25491/8947*e^3 - 87047/17894*e^2 + 428261/17894*e - 143753/8947, 413/8947*e^6 - 1806/8947*e^5 - 13483/8947*e^4 + 71264/8947*e^3 + 45807/8947*e^2 - 541056/8947*e + 485623/8947, -2211/8947*e^6 + 8152/8947*e^5 + 74781/8947*e^4 - 313966/8947*e^3 - 347718/8947*e^2 + 2322988/8947*e - 1886411/8947, -213/8947*e^6 + 1538/8947*e^5 + 7192/8947*e^4 - 56359/8947*e^3 - 24296/8947*e^2 + 418231/8947*e - 318521/8947, 1289/17894*e^6 - 5485/17894*e^5 - 39785/17894*e^4 + 105404/8947*e^3 + 43440/8947*e^2 - 1566641/17894*e + 823135/8947, -131/8947*e^6 + 1786/8947*e^5 + 2197/8947*e^4 - 69484/8947*e^3 + 62094/8947*e^2 + 562470/8947*e - 688949/8947, -5/8947*e^6 - 888/8947*e^5 + 1723/8947*e^4 + 34297/8947*e^3 - 60259/8947*e^2 - 273168/8947*e + 377412/8947, 1313/17894*e^6 - 1506/8947*e^5 - 23133/8947*e^4 + 62458/8947*e^3 + 281285/17894*e^2 - 999825/17894*e + 377222/8947, 822/8947*e^6 - 2533/8947*e^5 - 27377/8947*e^4 + 100179/8947*e^3 + 129298/8947*e^2 - 770984/8947*e + 630781/8947, -204/8947*e^6 + 1347/8947*e^5 + 5880/8947*e^4 - 48307/8947*e^3 + 7226/8947*e^2 + 317642/8947*e - 382309/8947, 550/8947*e^6 - 737/8947*e^5 - 19537/8947*e^4 + 29805/8947*e^3 + 141915/8947*e^2 - 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12361/8947*e^4 - 46532/8947*e^3 + 196126/8947*e^2 + 428114/8947*e - 679510/8947, -1509/8947*e^6 + 11148/8947*e^5 + 44021/8947*e^4 - 419564/8947*e^3 + 53188/8947*e^2 + 3137742/8947*e - 3229393/8947, -2983/8947*e^6 + 10618/8947*e^5 + 102822/8947*e^4 - 408182/8947*e^3 - 527557/8947*e^2 + 3016294/8947*e - 2533572/8947, -1600/8947*e^6 + 2144/8947*e^5 + 59275/8947*e^4 - 83452/8947*e^3 - 449445/8947*e^2 + 490515/8947*e - 57395/8947, 2151/17894*e^6 - 9861/17894*e^5 - 71999/17894*e^4 + 192772/8947*e^3 + 125450/8947*e^2 - 2943745/17894*e + 1556956/8947, 263/8947*e^6 - 1605/8947*e^5 - 6528/8947*e^4 + 62322/8947*e^3 - 44139/8947*e^2 - 469068/8947*e + 946325/8947, 3804/8947*e^6 - 15118/8947*e^5 - 128065/8947*e^4 + 576060/8947*e^3 + 549965/8947*e^2 - 4219475/8947*e + 3425933/8947, -269/778*e^6 + 695/778*e^5 + 9607/778*e^4 - 13617/389*e^3 - 30774/389*e^2 + 200161/778*e - 50776/389, -7/8947*e^6 - 4822/8947*e^5 + 5991/8947*e^4 + 169695/8947*e^3 - 238251/8947*e^2 - 1227032/8947*e + 1491074/8947, 3411/8947*e^6 - 9760/8947*e^5 - 121474/8947*e^4 + 376555/8947*e^3 + 754141/8947*e^2 - 2791528/8947*e + 1573814/8947, -12243/17894*e^6 + 24039/8947*e^5 + 206442/8947*e^4 - 931626/8947*e^3 - 1828609/17894*e^2 + 14057871/17894*e - 5780276/8947, -2119/8947*e^6 + 10176/8947*e^5 + 66340/8947*e^4 - 395685/8947*e^3 - 158704/8947*e^2 + 3031457/8947*e - 2743253/8947];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {59, 59, w^5 - w^4 - 4*w^3 + 3*w^2 + 3*w - 3}>] := 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;