/*
  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![20, 10, -11, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {16,4,1/2*w^3 + 1/2*w^2 - 5/2*w - 2}>;

primesArray := [
[4, 2, -w + 2],
[4, 2, 1/2*w^3 + 1/2*w^2 - 9/2*w - 4],
[5, 5, -1/2*w^3 - 3/2*w^2 + 7/2*w + 10],
[5, 5, -1/2*w^3 - 1/2*w^2 + 5/2*w + 3],
[19, 19, 1/2*w^3 + 1/2*w^2 - 9/2*w - 3],
[19, 19, w - 1],
[31, 31, 1/2*w^3 + 3/2*w^2 - 7/2*w - 6],
[31, 31, -w^3 - 2*w^2 + 7*w + 13],
[49, 7, -2*w^3 - 2*w^2 + 15*w + 9],
[49, 7, 1/2*w^3 + 3/2*w^2 - 9/2*w - 4],
[59, 59, -3/2*w^3 - 3/2*w^2 + 17/2*w + 8],
[59, 59, -1/2*w^3 - 5/2*w^2 + 11/2*w + 9],
[61, 61, -1/2*w^3 - 3/2*w^2 + 9/2*w + 9],
[61, 61, -3/2*w^3 - 5/2*w^2 + 23/2*w + 12],
[71, 71, -3/2*w^3 - 1/2*w^2 + 23/2*w - 1],
[71, 71, 3/2*w^3 + 3/2*w^2 - 19/2*w - 9],
[79, 79, -1/2*w^3 - 3/2*w^2 + 11/2*w + 4],
[79, 79, -5/2*w^3 - 7/2*w^2 + 37/2*w + 18],
[81, 3, -3],
[89, 89, w^3 - 7*w + 1],
[89, 89, -2*w^3 - 3*w^2 + 14*w + 17],
[89, 89, 1/2*w^3 - 1/2*w^2 - 7/2*w + 2],
[89, 89, -5/2*w^3 - 7/2*w^2 + 35/2*w + 18],
[101, 101, -2*w^2 + 11],
[101, 101, 3*w^3 + 5*w^2 - 21*w - 27],
[121, 11, -3/2*w^3 - 3/2*w^2 + 21/2*w + 7],
[121, 11, 3/2*w^3 + 3/2*w^2 - 21/2*w - 8],
[131, 131, -3/2*w^3 - 5/2*w^2 + 21/2*w + 16],
[131, 131, -3/2*w^3 - 5/2*w^2 + 19/2*w + 14],
[139, 139, -2*w^3 - w^2 + 16*w + 1],
[139, 139, 1/2*w^3 + 1/2*w^2 - 3/2*w - 8],
[149, 149, -3/2*w^3 - 7/2*w^2 + 21/2*w + 24],
[149, 149, -w^3 + w^2 + 5*w - 3],
[149, 149, -5*w^3 - 7*w^2 + 37*w + 39],
[149, 149, -3/2*w^3 - 7/2*w^2 + 21/2*w + 14],
[181, 181, -5/2*w^3 - 9/2*w^2 + 37/2*w + 27],
[181, 181, -5/2*w^3 - 7/2*w^2 + 33/2*w + 19],
[181, 181, 3/2*w^3 + 1/2*w^2 - 23/2*w - 2],
[181, 181, w^3 + 3*w^2 - 8*w - 13],
[191, 191, 1/2*w^3 + 5/2*w^2 - 7/2*w - 14],
[191, 191, -5/2*w^3 - 9/2*w^2 + 35/2*w + 24],
[199, 199, -1/2*w^3 - 5/2*w^2 + 7/2*w + 16],
[199, 199, 5/2*w^3 + 9/2*w^2 - 35/2*w - 22],
[211, 211, -2*w^3 - 4*w^2 + 14*w + 19],
[211, 211, -w^3 - 3*w^2 + 7*w + 19],
[229, 229, 3/2*w^3 + 7/2*w^2 - 21/2*w - 17],
[229, 229, -3/2*w^3 - 7/2*w^2 + 21/2*w + 21],
[229, 229, -1/2*w^3 - 3/2*w^2 + 13/2*w + 1],
[229, 229, 5/2*w^3 + 7/2*w^2 - 41/2*w - 24],
[241, 241, -1/2*w^3 - 5/2*w^2 + 7/2*w + 12],
[241, 241, 3/2*w^3 + 3/2*w^2 - 23/2*w - 3],
[241, 241, w^3 + w^2 - 6*w - 1],
[241, 241, -5/2*w^3 - 9/2*w^2 + 35/2*w + 26],
[251, 251, 2*w^3 + 2*w^2 - 13*w - 9],
[251, 251, -5/2*w^3 - 5/2*w^2 + 37/2*w + 11],
[269, 269, -2*w^3 - 3*w^2 + 12*w + 17],
[269, 269, 5/2*w^3 + 11/2*w^2 - 37/2*w - 21],
[271, 271, 3/2*w^3 + 5/2*w^2 - 23/2*w - 9],
[271, 271, 1/2*w^3 + 3/2*w^2 - 9/2*w - 12],
[281, 281, 5/2*w^3 + 9/2*w^2 - 39/2*w - 28],
[281, 281, 3/2*w^3 + 7/2*w^2 - 25/2*w - 14],
[311, 311, 1/2*w^3 + 7/2*w^2 - 5/2*w - 24],
[311, 311, 3*w^3 + 5*w^2 - 22*w - 27],
[311, 311, 3/2*w^3 + 5/2*w^2 - 17/2*w - 12],
[311, 311, 1/2*w^3 + 5/2*w^2 - 9/2*w - 13],
[349, 349, 3*w^3 + 4*w^2 - 21*w - 21],
[349, 349, -3/2*w^3 - 1/2*w^2 + 21/2*w + 2],
[359, 359, -w^3 - 3*w^2 + 7*w + 17],
[359, 359, -2*w^3 - 4*w^2 + 14*w + 21],
[361, 19, -2*w^3 - 2*w^2 + 14*w + 11],
[389, 389, -2*w^3 - 2*w^2 + 13*w + 11],
[389, 389, 5/2*w^3 + 5/2*w^2 - 37/2*w - 13],
[401, 401, 3/2*w^3 + 7/2*w^2 - 21/2*w - 19],
[401, 401, 5/2*w^3 + 9/2*w^2 - 37/2*w - 23],
[401, 401, -w^3 - 3*w^2 + 8*w + 17],
[431, 431, 5/2*w^3 + 5/2*w^2 - 29/2*w - 13],
[431, 431, -15/2*w^3 - 23/2*w^2 + 107/2*w + 61],
[439, 439, -3/2*w^3 + 1/2*w^2 + 21/2*w - 6],
[439, 439, -9/2*w^3 - 13/2*w^2 + 63/2*w + 32],
[449, 449, -w^2 - 2*w + 1],
[449, 449, -1/2*w^3 - 3/2*w^2 + 3/2*w + 14],
[461, 461, -2*w^3 - 2*w^2 + 12*w + 9],
[461, 461, -3*w^3 - 3*w^2 + 23*w + 13],
[479, 479, 7/2*w^3 + 9/2*w^2 - 47/2*w - 26],
[479, 479, 3/2*w^3 + 5/2*w^2 - 27/2*w - 16],
[479, 479, -7/2*w^3 - 9/2*w^2 + 51/2*w + 24],
[479, 479, 3/2*w^3 + 1/2*w^2 - 19/2*w - 3],
[491, 491, 2*w^3 + 4*w^2 - 15*w - 23],
[491, 491, -7/2*w^3 - 7/2*w^2 + 53/2*w + 17],
[491, 491, -1/2*w^3 - 5/2*w^2 + 11/2*w + 6],
[491, 491, -3/2*w^3 - 7/2*w^2 + 23/2*w + 17],
[499, 499, 3*w^2 - 19],
[499, 499, 3/2*w^3 + 5/2*w^2 - 19/2*w - 16],
[499, 499, -9/2*w^3 - 15/2*w^2 + 63/2*w + 38],
[499, 499, -1/2*w^3 + 1/2*w^2 + 9/2*w - 1],
[509, 509, 2*w^2 - w - 7],
[509, 509, 7/2*w^3 + 11/2*w^2 - 51/2*w - 33],
[521, 521, 4*w^3 + 5*w^2 - 32*w - 31],
[521, 521, -1/2*w^3 + 1/2*w^2 - 1/2*w + 4],
[541, 541, 1/2*w^3 - 7/2*w^2 - 3/2*w + 18],
[541, 541, -15/2*w^3 - 23/2*w^2 + 109/2*w + 62],
[541, 541, -w^3 - 3*w^2 + 7*w + 11],
[541, 541, 2*w^3 + 4*w^2 - 14*w - 27],
[569, 569, 1/2*w^3 + 5/2*w^2 - 7/2*w - 21],
[569, 569, -5/2*w^3 - 5/2*w^2 + 31/2*w + 14],
[571, 571, 2*w^2 + 2*w - 11],
[571, 571, 2*w^3 + 4*w^2 - 12*w - 23],
[601, 601, w^3 + 3*w^2 - 8*w - 9],
[601, 601, 3*w^3 + 2*w^2 - 23*w - 7],
[601, 601, -3/2*w^3 - 7/2*w^2 + 23/2*w + 19],
[601, 601, -2*w^3 - 4*w^2 + 15*w + 21],
[631, 631, -5/2*w^3 - 3/2*w^2 + 33/2*w + 3],
[631, 631, -13/2*w^3 - 19/2*w^2 + 101/2*w + 58],
[641, 641, 13/2*w^3 + 19/2*w^2 - 97/2*w - 52],
[641, 641, -3/2*w^3 - 9/2*w^2 + 23/2*w + 16],
[659, 659, 1/2*w^3 - 1/2*w^2 - 1/2*w + 2],
[659, 659, 3/2*w^3 + 7/2*w^2 - 15/2*w - 11],
[661, 661, -3/2*w^3 - 3/2*w^2 + 25/2*w + 3],
[661, 661, -1/2*w^3 - 1/2*w^2 + 3/2*w - 1],
[691, 691, -2*w^3 - 7*w^2 + 14*w + 49],
[691, 691, -1/2*w^3 - 7/2*w^2 + 13/2*w + 14],
[691, 691, -13/2*w^3 - 19/2*w^2 + 101/2*w + 59],
[691, 691, -7/2*w^3 - 13/2*w^2 + 49/2*w + 36],
[701, 701, 3/2*w^3 + 11/2*w^2 - 21/2*w - 38],
[701, 701, -2*w^3 - 2*w^2 + 10*w + 11],
[709, 709, 1/2*w^3 + 5/2*w^2 - 9/2*w - 17],
[709, 709, -3*w^3 - 3*w^2 + 22*w + 13],
[709, 709, -3*w^3 - 5*w^2 + 22*w + 23],
[709, 709, -5/2*w^3 - 5/2*w^2 + 33/2*w + 11],
[751, 751, -3/2*w^3 + 3/2*w^2 + 15/2*w - 4],
[751, 751, 15/2*w^3 + 21/2*w^2 - 111/2*w - 59],
[751, 751, 1/2*w^3 - 1/2*w^2 - 9/2*w - 2],
[751, 751, -3/2*w^3 - 5/2*w^2 + 19/2*w + 19],
[769, 769, -9/2*w^3 - 15/2*w^2 + 65/2*w + 38],
[769, 769, -1/2*w^3 - 7/2*w^2 + 9/2*w + 21],
[809, 809, -7/2*w^3 - 13/2*w^2 + 51/2*w + 42],
[809, 809, -5/2*w^3 - 3/2*w^2 + 27/2*w + 14],
[809, 809, -3*w^3 - 5*w^2 + 21*w + 29],
[809, 809, 2*w^2 - 9],
[811, 811, 3*w^3 + 5*w^2 - 20*w - 27],
[811, 811, 1/2*w^3 - 7/2*w^2 - 9/2*w + 31],
[811, 811, w^3 - w^2 - 2*w + 1],
[811, 811, 3/2*w^3 + 5/2*w^2 - 19/2*w - 18],
[821, 821, 9/2*w^3 + 13/2*w^2 - 67/2*w - 34],
[821, 821, 3/2*w^3 + 3/2*w^2 - 25/2*w - 1],
[829, 829, 1/2*w^3 + 5/2*w^2 - 1/2*w - 21],
[829, 829, 4*w^3 + 2*w^2 - 32*w - 3],
[839, 839, -1/2*w^3 - 1/2*w^2 + 3/2*w - 2],
[839, 839, -3/2*w^3 - 3/2*w^2 + 25/2*w + 2],
[841, 29, -5/2*w^3 - 5/2*w^2 + 35/2*w + 11],
[841, 29, 5/2*w^3 + 5/2*w^2 - 35/2*w - 14],
[881, 881, -9/2*w^3 - 13/2*w^2 + 63/2*w + 36],
[881, 881, 1/2*w^3 + 5/2*w^2 - 3/2*w - 21],
[911, 911, -1/2*w^3 + 3/2*w^2 + 7/2*w - 7],
[911, 911, 7/2*w^3 + 13/2*w^2 - 49/2*w - 38],
[911, 911, 7*w^3 + 11*w^2 - 51*w - 61],
[911, 911, -7/2*w^3 - 11/2*w^2 + 49/2*w + 31],
[919, 919, -1/2*w^3 + 7/2*w^2 + 3/2*w - 16],
[919, 919, 15/2*w^3 + 23/2*w^2 - 109/2*w - 64],
[929, 929, -3/2*w^3 - 7/2*w^2 + 19/2*w + 23],
[929, 929, -5/2*w^3 - 7/2*w^2 + 33/2*w + 21],
[941, 941, -1/2*w^3 - 7/2*w^2 + 11/2*w + 18],
[941, 941, -5*w^3 - 8*w^2 + 37*w + 43],
[961, 31, 5/2*w^3 + 5/2*w^2 - 35/2*w - 13],
[971, 971, 2*w^3 + w^2 - 14*w - 3],
[971, 971, -5/2*w^3 - 9/2*w^2 + 35/2*w + 31],
[971, 971, 7/2*w^3 + 9/2*w^2 - 49/2*w - 22],
[971, 971, 3/2*w^3 + 1/2*w^2 - 27/2*w + 6],
[991, 991, 5/2*w^3 + 7/2*w^2 - 39/2*w - 16],
[991, 991, 5/2*w^3 + 7/2*w^2 - 37/2*w - 14],
[1009, 1009, 1/2*w^3 + 7/2*w^2 - 9/2*w - 18],
[1009, 1009, 9/2*w^3 + 15/2*w^2 - 65/2*w - 41],
[1019, 1019, 2*w^3 + 5*w^2 - 14*w - 21],
[1019, 1019, 5/2*w^3 + 11/2*w^2 - 35/2*w - 36],
[1021, 1021, 1/2*w^3 + 3/2*w^2 - 7/2*w - 2],
[1021, 1021, w^3 + 2*w^2 - 7*w - 17],
[1039, 1039, -3/2*w^3 - 5/2*w^2 + 27/2*w + 8],
[1039, 1039, -7/2*w^3 - 13/2*w^2 + 51/2*w + 31],
[1039, 1039, -3*w^3 - 4*w^2 + 25*w + 19],
[1039, 1039, -4*w^3 - 6*w^2 + 29*w + 29],
[1051, 1051, 3/2*w^3 + 7/2*w^2 - 27/2*w - 13],
[1051, 1051, -7/2*w^3 - 9/2*w^2 + 53/2*w + 22],
[1061, 1061, 1/2*w^3 + 3/2*w^2 - 1/2*w - 17],
[1061, 1061, -3*w^3 - w^2 + 24*w - 3],
[1069, 1069, -7/2*w^3 - 9/2*w^2 + 47/2*w + 23],
[1069, 1069, 2*w^3 + 3*w^2 - 14*w - 23],
[1129, 1129, 3*w^3 + 4*w^2 - 23*w - 19],
[1129, 1129, 5/2*w^3 + 7/2*w^2 - 37/2*w - 13],
[1151, 1151, w^3 + w^2 - 4*w - 13],
[1151, 1151, -5*w^3 - 8*w^2 + 35*w + 43],
[1229, 1229, -3*w^3 - 4*w^2 + 19*w + 23],
[1229, 1229, -3/2*w^3 - 9/2*w^2 + 19/2*w + 31],
[1249, 1249, 3*w^3 + 6*w^2 - 21*w - 23],
[1249, 1249, 7/2*w^3 + 1/2*w^2 - 55/2*w + 7],
[1279, 1279, 2*w^3 + 2*w^2 - 17*w - 9],
[1279, 1279, -3*w^3 - 6*w^2 + 21*w + 29],
[1319, 1319, 3/2*w^3 + 9/2*w^2 - 19/2*w - 22],
[1319, 1319, -w^3 + w^2 + 9],
[1319, 1319, 5/2*w^3 + 11/2*w^2 - 33/2*w - 33],
[1319, 1319, 9*w^3 + 14*w^2 - 65*w - 77],
[1321, 1321, 3*w^3 + 3*w^2 - 16*w - 19],
[1321, 1321, -3*w^3 - 8*w^2 + 21*w + 53],
[1361, 1361, -11*w^3 - 17*w^2 + 79*w + 89],
[1361, 1361, -9/2*w^3 - 11/2*w^2 + 59/2*w + 24],
[1409, 1409, -3/2*w^3 - 1/2*w^2 + 15/2*w + 3],
[1409, 1409, -5*w^3 - 6*w^2 + 39*w + 31],
[1409, 1409, 7/2*w^3 + 13/2*w^2 - 51/2*w - 27],
[1409, 1409, 1/2*w^3 + 5/2*w^2 - 9/2*w - 21],
[1429, 1429, -1/2*w^3 - 1/2*w^2 + 13/2*w - 1],
[1429, 1429, 7/2*w^3 + 13/2*w^2 - 49/2*w - 34],
[1429, 1429, 1/2*w^3 - 5/2*w^2 - 5/2*w + 17],
[1429, 1429, 11/2*w^3 + 17/2*w^2 - 79/2*w - 42],
[1439, 1439, -17/2*w^3 - 25/2*w^2 + 125/2*w + 71],
[1439, 1439, 9/2*w^3 + 17/2*w^2 - 65/2*w - 51],
[1451, 1451, 3/2*w^3 - 3/2*w^2 - 15/2*w + 7],
[1451, 1451, -7/2*w^3 - 5/2*w^2 + 47/2*w + 7],
[1459, 1459, 3/2*w^3 + 11/2*w^2 - 25/2*w - 18],
[1459, 1459, -7/2*w^3 - 9/2*w^2 + 55/2*w + 22],
[1459, 1459, 3*w^3 + 5*w^2 - 22*w - 21],
[1459, 1459, w^3 + 7*w^2 - 5*w - 53],
[1471, 1471, -1/2*w^3 - 9/2*w^2 + 7/2*w + 37],
[1471, 1471, -21/2*w^3 - 31/2*w^2 + 151/2*w + 82],
[1481, 1481, -11/2*w^3 - 15/2*w^2 + 81/2*w + 38],
[1481, 1481, 3/2*w^3 - 1/2*w^2 - 17/2*w + 4],
[1489, 1489, -7/2*w^3 - 7/2*w^2 + 45/2*w + 22],
[1489, 1489, 9/2*w^3 + 9/2*w^2 - 67/2*w - 26],
[1499, 1499, 7/2*w^3 + 9/2*w^2 - 45/2*w - 26],
[1499, 1499, 7*w^3 + 11*w^2 - 49*w - 53],
[1511, 1511, -7/2*w^3 - 9/2*w^2 + 51/2*w + 19],
[1511, 1511, -3/2*w^3 - 1/2*w^2 + 19/2*w - 2],
[1511, 1511, -5*w^3 - 3*w^2 + 39*w + 9],
[1511, 1511, 1/2*w^3 - 9/2*w^2 - 5/2*w + 26],
[1559, 1559, -9/2*w^3 - 13/2*w^2 + 65/2*w + 31],
[1559, 1559, -3/2*w^3 - 5/2*w^2 + 27/2*w + 4],
[1559, 1559, -6*w^3 - 8*w^2 + 43*w + 37],
[1559, 1559, w^3 - w^2 - 6*w + 9],
[1571, 1571, 9/2*w^3 + 17/2*w^2 - 65/2*w - 39],
[1571, 1571, -2*w^3 - 6*w^2 + 15*w + 39],
[1601, 1601, -3*w^3 - 5*w^2 + 24*w + 33],
[1601, 1601, -7/2*w^3 - 9/2*w^2 + 51/2*w + 14],
[1609, 1609, 4*w^3 + 5*w^2 - 28*w - 23],
[1609, 1609, -3/2*w^3 - 3/2*w^2 + 13/2*w + 8],
[1609, 1609, -13/2*w^3 - 19/2*w^2 + 91/2*w + 48],
[1609, 1609, -5/2*w^3 - 3/2*w^2 + 35/2*w + 4],
[1619, 1619, 5/2*w^3 + 7/2*w^2 - 29/2*w - 14],
[1619, 1619, -11/2*w^3 - 17/2*w^2 + 75/2*w + 44],
[1621, 1621, 2*w^3 + 2*w^2 - 16*w - 3],
[1621, 1621, w^3 + w^2 - 5*w + 1],
[1669, 1669, -6*w^3 - 6*w^2 + 46*w + 31],
[1669, 1669, -1/2*w^3 - 9/2*w^2 + 15/2*w + 11],
[1681, 41, 3*w^3 + 3*w^2 - 21*w - 13],
[1681, 41, 3*w^3 + 3*w^2 - 21*w - 17],
[1699, 1699, 7/2*w^3 + 7/2*w^2 - 39/2*w - 23],
[1699, 1699, -7/2*w^3 - 17/2*w^2 + 49/2*w + 56],
[1709, 1709, -1/2*w^3 + 1/2*w^2 + 13/2*w - 1],
[1709, 1709, 1/2*w^3 + 3/2*w^2 - 1/2*w - 12],
[1721, 1721, 5/2*w^3 + 9/2*w^2 - 39/2*w - 19],
[1721, 1721, -3*w^3 - 3*w^2 + 23*w + 11],
[1741, 1741, 5/2*w^3 + 9/2*w^2 - 31/2*w - 26],
[1741, 1741, -3*w^3 - 5*w^2 + 21*w + 31],
[1759, 1759, w^3 + 5*w^2 - 6*w - 33],
[1759, 1759, 9/2*w^3 + 17/2*w^2 - 61/2*w - 41],
[1789, 1789, 5/2*w^3 + 11/2*w^2 - 35/2*w - 28],
[1789, 1789, 2*w^3 + 5*w^2 - 14*w - 29],
[1801, 1801, w^3 + 3*w^2 - 4*w - 23],
[1801, 1801, 3/2*w^3 + 9/2*w^2 - 21/2*w - 26],
[1801, 1801, 3*w^3 + 6*w^2 - 21*w - 31],
[1801, 1801, 11/2*w^3 + 17/2*w^2 - 79/2*w - 48],
[1811, 1811, 1/2*w^3 + 3/2*w^2 - 5/2*w - 1],
[1811, 1811, 1/2*w^3 + 3/2*w^2 - 5/2*w - 16],
[1831, 1831, -9/2*w^3 - 13/2*w^2 + 63/2*w + 37],
[1831, 1831, -w^3 - 3*w^2 + 5*w + 23],
[1849, 43, 6*w^3 + 8*w^2 - 44*w - 43],
[1849, 43, 1/2*w^3 - 3/2*w^2 + 1/2*w - 3],
[1861, 1861, 5/2*w^3 + 7/2*w^2 - 33/2*w - 23],
[1861, 1861, 5/2*w^3 + 9/2*w^2 - 33/2*w - 27],
[1861, 1861, -2*w^3 + 13*w - 1],
[1861, 1861, 2*w^3 + 3*w^2 - 12*w - 7],
[1871, 1871, 3/2*w^3 + 5/2*w^2 - 15/2*w - 14],
[1871, 1871, 3/2*w^3 + 1/2*w^2 - 27/2*w - 1],
[1901, 1901, -4*w^3 - 5*w^2 + 28*w + 27],
[1901, 1901, 5/2*w^3 + 3/2*w^2 - 35/2*w - 8],
[1931, 1931, -2*w^3 + w^2 + 10*w + 1],
[1931, 1931, 17/2*w^3 + 23/2*w^2 - 127/2*w - 66],
[1949, 1949, -w^3 - 2*w^2 + 3*w + 17],
[1949, 1949, -4*w^2 + 2*w + 17],
[1949, 1949, -w^3 - 5*w^2 + 7*w + 27],
[1949, 1949, -5*w^3 - 9*w^2 + 35*w + 49],
[1951, 1951, -13/2*w^3 - 17/2*w^2 + 103/2*w + 52],
[1951, 1951, 11/2*w^3 + 13/2*w^2 - 87/2*w - 41],
[1979, 1979, -15/2*w^3 - 19/2*w^2 + 119/2*w + 59],
[1979, 1979, 9/2*w^3 + 17/2*w^2 - 61/2*w - 47],
[1999, 1999, 3*w^3 + 3*w^2 - 20*w - 17],
[1999, 1999, 7/2*w^3 + 7/2*w^2 - 51/2*w - 19]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^5 - 2*x^4 - 11*x^3 + 5*x^2 + 32*x + 17;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 0, -e^4 + 4*e^3 + 4*e^2 - 15*e - 9, e, 2*e^4 - 7*e^3 - 12*e^2 + 27*e + 28, -e^4 + 3*e^3 + 8*e^2 - 13*e - 19, 4*e^4 - 14*e^3 - 21*e^2 + 48*e + 41, e^4 - 4*e^3 - 5*e^2 + 16*e + 14, -4*e^4 + 16*e^3 + 14*e^2 - 56*e - 27, e^4 - 4*e^3 - 2*e^2 + 10*e + 4, e^4 - 4*e^3 - 4*e^2 + 14*e + 19, -e^4 + 3*e^3 + 7*e^2 - 9*e - 16, -5*e^4 + 17*e^3 + 28*e^2 - 61*e - 56, 5*e^4 - 18*e^3 - 27*e^2 + 66*e + 65, -3*e^4 + 9*e^3 + 21*e^2 - 33*e - 44, 3*e^4 - 11*e^3 - 15*e^2 + 39*e + 30, -e^4 + 5*e^3 - 19*e + 1, 2*e^4 - 8*e^3 - 9*e^2 + 32*e + 23, e^3 - 5*e^2 + e + 11, -2*e^4 + 7*e^3 + 7*e^2 - 19*e - 4, -e^4 + 2*e^3 + 10*e^2 - 7*e - 21, e^4 - 3*e^3 - 7*e^2 + 10*e + 24, -e^4 + 4*e^3 + 6*e^2 - 18*e - 20, -2*e^4 + 5*e^3 + 19*e^2 - 23*e - 38, 2*e^4 - 6*e^3 - 16*e^2 + 28*e + 43, -6*e^4 + 20*e^3 + 37*e^2 - 77*e - 79, -3*e^4 + 12*e^3 + 11*e^2 - 40*e - 24, -e^4 + 4*e^3 + e^2 - 6*e + 4, 7*e^4 - 25*e^3 - 38*e^2 + 91*e + 81, -2*e^4 + 8*e^3 + 3*e^2 - 20*e + 5, 10*e^4 - 35*e^3 - 54*e^2 + 127*e + 120, -3*e^4 + 13*e^3 + 10*e^2 - 50*e - 29, 3*e^4 - 10*e^3 - 22*e^2 + 44*e + 54, -8*e^4 + 30*e^3 + 38*e^2 - 110*e - 79, -2*e^4 + 7*e^3 + 10*e^2 - 24*e - 20, -3*e^4 + 12*e^3 + 10*e^2 - 34*e - 14, 6*e^4 - 23*e^3 - 24*e^2 + 76*e + 42, -9*e^4 + 32*e^3 + 49*e^2 - 121*e - 108, e^3 + e^2 - 13*e, -2*e^4 + 6*e^3 + 15*e^2 - 24*e - 25, 7*e^4 - 24*e^3 - 41*e^2 + 88*e + 84, 3*e^4 - 10*e^3 - 23*e^2 + 52*e + 58, -6*e^4 + 24*e^3 + 25*e^2 - 92*e - 51, 2*e^4 - 5*e^3 - 20*e^2 + 19*e + 44, e^4 - 6*e^3 + 7*e^2 + 14*e - 18, -13*e^4 + 46*e^3 + 66*e^2 - 161*e - 131, -5*e^4 + 18*e^3 + 22*e^2 - 57*e - 39, e^4 - 4*e^3 - 3*e^2 + 10*e, -9*e^4 + 35*e^3 + 36*e^2 - 121*e - 63, -12*e^4 + 42*e^3 + 70*e^2 - 156*e - 155, -5*e^4 + 20*e^3 + 15*e^2 - 66*e - 28, -6*e^4 + 22*e^3 + 29*e^2 - 78*e - 67, 5*e^4 - 19*e^3 - 23*e^2 + 67*e + 47, -10*e^4 + 36*e^3 + 50*e^2 - 122*e - 92, -3*e^4 + 10*e^3 + 26*e^2 - 54*e - 69, 3*e^4 - 11*e^3 - 18*e^2 + 44*e + 53, -8*e^4 + 30*e^3 + 37*e^2 - 109*e - 83, -2*e^4 + 5*e^3 + 17*e^2 - 15*e - 25, -e^4 + 4*e^3 + 2*e^2 - 4*e - 3, 9*e^4 - 32*e^3 - 45*e^2 + 115*e + 94, 2*e^4 - 9*e^3 - 4*e^2 + 28*e + 16, e^4 - 5*e^3 - 5*e^2 + 25*e + 20, 5*e^4 - 19*e^3 - 16*e^2 + 55*e + 21, -13*e^4 + 49*e^3 + 65*e^2 - 185*e - 156, 9*e^4 - 30*e^3 - 55*e^2 + 114*e + 110, -3*e^4 + 11*e^3 + 10*e^2 - 29*e + 4, 8*e^4 - 30*e^3 - 37*e^2 + 102*e + 76, -9*e^4 + 33*e^3 + 46*e^2 - 121*e - 83, -5*e^4 + 14*e^3 + 37*e^2 - 50*e - 76, 6*e^4 - 21*e^3 - 35*e^2 + 88*e + 83, 9*e^4 - 31*e^3 - 50*e^2 + 111*e + 114, 19*e^4 - 66*e^3 - 105*e^2 + 238*e + 223, -2*e^2, 15*e^4 - 53*e^3 - 82*e^2 + 197*e + 198, 2*e^4 - 9*e^3 - 4*e^2 + 27*e + 19, -9*e^4 + 32*e^3 + 53*e^2 - 130*e - 132, -12*e^4 + 45*e^3 + 56*e^2 - 169*e - 124, -6*e^4 + 21*e^3 + 32*e^2 - 75*e - 72, 5*e^4 - 20*e^3 - 17*e^2 + 72*e + 22, -3*e^4 + 13*e^3 + 7*e^2 - 49*e - 12, -6*e^4 + 23*e^3 + 31*e^2 - 97*e - 67, -5*e^4 + 18*e^3 + 27*e^2 - 64*e - 44, -12*e^4 + 45*e^3 + 64*e^2 - 173*e - 166, -6*e^4 + 20*e^3 + 37*e^2 - 76*e - 75, 3*e^4 - 14*e^3 - 9*e^2 + 52*e + 48, 9*e^4 - 34*e^3 - 43*e^2 + 118*e + 100, -3*e^4 + 9*e^3 + 32*e^2 - 53*e - 93, -4*e^4 + 12*e^3 + 32*e^2 - 52*e - 74, -3*e^4 + 12*e^3 + 17*e^2 - 54*e - 48, -9*e^4 + 29*e^3 + 58*e^2 - 103*e - 129, 14*e^4 - 50*e^3 - 74*e^2 + 178*e + 170, -7*e^4 + 23*e^3 + 38*e^2 - 71*e - 71, 7*e^4 - 29*e^3 - 29*e^2 + 113*e + 66, -17*e^4 + 59*e^3 + 88*e^2 - 203*e - 171, -5*e^4 + 17*e^3 + 29*e^2 - 57*e - 72, -9*e^4 + 31*e^3 + 50*e^2 - 114*e - 99, -e^3 + 16*e, 9*e^4 - 35*e^3 - 32*e^2 + 117*e + 55, 5*e^4 - 19*e^3 - 20*e^2 + 61*e + 39, 12*e^4 - 43*e^3 - 63*e^2 + 148*e + 135, 15*e^4 - 50*e^3 - 88*e^2 + 177*e + 177, -4*e^4 + 13*e^3 + 23*e^2 - 48*e - 55, 17*e^4 - 63*e^3 - 79*e^2 + 222*e + 156, 2*e^4 - 14*e^3 + 13*e^2 + 44*e - 22, -7*e^4 + 32*e^3 + 17*e^2 - 120*e - 37, 10*e^4 - 37*e^3 - 45*e^2 + 131*e + 99, -13*e^4 + 47*e^3 + 61*e^2 - 163*e - 110, -22*e^4 + 80*e^3 + 116*e^2 - 298*e - 265, 6*e^4 - 25*e^3 - 19*e^2 + 91*e + 50, 10*e^4 - 34*e^3 - 59*e^2 + 132*e + 115, -13*e^4 + 51*e^3 + 58*e^2 - 187*e - 147, 3*e^4 - 6*e^3 - 29*e^2 + 18*e + 52, -2*e^3 + 9*e^2 - 4*e - 25, 21*e^4 - 77*e^3 - 109*e^2 + 285*e + 240, 2*e^4 - 8*e^3 - 6*e^2 + 26*e + 4, -4*e^4 + 15*e^3 + 16*e^2 - 45*e - 2, 6*e^4 - 20*e^3 - 35*e^2 + 74*e + 57, 9*e^4 - 33*e^3 - 39*e^2 + 107*e + 52, e^4 - 3*e^3 - e^2 - 3*e + 6, 15*e^4 - 52*e^3 - 85*e^2 + 182*e + 178, 2*e^4 - 4*e^3 - 17*e^2 + 12*e + 5, 10*e^4 - 39*e^3 - 40*e^2 + 139*e + 78, 11*e^4 - 39*e^3 - 58*e^2 + 133*e + 101, 5*e^4 - 16*e^3 - 33*e^2 + 66*e + 74, -4*e^4 + 17*e^3 + 8*e^2 - 49*e + 10, e^4 - 5*e^3 + 2*e^2 + 15*e - 4, 21*e^4 - 76*e^3 - 112*e^2 + 281*e + 261, -6*e^4 + 19*e^3 + 40*e^2 - 75*e - 53, 8*e^4 - 32*e^3 - 26*e^2 + 107*e + 42, -e^4 + 5*e^3 - 4*e^2 - 15*e + 35, 11*e^4 - 40*e^3 - 57*e^2 + 142*e + 114, -2*e^4 + 12*e^3 - 2*e^2 - 54*e + 2, 7*e^4 - 27*e^3 - 31*e^2 + 103*e + 90, -5*e^4 + 22*e^3 + 7*e^2 - 62*e - 2, 5*e^4 - 21*e^3 - 12*e^2 + 65*e + 25, 12*e^4 - 45*e^3 - 59*e^2 + 169*e + 127, -11*e^4 + 41*e^3 + 53*e^2 - 143*e - 108, 7*e^4 - 28*e^3 - 29*e^2 + 104*e + 57, -10*e^4 + 38*e^3 + 39*e^2 - 120*e - 64, -12*e^4 + 45*e^3 + 56*e^2 - 161*e - 120, 6*e^4 - 23*e^3 - 29*e^2 + 83*e + 53, 8*e^4 - 27*e^3 - 49*e^2 + 103*e + 127, -17*e^4 + 59*e^3 + 90*e^2 - 209*e - 175, 4*e^4 - 14*e^3 - 17*e^2 + 33*e + 9, 3*e^4 - 10*e^3 - 11*e^2 + 25*e + 2, 21*e^4 - 75*e^3 - 118*e^2 + 281*e + 272, 3*e^4 - 12*e^3 - 7*e^2 + 26*e + 11, -11*e^4 + 40*e^3 + 53*e^2 - 146*e - 94, 11*e^4 - 42*e^3 - 53*e^2 + 152*e + 122, 4*e^4 - 16*e^3 - 22*e^2 + 70*e + 58, -5*e^4 + 16*e^3 + 28*e^2 - 52*e - 41, -18*e^4 + 68*e^3 + 83*e^2 - 244*e - 181, -2*e^4 + 10*e^3 + 3*e^2 - 46*e + 19, 4*e^4 - 15*e^3 - 12*e^2 + 37*e + 28, -19*e^4 + 67*e^3 + 107*e^2 - 249*e - 248, -9*e^4 + 28*e^3 + 64*e^2 - 122*e - 141, e^4 - 4*e^3 + 3*e^2 + 4*e - 16, -5*e^4 + 23*e^3 + 3*e^2 - 73*e - 8, -6*e^4 + 23*e^3 + 25*e^2 - 83*e - 19, e^4 - 5*e^3 + 5*e^2 + 21*e - 34, 5*e^4 - 23*e^3 - 5*e^2 + 67*e - 8, 14*e^4 - 49*e^3 - 83*e^2 + 186*e + 199, -3*e^4 + 6*e^3 + 34*e^2 - 31*e - 45, 15*e^4 - 58*e^3 - 62*e^2 + 201*e + 115, 20*e^4 - 69*e^3 - 113*e^2 + 249*e + 243, 16*e^4 - 52*e^3 - 108*e^2 + 202*e + 230, 15*e^4 - 58*e^3 - 64*e^2 + 216*e + 155, 11*e^4 - 39*e^3 - 61*e^2 + 143*e + 120, 19*e^4 - 68*e^3 - 97*e^2 + 240*e + 192, -10*e^4 + 35*e^3 + 62*e^2 - 145*e - 142, 16*e^4 - 55*e^3 - 92*e^2 + 192*e + 204, 12*e^4 - 38*e^3 - 87*e^2 + 159*e + 201, -2*e^4 + 7*e^3 + 5*e^2 - 17*e + 15, 8*e^4 - 36*e^3 - 22*e^2 + 138*e + 46, -12*e^4 + 41*e^3 + 70*e^2 - 150*e - 164, 7*e^4 - 24*e^3 - 37*e^2 + 81*e + 52, 3*e^4 - 11*e^3 - 20*e^2 + 59*e + 37, -4*e^3 + 22*e^2 - 56, 10*e^4 - 35*e^3 - 45*e^2 + 115*e + 55, -e^4 + 13*e^2 + 12*e - 22, 18*e^4 - 67*e^3 - 79*e^2 + 221*e + 139, -13*e^4 + 45*e^3 + 83*e^2 - 177*e - 198, -18*e^4 + 63*e^3 + 94*e^2 - 213*e - 175, 3*e^4 - 10*e^3 - 21*e^2 + 50*e + 71, -e^4 - 2*e^3 + 20*e^2 - 15, -2*e^3 + 14*e^2 - 10*e - 12, 4*e^4 - 19*e^3 - 2*e^2 + 56*e - 28, 33*e^4 - 115*e^3 - 176*e^2 + 408*e + 359, -16*e^4 + 61*e^3 + 72*e^2 - 227*e - 146, 13*e^4 - 50*e^3 - 53*e^2 + 162*e + 98, -4*e^4 + 14*e^3 + 18*e^2 - 44*e - 42, 17*e^4 - 64*e^3 - 70*e^2 + 216*e + 119, 26*e^4 - 94*e^3 - 131*e^2 + 335*e + 261, -10*e^4 + 38*e^3 + 37*e^2 - 133*e - 39, -4*e^4 + 18*e^3 + 2*e^2 - 52*e + 6, e^4 - 12*e^3 + 18*e^2 + 52*e - 29, -e^4 + 5*e^3 + 7*e^2 - 15*e - 68, -22*e^4 + 84*e^3 + 94*e^2 - 296*e - 188, 6*e^4 - 26*e^3 - 14*e^2 + 98*e + 14, e^4 - 5*e^3 + 7*e^2 - e - 60, 15*e^4 - 53*e^3 - 85*e^2 + 202*e + 216, 24*e^4 - 88*e^3 - 124*e^2 + 325*e + 278, -26*e^4 + 96*e^3 + 129*e^2 - 347*e - 269, 3*e^4 - 15*e^3 - 4*e^2 + 58*e + 3, 2*e^4 - 7*e^3 - 11*e^2 + 35*e + 33, -11*e^4 + 38*e^3 + 61*e^2 - 128*e - 96, -14*e^4 + 55*e^3 + 60*e^2 - 195*e - 156, -18*e^4 + 60*e^3 + 116*e^2 - 232*e - 264, -9*e^4 + 39*e^3 + 28*e^2 - 148*e - 71, -16*e^4 + 55*e^3 + 86*e^2 - 200*e - 152, -3*e^4 + 10*e^3 + 15*e^2 - 32*e - 34, 13*e^4 - 40*e^3 - 101*e^2 + 166*e + 218, -10*e^4 + 40*e^3 + 38*e^2 - 160*e - 68, 12*e^4 - 44*e^3 - 66*e^2 + 164*e + 146, -30*e^4 + 105*e^3 + 172*e^2 - 393*e - 380, -7*e^4 + 30*e^3 + 27*e^2 - 120*e - 42, 30*e^4 - 107*e^3 - 167*e^2 + 401*e + 387, -4*e^4 + 22*e^3 - 3*e^2 - 74*e - 5, 5*e^4 - 12*e^3 - 47*e^2 + 38*e + 108, -10*e^4 + 40*e^3 + 36*e^2 - 142*e - 70, -10*e^4 + 31*e^3 + 69*e^2 - 105*e - 165, 15*e^4 - 48*e^3 - 108*e^2 + 200*e + 235, 22*e^4 - 74*e^3 - 134*e^2 + 275*e + 272, 6*e^4 - 19*e^3 - 29*e^2 + 42*e + 37, 9*e^4 - 33*e^3 - 40*e^2 + 115*e + 46, -5*e^4 + 27*e^3 - 4*e^2 - 105*e + 10, -6*e^4 + 27*e^3 - 77*e + 10, -14*e^4 + 53*e^3 + 64*e^2 - 191*e - 126, -11*e^4 + 44*e^3 + 49*e^2 - 160*e - 126, -3*e^4 + 14*e^3 + 21*e^2 - 82*e - 70, 9*e^4 - 29*e^3 - 56*e^2 + 87*e + 111, 23*e^4 - 80*e^3 - 127*e^2 + 278*e + 274, 14*e^4 - 53*e^3 - 64*e^2 + 179*e + 158, -24*e^4 + 87*e^3 + 121*e^2 - 301*e - 265, 11*e^4 - 38*e^3 - 66*e^2 + 146*e + 123, 18*e^4 - 63*e^3 - 98*e^2 + 225*e + 188, 5*e^4 - 26*e^3 + 90*e + 15, 8*e^4 - 31*e^3 - 31*e^2 + 101*e + 55, 8*e^4 - 30*e^3 - 45*e^2 + 125*e + 141, 11*e^4 - 38*e^3 - 55*e^2 + 127*e + 82, -5*e^4 + 20*e^3 + 33*e^2 - 105*e - 64, 9*e^4 - 32*e^3 - 48*e^2 + 121*e + 87, 7*e^4 - 30*e^3 - 12*e^2 + 93*e - 11, 31*e^4 - 108*e^3 - 179*e^2 + 409*e + 404, -e^4 + 3*e^3 + 18*e^2 - 35*e - 87, -13*e^4 + 41*e^3 + 94*e^2 - 169*e - 211, e^4 - 5*e^3 + e^2 + 3*e - 19, -17*e^4 + 56*e^3 + 110*e^2 - 206*e - 256, 15*e^4 - 53*e^3 - 80*e^2 + 184*e + 151, 20*e^4 - 69*e^3 - 118*e^2 + 258*e + 282, -15*e^4 + 51*e^3 + 89*e^2 - 193*e - 168, 4*e^4 - 10*e^3 - 36*e^2 + 20*e + 92, 12*e^4 - 43*e^3 - 79*e^2 + 185*e + 209, -36*e^4 + 129*e^3 + 185*e^2 - 463*e - 383, 4*e^4 - 11*e^3 - 22*e^2 + 15*e + 36, -13*e^4 + 49*e^3 + 72*e^2 - 195*e - 203, -13*e^4 + 42*e^3 + 77*e^2 - 141*e - 134, 21*e^4 - 77*e^3 - 102*e^2 + 270*e + 205, -23*e^4 + 82*e^3 + 122*e^2 - 288*e - 243, -17*e^4 + 58*e^3 + 94*e^2 - 196*e - 193, 17*e^4 - 60*e^3 - 87*e^2 + 194*e + 178, 17*e^4 - 63*e^3 - 80*e^2 + 225*e + 149, -15*e^4 + 59*e^3 + 66*e^2 - 219*e - 130, -21*e^4 + 76*e^3 + 107*e^2 - 280*e - 199, -9*e^4 + 31*e^3 + 50*e^2 - 100*e - 129, 8*e^4 - 27*e^3 - 52*e^2 + 116*e + 82, -15*e^4 + 55*e^3 + 72*e^2 - 190*e - 173, -7*e^4 + 17*e^3 + 68*e^2 - 72*e - 133, -e^4 + 29*e^2 - 28*e - 62, -23*e^4 + 85*e^3 + 112*e^2 - 301*e - 205, 9*e^4 - 27*e^3 - 65*e^2 + 111*e + 154, 10*e^4 - 39*e^3 - 31*e^2 + 129*e + 29, e^4 - 2*e^3 - 13*e^2 + 35*e + 18, -13*e^4 + 40*e^3 + 89*e^2 - 149*e - 150, -28*e^4 + 93*e^3 + 162*e^2 - 313*e - 344, 32*e^4 - 114*e^3 - 177*e^2 + 422*e + 397, -3*e^4 + 9*e^3 + 7*e^2 - 13*e + 23, 22*e^4 - 71*e^3 - 139*e^2 + 257*e + 278, 15*e^4 - 56*e^3 - 67*e^2 + 202*e + 134, -5*e^4 + 15*e^3 + 32*e^2 - 33*e - 75, -4*e^4 + 21*e^3 - 89*e + 6, -7*e^4 + 27*e^3 + 34*e^2 - 109*e - 47, 27*e^4 - 102*e^3 - 130*e^2 + 380*e + 291, -28*e^4 + 95*e^3 + 165*e^2 - 347*e - 349, 5*e^4 - 15*e^3 - 31*e^2 + 41*e + 68, 20*e^4 - 74*e^3 - 96*e^2 + 270*e + 182, -6*e^4 + 28*e^3 + e^2 - 73*e + 3, -6*e^4 + 21*e^3 + 46*e^2 - 112*e - 104, 19*e^4 - 72*e^3 - 75*e^2 + 236*e + 130, -37*e^4 + 130*e^3 + 205*e^2 - 466*e - 434, -e^4 + 5*e^3 + 6*e^2 - 43*e - 51, -11*e^4 + 31*e^3 + 88*e^2 - 125*e - 163, -14*e^4 + 58*e^3 + 46*e^2 - 230*e - 82, 4*e^4 - 15*e^3 - 23*e^2 + 67*e + 39];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {4,2,-1/2*w^3 - 1/2*w^2 + 9/2*w + 4}>] := 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;