/*
  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, 2, -5, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {1, 1, 1}>;

primesArray := [
[2, 2, -w + 1],
[7, 7, -w + 2],
[8, 2, -w^3 + 5*w + 3],
[11, 11, w^3 - w^2 - 5*w + 4],
[11, 11, w^3 - w^2 - 4*w + 1],
[17, 17, -w^3 + w^2 + 5*w],
[25, 5, -w^2 + w + 3],
[25, 5, -w^2 + 2],
[29, 29, w^3 - 2*w^2 - 4*w + 4],
[29, 29, -w^3 + 4*w + 2],
[37, 37, 4*w^3 - 2*w^2 - 21*w - 4],
[43, 43, 4*w^3 - 2*w^2 - 20*w - 3],
[47, 47, -w^3 + 6*w],
[53, 53, w^3 - w^2 - 5*w - 2],
[81, 3, -3],
[83, 83, 2*w^3 - w^2 - 10*w - 4],
[89, 89, w^3 - 2*w^2 - 4*w + 2],
[89, 89, 2*w - 3],
[101, 101, 6*w^3 - 3*w^2 - 31*w - 5],
[107, 107, -w^3 + w^2 + 4*w - 5],
[107, 107, 3*w^3 - 2*w^2 - 14*w + 2],
[113, 113, 3*w^3 - 2*w^2 - 16*w - 2],
[121, 11, w^3 - w^2 - 7*w + 6],
[127, 127, 2*w^3 + w^2 - 11*w - 11],
[131, 131, -2*w^3 + w^2 + 8*w - 2],
[139, 139, w^3 - w^2 - 3*w + 6],
[149, 149, w^3 - 6*w + 2],
[149, 149, 2*w^3 - 2*w^2 - 11*w + 2],
[151, 151, w^2 - 2*w - 4],
[157, 157, w^3 + w^2 - 7*w - 4],
[163, 163, 2*w^2 - 7],
[167, 167, w^2 - 4*w - 2],
[167, 167, -2*w^3 + 2*w^2 + 10*w - 1],
[173, 173, w^2 - w - 7],
[179, 179, 2*w^3 - 2*w^2 - 8*w + 3],
[181, 181, w^3 + w^2 - 4*w - 5],
[191, 191, -w^3 + w^2 + 2*w - 3],
[193, 193, -2*w^3 + 2*w^2 + 7*w - 4],
[193, 193, -w^3 + w^2 + 6*w + 3],
[193, 193, 2*w^3 - 3*w^2 - 8*w + 4],
[193, 193, 2*w^3 - 11*w - 2],
[197, 197, 3*w^3 - 2*w^2 - 14*w],
[199, 199, -w^3 + 8*w - 2],
[199, 199, -5*w^3 + 2*w^2 + 26*w + 4],
[223, 223, 2*w^3 - w^2 - 9*w + 3],
[223, 223, 2*w^2 - 3*w - 4],
[229, 229, w^3 - w^2 - 3*w - 4],
[233, 233, -w - 4],
[239, 239, -w^3 - w^2 + 5*w + 4],
[241, 241, 2*w^3 - 2*w^2 - 7*w],
[241, 241, -2*w^3 + w^2 + 10*w - 2],
[251, 251, 2*w^2 - w - 8],
[251, 251, -3*w^3 + 3*w^2 + 14*w - 3],
[257, 257, -w^2 - 2],
[257, 257, -4*w^3 + 5*w^2 + 17*w - 11],
[257, 257, -3*w^3 + w^2 + 13*w],
[257, 257, -2*w^3 + 3*w^2 + 7*w - 7],
[269, 269, -w^3 - w^2 + 6*w + 5],
[269, 269, w^2 + w - 5],
[271, 271, 3*w^3 - w^2 - 16*w - 7],
[283, 283, 4*w^3 - w^2 - 20*w - 8],
[283, 283, w^2 - 2*w - 6],
[283, 283, 2*w^3 - 12*w - 7],
[283, 283, 3*w^3 - 3*w^2 - 13*w + 6],
[307, 307, w^3 - 6*w - 6],
[311, 311, 2*w^3 - w^2 - 13*w + 5],
[313, 313, -2*w^3 + 3*w^2 + 7*w + 1],
[337, 337, w^3 - 8*w],
[337, 337, 3*w^3 - 3*w^2 - 13*w + 4],
[343, 7, -4*w^3 + 3*w^2 + 19*w - 5],
[349, 349, 2*w^3 - w^2 - 8*w - 4],
[359, 359, w^3 + w^2 - 2*w - 3],
[359, 359, 4*w^3 - 4*w^2 - 20*w + 11],
[373, 373, -8*w^3 + 2*w^2 + 43*w + 16],
[373, 373, 2*w^3 - 10*w - 1],
[379, 379, w^3 + w^2 - 5*w - 10],
[383, 383, 2*w^3 - 3*w^2 - 12*w + 8],
[389, 389, -2*w^3 + 2*w^2 + 7*w - 2],
[389, 389, -3*w^3 + w^2 + 18*w - 1],
[397, 397, 5*w^3 - 26*w - 14],
[397, 397, 4*w^3 - 3*w^2 - 19*w - 1],
[409, 409, -5*w^3 + 6*w^2 + 22*w - 12],
[419, 419, -2*w^3 + w^2 + 12*w],
[419, 419, -6*w^3 + 4*w^2 + 31*w],
[431, 431, 2*w^2 - 5],
[439, 439, 5*w^3 - 3*w^2 - 24*w + 1],
[443, 443, -3*w^3 + w^2 + 13*w + 2],
[443, 443, -w^3 + 3*w^2 + 4*w - 9],
[457, 457, -8*w^3 + 3*w^2 + 43*w + 11],
[463, 463, -3*w^3 + 3*w^2 + 12*w - 1],
[467, 467, -7*w^3 + 3*w^2 + 37*w + 6],
[467, 467, -4*w^3 + 3*w^2 + 20*w],
[479, 479, -2*w^3 + 4*w^2 + 9*w - 10],
[479, 479, 4*w^3 - 2*w^2 - 19*w - 2],
[487, 487, 2*w^3 - 3*w^2 - 12*w + 4],
[487, 487, w^2 + w - 7],
[499, 499, 2*w^2 - w - 4],
[541, 541, -w^3 + 3*w^2 + 3*w - 8],
[547, 547, -w^3 + 2*w^2 + 6*w - 8],
[547, 547, -2*w^3 + 2*w^2 + 12*w - 1],
[569, 569, 4*w^3 - 3*w^2 - 21*w - 1],
[569, 569, -w^3 + 3*w^2 - 5],
[587, 587, 7*w^3 - 4*w^2 - 36*w - 4],
[587, 587, -2*w^3 + 14*w + 3],
[593, 593, -3*w^3 + w^2 + 13*w - 2],
[601, 601, 5*w^3 - w^2 - 28*w - 13],
[601, 601, 8*w^3 - 3*w^2 - 40*w - 8],
[613, 613, -2*w^3 + 3*w^2 + 11*w - 3],
[613, 613, 4*w^3 - w^2 - 19*w - 7],
[617, 617, -2*w^3 + 3*w^2 + 8*w - 2],
[619, 619, -w^3 + 3*w^2 + 3*w - 6],
[641, 641, -4*w^3 + 2*w^2 + 22*w + 3],
[643, 643, -w^3 + 3*w^2 + 4*w - 7],
[643, 643, 2*w^3 - 3*w^2 - 11*w + 13],
[653, 653, 2*w^3 - 9*w - 6],
[659, 659, -3*w^3 + 3*w^2 + 15*w - 2],
[673, 673, -w^3 + 2*w^2 + 6*w - 10],
[677, 677, -2*w^3 + 3*w^2 + 9*w - 3],
[683, 683, -3*w^3 + 3*w^2 + 16*w - 5],
[691, 691, -w^3 + w^2 + 8*w - 3],
[691, 691, w^3 - w^2 - 5*w - 4],
[701, 701, -2*w^3 - w^2 + 13*w + 9],
[709, 709, -5*w^3 + 2*w^2 + 24*w + 4],
[709, 709, -2*w^3 + 4*w^2 + 6*w - 3],
[719, 719, -w^3 + 2*w^2 + 4*w - 10],
[739, 739, -3*w^3 + 4*w^2 + 12*w - 4],
[739, 739, 5*w^3 - w^2 - 25*w - 10],
[743, 743, -3*w^3 + 18*w + 8],
[743, 743, -2*w^3 + 3*w^2 + 7*w - 9],
[761, 761, 2*w^3 - 3*w^2 - 12*w + 10],
[769, 769, -2*w^3 + 14*w - 3],
[773, 773, -w^3 + 4*w^2 + 2*w - 4],
[787, 787, -6*w^3 + 4*w^2 + 29*w - 2],
[787, 787, -3*w^3 + 2*w^2 + 14*w - 10],
[797, 797, 3*w^3 - w^2 - 15*w],
[797, 797, -2*w^3 + 5*w^2 + 5*w - 11],
[809, 809, 6*w^3 - 32*w - 17],
[811, 811, 5*w^3 - 28*w - 18],
[811, 811, -2*w^3 + 2*w^2 + 12*w - 5],
[821, 821, -4*w^3 + 21*w + 8],
[823, 823, -3*w^3 + 3*w^2 + 14*w - 1],
[827, 827, 6*w^3 - 2*w^2 - 30*w - 5],
[827, 827, -4*w^3 + 4*w^2 + 22*w - 13],
[829, 829, 5*w^3 - w^2 - 27*w - 6],
[829, 829, w^3 + 2*w^2 - 8*w - 4],
[841, 29, -2*w^3 + 3*w^2 + 8*w],
[853, 853, -w^3 + 3*w^2 + 7*w - 2],
[853, 853, -2*w^3 + 11*w],
[863, 863, -w^3 + w^2 + 4*w - 7],
[863, 863, 2*w - 7],
[877, 877, 2*w^3 + w^2 - 10*w - 10],
[877, 877, -3*w^3 + w^2 + 18*w + 3],
[883, 883, 3*w^2 - 3*w - 11],
[919, 919, 3*w^3 - 3*w^2 - 17*w + 14],
[919, 919, -2*w^3 + 2*w^2 + 12*w - 3],
[937, 937, -w^2 + 2*w - 4],
[941, 941, 4*w^3 - 3*w^2 - 18*w + 4],
[941, 941, w^3 + w^2 - 4*w - 7],
[941, 941, 7*w^3 - 5*w^2 - 34*w + 3],
[941, 941, 4*w^3 - 2*w^2 - 18*w - 3],
[953, 953, 3*w^3 - 3*w^2 - 10*w - 1],
[961, 31, 4*w^3 - 3*w^2 - 21*w + 7],
[961, 31, 2*w^2 + w - 8],
[967, 967, w^3 + w^2 - 5*w - 12],
[967, 967, 2*w^3 - 8*w - 5],
[971, 971, w^2 + 2*w - 6],
[977, 977, w^2 + 3*w - 5],
[983, 983, w^3 + 2*w^2 - 4*w - 6],
[991, 991, -4*w^3 + 4*w^2 + 19*w - 4],
[1009, 1009, -w^3 - w^2 + 8*w + 7],
[1013, 1013, -3*w^3 + 4*w^2 + 10*w - 4],
[1013, 1013, -2*w^3 + w^2 + 13*w + 1],
[1021, 1021, -4*w^3 + 2*w^2 + 20*w - 1],
[1033, 1033, w^3 + w^2 - 8*w - 11],
[1033, 1033, -2*w^3 + w^2 + 13*w - 3],
[1049, 1049, 3*w^3 - 2*w^2 - 16*w + 6],
[1061, 1061, 3*w^3 - w^2 - 11*w - 4],
[1063, 1063, 6*w^3 - w^2 - 32*w - 16],
[1091, 1091, 6*w^3 - 3*w^2 - 29*w - 5],
[1091, 1091, -6*w^3 + 3*w^2 + 32*w + 2],
[1093, 1093, -10*w^3 + 3*w^2 + 53*w + 19],
[1093, 1093, -4*w^3 + 6*w^2 + 19*w - 12],
[1097, 1097, 4*w^3 - 2*w^2 - 19*w + 2],
[1123, 1123, -4*w^3 + 5*w^2 + 18*w - 8],
[1123, 1123, 4*w^3 - 3*w^2 - 20*w - 2],
[1129, 1129, 2*w^3 - 10*w + 5],
[1129, 1129, -w^3 + 2*w^2 + 2*w - 12],
[1151, 1151, 11*w^3 - 5*w^2 - 57*w - 12],
[1153, 1153, 6*w^3 - 4*w^2 - 31*w - 2],
[1163, 1163, w^3 - 4*w^2 - 6*w + 12],
[1163, 1163, 4*w^3 - 3*w^2 - 20*w - 4],
[1171, 1171, w^3 - w^2 - w - 6],
[1181, 1181, -5*w^3 + 5*w^2 + 26*w - 13],
[1181, 1181, 5*w^3 - 5*w^2 - 22*w + 11],
[1187, 1187, -w^3 - w^2 + 11*w + 2],
[1187, 1187, 3*w^3 - w^2 - 18*w + 3],
[1193, 1193, 12*w^3 - 5*w^2 - 61*w - 13],
[1193, 1193, 2*w^3 - 9*w - 8],
[1201, 1201, 10*w^3 - 3*w^2 - 51*w - 17],
[1213, 1213, -5*w^3 + 7*w^2 + 20*w - 11],
[1217, 1217, 2*w^3 - 13*w - 8],
[1229, 1229, 4*w^3 - 4*w^2 - 16*w + 1],
[1237, 1237, 2*w^3 - 13*w + 2],
[1237, 1237, -8*w^3 + 4*w^2 + 42*w + 9],
[1249, 1249, 4*w^3 - 4*w^2 - 21*w + 6],
[1249, 1249, 3*w^3 - 2*w^2 - 12*w],
[1259, 1259, 4*w + 5],
[1259, 1259, -w^3 - 2*w^2 + 8*w + 12],
[1279, 1279, -w^3 + w^2 + 9*w - 4],
[1283, 1283, -10*w^3 + 5*w^2 + 52*w + 6],
[1291, 1291, 3*w^3 + w^2 - 16*w - 11],
[1301, 1301, 5*w^3 - 26*w - 12],
[1301, 1301, 4*w^3 - 3*w^2 - 22*w],
[1321, 1321, -w - 6],
[1327, 1327, w^3 + 2*w^2 - 8*w - 6],
[1361, 1361, 2*w^3 - 3*w^2 - 12*w],
[1367, 1367, 4*w^3 - 22*w - 15],
[1381, 1381, -5*w^3 + 2*w^2 + 26*w + 2],
[1381, 1381, w^3 - w^2 - 6*w - 5],
[1399, 1399, -w^3 + 6*w - 6],
[1399, 1399, -2*w^3 + 3*w^2 + 11*w - 1],
[1423, 1423, 2*w^3 + w^2 - 12*w - 14],
[1423, 1423, 3*w^3 - 14*w - 8],
[1427, 1427, -4*w^3 + w^2 + 18*w],
[1447, 1447, -5*w^3 + w^2 + 29*w + 10],
[1447, 1447, -4*w^3 + 2*w^2 + 22*w - 3],
[1453, 1453, 6*w^3 - 3*w^2 - 29*w - 3],
[1453, 1453, 4*w^3 - 4*w^2 - 22*w + 1],
[1459, 1459, 6*w^3 - 7*w^2 - 26*w + 12],
[1471, 1471, -w^3 + w^2 + w - 6],
[1483, 1483, 6*w^3 - 3*w^2 - 34*w - 8],
[1489, 1489, -2*w^3 - w^2 + 8*w - 2],
[1493, 1493, 3*w^3 - w^2 - 10*w + 3],
[1493, 1493, 3*w^3 - 5*w^2 - 12*w + 7],
[1511, 1511, 8*w^3 - 3*w^2 - 41*w - 7],
[1523, 1523, -w^3 + 4*w^2 + 4*w - 6],
[1543, 1543, -w^3 + w^2 + 5*w - 8],
[1543, 1543, -3*w^3 + 2*w^2 + 16*w - 8],
[1553, 1553, w^3 + w^2 - 8*w - 9],
[1559, 1559, 3*w^3 - 3*w^2 - 15*w - 2],
[1559, 1559, -3*w^3 + 3*w^2 + 11*w - 4],
[1567, 1567, w^3 - w^2 - 3*w - 6],
[1567, 1567, 2*w^3 - 11*w - 10],
[1567, 1567, -w^3 + 2*w^2 + 8*w - 8],
[1567, 1567, w^3 + w^2 - 2*w - 5],
[1579, 1579, w^2 + 2*w - 10],
[1579, 1579, w^3 + w^2 - 9*w - 6],
[1597, 1597, -2*w^3 + 5*w^2 + 7*w - 5],
[1597, 1597, 2*w^3 - 4*w^2 - 10*w + 5],
[1607, 1607, -8*w^3 + 3*w^2 + 40*w + 6],
[1609, 1609, 3*w^2 - 4*w - 6],
[1609, 1609, -2*w^3 - w^2 + 14*w + 8],
[1613, 1613, -3*w^3 + 3*w^2 + 10*w - 5],
[1613, 1613, 2*w^3 - 10*w + 3],
[1627, 1627, -5*w^3 + 2*w^2 + 28*w + 2],
[1627, 1627, -3*w^3 + w^2 + 13*w - 4],
[1627, 1627, 4*w^3 - 5*w^2 - 16*w + 4],
[1627, 1627, -3*w^3 - w^2 + 17*w + 4],
[1663, 1663, -4*w^3 + w^2 + 22*w + 2],
[1667, 1667, 2*w^3 - 2*w^2 - 8*w - 5],
[1669, 1669, 2*w^3 - 2*w^2 - 13*w + 6],
[1669, 1669, -4*w^3 + 2*w^2 + 21*w - 2],
[1693, 1693, w^3 - w^2 - 2*w + 9],
[1693, 1693, -w^3 + w^2 + 9*w - 2],
[1697, 1697, 6*w^3 - 4*w^2 - 29*w - 4],
[1697, 1697, -2*w^3 + 11*w - 2],
[1721, 1721, -4*w^3 + 4*w^2 + 14*w - 11],
[1721, 1721, w^3 - 6*w - 8],
[1733, 1733, 4*w^3 - 2*w^2 - 17*w + 6],
[1741, 1741, 5*w^3 - 4*w^2 - 28*w + 14],
[1747, 1747, -w^3 - 3*w^2 + 6*w + 17],
[1787, 1787, 7*w^3 - 5*w^2 - 36*w + 3],
[1789, 1789, -w^3 - w^2 + 11*w],
[1789, 1789, w^3 + 2*w^2 - 6*w - 8],
[1811, 1811, 4*w^3 - 2*w^2 - 17*w + 2],
[1847, 1847, 6*w^3 - 5*w^2 - 32*w + 2],
[1847, 1847, -2*w^3 + 3*w^2 + 15*w + 1],
[1861, 1861, 2*w^3 - 3*w^2 - 13*w + 11],
[1861, 1861, -4*w^3 + 3*w^2 + 17*w - 5],
[1879, 1879, -8*w^3 + 5*w^2 + 39*w - 1],
[1933, 1933, 5*w^3 - 5*w^2 - 22*w + 7],
[1949, 1949, 3*w^3 - 3*w^2 - 17*w + 4],
[1951, 1951, -4*w^3 + 3*w^2 + 23*w - 13],
[1973, 1973, 9*w^3 - w^2 - 47*w - 22],
[1973, 1973, -3*w^3 + 12*w - 2],
[1973, 1973, w^2 - 2*w - 10],
[1973, 1973, w^3 - w^2 - 10*w + 5],
[1979, 1979, 5*w^3 - 3*w^2 - 23*w - 2],
[1979, 1979, 5*w^3 - w^2 - 27*w - 14],
[1987, 1987, 7*w^3 - w^2 - 35*w - 14],
[1993, 1993, -w^3 + 3*w^2 - 7],
[1993, 1993, 3*w^2 - w - 5],
[1993, 1993, -10*w^3 + 5*w^2 + 53*w + 9],
[1993, 1993, -2*w^3 + 14*w - 7],
[1997, 1997, -7*w^3 + 4*w^2 + 36*w + 6]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x;
K := Rationals(); e := 1;

heckeEigenvaluesArray := [-1, 0, -3, 4, 4, 2, 2, 2, -2, -2, 6, 4, -8, -2, 10, 4, -6, 18, -10, 4, -12, 2, 10, -8, 12, -4, 6, -10, 8, -18, 20, -24, 8, -18, -20, -18, 8, 18, 10, -14, -14, -18, -8, 16, -8, -8, 6, 18, -8, 2, 18, -12, -4, 18, -30, -14, 18, 30, 14, -8, 28, -12, -20, -4, -28, 0, 26, -22, 2, 24, -2, 32, 16, 22, -10, 20, -24, -34, 30, -2, -10, -22, 4, 4, 8, 40, -12, -20, -22, 40, 20, -28, 0, 8, 16, 16, -4, 30, -20, -12, 10, -6, -36, 28, -30, 34, 42, -42, -2, -22, 4, 50, -4, -20, -34, 36, 34, 30, -20, 36, 4, 30, -10, -34, -40, 4, -20, 24, 32, 42, 50, -18, 20, 4, 14, -42, -38, -44, -20, -42, -8, -20, -44, 14, -34, 42, 38, 6, -32, 0, 14, -10, -4, -8, 16, 18, -18, 30, 38, 6, -6, -6, 18, -56, 16, -60, -30, -32, 32, -22, -42, -58, -34, -46, 10, -30, -42, -32, 60, 36, -18, 22, -6, -44, 28, -6, -54, -32, 10, 4, -36, -4, 30, 30, -12, 12, -54, -54, 34, -66, 2, -66, -58, -58, 10, -62, 28, 12, 24, 36, -68, 22, 30, -22, 8, 66, -24, 22, 38, -56, 64, 64, 8, -44, 72, -32, 14, 14, -52, 16, 44, -14, -2, -66, 0, 12, -16, 64, 34, -56, 0, -16, 32, -32, -24, -12, -68, 30, -2, -32, 26, -38, 22, -18, 36, 44, 44, -12, 40, -60, -26, -50, 62, 30, 74, 66, 58, -54, -66, 70, 28, -36, 70, -26, 60, 24, -8, 22, -26, 0, 46, -34, -16, -42, 54, 6, 54, 4, 60, 76, 58, 10, 10, -54, 78];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();

// 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;