/*
  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![-28, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {11, 11, 4*w + 19}>;

primesArray := [
[2, 2, -w + 6],
[2, 2, w + 5],
[7, 7, 6*w - 35],
[7, 7, -6*w - 29],
[9, 3, 3],
[11, 11, 4*w + 19],
[11, 11, 4*w - 23],
[13, 13, -2*w + 11],
[13, 13, 2*w + 9],
[25, 5, -5],
[31, 31, 2*w - 13],
[31, 31, -2*w - 11],
[41, 41, -8*w - 39],
[41, 41, 8*w - 47],
[53, 53, -26*w - 125],
[53, 53, 26*w - 151],
[61, 61, -14*w + 81],
[61, 61, -14*w - 67],
[83, 83, 2*w - 15],
[83, 83, -2*w - 13],
[97, 97, 2*w - 5],
[97, 97, -2*w - 3],
[109, 109, 2*w - 3],
[109, 109, -2*w - 1],
[113, 113, 2*w - 1],
[127, 127, 8*w - 45],
[127, 127, 8*w + 37],
[131, 131, -50*w + 291],
[131, 131, 50*w + 241],
[139, 139, 6*w - 37],
[139, 139, -6*w - 31],
[149, 149, 20*w + 97],
[149, 149, 20*w - 117],
[157, 157, -12*w - 59],
[157, 157, 12*w - 71],
[163, 163, 4*w - 19],
[163, 163, 4*w + 15],
[173, 173, 4*w + 23],
[173, 173, 4*w - 27],
[211, 211, 2*w - 19],
[211, 211, -2*w - 17],
[227, 227, -4*w - 13],
[227, 227, 4*w - 17],
[233, 233, 6*w + 25],
[233, 233, -6*w + 31],
[239, 239, -14*w - 69],
[239, 239, 14*w - 83],
[241, 241, 46*w + 221],
[241, 241, -46*w + 267],
[251, 251, 22*w - 129],
[251, 251, 22*w + 107],
[257, 257, -34*w + 197],
[257, 257, -34*w - 163],
[277, 277, 4*w - 29],
[277, 277, -4*w - 25],
[283, 283, 4*w - 15],
[283, 283, -4*w - 11],
[289, 17, -17],
[307, 307, 68*w - 395],
[307, 307, 68*w + 327],
[311, 311, 10*w - 61],
[311, 311, -10*w - 51],
[313, 313, -32*w - 155],
[313, 313, 32*w - 187],
[317, 317, -18*w - 85],
[317, 317, 18*w - 103],
[331, 331, -4*w - 9],
[331, 331, 4*w - 13],
[337, 337, -16*w - 79],
[337, 337, 16*w - 95],
[347, 347, -12*w + 67],
[347, 347, 12*w + 55],
[353, 353, 14*w - 79],
[353, 353, 14*w + 65],
[361, 19, -19],
[367, 367, -32*w - 153],
[367, 367, -32*w + 185],
[383, 383, 56*w + 269],
[383, 383, 56*w - 325],
[389, 389, -4*w - 27],
[389, 389, 4*w - 31],
[401, 401, 8*w - 51],
[401, 401, -8*w - 43],
[421, 421, 12*w - 73],
[421, 421, -12*w - 61],
[439, 439, -8*w - 33],
[439, 439, 8*w - 41],
[443, 443, -4*w - 1],
[443, 443, 4*w - 5],
[461, 461, -30*w + 173],
[461, 461, 30*w + 143],
[463, 463, 2*w - 25],
[463, 463, -2*w - 23],
[467, 467, 34*w + 165],
[467, 467, 34*w - 199],
[503, 503, -26*w - 127],
[503, 503, 26*w - 153],
[509, 509, 4*w - 33],
[509, 509, -4*w - 29],
[521, 521, -10*w + 53],
[521, 521, 10*w + 43],
[529, 23, -23],
[547, 547, 14*w - 85],
[547, 547, -14*w - 71],
[557, 557, 66*w + 317],
[557, 557, 66*w - 383],
[563, 563, 2*w - 27],
[563, 563, -2*w - 25],
[569, 569, -64*w + 373],
[569, 569, 64*w + 309],
[587, 587, 12*w + 53],
[587, 587, -12*w + 65],
[593, 593, 8*w + 45],
[593, 593, 8*w - 53],
[601, 601, -26*w - 123],
[601, 601, 26*w - 149],
[617, 617, 6*w - 23],
[617, 617, -6*w - 17],
[647, 647, 24*w - 137],
[647, 647, -24*w - 113],
[653, 653, 28*w - 165],
[653, 653, -28*w - 137],
[677, 677, -22*w - 103],
[677, 677, 22*w - 125],
[691, 691, 20*w - 113],
[691, 691, 20*w + 93],
[709, 709, -10*w - 41],
[709, 709, 10*w - 51],
[719, 719, -8*w + 37],
[719, 719, -8*w - 29],
[727, 727, -22*w - 109],
[727, 727, 22*w - 131],
[739, 739, 46*w - 269],
[739, 739, -46*w - 223],
[761, 761, -6*w - 13],
[761, 761, 6*w - 19],
[769, 769, 110*w - 639],
[769, 769, 110*w + 529],
[773, 773, 4*w - 37],
[773, 773, -4*w - 33],
[787, 787, 2*w - 31],
[787, 787, -2*w - 29],
[809, 809, 56*w + 271],
[809, 809, -56*w + 327],
[821, 821, 6*w - 17],
[821, 821, -6*w - 11],
[823, 823, 38*w - 223],
[823, 823, -38*w - 185],
[827, 827, 132*w - 767],
[827, 827, 132*w + 635],
[841, 29, -29],
[853, 853, -76*w + 443],
[853, 853, 76*w + 367],
[863, 863, 14*w - 87],
[863, 863, -14*w - 73],
[911, 911, 2*w - 33],
[911, 911, -2*w - 31],
[919, 919, -6*w - 41],
[919, 919, 6*w - 47],
[929, 929, 50*w + 239],
[929, 929, 50*w - 289],
[953, 953, 6*w - 11],
[953, 953, -6*w - 5],
[967, 967, -8*w - 25],
[967, 967, 8*w - 33],
[991, 991, 16*w + 71],
[991, 991, -16*w + 87]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^16 - 2*x^15 - 21*x^14 + 38*x^13 + 178*x^12 - 280*x^11 - 781*x^10 + 1012*x^9 + 1884*x^8 - 1880*x^7 - 2438*x^6 + 1731*x^5 + 1543*x^4 - 679*x^3 - 368*x^2 + 65*x + 11;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [-25/6212*e^15 - 45/12424*e^14 + 3249/12424*e^13 - 2883/12424*e^12 - 22685/6212*e^11 + 50151/12424*e^10 + 260119/12424*e^9 - 277285/12424*e^8 - 86181/1553*e^7 + 628165/12424*e^6 + 816877/12424*e^5 - 144597/3106*e^4 - 47237/1553*e^3 + 211201/12424*e^2 + 14703/6212*e - 21713/12424, e, -187/3106*e^15 - 13/3106*e^14 + 5287/3106*e^13 - 1247/3106*e^12 - 55383/3106*e^11 + 20493/3106*e^10 + 275517/3106*e^9 - 109439/3106*e^8 - 679465/3106*e^7 + 234617/3106*e^6 + 392581/1553*e^5 - 187693/3106*e^4 - 368659/3106*e^3 + 37339/3106*e^2 + 21227/1553*e + 1941/3106, -1715/6212*e^15 + 5445/6212*e^14 + 29287/6212*e^13 - 49987/3106*e^12 - 183339/6212*e^11 + 705915/6212*e^10 + 498765/6212*e^9 - 602834/1553*e^8 - 477617/6212*e^7 + 4108199/6212*e^6 - 98555/3106*e^5 - 1597759/3106*e^4 + 441489/6212*e^3 + 440699/3106*e^2 - 90277/6212*e - 18061/3106, -515/1553*e^15 + 5911/6212*e^14 + 36641/6212*e^13 - 109151/6212*e^12 - 60425/1553*e^11 + 771951/6212*e^10 + 702227/6212*e^9 - 2613973/6212*e^8 - 361361/3106*e^7 + 4310781/6212*e^6 - 355057/6212*e^5 - 1539821/3106*e^4 + 415493/3106*e^3 + 688933/6212*e^2 - 96503/3106*e - 24585/6212, -1, 1815/6212*e^15 - 12263/12424*e^14 - 63805/12424*e^13 + 228563/12424*e^12 + 211959/6212*e^11 - 1638835/12424*e^10 - 1325179/12424*e^9 + 5672461/12424*e^8 + 491087/3106*e^7 - 9721161/12424*e^6 - 1178965/12424*e^5 + 1868653/3106*e^4 + 50771/3106*e^3 - 1888561/12424*e^2 - 15125/6212*e + 36409/12424, -1875/6212*e^15 + 12155/12424*e^14 + 66633/12424*e^13 - 231755/12424*e^12 - 216707/6212*e^11 + 1702047/12424*e^10 + 1186631/12424*e^9 - 6021133/12424*e^8 - 209633/3106*e^7 + 10446045/12424*e^6 - 1646255/12424*e^5 - 998667/1553*e^4 + 541233/3106*e^3 + 2058753/12424*e^2 - 186265/6212*e - 97217/12424, 773/6212*e^15 - 2255/6212*e^14 - 14231/6212*e^13 + 10343/1553*e^12 + 101341/6212*e^11 - 289525/6212*e^10 - 352353/6212*e^9 + 483489/3106*e^8 + 619715/6212*e^7 - 1585669/6212*e^6 - 129990/1553*e^5 + 299593/1553*e^4 + 227059/6212*e^3 - 175233/3106*e^2 - 63385/6212*e + 6791/1553, 2085/6212*e^15 - 1278/1553*e^14 - 19521/3106*e^13 + 89627/6212*e^12 + 289233/6212*e^11 - 295627/3106*e^10 - 546207/3106*e^9 + 1826251/6212*e^8 + 2246173/6212*e^7 - 673427/1553*e^6 - 2406953/6212*e^5 + 432217/1553*e^4 + 1145465/6212*e^3 - 312327/6212*e^2 - 157145/6212*e - 15031/6212, 693/6212*e^15 - 970/1553*e^14 - 4361/3106*e^13 + 71857/6212*e^12 + 22537/6212*e^11 - 256991/3106*e^10 + 55369/3106*e^9 + 1789017/6212*e^8 - 645535/6212*e^7 - 781493/1553*e^6 + 1024031/6212*e^5 + 1251219/3106*e^4 - 450255/6212*e^3 - 724129/6212*e^2 - 80319/6212*e + 55475/6212, 501/3106*e^15 - 784/1553*e^14 - 8235/3106*e^13 + 14273/1553*e^12 + 46479/3106*e^11 - 99575/1553*e^10 - 85159/3106*e^9 + 334012/1553*e^8 - 110235/3106*e^7 - 551966/1553*e^6 + 280834/1553*e^5 + 805783/3106*e^4 - 289203/1553*e^3 - 182221/3106*e^2 + 160443/3106*e + 1299/1553, -2039/6212*e^15 + 1366/1553*e^14 + 19859/3106*e^13 - 108903/6212*e^12 - 292219/6212*e^11 + 419813/3106*e^10 + 489573/3106*e^9 - 3126323/6212*e^8 - 1327247/6212*e^7 + 1425263/1553*e^6 + 68695/6212*e^5 - 2271205/3106*e^4 + 867885/6212*e^3 + 1173503/6212*e^2 - 258407/6212*e - 32269/6212, 3005/6212*e^15 - 19439/12424*e^14 - 96081/12424*e^13 + 341567/12424*e^12 + 266785/6212*e^11 - 2266163/12424*e^10 - 1079711/12424*e^9 + 7065321/12424*e^8 - 23470/1553*e^7 - 10453369/12424*e^6 + 3030955/12424*e^5 + 1572883/3106*e^4 - 649847/3106*e^3 - 770689/12424*e^2 + 154071/6212*e - 66227/12424, 2993/3106*e^15 - 9575/3106*e^14 - 26286/1553*e^13 + 89037/1553*e^12 + 342243/3106*e^11 - 1269481/3106*e^10 - 491868/1553*e^9 + 2168129/1553*e^8 + 1024735/3106*e^7 - 7224811/3106*e^6 + 381135/3106*e^5 + 2630209/1553*e^4 - 468705/1553*e^3 - 1236297/3106*e^2 + 70097/1553*e + 23188/1553, -631/3106*e^15 + 7357/12424*e^14 + 41571/12424*e^13 - 126463/12424*e^12 - 61943/3106*e^11 + 815309/12424*e^10 + 625989/12424*e^9 - 2451413/12424*e^8 - 242819/6212*e^7 + 3480267/12424*e^6 - 566647/12424*e^5 - 502521/3106*e^4 + 594733/6212*e^3 + 211041/12424*e^2 - 71656/1553*e + 33083/12424, 3063/6212*e^15 - 11065/6212*e^14 - 49045/6212*e^13 + 103945/3106*e^12 + 259779/6212*e^11 - 1507727/6212*e^10 - 358331/6212*e^9 + 1322049/1553*e^8 - 1104235/6212*e^7 - 9112139/6212*e^6 + 918840/1553*e^5 + 3374877/3106*e^4 - 3001555/6212*e^3 - 370260/1553*e^2 + 508707/6212*e + 23323/3106, -4535/6212*e^15 + 6889/3106*e^14 + 39331/3106*e^13 - 247977/6212*e^12 - 505887/6212*e^11 + 423221/1553*e^10 + 720323/3106*e^9 - 5456933/6212*e^8 - 1487299/6212*e^7 + 4204963/3106*e^6 - 663377/6212*e^5 - 2742945/3106*e^4 + 1669639/6212*e^3 + 999963/6212*e^2 - 402225/6212*e + 11793/6212, 4993/6212*e^15 - 26421/12424*e^14 - 183363/12424*e^13 + 476525/12424*e^12 + 650633/6212*e^11 - 3269553/12424*e^10 - 4509053/12424*e^9 + 10664763/12424*e^8 + 1979049/3106*e^7 - 16915459/12424*e^6 - 6544515/12424*e^5 + 1488772/1553*e^4 + 291849/1553*e^3 - 2846307/12424*e^2 - 223827/6212*e + 163423/12424, 5731/6212*e^15 - 15497/6212*e^14 - 103017/6212*e^13 + 138187/3106*e^12 + 707791/6212*e^11 - 1868075/6212*e^10 - 2324783/6212*e^9 + 1492149/1553*e^8 + 3683965/6212*e^7 - 9175055/6212*e^6 - 582556/1553*e^5 + 3035119/3106*e^4 + 211173/6212*e^3 - 290125/1553*e^2 + 43351/6212*e - 6585/3106, 190/1553*e^15 - 3975/6212*e^14 - 11181/6212*e^13 + 74571/6212*e^12 + 12447/1553*e^11 - 533383/6212*e^10 - 11363/6212*e^9 + 1806029/6212*e^8 - 227687/3106*e^7 - 2909033/6212*e^6 + 1109789/6212*e^5 + 975111/3106*e^4 - 408237/3106*e^3 - 387833/6212*e^2 + 84319/3106*e + 53293/6212, 1189/1553*e^15 - 10939/6212*e^14 - 94793/6212*e^13 + 206955/6212*e^12 + 185613/1553*e^11 - 1505895/6212*e^10 - 2887523/6212*e^9 + 5280329/6212*e^8 + 2891853/3106*e^7 - 9156489/6212*e^6 - 5628039/6212*e^5 + 3624919/3106*e^4 + 1245495/3106*e^3 - 2080789/6212*e^2 - 230507/3106*e + 70481/6212, -673/1553*e^15 + 7827/6212*e^14 + 44909/6212*e^13 - 128447/6212*e^12 - 72721/1553*e^11 + 773975/6212*e^10 + 985511/6212*e^9 - 2123297/6212*e^8 - 1033217/3106*e^7 + 2809789/6212*e^6 + 2724343/6212*e^5 - 1016545/3106*e^4 - 860489/3106*e^3 + 825757/6212*e^2 + 110091/3106*e - 60745/6212, -1053/3106*e^15 + 21989/12424*e^14 + 54847/12424*e^13 - 404935/12424*e^12 - 38601/3106*e^11 + 2859509/12424*e^10 - 700063/12424*e^9 - 9689293/12424*e^8 + 2329373/6212*e^7 + 16013923/12424*e^6 - 8713843/12424*e^5 - 2818187/3106*e^4 + 2785551/6212*e^3 + 1995885/12424*e^2 - 143419/3106*e + 115315/12424, -5891/6212*e^15 + 5003/1553*e^14 + 50029/3106*e^13 - 369151/6212*e^12 - 623131/6212*e^11 + 1306709/3106*e^10 + 846653/3106*e^9 - 8898103/6212*e^8 - 1676599/6212*e^7 + 3722272/1553*e^6 - 394673/6212*e^5 - 5483101/3106*e^4 + 984225/6212*e^3 + 2539231/6212*e^2 - 27523/6212*e - 18729/6212, -3241/3106*e^15 + 9973/3106*e^14 + 55207/3106*e^13 - 89540/1553*e^12 - 343025/3106*e^11 + 1219557/3106*e^10 + 902503/3106*e^9 - 1960336/1553*e^8 - 659177/3106*e^7 + 6015715/3106*e^6 - 540523/1553*e^5 - 1930665/1553*e^4 + 1625061/3106*e^3 + 324024/1553*e^2 - 415079/3106*e + 6950/1553, -259/1553*e^15 + 5279/12424*e^14 + 37545/12424*e^13 - 96425/12424*e^12 - 31263/1553*e^11 + 659623/12424*e^10 + 712599/12424*e^9 - 2039443/12424*e^8 - 313767/6212*e^7 + 2565017/12424*e^6 - 522657/12424*e^5 - 88277/3106*e^4 + 270505/6212*e^3 - 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1092834/1553*e^6 - 5223715/6212*e^5 + 528670/1553*e^4 + 338687/6212*e^3 + 177975/6212*e^2 + 598721/6212*e - 54005/6212, 6115/3106*e^15 - 57325/6212*e^14 - 159839/6212*e^13 + 1019509/6212*e^12 + 240597/3106*e^11 - 6888585/6212*e^10 + 1633195/6212*e^9 + 22128439/6212*e^8 - 2922913/1553*e^7 - 34602391/6212*e^6 + 22137949/6212*e^5 + 5929137/1553*e^4 - 3776885/1553*e^3 - 5120703/6212*e^2 + 1204901/3106*e + 227099/6212, 3361/6212*e^15 - 6759/6212*e^14 - 70459/6212*e^13 + 36250/1553*e^12 + 569941/6212*e^11 - 1220649/6212*e^10 - 2233093/6212*e^9 + 2527581/3106*e^8 + 4419099/6212*e^7 - 10501965/6212*e^6 - 1111442/1553*e^5 + 2467642/1553*e^4 + 2504675/6212*e^3 - 1677921/3106*e^2 - 722717/6212*e + 62976/1553, 1003/3106*e^15 - 5649/6212*e^14 - 41891/6212*e^13 + 127593/6212*e^12 + 160955/3106*e^11 - 1112809/6212*e^10 - 1071757/6212*e^9 + 4679103/6212*e^8 + 309509/1553*e^7 - 9632223/6212*e^6 + 489173/6212*e^5 + 2186034/1553*e^4 - 278501/1553*e^3 - 2766047/6212*e^2 + 104493/3106*e + 250671/6212, -2972/1553*e^15 + 25641/6212*e^14 + 239679/6212*e^13 - 486119/6212*e^12 - 473518/1553*e^11 + 3530061/6212*e^10 + 7379885/6212*e^9 - 12221125/6212*e^8 - 7282343/3106*e^7 + 20351323/6212*e^6 + 13447065/6212*e^5 - 3584573/1553*e^4 - 2640497/3106*e^3 + 2828585/6212*e^2 + 219927/1553*e + 36899/6212, -23587/6212*e^15 + 127131/12424*e^14 + 875885/12424*e^13 - 2323603/12424*e^12 - 3149503/6212*e^11 + 16215839/12424*e^10 + 22106483/12424*e^9 - 54076765/12424*e^8 - 9713397/3106*e^7 + 88382757/12424*e^6 + 30543709/12424*e^5 - 8146404/1553*e^4 - 1049123/1553*e^3 + 16950789/12424*e^2 + 291809/6212*e - 793617/12424, -3226/1553*e^15 + 7657/1553*e^14 + 64948/1553*e^13 - 296795/3106*e^12 - 508009/1553*e^11 + 1103722/1553*e^10 + 1922283/1553*e^9 - 7839591/3106*e^8 - 3517654/1553*e^7 + 6702381/1553*e^6 + 2597856/1553*e^5 - 9740225/3106*e^4 - 376135/1553*e^3 + 2165159/3106*e^2 - 173489/3106*e - 107639/3106, 5071/3106*e^15 - 30629/6212*e^14 - 182691/6212*e^13 + 565779/6212*e^12 + 624503/3106*e^11 - 3995913/6212*e^10 - 4004053/6212*e^9 + 13470521/6212*e^8 + 1463139/1553*e^7 - 22019227/6212*e^6 - 2651203/6212*e^5 + 7775569/3106*e^4 - 166650/1553*e^3 - 3376293/6212*e^2 + 29861/1553*e + 151157/6212, -6425/6212*e^15 + 8971/6212*e^14 + 138733/6212*e^13 - 39232/1553*e^12 - 1214529/6212*e^11 + 1036081/6212*e^10 + 5501575/6212*e^9 - 1639125/3106*e^8 - 13514283/6212*e^7 + 5477129/6212*e^6 + 8502999/3106*e^5 - 1352509/1553*e^4 - 9251653/6212*e^3 + 690666/1553*e^2 + 1331143/6212*e - 65265/1553, 14279/6212*e^15 - 11036/1553*e^14 - 65737/1553*e^13 + 850691/6212*e^12 + 1819891/6212*e^11 - 3162195/3106*e^10 - 1430603/1553*e^9 + 22663907/6212*e^8 + 7348475/6212*e^7 - 9927121/1553*e^6 - 844329/6212*e^5 + 15045195/3106*e^4 - 2985719/6212*e^3 - 6857633/6212*e^2 + 308601/6212*e - 2163/6212, 3727/1553*e^15 - 112625/12424*e^14 - 478307/12424*e^13 + 2097315/12424*e^12 + 324644/1553*e^11 - 15008985/12424*e^10 - 4339045/12424*e^9 + 51656393/12424*e^8 - 3420711/6212*e^7 - 87011199/12424*e^6 + 28553371/12424*e^5 + 7953370/1553*e^4 - 12091629/6212*e^3 - 14499417/12424*e^2 + 1006865/3106*e + 608193/12424];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {11, 11, 4*w + 19}>] := 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;