/*
  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![-49, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {7,7,-w - 6}>;

primesArray := [
[4, 2, 2],
[7, 7, w - 7],
[7, 7, w + 6],
[9, 3, 3],
[19, 19, w + 5],
[19, 19, w - 6],
[23, 23, w + 8],
[23, 23, -w + 9],
[25, 5, 5],
[29, 29, -w - 4],
[29, 29, w - 5],
[37, 37, -w - 3],
[37, 37, w - 4],
[41, 41, -w - 9],
[41, 41, w - 10],
[43, 43, -w - 2],
[43, 43, w - 3],
[47, 47, -w - 1],
[47, 47, w - 2],
[53, 53, 2*w - 13],
[53, 53, -2*w - 11],
[59, 59, -4*w - 25],
[59, 59, -4*w + 29],
[61, 61, -w - 10],
[61, 61, w - 11],
[83, 83, -w - 11],
[83, 83, w - 12],
[97, 97, 2*w - 11],
[97, 97, -2*w - 9],
[101, 101, 3*w - 20],
[101, 101, -3*w - 17],
[107, 107, -w - 12],
[107, 107, w - 13],
[109, 109, -5*w - 31],
[109, 109, -5*w + 36],
[121, 11, -11],
[127, 127, 2*w - 19],
[127, 127, -2*w - 17],
[137, 137, -3*w - 16],
[137, 137, 3*w - 19],
[157, 157, -3*w - 23],
[157, 157, 3*w - 26],
[163, 163, -4*w + 27],
[163, 163, 4*w + 23],
[169, 13, -13],
[173, 173, -6*w - 37],
[173, 173, -6*w + 43],
[181, 181, 2*w - 5],
[181, 181, -2*w - 3],
[191, 191, -w - 15],
[191, 191, w - 16],
[193, 193, 2*w - 3],
[193, 193, -2*w - 1],
[197, 197, 2*w - 1],
[223, 223, -w - 16],
[223, 223, w - 17],
[233, 233, -3*w - 13],
[233, 233, 3*w - 16],
[239, 239, -5*w + 34],
[239, 239, -5*w - 29],
[251, 251, 5*w - 41],
[251, 251, 5*w + 36],
[257, 257, -w - 17],
[257, 257, w - 18],
[289, 17, -17],
[293, 293, -w - 18],
[293, 293, w - 19],
[311, 311, -3*w - 10],
[311, 311, 3*w - 13],
[313, 313, -3*w - 26],
[313, 313, 3*w - 29],
[331, 331, -w - 19],
[331, 331, w - 20],
[347, 347, 4*w - 23],
[347, 347, -4*w - 19],
[353, 353, 3*w - 11],
[353, 353, -3*w - 8],
[379, 379, 2*w - 25],
[379, 379, -2*w - 23],
[401, 401, 3*w - 8],
[401, 401, -3*w - 5],
[409, 409, 5*w - 43],
[409, 409, 5*w + 38],
[419, 419, -5*w - 26],
[419, 419, 5*w - 31],
[431, 431, 3*w - 5],
[431, 431, -3*w - 2],
[433, 433, -7*w + 48],
[433, 433, -7*w - 41],
[443, 443, 3*w - 2],
[443, 443, 3*w - 1],
[449, 449, -9*w - 55],
[449, 449, -9*w + 64],
[457, 457, -w - 22],
[457, 457, w - 23],
[479, 479, 2*w - 27],
[479, 479, -2*w - 25],
[487, 487, -3*w - 29],
[487, 487, 3*w - 32],
[491, 491, -5*w - 39],
[491, 491, 5*w - 44],
[499, 499, 4*w - 19],
[499, 499, -4*w - 15],
[503, 503, -w - 23],
[503, 503, w - 24],
[521, 521, 11*w - 86],
[521, 521, -7*w + 47],
[557, 557, 7*w + 51],
[557, 557, 7*w - 58],
[563, 563, -4*w - 13],
[563, 563, 4*w - 17],
[569, 569, -10*w - 61],
[569, 569, -10*w + 71],
[587, 587, 2*w - 29],
[587, 587, -2*w - 27],
[601, 601, -w - 25],
[601, 601, w - 26],
[607, 607, -7*w - 39],
[607, 607, 7*w - 46],
[613, 613, 3*w - 34],
[613, 613, -3*w - 31],
[617, 617, -6*w - 31],
[617, 617, 6*w - 37],
[619, 619, 4*w - 15],
[619, 619, -4*w - 11],
[631, 631, 5*w - 27],
[631, 631, -5*w - 22],
[653, 653, -w - 26],
[653, 653, w - 27],
[661, 661, 5*w - 46],
[661, 661, -5*w - 41],
[683, 683, -9*w + 62],
[683, 683, -9*w - 53],
[691, 691, 7*w - 45],
[691, 691, -7*w - 38],
[727, 727, -6*w - 47],
[727, 727, 6*w - 53],
[733, 733, 4*w - 41],
[733, 733, -4*w - 37],
[739, 739, -4*w - 5],
[739, 739, 4*w - 9],
[751, 751, 8*w - 53],
[751, 751, -8*w - 45],
[769, 769, 5*w - 24],
[769, 769, -5*w - 19],
[773, 773, 7*w - 44],
[773, 773, -7*w - 37],
[787, 787, 4*w - 3],
[787, 787, 4*w - 1],
[797, 797, -9*w - 52],
[797, 797, -9*w + 61],
[811, 811, -5*w - 18],
[811, 811, 5*w - 23],
[821, 821, -w - 29],
[821, 821, w - 30],
[827, 827, 2*w - 33],
[827, 827, -2*w - 31],
[829, 829, -10*w + 69],
[829, 829, -10*w - 59],
[839, 839, 5*w - 48],
[839, 839, -5*w - 43],
[853, 853, -7*w - 36],
[853, 853, 7*w - 43],
[881, 881, -w - 30],
[881, 881, w - 31],
[961, 31, -31],
[991, 991, -5*w - 13],
[991, 991, 5*w - 18]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^10 + 7*x^9 + 6*x^8 - 46*x^7 - 83*x^6 + 34*x^5 + 93*x^4 - 7*x^3 - 20*x^2 + x + 1;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 255/47*e^9 + 1835/47*e^8 + 1911/47*e^7 - 11206/47*e^6 - 23236/47*e^5 + 3126/47*e^4 + 22600/47*e^3 + 3391/47*e^2 - 2662/47*e - 384/47, 1, -294/47*e^9 - 2182/47*e^8 - 2660/47*e^7 + 12561/47*e^6 + 29790/47*e^5 + 1499/47*e^4 - 28271/47*e^3 - 8953/47*e^2 + 3496/47*e + 926/47, 102/47*e^9 + 828/47*e^8 + 1413/47*e^7 - 3956/47*e^6 - 13515/47*e^5 - 6138/47*e^4 + 11860/47*e^3 + 8820/47*e^2 - 1281/47*e - 1009/47, -32/47*e^9 - 210/47*e^8 - 106/47*e^7 + 1489/47*e^6 + 2031/47*e^5 - 1721/47*e^4 - 2132/47*e^3 + 675/47*e^2 + 1/47*e - 53/47, -273/47*e^9 - 2006/47*e^8 - 2329/47*e^7 + 11788/47*e^6 + 26749/47*e^5 - 290/47*e^4 - 25644/47*e^3 - 6504/47*e^2 + 3253/47*e + 645/47, 439/47*e^9 + 3254/47*e^8 + 3954/47*e^7 - 18722/47*e^6 - 44326/47*e^5 - 2359/47*e^4 + 41909/47*e^3 + 13692/47*e^2 - 5288/47*e - 1595/47, 118/47*e^9 + 839/47*e^8 + 808/47*e^7 - 5288/47*e^6 - 10324/47*e^5 + 2595/47*e^4 + 10576/47*e^3 + 234/47*e^2 - 1493/47*e - 66/47, 160/47*e^9 + 1191/47*e^8 + 1470/47*e^7 - 6834/47*e^6 - 16406/47*e^5 - 983/47*e^4 + 15877/47*e^3 + 5085/47*e^2 - 2684/47*e - 534/47, -229/47*e^9 - 1635/47*e^8 - 1631/47*e^7 + 10099/47*e^6 + 20214/47*e^5 - 3640/47*e^4 - 19305/47*e^3 - 1845/47*e^2 + 2153/47*e + 148/47, -713/47*e^9 - 5293/47*e^8 - 6489/47*e^7 + 30276/47*e^6 + 72265/47*e^5 + 5010/47*e^4 - 67273/47*e^3 - 23202/47*e^2 + 7673/47*e + 2560/47, -385/47*e^9 - 2788/47*e^8 - 2982/47*e^7 + 16976/47*e^6 + 35949/47*e^5 - 4363/47*e^4 - 36067/47*e^3 - 5810/47*e^2 + 5113/47*e + 671/47, 419/47*e^9 + 3111/47*e^8 + 3829/47*e^7 - 17715/47*e^6 - 42428/47*e^5 - 3323/47*e^4 + 38767/47*e^3 + 13121/47*e^2 - 4271/47*e - 1258/47, 257/47*e^9 + 1948/47*e^8 + 2605/47*e^7 - 10738/47*e^6 - 27778/47*e^5 - 4542/47*e^4 + 25330/47*e^3 + 10813/47*e^2 - 2618/47*e - 1353/47, 339/47*e^9 + 2539/47*e^8 + 3235/47*e^7 - 14298/47*e^6 - 35353/47*e^5 - 3889/47*e^4 + 32779/47*e^3 + 12388/47*e^2 - 3775/47*e - 1743/47, -388/47*e^9 - 2840/47*e^8 - 3224/47*e^7 + 16885/47*e^6 + 37592/47*e^5 - 1697/47*e^4 - 36966/47*e^3 - 8248/47*e^2 + 5047/47*e + 926/47, -641/47*e^9 - 4703/47*e^8 - 5428/47*e^7 + 27666/47*e^6 + 62490/47*e^5 - 835/47*e^4 - 59750/47*e^3 - 15356/47*e^2 + 7330/47*e + 1469/47, -234/47*e^9 - 1659/47*e^8 - 1580/47*e^7 + 10433/47*e^6 + 20195/47*e^5 - 4915/47*e^4 - 19973/47*e^3 - 989/47*e^2 + 2466/47*e + 244/47, -290/47*e^9 - 2238/47*e^8 - 3246/47*e^7 + 11711/47*e^6 + 33114/47*e^5 + 9428/47*e^4 - 28639/47*e^3 - 15917/47*e^2 + 2738/47*e + 1526/47, 1312/47*e^9 + 9597/47*e^8 + 10926/47*e^7 - 56678/47*e^6 - 126511/47*e^5 + 3304/47*e^4 + 120171/47*e^3 + 29383/47*e^2 - 14141/47*e - 3279/47, 38/47*e^9 + 267/47*e^8 + 214/47*e^7 - 1871/47*e^6 - 3249/47*e^5 + 2076/47*e^4 + 4729/47*e^3 - 922/47*e^2 - 1890/47*e + 154/47, -10/47*e^9 - 48/47*e^8 + 102/47*e^7 + 668/47*e^6 - 38/47*e^5 - 2597/47*e^4 - 1524/47*e^3 + 1994/47*e^2 + 1378/47*e - 184/47, -693/47*e^9 - 5056/47*e^8 - 5706/47*e^7 + 29833/47*e^6 + 66090/47*e^5 - 1640/47*e^4 - 61217/47*e^3 - 15205/47*e^2 + 6139/47*e + 1800/47, -692/47*e^9 - 5164/47*e^8 - 6487/47*e^7 + 29221/47*e^6 + 71386/47*e^5 + 7122/47*e^4 - 66244/47*e^3 - 25124/47*e^2 + 7618/47*e + 2937/47, 316/47*e^9 + 2250/47*e^8 + 2210/47*e^7 - 13993/47*e^6 - 27817/47*e^5 + 5380/47*e^4 + 27657/47*e^3 + 3645/47*e^2 - 3341/47*e - 681/47, 413/47*e^9 + 3054/47*e^8 + 3674/47*e^7 - 17615/47*e^6 - 41304/47*e^5 - 1845/47*e^4 + 38614/47*e^3 + 12193/47*e^2 - 4638/47*e - 1641/47, 126/47*e^9 + 868/47*e^8 + 670/47*e^7 - 5813/47*e^6 - 9833/47*e^5 + 4917/47*e^4 + 10827/47*e^3 - 1427/47*e^2 - 1740/47*e + 476/47, -527/47*e^9 - 3855/47*e^8 - 4363/47*e^7 + 22946/47*e^6 + 50957/47*e^5 - 2503/47*e^4 - 50263/47*e^3 - 11025/47*e^2 + 7535/47*e + 897/47, 453/47*e^9 + 3293/47*e^8 + 3642/47*e^7 - 19582/47*e^6 - 42562/47*e^5 + 2245/47*e^4 + 39117/47*e^3 + 8071/47*e^2 - 3476/47*e - 905/47, -1226/47*e^9 - 9015/47*e^8 - 10553/47*e^7 + 52597/47*e^6 + 120333/47*e^5 + 1283/47*e^4 - 113090/47*e^3 - 31670/47*e^2 + 13166/47*e + 3348/47, 1119/47*e^9 + 8210/47*e^8 + 9473/47*e^7 - 48307/47*e^6 - 109046/47*e^5 + 1653/47*e^4 + 104181/47*e^3 + 26056/47*e^2 - 13311/47*e - 2854/47, -1080/47*e^9 - 7910/47*e^8 - 9053/47*e^7 + 46670/47*e^6 + 104654/47*e^5 - 2377/47*e^4 - 100061/47*e^3 - 24677/47*e^2 + 12524/47*e + 2406/47, 1153/47*e^9 + 8486/47*e^8 + 9991/47*e^7 - 49328/47*e^6 - 113410/47*e^5 - 2367/47*e^4 + 105377/47*e^3 + 30453/47*e^2 - 11435/47*e - 3535/47, -90/47*e^9 - 573/47*e^8 - 163/47*e^7 + 4320/47*e^6 + 4687/47*e^5 - 6735/47*e^4 - 4457/47*e^3 + 5209/47*e^2 - 382/47*e - 810/47, 795/47*e^9 + 5931/47*e^8 + 7448/47*e^7 - 33507/47*e^6 - 81767/47*e^5 - 8399/47*e^4 + 74675/47*e^3 + 28302/47*e^2 - 7749/47*e - 3279/47, e^9 + 7*e^8 + 6*e^7 - 47*e^6 - 88*e^5 + 37*e^4 + 128*e^3 + 8*e^2 - 53*e - 7, -266/47*e^9 - 2010/47*e^8 - 2673/47*e^7 + 11076/47*e^6 + 28665/47*e^5 + 4832/47*e^4 - 26758/47*e^3 - 11876/47*e^2 + 3783/47*e + 1554/47, 469/47*e^9 + 3398/47*e^8 + 3648/47*e^7 - 20632/47*e^6 - 43789/47*e^5 + 4962/47*e^4 + 43332/47*e^3 + 7287/47*e^2 - 5709/47*e - 1184/47, 1348/47*e^9 + 9845/47*e^8 + 11104/47*e^7 - 58406/47*e^6 - 129260/47*e^5 + 5293/47*e^4 + 123392/47*e^3 + 27760/47*e^2 - 14712/47*e - 2673/47, 1838/47*e^9 + 13419/47*e^8 + 15130/47*e^7 - 79576/47*e^6 - 176278/47*e^5 + 6586/47*e^4 + 168834/47*e^3 + 40504/47*e^2 - 20288/47*e - 4467/47, 696/47*e^9 + 5249/47*e^8 + 6888/47*e^7 - 29178/47*e^6 - 74266/47*e^5 - 10802/47*e^4 + 68790/47*e^3 + 28782/47*e^2 - 8000/47*e - 3700/47, 2148/47*e^9 + 15612/47*e^8 + 17185/47*e^7 - 93422/47*e^6 - 202689/47*e^5 + 13491/47*e^4 + 194458/47*e^3 + 41388/47*e^2 - 22821/47*e - 4920/47, 587/47*e^9 + 4331/47*e^8 + 5161/47*e^7 - 25074/47*e^6 - 58343/47*e^5 - 1984/47*e^4 + 54895/47*e^3 + 16686/47*e^2 - 6873/47*e - 2237/47, -745/47*e^9 - 5503/47*e^8 - 6595/47*e^7 + 31718/47*e^6 + 74014/47*e^5 + 3242/47*e^4 - 67572/47*e^3 - 20788/47*e^2 + 6781/47*e + 2366/47, -2243/47*e^9 - 16397/47*e^8 - 18613/47*e^7 + 96948/47*e^6 + 215911/47*e^5 - 6367/47*e^4 - 205740/47*e^3 - 49658/47*e^2 + 25337/47*e + 5099/47, -680/47*e^9 - 5097/47*e^8 - 6506/47*e^7 + 28739/47*e^6 + 71159/47*e^5 + 7503/47*e^4 - 66737/47*e^3 - 24067/47*e^2 + 8587/47*e + 2622/47, 127/47*e^9 + 854/47*e^8 + 547/47*e^7 - 5908/47*e^6 - 9143/47*e^5 + 5783/47*e^4 + 10829/47*e^3 - 395/47*e^2 - 1953/47*e - 831/47, -1463/47*e^9 - 10773/47*e^8 - 12657/47*e^7 + 62939/47*e^6 + 144380/47*e^5 + 914/47*e^4 - 137722/47*e^3 - 37024/47*e^2 + 17775/47*e + 3988/47, 114/47*e^9 + 707/47*e^8 + 78/47*e^7 - 5613/47*e^6 - 5282/47*e^5 + 10176/47*e^4 + 6432/47*e^3 - 7795/47*e^2 - 1064/47*e + 1167/47, -737/47*e^9 - 5286/47*e^8 - 5370/47*e^7 + 32697/47*e^6 + 66468/47*e^5 - 11873/47*e^4 - 66663/47*e^3 - 7080/47*e^2 + 9354/47*e + 840/47, 406/47*e^9 + 3011/47*e^8 + 3642/47*e^7 - 17467/47*e^6 - 41105/47*e^5 - 1139/47*e^4 + 39963/47*e^3 + 11173/47*e^2 - 5168/47*e - 341/47, 1451/47*e^9 + 10565/47*e^8 + 11736/47*e^7 - 63021/47*e^6 - 137714/47*e^5 + 8011/47*e^4 + 131870/47*e^3 + 27930/47*e^2 - 16065/47*e - 3109/47, 761/47*e^9 + 5655/47*e^8 + 6930/47*e^7 - 32486/47*e^6 - 77309/47*e^5 - 4050/47*e^4 + 72774/47*e^3 + 21649/47*e^2 - 8920/47*e - 1282/47, -1591/47*e^9 - 11566/47*e^8 - 12752/47*e^7 + 69130/47*e^6 + 150107/47*e^5 - 9730/47*e^4 - 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186737/47*e^6 - 420411/47*e^5 + 6183/47*e^4 + 399136/47*e^3 + 102119/47*e^2 - 46539/47*e - 11837/47, -1479/47*e^9 - 10925/47*e^8 - 13133/47*e^7 + 62861/47*e^6 + 147628/47*e^5 + 8020/47*e^4 - 137331/47*e^3 - 46580/47*e^2 + 16154/47*e + 5724/47, 3517/47*e^9 + 25727/47*e^8 + 29325/47*e^7 - 151708/47*e^6 - 338985/47*e^5 + 7219/47*e^4 + 319678/47*e^3 + 80809/47*e^2 - 35426/47*e - 9754/47, -44/47*e^9 - 465/47*e^8 - 1356/47*e^7 + 1125/47*e^6 + 10765/47*e^5 + 10729/47*e^4 - 8924/47*e^3 - 10346/47*e^2 + 1100/47*e + 403/47, 832/47*e^9 + 5977/47*e^8 + 6140/47*e^7 - 36740/47*e^6 - 75178/47*e^5 + 12222/47*e^4 + 73245/47*e^3 + 6843/47*e^2 - 8815/47*e - 32/47, -837/47*e^9 - 6236/47*e^8 - 7687/47*e^7 + 35899/47*e^6 + 85734/47*e^5 + 3940/47*e^4 - 82185/47*e^3 - 23471/47*e^2 + 11572/47*e + 1679/47, -1475/47*e^9 - 10558/47*e^8 - 10711/47*e^7 + 64878/47*e^6 + 131823/47*e^5 - 20993/47*e^4 - 127312/47*e^3 - 15662/47*e^2 + 15067/47*e + 2423/47, -3091/47*e^9 - 22526/47*e^8 - 25135/47*e^7 + 134127/47*e^6 + 294196/47*e^5 - 15290/47*e^4 - 281132/47*e^3 - 61357/47*e^2 + 34317/47*e + 5739/47, -3317/47*e^9 - 24391/47*e^8 - 28498/47*e^7 + 142672/47*e^6 + 325833/47*e^5 + 1199/47*e^4 - 309690/47*e^3 - 84734/47*e^2 + 38181/47*e + 9204/47, 8/47*e^9 - 300/47*e^8 - 2441/47*e^7 - 2499/47*e^6 + 15484/47*e^5 + 29065/47*e^4 - 9995/47*e^3 - 28357/47*e^2 + 787/47*e + 2892/47, -485/47*e^9 - 3268/47*e^8 - 2056/47*e^7 + 22810/47*e^6 + 34159/47*e^5 - 25210/47*e^4 - 37677/47*e^3 + 13002/47*e^2 + 5827/47*e - 1686/47, -3426/47*e^9 - 25309/47*e^8 - 30319/47*e^7 + 146259/47*e^6 + 341850/47*e^5 + 13542/47*e^4 - 321094/47*e^3 - 99838/47*e^2 + 38556/47*e + 11043/47, 2364/47*e^9 + 17241/47*e^8 + 19334/47*e^7 - 102474/47*e^6 - 225998/47*e^5 + 10197/47*e^4 + 217732/47*e^3 + 49745/47*e^2 - 28785/47*e - 5890/47, -2645/47*e^9 - 19276/47*e^8 - 21478/47*e^7 + 114928/47*e^6 + 251598/47*e^5 - 14172/47*e^4 - 240196/47*e^3 - 51580/47*e^2 + 26692/47*e + 5758/47, 1210/47*e^9 + 8722/47*e^8 + 9184/47*e^7 - 52910/47*e^6 - 110411/47*e^5 + 12873/47*e^4 + 103799/47*e^3 + 16192/47*e^2 - 10087/47*e - 1753/47, 37/47*e^9 + 422/47*e^8 + 1418/47*e^7 - 319/47*e^6 - 10049/47*e^5 - 14300/47*e^4 + 3787/47*e^3 + 12569/47*e^2 + 485/47*e - 278/47, -1360/47*e^9 - 9630/47*e^8 - 9111/47*e^7 + 60627/47*e^6 + 116750/47*e^5 - 29127/47*e^4 - 114815/47*e^3 - 4330/47*e^2 + 12615/47*e - 302/47, -1852/47*e^9 - 13317/47*e^8 - 13878/47*e^7 + 81000/47*e^6 + 168028/47*e^5 - 20684/47*e^4 - 159462/47*e^3 - 25342/47*e^2 + 16737/47*e + 2696/47, 1047/47*e^9 + 7761/47*e^8 + 9446/47*e^7 - 44616/47*e^6 - 105851/47*e^5 - 5615/47*e^4 + 100653/47*e^3 + 31370/47*e^2 - 14237/47*e - 2703/47];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {7,7,-w - 6}>] := -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;