/*
  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, -6, 0, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {17, 17, -w^3 + w^2 + 6*w - 1}>;

primesArray := [
[2, 2, w + 1],
[3, 3, -w^3 + w^2 + 5*w - 2],
[11, 11, -w^3 + 5*w + 1],
[11, 11, -w + 2],
[13, 13, -w^3 + w^2 + 4*w + 1],
[17, 17, -w^3 + w^2 + 6*w - 1],
[17, 17, -w^2 - w + 3],
[23, 23, w^3 - 6*w],
[27, 3, w^3 + w^2 - 5*w - 4],
[41, 41, -w^3 + w^2 + 5*w],
[41, 41, 2*w^3 - 11*w - 4],
[53, 53, 2*w^3 - 2*w^2 - 11*w + 6],
[59, 59, 2*w^3 - 11*w - 2],
[67, 67, w^3 - 7*w - 1],
[71, 71, 3*w^3 - 2*w^2 - 15*w + 1],
[79, 79, -3*w^3 + w^2 + 16*w + 3],
[89, 89, -4*w^3 + 2*w^2 + 22*w - 3],
[101, 101, -2*w^3 + 13*w + 6],
[101, 101, w^3 + w^2 - 6*w - 3],
[101, 101, -3*w^3 + 2*w^2 + 17*w - 3],
[101, 101, w^3 - w^2 - 8*w - 3],
[107, 107, 2*w^3 - 3*w^2 - 6*w],
[109, 109, -w^3 + w^2 + 4*w - 3],
[113, 113, w^3 - 8*w - 4],
[113, 113, 7*w^3 - 4*w^2 - 39*w + 7],
[121, 11, w^3 - w^2 - 6*w - 1],
[127, 127, -2*w^3 + w^2 + 9*w + 3],
[127, 127, 2*w^3 - 13*w],
[131, 131, 6*w^3 - 3*w^2 - 34*w + 6],
[139, 139, w^2 - 2*w - 4],
[149, 149, 3*w^3 - w^2 - 18*w - 3],
[151, 151, -2*w^3 + 2*w^2 + 9*w - 4],
[163, 163, 3*w^3 - 2*w^2 - 16*w + 2],
[163, 163, 2*w^3 - 10*w + 1],
[167, 167, 3*w^3 - 18*w - 4],
[173, 173, -3*w^3 + w^2 + 18*w - 3],
[193, 193, 4*w^3 - 3*w^2 - 23*w + 9],
[197, 197, 3*w^3 - w^2 - 17*w + 2],
[197, 197, -3*w^3 - 2*w^2 + 15*w + 9],
[199, 199, 2*w^3 - w^2 - 8*w - 6],
[223, 223, -6*w^3 + 3*w^2 + 35*w - 7],
[227, 227, 2*w^3 - 12*w - 1],
[227, 227, -w^3 + w^2 + 7*w - 8],
[227, 227, 3*w^3 - w^2 - 18*w - 1],
[227, 227, -4*w^3 - 2*w^2 + 21*w + 14],
[229, 229, -w^3 + 2*w^2 + 3*w - 5],
[233, 233, w^3 - 3*w - 3],
[233, 233, -3*w^3 + 3*w^2 + 15*w - 8],
[241, 241, 4*w^2 - 7*w - 8],
[241, 241, w^3 + w^2 - 4*w - 5],
[251, 251, 2*w^3 - w^2 - 13*w - 1],
[251, 251, 2*w^3 - 9*w - 6],
[257, 257, w^3 - 8*w],
[263, 263, -w^3 + 2*w^2 + 5*w - 7],
[269, 269, 3*w^3 - 3*w^2 - 12*w - 1],
[271, 271, 2*w^3 - w^2 - 12*w - 2],
[271, 271, 9*w^3 - 5*w^2 - 50*w + 9],
[277, 277, w^3 - 2*w^2 - 6*w + 6],
[277, 277, w^3 + w^2 - 7*w - 2],
[281, 281, 4*w^3 - 2*w^2 - 24*w + 5],
[281, 281, -7*w^3 + 4*w^2 + 40*w - 12],
[289, 17, -5*w^3 + 5*w^2 + 26*w - 15],
[293, 293, -w^3 + 2*w^2 + 4*w - 4],
[293, 293, -9*w^3 + 5*w^2 + 51*w - 12],
[307, 307, -2*w^3 + 2*w^2 + 12*w - 7],
[311, 311, -4*w^3 + 24*w + 11],
[313, 313, 2*w^3 - 9*w - 4],
[317, 317, 2*w^3 - 4*w^2 - 2*w - 3],
[317, 317, 2*w^3 - 14*w - 7],
[331, 331, -3*w^3 + 19*w + 3],
[349, 349, -w^3 - 2*w^2 + 8*w + 8],
[349, 349, w^3 + w^2 - 5*w - 8],
[361, 19, -w^3 + w^2 + 7*w - 6],
[361, 19, w^3 + w^2 - 3*w - 4],
[373, 373, 2*w^3 - w^2 - 11*w - 3],
[379, 379, -4*w^3 + 25*w + 14],
[383, 383, -3*w^3 + w^2 + 15*w - 2],
[383, 383, 3*w^3 - 4*w^2 - 10*w],
[401, 401, 4*w^3 - w^2 - 24*w - 4],
[409, 409, w^2 + 5*w + 5],
[419, 419, w^2 - 2*w - 6],
[419, 419, -6*w^3 + 3*w^2 + 34*w - 8],
[433, 433, 3*w^3 - 16*w - 6],
[433, 433, 3*w^3 - w^2 - 16*w - 5],
[443, 443, -w^3 + 2*w^2 + w + 3],
[449, 449, 2*w^2 - 2*w - 5],
[457, 457, -4*w^3 + 4*w^2 + 20*w - 9],
[457, 457, w^2 + w - 7],
[463, 463, w^3 - 7*w - 7],
[463, 463, w^3 + 2*w^2 - 5*w - 9],
[487, 487, w^3 + 2*w^2 - 5*w - 5],
[487, 487, -w^3 + w^2 + 6*w - 7],
[509, 509, -2*w^3 - 2*w^2 + 13*w + 10],
[509, 509, 3*w^3 - 17*w - 3],
[509, 509, -5*w^3 + 3*w^2 + 30*w - 11],
[509, 509, -w^3 - 2*w^2 + 4*w + 6],
[521, 521, -2*w^3 - w^2 + 9*w + 7],
[541, 541, -2*w^3 - 2*w^2 + 12*w + 9],
[541, 541, -2*w^3 + 12*w + 9],
[547, 547, 2*w^3 + w^2 - 7*w - 3],
[547, 547, 5*w^3 - 3*w^2 - 30*w + 3],
[557, 557, w^3 + 2*w^2 - 5*w - 11],
[557, 557, -w^3 + w^2 + 3*w - 4],
[563, 563, 3*w^3 - w^2 - 15*w - 4],
[569, 569, 2*w^2 - w - 8],
[577, 577, 4*w^3 - 22*w - 7],
[593, 593, -3*w^3 + w^2 + 17*w + 4],
[607, 607, -w^3 - 3*w^2 + w + 4],
[613, 613, 3*w^3 - 2*w^2 - 14*w],
[613, 613, w^2 - 3*w - 5],
[619, 619, -w^3 + 2*w^2 + 4*w - 10],
[625, 5, -5],
[641, 641, -3*w^3 - 3*w^2 + 12*w + 7],
[643, 643, 2*w^3 + 2*w^2 - 14*w - 13],
[643, 643, 3*w^3 - 19*w - 7],
[647, 647, w^3 - 5*w - 7],
[653, 653, -3*w^3 + 2*w^2 + 14*w - 2],
[659, 659, -6*w^3 + 2*w^2 + 34*w - 1],
[659, 659, -2*w^3 + w^2 + 17*w + 9],
[683, 683, w^3 + 2*w^2 - 7*w - 7],
[691, 691, 3*w^3 - 15*w - 7],
[701, 701, w^3 + 2*w^2 - 6*w - 10],
[701, 701, -w^3 + 3*w^2 + 6*w - 13],
[701, 701, 5*w^3 - 2*w^2 - 30*w + 4],
[701, 701, 4*w^3 - 2*w^2 - 21*w + 2],
[727, 727, -2*w^3 - 3*w^2 + 9*w + 7],
[743, 743, 3*w - 4],
[751, 751, w^3 - 9*w - 3],
[757, 757, w^3 - 5*w^2 + 4*w + 7],
[757, 757, 4*w^3 - 5*w^2 - 11*w - 5],
[761, 761, 4*w^3 - 5*w^2 - 20*w + 16],
[769, 769, -3*w^3 + 16*w + 12],
[773, 773, 2*w^3 + 2*w^2 - 11*w - 10],
[773, 773, w^3 - 3*w - 5],
[773, 773, -w^3 + 2*w^2 + 9*w + 3],
[773, 773, 5*w^3 - w^2 - 27*w],
[787, 787, -4*w^3 + 3*w^2 + 22*w - 4],
[787, 787, -2*w^3 + w^2 + 14*w - 6],
[797, 797, 2*w^3 - w^2 - 14*w + 2],
[797, 797, -3*w^3 + 2*w^2 + 19*w - 7],
[811, 811, 2*w^3 + w^2 - 14*w - 12],
[811, 811, 2*w^3 + 2*w^2 - 8*w - 3],
[829, 829, -2*w^3 + 14*w + 11],
[857, 857, -3*w^3 + 3*w^2 + 14*w - 7],
[859, 859, 3*w^3 - w^2 - 15*w],
[859, 859, -11*w^3 + 7*w^2 + 60*w - 15],
[863, 863, 2*w^2 - 2*w - 13],
[863, 863, 2*w^3 + w^2 - 12*w - 4],
[877, 877, -6*w^3 - 2*w^2 + 32*w + 19],
[887, 887, 3*w^3 + w^2 - 14*w - 7],
[887, 887, 2*w^3 - w^2 - 15*w - 5],
[911, 911, 3*w^3 - 18*w - 2],
[919, 919, w^3 - w^2 - 6*w - 5],
[919, 919, -4*w^3 + w^2 + 24*w - 2],
[941, 941, 3*w^3 - 3*w^2 - 13*w],
[947, 947, 2*w^3 - 2*w^2 - 10*w - 1],
[947, 947, -3*w^3 + 2*w^2 + 14*w + 6],
[953, 953, -4*w^3 + 3*w^2 + 21*w - 3],
[953, 953, 4*w^3 - w^2 - 23*w + 1],
[961, 31, -2*w^3 + 3*w^2 + 12*w - 8],
[961, 31, 3*w^2 - 4*w - 6],
[967, 967, -5*w^3 - 3*w^2 + 23*w + 14],
[971, 971, 5*w^3 - w^2 - 27*w - 8],
[971, 971, -9*w^3 + 6*w^2 + 50*w - 12],
[983, 983, -w^3 + w^2 + 10*w + 3],
[997, 997, 2*w^3 + w^2 - 11*w - 3],
[997, 997, w^3 + 2*w^2 - 6*w - 8],
[997, 997, -5*w^3 + 4*w^2 + 29*w - 15]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^21 - 5*x^20 - 19*x^19 + 125*x^18 + 110*x^17 - 1294*x^16 + 81*x^15 + 7211*x^14 - 3631*x^13 - 23611*x^12 + 17397*x^11 + 46651*x^10 - 40136*x^9 - 54932*x^8 + 50361*x^7 + 36489*x^6 - 33877*x^5 - 12175*x^4 + 10879*x^3 + 1695*x^2 - 1160*x - 132;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, -6164045801/69076492302*e^20 + 686346065/1817802429*e^19 + 133867043089/69076492302*e^18 - 326823799999/34538246151*e^17 - 556970894230/34538246151*e^16 + 3395389645604/34538246151*e^15 + 4233496691165/69076492302*e^14 - 19023315165733/34538246151*e^13 - 1835108679687/23025497434*e^12 + 62812100875865/34538246151*e^11 - 3325689811951/23025497434*e^10 - 41924625333129/11512748717*e^9 + 20890140678749/34538246151*e^8 + 151332124291301/34538246151*e^7 - 51253611392227/69076492302*e^6 - 104070547861208/34538246151*e^5 + 8434597468789/23025497434*e^4 + 12127470519381/11512748717*e^3 - 2954895219527/69076492302*e^2 - 83220125316/605934143*e - 138616451434/11512748717, -583245683/69076492302*e^20 + 115350515/1817802429*e^19 + 10776687649/69076492302*e^18 - 61425273955/34538246151*e^17 - 24001399546/34538246151*e^16 + 724828106180/34538246151*e^15 - 316276783339/69076492302*e^14 - 4677162532576/34538246151*e^13 + 1413627421409/23025497434*e^12 + 17934495364847/34538246151*e^11 - 6372214529029/23025497434*e^10 - 13854354489566/11512748717*e^9 + 22087690785179/34538246151*e^8 + 56615728125188/34538246151*e^7 - 54608496685039/69076492302*e^6 - 41967409941242/34538246151*e^5 + 11166937553737/23025497434*e^4 + 4845120650944/11512748717*e^3 - 7585908533297/69076492302*e^2 - 29694804435/605934143*e - 6612810294/11512748717, 2464279611/23025497434*e^20 - 5777290287/11512748717*e^19 - 53050457509/23025497434*e^18 + 7892170271/605934143*e^17 + 213794329078/11512748717*e^16 - 1629120251421/11512748717*e^15 - 1440115538303/23025497434*e^14 + 9658186061674/11512748717*e^13 + 404524650423/23025497434*e^12 - 34178035375841/11512748717*e^11 + 10982295438051/23025497434*e^10 + 74142585836273/11512748717*e^9 - 15875026175250/11512748717*e^8 - 96998778465325/11512748717*e^7 + 37669008587411/23025497434*e^6 + 71758287130972/11512748717*e^5 - 19486071987861/23025497434*e^4 - 26121031883749/11512748717*e^3 + 2761069520015/23025497434*e^2 + 3330481250870/11512748717*e + 300488228586/11512748717, -1409686311/23025497434*e^20 + 492944632/1817802429*e^19 + 92816677679/69076492302*e^18 - 240407195135/34538246151*e^17 - 390512350676/34538246151*e^16 + 2570843171704/34538246151*e^15 + 2998354724405/69076492302*e^14 - 14901063278431/34538246151*e^13 - 3905392872043/69076492302*e^12 + 17023667223636/11512748717*e^11 - 7176572989639/69076492302*e^10 - 35311790635784/11512748717*e^9 + 4771048260313/11512748717*e^8 + 130266232710934/34538246151*e^7 - 30737535966727/69076492302*e^6 - 88510632136630/34538246151*e^5 + 10027753773757/69076492302*e^4 + 9616679414083/11512748717*e^3 + 314300768513/23025497434*e^2 - 178667765219/1817802429*e - 84434656672/11512748717, -1, 1284290887/11512748717*e^20 - 5923646581/11512748717*e^19 - 27697876720/11512748717*e^18 + 152800325763/11512748717*e^17 + 225405738858/11512748717*e^16 - 1647987527671/11512748717*e^15 - 794162696915/11512748717*e^14 + 9689145198428/11512748717*e^13 + 573941938040/11512748717*e^12 - 33987536982034/11512748717*e^11 + 4049259233101/11512748717*e^10 + 73139244017682/11512748717*e^9 - 12118803749511/11512748717*e^8 - 95176701847519/11512748717*e^7 + 13062126429002/11512748717*e^6 + 70366012682823/11512748717*e^5 - 272027290474/605934143*e^4 - 25726130631720/11512748717*e^3 - 67959207962/11512748717*e^2 + 3334357714791/11512748717*e + 372418855194/11512748717, -5969395343/69076492302*e^20 + 11494061935/34538246151*e^19 + 142724955635/69076492302*e^18 - 300021167210/34538246151*e^17 - 689116152998/34538246151*e^16 + 3266708276542/34538246151*e^15 + 2282897531151/23025497434*e^14 - 6427468714576/11512748717*e^13 - 18289621283381/69076492302*e^12 + 67173977360195/34538246151*e^11 + 1252698982195/3635604858*e^10 - 46973882022553/11512748717*e^9 - 3225977142712/34538246151*e^8 + 173830223465623/34538246151*e^7 - 5660539302975/23025497434*e^6 - 117235009511692/34538246151*e^5 + 17013356832029/69076492302*e^4 + 12422075282002/11512748717*e^3 - 4655329568855/69076492302*e^2 - 3976198634101/34538246151*e - 54208757866/11512748717, -19124591179/69076492302*e^20 + 37026955400/34538246151*e^19 + 444737288767/69076492302*e^18 - 945150201667/34538246151*e^17 - 2079272161453/34538246151*e^16 + 10041684051599/34538246151*e^15 + 6659468905555/23025497434*e^14 - 19262544811360/11512748717*e^13 - 52198944758461/69076492302*e^12 + 196692285007963/34538246151*e^11 + 71683819084379/69076492302*e^10 - 135388507955981/11512748717*e^9 - 21713005922546/34538246151*e^8 + 500443828999934/34538246151*e^7 + 997698050841/23025497434*e^6 - 344644807113428/34538246151*e^5 + 3854887905997/69076492302*e^4 + 38115150483635/11512748717*e^3 + 2811792803219/69076492302*e^2 - 12604312606175/34538246151*e - 405032235126/11512748717, 11873991217/34538246151*e^20 - 52014674905/34538246151*e^19 - 261964031653/34538246151*e^18 + 1339096960739/34538246151*e^17 + 2218539077426/34538246151*e^16 - 14389032289063/34538246151*e^15 - 2851168373646/11512748717*e^14 + 28020183591036/11512748717*e^13 + 10631825091976/34538246151*e^12 - 291877239744335/34538246151*e^11 + 26428697914135/34538246151*e^10 + 206252720890539/11512748717*e^9 - 106869501618233/34538246151*e^8 - 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349374145786669/69076492302*e^10 - 456188884172641/11512748717*e^9 + 124684298890019/11512748717*e^8 + 1807548615422632/34538246151*e^7 - 725762228628043/69076492302*e^6 - 1348218085853275/34538246151*e^5 + 275015573770387/69076492302*e^4 + 165047649916367/11512748717*e^3 - 711692302557/23025497434*e^2 - 65165466577286/34538246151*e - 2487182648582/11512748717, -16105536536/34538246151*e^20 + 66542476240/34538246151*e^19 + 381355671583/34538246151*e^18 - 1759120856822/34538246151*e^17 - 3642012089255/34538246151*e^16 + 19527383885026/34538246151*e^15 + 17866243672754/34538246151*e^14 - 118668483588407/34538246151*e^13 - 15613467984759/11512748717*e^12 + 431689032524389/34538246151*e^11 + 19185266211455/11512748717*e^10 - 321529559653564/11512748717*e^9 - 818796989729/34538246151*e^8 + 1301422865246239/34538246151*e^7 - 81609574500343/34538246151*e^6 - 993648616966366/34538246151*e^5 + 28844613898456/11512748717*e^4 + 124191369384143/11512748717*e^3 - 26102679018212/34538246151*e^2 - 16000968730272/11512748717*e - 930237752724/11512748717, -7109051496/11512748717*e^20 + 31773090908/11512748717*e^19 + 156999496432/11512748717*e^18 - 823196735450/11512748717*e^17 - 1334789649394/11512748717*e^16 + 8921226545667/11512748717*e^15 + 5226910020890/11512748717*e^14 - 2774024693345/605934143*e^13 - 7257518688422/11512748717*e^12 + 185624344959527/11512748717*e^11 - 11556415138692/11512748717*e^10 - 400043192245210/11512748717*e^9 + 52213616297131/11512748717*e^8 + 518719867236500/11512748717*e^7 - 64049101562398/11512748717*e^6 - 379022432948776/11512748717*e^5 + 28843229631680/11512748717*e^4 + 135522718913899/11512748717*e^3 - 36067498509/605934143*e^2 - 16932033247622/11512748717*e - 1830084278820/11512748717, -87776898853/69076492302*e^20 + 10662818878/1817802429*e^19 + 1940069543237/69076492302*e^18 - 5304016523312/34538246151*e^17 - 8232617338727/34538246151*e^16 + 58204720912426/34538246151*e^15 + 63765883916161/69076492302*e^14 - 348968963782202/34538246151*e^13 - 27328805280223/23025497434*e^12 + 1249842290320384/34538246151*e^11 - 58754844417083/23025497434*e^10 - 914650078383340/11512748717*e^9 + 359166496204669/34538246151*e^8 + 3630340015739107/34538246151*e^7 - 873481329643811/69076492302*e^6 - 2713952405581339/34538246151*e^5 + 136259189508365/23025497434*e^4 + 333160467861161/11512748717*e^3 - 26346831484141/69076492302*e^2 - 2301475115002/605934143*e - 4026444055376/11512748717, -6762597202/11512748717*e^20 + 89625410252/34538246151*e^19 + 431738159786/34538246151*e^18 - 2253074116027/34538246151*e^17 - 3447773714614/34538246151*e^16 + 23501653399307/34538246151*e^15 + 11753308357634/34538246151*e^14 - 132352174944941/34538246151*e^13 - 6934346087392/34538246151*e^12 + 146574910865029/11512748717*e^11 - 63513015883060/34538246151*e^10 - 295424557826863/11512748717*e^9 + 59337155914370/11512748717*e^8 + 1071592579582871/34538246151*e^7 - 180263467375426/34538246151*e^6 - 736253681489450/34538246151*e^5 + 59735335006192/34538246151*e^4 + 84752170688076/11512748717*e^3 + 2903029660320/11512748717*e^2 - 32606278430554/34538246151*e - 89522151246/605934143, 88351741541/34538246151*e^20 - 388092720112/34538246151*e^19 - 1908691793917/34538246151*e^18 + 9840055765178/34538246151*e^17 + 15650771986844/34538246151*e^16 - 103783419419686/34538246151*e^15 - 56734149205052/34538246151*e^14 + 592894491702974/34538246151*e^13 + 17838911521569/11512748717*e^12 - 2006013636192160/34538246151*e^11 + 77725008722219/11512748717*e^10 + 1377954959615418/11512748717*e^9 - 774241670060302/34538246151*e^8 - 5124915694573360/34538246151*e^7 + 47869121373841/1817802429*e^6 + 3609012383380744/34538246151*e^5 - 146576329599479/11512748717*e^4 - 423130313911408/11512748717*e^3 + 50658851979296/34538246151*e^2 + 54364027935384/11512748717*e + 4808878351882/11512748717];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {17, 17, -w^3 + w^2 + 6*w - 1}>] := 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;