/* 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 := PolynomialRing(Rationals()); g := P![44, 14, -13, -2, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [4, 2, w^2 - 2*w - 6], [4, 2, -w^2 + 7], [5, 5, -1/2*w^3 + 2*w^2 + 7/2*w - 14], [5, 5, 1/2*w^3 + 1/2*w^2 - 6*w - 9], [11, 11, 1/2*w^3 - 2*w^2 - 5/2*w + 11], [11, 11, 1/2*w^3 + 1/2*w^2 - 5*w - 7], [31, 31, 1/2*w^2 + 1/2*w - 4], [31, 31, -1/2*w^2 + 3/2*w + 3], [41, 41, 1/2*w^2 + 1/2*w - 6], [41, 41, 2*w^3 - 15/2*w^2 - 25/2*w + 50], [41, 41, 5/2*w^2 - 1/2*w - 17], [41, 41, 1/2*w^2 - 3/2*w - 5], [61, 61, -1/2*w^3 + w^2 + 7/2*w - 1], [61, 61, -1/2*w^3 + 1/2*w^2 + 4*w - 3], [71, 71, 1/2*w^3 + w^2 - 11/2*w - 13], [71, 71, -1/2*w^3 + 5/2*w^2 + 2*w - 17], [81, 3, -3], [89, 89, -w^3 + 3/2*w^2 + 13/2*w - 9], [89, 89, w^3 - 7/2*w^2 - 11/2*w + 20], [89, 89, -w^3 - 1/2*w^2 + 19/2*w + 12], [89, 89, 1/2*w^3 + 2*w^2 - 17/2*w - 19], [109, 109, 1/2*w^3 + 3/2*w^2 - 7*w - 15], [109, 109, -1/2*w^3 + 1/2*w^2 + 4*w - 5], [121, 11, -3/2*w^2 + 3/2*w + 10], [131, 131, 3/2*w^3 - 13/2*w^2 - 9*w + 43], [131, 131, -3/2*w^3 - 2*w^2 + 35/2*w + 29], [139, 139, -3/2*w^3 + 11/2*w^2 + 10*w - 39], [139, 139, 1/2*w^3 + w^2 - 11/2*w - 9], [139, 139, -1/2*w^3 + 5/2*w^2 + 2*w - 13], [139, 139, -3/2*w^3 - w^2 + 33/2*w + 25], [151, 151, -1/2*w^3 + 3/2*w^2 + 3*w - 5], [151, 151, -1/2*w^3 + 9/2*w + 1], [179, 179, 5/2*w^2 - 3/2*w - 20], [179, 179, -w^3 + 5/2*w^2 + 11/2*w - 5], [179, 179, -w^3 + 1/2*w^2 + 15/2*w - 2], [179, 179, w^3 + 1/2*w^2 - 19/2*w - 10], [181, 181, 1/2*w^2 - 3/2*w - 8], [181, 181, 3/2*w^2 - 1/2*w - 13], [181, 181, -3/2*w^2 + 5/2*w + 12], [181, 181, 1/2*w^2 + 1/2*w - 9], [191, 191, w^3 + 1/2*w^2 - 17/2*w - 9], [191, 191, 1/2*w^3 - w^2 - 5/2*w + 8], [199, 199, -1/2*w^3 + 7/2*w^2 + 3*w - 23], [199, 199, -1/2*w^3 - 2*w^2 + 17/2*w + 17], [211, 211, w^3 - 5/2*w^2 - 9/2*w + 3], [211, 211, -w^3 + 1/2*w^2 + 13/2*w - 3], [229, 229, 3/2*w^3 - 2*w^2 - 21/2*w - 6], [229, 229, -w^3 + 3*w^2 + 8*w - 23], [239, 239, -w^3 + 3*w^2 + 4*w - 9], [239, 239, w^3 - 9*w - 7], [239, 239, 1/2*w^3 - 3/2*w^2 - 2*w + 13], [239, 239, -w^3 + 7*w + 3], [241, 241, 1/2*w^3 + 2*w^2 - 15/2*w - 16], [241, 241, -1/2*w^3 + 7/2*w^2 + 2*w - 21], [251, 251, w^3 - 5/2*w^2 - 9/2*w + 10], [251, 251, w^3 - 9*w - 9], [269, 269, w^3 - 1/2*w^2 - 17/2*w - 10], [269, 269, w^3 - 5/2*w^2 - 13/2*w + 18], [281, 281, -1/2*w^3 + 3*w^2 + 3/2*w - 19], [281, 281, 1/2*w^3 + 3/2*w^2 - 6*w - 15], [289, 17, w^3 - 3/2*w^2 - 15/2*w - 1], [289, 17, -w^3 + 3/2*w^2 + 15/2*w - 9], [331, 331, 3/2*w^2 - 1/2*w - 14], [331, 331, -3/2*w^2 + 5/2*w + 13], [349, 349, -w^3 + 3/2*w^2 + 11/2*w - 1], [349, 349, w^3 - 5/2*w^2 - 13/2*w + 14], [359, 359, -w^3 + 5/2*w^2 + 11/2*w - 14], [359, 359, w^3 - 1/2*w^2 - 15/2*w - 7], [361, 19, 2*w^2 - 2*w - 15], [361, 19, -2*w^2 + 2*w + 13], [379, 379, 5/2*w^2 - 3/2*w - 16], [379, 379, 5/2*w^2 - 7/2*w - 15], [389, 389, 7/2*w^2 - 1/2*w - 26], [389, 389, 1/2*w^3 - 3/2*w^2 - 5*w + 5], [389, 389, 1/2*w^3 + 2*w^2 - 11/2*w - 18], [389, 389, 3/2*w^3 - 1/2*w^2 - 13*w - 15], [409, 409, -w^3 + 7/2*w^2 + 9/2*w - 19], [409, 409, w^3 + 1/2*w^2 - 17/2*w - 12], [439, 439, -1/2*w^3 + 5/2*w^2 + w - 15], [439, 439, 1/2*w^3 + w^2 - 9/2*w - 12], [461, 461, 1/2*w^3 + 2*w^2 - 15/2*w - 18], [461, 461, -1/2*w^3 + 7/2*w^2 + 2*w - 23], [479, 479, -1/2*w^3 + 2*w^2 + 7/2*w - 10], [479, 479, 1/2*w^3 - 2*w^2 - 5/2*w + 7], [491, 491, -2*w^3 + 1/2*w^2 + 29/2*w - 1], [491, 491, 2*w^3 - 11/2*w^2 - 19/2*w + 12], [499, 499, -w^3 + 5/2*w^2 + 13/2*w - 13], [499, 499, w^3 - 1/2*w^2 - 17/2*w - 5], [509, 509, -w^3 + 3/2*w^2 + 15/2*w - 2], [509, 509, w^3 - 3/2*w^2 - 15/2*w + 6], [521, 521, -1/2*w^3 + 2*w^2 + 9/2*w - 15], [521, 521, 1/2*w^3 + 1/2*w^2 - 7*w - 9], [529, 23, -w^3 + 2*w^2 + 5*w - 9], [529, 23, -3/2*w^2 + 7/2*w + 12], [541, 541, 3/2*w^3 + 1/2*w^2 - 14*w - 17], [541, 541, -3/2*w^3 + 5*w^2 + 17/2*w - 29], [569, 569, -2*w^3 + 1/2*w^2 + 35/2*w + 18], [569, 569, -w^3 - 5/2*w^2 + 27/2*w + 27], [571, 571, -w^3 + w^2 + 8*w + 7], [571, 571, -1/2*w^3 + 2*w^2 + 3/2*w - 4], [571, 571, 1/2*w^3 + 1/2*w^2 - 4*w - 1], [571, 571, -4*w^3 - 7/2*w^2 + 91/2*w + 68], [599, 599, -1/2*w^3 - 5/2*w^2 + 10*w + 21], [599, 599, 2*w^3 + 5/2*w^2 - 47/2*w - 37], [599, 599, 2*w^3 - 17/2*w^2 - 25/2*w + 56], [599, 599, -1/2*w^3 + 4*w^2 + 7/2*w - 28], [601, 601, -w^3 - 3/2*w^2 + 23/2*w + 18], [601, 601, 1/2*w^3 + 7/2*w^2 - 5*w - 27], [601, 601, 1/2*w^3 - 5*w^2 + 7/2*w + 28], [601, 601, 2*w^3 - 3*w^2 - 13*w + 21], [619, 619, -w^3 + 5/2*w^2 + 9/2*w - 8], [619, 619, w^3 - 1/2*w^2 - 13/2*w - 2], [631, 631, -5/2*w^3 + 1/2*w^2 + 18*w - 1], [631, 631, -5/2*w^3 + 7*w^2 + 23/2*w - 15], [641, 641, 5/2*w^2 - 1/2*w - 20], [641, 641, -5/2*w^2 + 9/2*w + 18], [659, 659, w^3 - 7/2*w^2 - 15/2*w + 28], [659, 659, w^3 + 2*w^2 - 11*w - 21], [661, 661, -w^3 + 15/2*w^2 + 11/2*w - 52], [661, 661, -3/2*w^3 + 1/2*w^2 + 13*w + 5], [661, 661, 3/2*w^3 - 4*w^2 - 19/2*w + 17], [661, 661, -w^3 - 9/2*w^2 + 35/2*w + 40], [691, 691, 2*w^3 - 9/2*w^2 - 21/2*w + 5], [691, 691, -5/2*w^3 - w^2 + 55/2*w + 37], [701, 701, w^3 - 2*w^2 - 7*w + 3], [701, 701, w^3 - w^2 - 8*w + 5], [709, 709, -11/2*w^2 + 3/2*w + 40], [709, 709, -3/2*w^3 - 3/2*w^2 + 16*w + 23], [739, 739, 1/2*w^3 - 9/2*w^2 + 3*w + 25], [739, 739, 1/2*w^3 + 3*w^2 - 9/2*w - 24], [751, 751, -7/2*w^3 + 12*w^2 + 47/2*w - 83], [751, 751, -3/2*w^3 + 23/2*w + 3], [751, 751, -3/2*w^3 + 9/2*w^2 + 7*w - 13], [751, 751, 7/2*w^3 + 3/2*w^2 - 37*w - 51], [761, 761, -3/2*w^3 - 1/2*w^2 + 14*w + 19], [761, 761, -w^3 + 3/2*w^2 + 15/2*w - 4], [761, 761, -3/2*w^3 + 5*w^2 + 17/2*w - 31], [769, 769, -3*w^3 - 5/2*w^2 + 69/2*w + 51], [769, 769, -1/2*w^3 - 4*w^2 + 9/2*w + 27], [769, 769, -w^3 - 5/2*w^2 + 29/2*w + 25], [769, 769, 3*w^3 - 23/2*w^2 - 41/2*w + 80], [809, 809, 1/2*w^3 + 2*w^2 - 13/2*w - 17], [809, 809, 1/2*w^3 - 7/2*w^2 - w + 21], [821, 821, 1/2*w^3 - 1/2*w^2 - 6*w + 3], [821, 821, -1/2*w^3 + w^2 + 11/2*w - 3], [829, 829, -3/2*w^3 + 3*w^2 + 23/2*w - 10], [829, 829, -w^3 + 2*w^2 + 5*w + 1], [829, 829, 7/2*w^2 - 3/2*w - 28], [829, 829, 3/2*w^3 - 3/2*w^2 - 13*w + 3], [839, 839, -w^3 - 7/2*w^2 + 17/2*w + 27], [839, 839, 2*w^3 + 1/2*w^2 - 43/2*w - 27], [839, 839, 2*w^3 - 13/2*w^2 - 29/2*w + 46], [839, 839, -w^3 - 3/2*w^2 + 19/2*w + 14], [841, 29, 5/2*w^2 - 5/2*w - 19], [841, 29, 5/2*w^2 - 5/2*w - 16], [859, 859, 1/2*w^3 + w^2 - 5/2*w - 12], [859, 859, w^3 + 3/2*w^2 - 19/2*w - 19], [859, 859, -w^3 + 9/2*w^2 + 7/2*w - 26], [859, 859, 1/2*w^3 - 5/2*w^2 + w + 13], [881, 881, -1/2*w^3 + 1/2*w^2 + 6*w + 1], [881, 881, 1/2*w^3 - w^2 - 11/2*w + 7], [911, 911, -1/2*w^3 + 5/2*w^2 + 3*w - 13], [911, 911, 1/2*w^3 + w^2 - 13/2*w - 8], [941, 941, -2*w^3 + 7/2*w^2 + 27/2*w - 21], [941, 941, 3/2*w^3 - 7*w^2 - 21/2*w + 51], [941, 941, 3/2*w^3 + 5/2*w^2 - 20*w - 35], [941, 941, -2*w^3 + 13/2*w^2 + 29/2*w - 48], [961, 31, -w^2 + w + 13], [1009, 1009, -5/2*w^2 - 1/2*w + 18], [1009, 1009, 3/2*w^3 - 3/2*w^2 - 12*w - 5], [1021, 1021, w^3 + w^2 - 10*w - 19], [1021, 1021, w^3 - 5/2*w^2 - 9/2*w + 12], [1031, 1031, -1/2*w^3 + 3/2*w^2 + 5*w - 9], [1031, 1031, -w^3 + 3/2*w^2 + 13/2*w - 2], [1049, 1049, -3/2*w^3 - 1/2*w^2 + 16*w + 23], [1049, 1049, -2*w^3 + 9/2*w^2 + 23/2*w - 6], [1049, 1049, -2*w^3 + 3/2*w^2 + 29/2*w - 8], [1049, 1049, 3/2*w^3 - 5*w^2 - 21/2*w + 37], [1051, 1051, -2*w^3 + 11/2*w^2 + 17/2*w - 10], [1051, 1051, -3*w^3 - 1/2*w^2 + 59/2*w + 36], [1051, 1051, -3*w^3 + 19/2*w^2 + 39/2*w - 62], [1051, 1051, 2*w^3 - 1/2*w^2 - 27/2*w + 2], [1061, 1061, 11/2*w^2 - 3/2*w - 38], [1061, 1061, 11/2*w^2 - 19/2*w - 34], [1069, 1069, 1/2*w^3 - 4*w^2 - 5/2*w + 25], [1069, 1069, 2*w^3 - 20*w - 25], [1069, 1069, -2*w^3 + 6*w^2 + 14*w - 43], [1069, 1069, 1/2*w^3 + 5/2*w^2 - 9*w - 19], [1109, 1109, -5/2*w^3 + 13/2*w^2 + 12*w - 13], [1109, 1109, -5/2*w^3 + w^2 + 35/2*w - 3], [1151, 1151, 13/2*w^2 - 3/2*w - 46], [1151, 1151, 1/2*w^3 + 3/2*w^2 - 5*w - 17], [1151, 1151, 1/2*w^3 - 3*w^2 - 1/2*w + 20], [1151, 1151, 13/2*w^2 - 23/2*w - 41], [1171, 1171, w^3 - 3/2*w^2 - 13/2*w + 12], [1171, 1171, 1/2*w^3 - 1/2*w^2 - 6*w + 1], [1171, 1171, -1/2*w^3 + w^2 + 11/2*w - 5], [1171, 1171, -1/2*w^3 + 5*w^2 - 7/2*w - 26], [1201, 1201, 1/2*w^3 + 1/2*w^2 - 6*w - 3], [1201, 1201, -1/2*w^3 + 2*w^2 + 7/2*w - 8], [1229, 1229, 1/2*w^3 + 5/2*w^2 - 8*w - 21], [1229, 1229, -1/2*w^3 + 4*w^2 + 3/2*w - 26], [1249, 1249, -w^3 + 7/2*w^2 + 9/2*w - 12], [1249, 1249, w^3 + 1/2*w^2 - 17/2*w - 5], [1279, 1279, 1/2*w^3 + 3/2*w^2 - 3*w - 15], [1279, 1279, -1/2*w^3 + 3*w^2 - 3/2*w - 16], [1289, 1289, 5/2*w^2 - 9/2*w - 19], [1289, 1289, w^3 - 9/2*w^2 - 15/2*w + 32], [1289, 1289, -w^3 - 3/2*w^2 + 27/2*w + 21], [1289, 1289, 5/2*w^2 - 1/2*w - 21], [1291, 1291, -1/2*w^3 + 5*w^2 - 9/2*w - 23], [1291, 1291, 1/2*w^3 + 7/2*w^2 - 4*w - 23], [1301, 1301, -3/2*w^3 + 2*w^2 + 21/2*w - 10], [1301, 1301, -3/2*w^3 + 5/2*w^2 + 10*w - 1], [1319, 1319, 4*w^3 - 29/2*w^2 - 49/2*w + 93], [1319, 1319, -4*w^3 - 5/2*w^2 + 83/2*w + 58], [1321, 1321, -17/2*w^2 + 31/2*w + 52], [1321, 1321, 17/2*w^2 - 3/2*w - 59], [1361, 1361, -3*w^3 - 7/2*w^2 + 71/2*w + 58], [1361, 1361, -3/2*w^3 - 3*w^2 + 39/2*w + 34], [1369, 37, 3/2*w^3 - 1/2*w^2 - 13*w - 17], [1369, 37, 3/2*w^3 + 1/2*w^2 - 11*w - 3], [1381, 1381, w^3 - 5*w^2 - 2*w + 27], [1381, 1381, w^3 + 2*w^2 - 9*w - 21], [1399, 1399, w^3 + 5/2*w^2 - 19/2*w - 25], [1399, 1399, w^3 - 11/2*w^2 - 3/2*w + 31], [1439, 1439, -2*w^3 + 13/2*w^2 + 23/2*w - 40], [1439, 1439, 4*w^3 + 3*w^2 - 43*w - 65], [1451, 1451, 1/2*w^3 + 9/2*w^2 - 5*w - 35], [1451, 1451, -1/2*w^3 + 6*w^2 - 11/2*w - 35], [1459, 1459, -3/2*w^3 + 9/2*w^2 + 9*w - 25], [1459, 1459, -3/2*w^3 + 1/2*w^2 + 10*w + 7], [1471, 1471, 3/2*w^3 - 11/2*w^2 - 7*w + 31], [1471, 1471, -3/2*w^3 - w^2 + 27/2*w + 20], [1489, 1489, -3*w^3 - 3*w^2 + 34*w + 51], [1489, 1489, 1/2*w^3 + 5/2*w^2 - 6*w - 25], [1489, 1489, -1/2*w^3 + 4*w^2 - 1/2*w - 28], [1489, 1489, 3*w^3 - 12*w^2 - 19*w + 79], [1499, 1499, 1/2*w^3 - 7/2*w^2 + 2*w + 19], [1499, 1499, 1/2*w^3 + 5/2*w^2 - 6*w - 21], [1499, 1499, -1/2*w^3 + 4*w^2 - 1/2*w - 24], [1499, 1499, -w^3 + 5/2*w^2 + 11/2*w - 17], [1511, 1511, -2*w^3 + 15/2*w^2 + 17/2*w - 37], [1511, 1511, -2*w^3 - 3/2*w^2 + 35/2*w + 23], [1531, 1531, 1/2*w^3 - 3*w^2 - 9/2*w + 16], [1531, 1531, -2*w^3 + 9/2*w^2 + 23/2*w - 8], [1531, 1531, -2*w^3 + 3/2*w^2 + 29/2*w - 6], [1531, 1531, w^3 + 5/2*w^2 - 21/2*w - 25], [1549, 1549, -1/2*w^3 + 1/2*w^2 + 3*w - 7], [1549, 1549, 1/2*w^3 - w^2 - 5/2*w - 4], [1579, 1579, w^3 + 3/2*w^2 - 19/2*w - 13], [1579, 1579, -w^3 + 9/2*w^2 + 7/2*w - 20], [1609, 1609, -11/2*w^2 + 1/2*w + 37], [1609, 1609, 11/2*w^2 - 21/2*w - 32], [1619, 1619, 1/2*w^3 - 3/2*w^2 - w + 15], [1619, 1619, w^3 - 3/2*w^2 - 21/2*w + 1], [1621, 1621, -2*w^3 + 15/2*w^2 + 23/2*w - 49], [1621, 1621, 1/2*w^3 + 3/2*w^2 - 9*w - 19], [1669, 1669, 1/2*w^3 + 5/2*w^2 - 7*w - 23], [1669, 1669, 1/2*w^3 - 4*w^2 - 1/2*w + 27], [1699, 1699, -w^3 + 1/2*w^2 + 17/2*w - 2], [1699, 1699, -w^3 + 5/2*w^2 + 13/2*w - 6], [1709, 1709, 1/2*w^3 + 3/2*w^2 - 2*w - 15], [1709, 1709, -1/2*w^3 + 3*w^2 - 5/2*w - 15], [1721, 1721, 5/2*w^3 - w^2 - 45/2*w - 20], [1721, 1721, -5/2*w^3 + 13/2*w^2 + 17*w - 41], [1741, 1741, -w^3 + 5/2*w^2 + 13/2*w - 3], [1741, 1741, -5/2*w^3 - 3*w^2 + 61/2*w + 48], [1741, 1741, -5*w^3 + 35/2*w^2 + 65/2*w - 116], [1741, 1741, -w^3 + 5*w^2 + 6*w - 31], [1759, 1759, 4*w^3 - 16*w^2 - 26*w + 111], [1759, 1759, 3*w^3 + 3/2*w^2 - 61/2*w - 43], [1789, 1789, w^3 + 1/2*w^2 - 17/2*w - 14], [1789, 1789, -w^3 + 7/2*w^2 + 9/2*w - 21], [1801, 1801, w^3 + 5/2*w^2 - 23/2*w - 24], [1801, 1801, w^3 + 11/2*w^2 - 15/2*w - 38], [1831, 1831, 13/2*w^2 - 1/2*w - 46], [1831, 1831, -3/2*w^3 + 8*w^2 + 19/2*w - 53], [1831, 1831, 9/2*w^3 - 33/2*w^2 - 28*w + 109], [1831, 1831, -13/2*w^2 + 25/2*w + 40], [1861, 1861, 5/2*w^2 - 9/2*w - 8], [1861, 1861, 5/2*w^2 - 1/2*w - 10], [1871, 1871, -1/2*w^3 - 1/2*w^2 + 7*w + 15], [1871, 1871, -1/2*w^3 - 4*w^2 + 7/2*w + 26], [1879, 1879, 1/2*w^3 - 9/2*w^2 - w + 25], [1879, 1879, -w^3 - 5/2*w^2 + 23/2*w + 27], [1879, 1879, w^3 - 11/2*w^2 - 7/2*w + 35], [1879, 1879, 1/2*w^3 + 3*w^2 - 17/2*w - 20], [1889, 1889, w^3 + 5/2*w^2 - 25/2*w - 27], [1889, 1889, -w^3 + 11/2*w^2 + 9/2*w - 36], [1901, 1901, -3*w^3 - w^2 + 32*w + 41], [1901, 1901, 3*w^3 - 10*w^2 - 21*w + 69], [1931, 1931, 2*w^3 - 15/2*w^2 - 13/2*w + 26], [1931, 1931, -w^3 + 11/2*w^2 + 5/2*w - 31], [1951, 1951, -w^3 + 1/2*w^2 + 13/2*w + 7], [1951, 1951, 2*w^2 - 19], [1979, 1979, -1/2*w^3 + 4*w^2 + 1/2*w - 25], [1979, 1979, 7/2*w^3 + w^2 - 73/2*w - 47], [1979, 1979, 7/2*w^3 - 23/2*w^2 - 24*w + 79], [1979, 1979, 1/2*w^3 + 5/2*w^2 - 7*w - 21], [1999, 1999, -w^3 + 15/2*w^2 + 11/2*w - 54], [1999, 1999, -w^3 + 15/2*w^2 - 9/2*w - 37]]; primes := [ideal : I in primesArray]; heckePol := x^12 - 40*x^10 - 2*x^9 + 557*x^8 + 44*x^7 - 3076*x^6 - 288*x^5 + 5367*x^4 + 964*x^3 - 2092*x^2 + 50*x + 115; K := NumberField(heckePol); heckeEigenvaluesArray := [e, 1, 1, -294555/24596968*e^11 + 31439/12298484*e^10 + 5790205/12298484*e^9 - 1619631/24596968*e^8 - 78762137/12298484*e^7 + 6516651/12298484*e^6 + 418123553/12298484*e^5 - 13573379/12298484*e^4 - 119425033/2236088*e^3 - 21527029/3074621*e^2 + 95459047/6149242*e + 17288793/24596968, -9145/3074621*e^11 - 5751/6149242*e^10 + 2955141/24596968*e^9 + 987935/24596968*e^8 - 20816929/12298484*e^7 - 7181919/12298484*e^6 + 116985829/12298484*e^5 + 42197417/12298484*e^4 - 19439931/1118044*e^3 - 100117591/12298484*e^2 + 229833405/24596968*e + 39133279/24596968, -42285/12298484*e^11 - 167799/24596968*e^10 + 3450905/24596968*e^9 + 1735925/6149242*e^8 - 24557333/12298484*e^7 - 48825563/12298484*e^6 + 140487075/12298484*e^5 + 259324905/12298484*e^4 - 12180077/559022*e^3 - 744775023/24596968*e^2 + 117112481/24596968*e + 41013227/12298484, -271757/24596968*e^11 - 5491/3074621*e^10 + 10671217/24596968*e^9 + 423337/3074621*e^8 - 73425955/12298484*e^7 - 33215925/12298484*e^6 + 410359843/12298484*e^5 + 223866559/12298484*e^4 - 144646751/2236088*e^3 - 448680415/12298484*e^2 + 697466409/24596968*e + 91830477/12298484, 435231/24596968*e^11 + 147641/6149242*e^10 - 8805429/12298484*e^9 - 23882657/24596968*e^8 + 124192745/12298484*e^7 + 163214407/12298484*e^6 - 698272027/12298484*e^5 - 844439441/12298484*e^4 + 228340109/2236088*e^3 + 1268037541/12298484*e^2 - 72268506/3074621*e - 205029681/24596968, 186981/24596968*e^11 - 25242/3074621*e^10 - 3643945/12298484*e^9 + 7679593/24596968*e^8 + 48632405/12298484*e^7 - 50876465/12298484*e^6 - 245974101/12298484*e^5 + 255383903/12298484*e^4 + 58913003/2236088*e^3 - 260186537/12298484*e^2 - 55483107/6149242*e + 97748029/24596968, 180959/3074621*e^11 + 23447/3074621*e^10 - 28725251/12298484*e^9 - 5576111/12298484*e^8 + 197326137/6149242*e^7 + 47439929/6149242*e^6 - 529491506/3074621*e^5 - 147482283/3074621*e^4 + 152298059/559022*e^3 + 713858887/6149242*e^2 - 692723221/12298484*e - 128876193/12298484, -371863/24596968*e^11 - 69353/24596968*e^10 + 14965847/24596968*e^9 + 3007453/24596968*e^8 - 51839399/6149242*e^7 - 10622217/6149242*e^6 + 275479419/6149242*e^5 + 32378460/3074621*e^4 - 143920887/2236088*e^3 - 926019491/24596968*e^2 + 233488285/24596968*e + 279389379/24596968, 913511/24596968*e^11 + 76941/24596968*e^10 - 18296031/12298484*e^9 - 1064557/6149242*e^8 + 253943223/12298484*e^7 + 32996077/12298484*e^6 - 1378362119/12298484*e^5 - 192028055/12298484*e^4 + 403391269/2236088*e^3 + 1214721873/24596968*e^2 - 150311196/3074621*e + 12897957/12298484, -320253/24596968*e^11 - 46735/12298484*e^10 + 6500473/12298484*e^9 + 3858341/24596968*e^8 - 92319217/12298484*e^7 - 25450213/12298484*e^6 + 526265557/12298484*e^5 + 118285011/12298484*e^4 - 178925211/2236088*e^3 - 85329575/6149242*e^2 + 198100383/6149242*e - 135758999/24596968, -210333/24596968*e^11 - 21232/3074621*e^10 + 8313851/24596968*e^9 + 1801749/6149242*e^8 - 56544145/12298484*e^7 - 52264515/12298484*e^6 + 293740373/12298484*e^5 + 302835009/12298484*e^4 - 70160491/2236088*e^3 - 633619125/12298484*e^2 - 237845133/24596968*e + 159549073/12298484, -1465535/24596968*e^11 - 23219/12298484*e^10 + 57918917/24596968*e^9 + 3251543/12298484*e^8 - 396314639/12298484*e^7 - 69372131/12298484*e^6 + 2122204757/12298484*e^5 + 481441091/12298484*e^4 - 615567233/2236088*e^3 - 621889483/6149242*e^2 + 1512536217/24596968*e + 28206659/6149242, -20083/1118044*e^11 - 57009/2236088*e^10 + 1621403/2236088*e^9 + 1132977/1118044*e^8 - 5646265/559022*e^7 - 7654679/559022*e^6 + 30509761/559022*e^5 + 19877992/279511*e^4 - 93658493/1118044*e^3 - 255917523/2236088*e^2 - 3911963/2236088*e + 19228943/1118044, 188339/12298484*e^11 + 177613/24596968*e^10 - 3809259/6149242*e^9 - 7920381/24596968*e^8 + 107394117/12298484*e^7 + 57699547/12298484*e^6 - 601517369/12298484*e^5 - 310299879/12298484*e^4 + 24068546/279511*e^3 + 1019362885/24596968*e^2 - 260287145/12298484*e - 18186101/24596968, -83735/3074621*e^11 - 333349/24596968*e^10 + 26365775/24596968*e^9 + 1979452/3074621*e^8 - 45080304/3074621*e^7 - 30704956/3074621*e^6 + 244247155/3074621*e^5 + 178292720/3074621*e^4 - 75352537/559022*e^3 - 2523018259/24596968*e^2 + 682606421/24596968*e + 26997515/3074621, 2090973/24596968*e^11 + 702357/24596968*e^10 - 83431019/24596968*e^9 - 32042919/24596968*e^8 + 288777701/6149242*e^7 + 118998189/6149242*e^6 - 785923573/3074621*e^5 - 668842047/6149242*e^4 + 942095397/2236088*e^3 + 5275497559/24596968*e^2 - 2396861109/24596968*e - 402005405/24596968, 12849/6149242*e^11 + 39087/3074621*e^10 - 355134/3074621*e^9 - 1369493/3074621*e^8 + 6778540/3074621*e^7 + 15983432/3074621*e^6 - 54071002/3074621*e^5 - 69003816/3074621*e^4 + 30309111/559022*e^3 + 85320211/3074621*e^2 - 130312925/3074621*e - 1708125/3074621, 1094245/24596968*e^11 + 239003/24596968*e^10 - 43839723/24596968*e^9 - 11306125/24596968*e^8 + 76222471/3074621*e^7 + 42268905/6149242*e^6 - 416874350/3074621*e^5 - 119008999/3074621*e^4 + 500547073/2236088*e^3 + 2107546361/24596968*e^2 - 1247869181/24596968*e - 152971155/24596968, -147157/3074621*e^11 - 547351/24596968*e^10 + 46906535/24596968*e^9 + 11831051/12298484*e^8 - 161687981/6149242*e^7 - 84866737/6149242*e^6 + 870716753/6149242*e^5 + 469014483/6149242*e^4 - 62990847/279511*e^3 - 3732174357/24596968*e^2 + 1106516689/24596968*e + 298686655/12298484, -261315/3074621*e^11 - 366511/24596968*e^10 + 82713955/24596968*e^9 + 4740577/6149242*e^8 - 565259857/12298484*e^7 - 150906303/12298484*e^6 + 3000409257/12298484*e^5 + 909986655/12298484*e^4 - 416485237/1118044*e^3 - 4451058039/24596968*e^2 + 1649039923/24596968*e + 277949785/12298484, -767049/24596968*e^11 + 291535/24596968*e^10 + 3803732/3074621*e^9 - 2341345/6149242*e^8 - 210206241/12298484*e^7 + 53707663/12298484*e^6 + 1152185233/12298484*e^5 - 254323757/12298484*e^4 - 360953131/2236088*e^3 + 500168459/24596968*e^2 + 666623225/12298484*e - 150407117/12298484, 176247/6149242*e^11 - 91561/12298484*e^10 - 27505339/24596968*e^9 + 5830423/24596968*e^8 + 182937295/12298484*e^7 - 33996111/12298484*e^6 - 907620843/12298484*e^5 + 151283389/12298484*e^4 + 93733603/1118044*e^3 + 20242234/3074621*e^2 + 273761853/24596968*e + 155482639/24596968, 172212/3074621*e^11 + 536331/12298484*e^10 - 6938819/3074621*e^9 - 21972031/12298484*e^8 + 97334278/3074621*e^7 + 150501281/6149242*e^6 - 542195928/3074621*e^5 - 775889995/6149242*e^4 + 86814804/279511*e^3 + 2458846179/12298484*e^2 - 277477999/3074621*e - 198962523/12298484, 177281/12298484*e^11 + 274211/24596968*e^10 - 13805607/24596968*e^9 - 2905021/6149242*e^8 + 22918954/3074621*e^7 + 41572381/6149242*e^6 - 113562010/3074621*e^5 - 116483493/3074621*e^4 + 44326067/1118044*e^3 + 1849029945/24596968*e^2 + 798484787/24596968*e - 107170145/6149242, -88079/3074621*e^11 + 168777/24596968*e^10 + 14064793/12298484*e^9 - 5671329/24596968*e^8 - 193514129/12298484*e^7 + 35121885/12298484*e^6 + 1023991575/12298484*e^5 - 159289923/12298484*e^4 - 134451113/1118044*e^3 - 279763915/24596968*e^2 + 56051206/3074621*e + 88728375/24596968, -4189/1118044*e^11 - 2358/279511*e^10 + 41118/279511*e^9 + 368763/1118044*e^8 - 554380/279511*e^7 - 2476223/559022*e^6 + 5681999/559022*e^5 + 6494323/279511*e^4 - 14867003/1118044*e^3 - 21215871/559022*e^2 + 1372325/559022*e + 3205685/1118044, -1127205/24596968*e^11 - 430919/24596968*e^10 + 45325727/24596968*e^9 + 19100713/24596968*e^8 - 79521909/3074621*e^7 - 34392288/3074621*e^6 + 891645597/6149242*e^5 + 184107639/3074621*e^4 - 586507793/2236088*e^3 - 2636574713/24596968*e^2 + 2194461557/24596968*e + 262594655/24596968, -151848/3074621*e^11 - 294873/12298484*e^10 + 23939543/12298484*e^9 + 6852899/6149242*e^8 - 81288771/3074621*e^7 - 105235651/6149242*e^6 + 426346174/3074621*e^5 + 621076983/6149242*e^4 - 56755009/279511*e^3 - 2498158841/12298484*e^2 + 92981465/12298484*e + 99115123/3074621, 933513/12298484*e^11 + 462809/12298484*e^10 - 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522468961/12298484*e - 814690955/24596968, -11532/279511*e^11 - 16691/2236088*e^10 + 1852819/1118044*e^9 + 738893/2236088*e^8 - 25840235/1118044*e^7 - 5159475/1118044*e^6 + 141871201/1118044*e^5 + 27971341/1118044*e^4 - 237566097/1118044*e^3 - 152587567/2236088*e^2 + 16783013/279511*e + 15917265/2236088, 1255231/12298484*e^11 + 678615/12298484*e^10 - 50132865/12298484*e^9 - 29562965/12298484*e^8 + 173954105/3074621*e^7 + 106685253/3074621*e^6 - 954488933/3074621*e^5 - 580506211/3074621*e^4 + 592552163/1118044*e^3 + 4025752933/12298484*e^2 - 1709525487/12298484*e - 301512407/12298484, 441407/12298484*e^11 + 16333/3074621*e^10 - 17525125/12298484*e^9 - 1665649/6149242*e^8 + 120826927/6149242*e^7 + 12313129/3074621*e^6 - 327966806/3074621*e^5 - 120994487/6149242*e^4 + 196577661/1118044*e^3 + 91819916/3074621*e^2 - 514928655/12298484*e + 53226498/3074621, -2003525/24596968*e^11 - 83475/3074621*e^10 + 39775553/12298484*e^9 + 31532777/24596968*e^8 - 546921797/12298484*e^7 - 240491239/12298484*e^6 + 2942067705/12298484*e^5 + 1380755775/12298484*e^4 - 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976928659/12298484*e^7 - 122953437/12298484*e^6 + 5278771719/12298484*e^5 + 918120219/12298484*e^4 - 1582039375/2236088*e^3 - 1355096911/6149242*e^2 + 2231528281/12298484*e + 1150363219/24596968, -1829991/12298484*e^11 + 855321/12298484*e^10 + 143435223/24596968*e^9 - 57684329/24596968*e^8 - 965447685/12298484*e^7 + 338482783/12298484*e^6 + 4953261109/12298484*e^5 - 1458613131/12298484*e^4 - 299940505/559022*e^3 + 59234646/3074621*e^2 + 925363171/24596968*e - 517354945/24596968, 836085/12298484*e^11 - 170163/24596968*e^10 - 33603543/12298484*e^9 + 5848737/24596968*e^8 + 465513835/12298484*e^7 - 44410373/12298484*e^6 - 2477376079/12298484*e^5 + 278280597/12298484*e^4 + 80829779/279511*e^3 + 189352165/24596968*e^2 - 152361851/6149242*e - 12711995/24596968, -146279/559022*e^11 - 12095/1118044*e^10 + 23306869/2236088*e^9 + 2257787/2236088*e^8 - 160890127/1118044*e^7 - 21696367/1118044*e^6 + 870621791/1118044*e^5 + 144976043/1118044*e^4 - 1417359325/1118044*e^3 - 217860397/559022*e^2 + 844636753/2236088*e + 58695615/2236088, 1818445/24596968*e^11 - 12054/3074621*e^10 - 35566067/12298484*e^9 - 793721/24596968*e^8 + 236286885/6149242*e^7 + 8192950/3074621*e^6 - 1160414691/6149242*e^5 - 92021502/3074621*e^4 + 448277729/2236088*e^3 + 453043524/3074621*e^2 + 801155563/12298484*e - 953049255/24596968, 904317/6149242*e^11 + 618455/12298484*e^10 - 143178859/24596968*e^9 - 56302965/24596968*e^8 + 245131946/3074621*e^7 + 206381635/6149242*e^6 - 2620817649/6149242*e^5 - 562555843/3074621*e^4 + 373957135/559022*e^3 + 4215309977/12298484*e^2 - 2945260665/24596968*e - 1158035671/24596968, 3736331/24596968*e^11 + 1267119/24596968*e^10 - 18410564/3074621*e^9 - 14553285/6149242*e^8 + 996384065/12298484*e^7 + 437679587/12298484*e^6 - 5147182933/12298484*e^5 - 2540711205/12298484*e^4 + 1279798045/2236088*e^3 + 11005360819/24596968*e^2 - 8966097/12298484*e - 974250733/12298484, -498325/24596968*e^11 - 185694/3074621*e^10 + 19509935/24596968*e^9 + 15952921/6149242*e^8 - 132810433/12298484*e^7 - 463230909/12298484*e^6 + 731708273/12298484*e^5 + 2514004499/12298484*e^4 - 254757187/2236088*e^3 - 3525988999/12298484*e^2 - 214702441/24596968*e + 561779507/12298484, 1251653/6149242*e^11 + 109115/3074621*e^10 - 99478923/12298484*e^9 - 24841159/12298484*e^8 + 687222687/6149242*e^7 + 104255260/3074621*e^6 - 1877255946/3074621*e^5 - 1259253265/6149242*e^4 + 290145594/279511*e^3 + 1283891606/3074621*e^2 - 3718945717/12298484*e - 99605787/12298484, -2122319/24596968*e^11 - 3118453/24596968*e^10 + 85864403/24596968*e^9 + 130551913/24596968*e^8 - 152516636/3074621*e^7 - 231715339/3074621*e^6 + 882859086/3074621*e^5 + 2489705307/6149242*e^4 - 1281899179/2236088*e^3 - 14837779051/24596968*e^2 + 4456783189/24596968*e + 2003828851/24596968, 3471299/24596968*e^11 - 435055/12298484*e^10 - 136765373/24596968*e^9 + 5203129/6149242*e^8 + 930624787/12298484*e^7 - 60837371/12298484*e^6 - 4923742631/12298484*e^5 - 127769623/12298484*e^4 + 1376638997/2236088*e^3 + 1069099871/6149242*e^2 - 3208540925/24596968*e - 677649903/12298484, 1880565/24596968*e^11 + 289353/12298484*e^10 - 9232274/3074621*e^9 - 28514075/24596968*e^8 + 497208883/12298484*e^7 + 225862047/12298484*e^6 - 2540372925/12298484*e^5 - 1376017103/12298484*e^4 + 593789359/2236088*e^3 + 1553650885/6149242*e^2 + 691561445/12298484*e - 1160985979/24596968, -8493951/24596968*e^11 - 1394711/24596968*e^10 + 334819521/24596968*e^9 + 78737581/24596968*e^8 - 569500095/3074621*e^7 - 166215998/3074621*e^6 + 6009749507/6149242*e^5 + 1052091922/3074621*e^4 - 3292744619/2236088*e^3 - 20517659905/24596968*e^2 + 5491132563/24596968*e + 3456378571/24596968, 75405/559022*e^11 + 56787/2236088*e^10 - 12166405/2236088*e^9 - 349570/279511*e^8 + 21368173/279511*e^7 + 10610989/559022*e^6 - 119086676/279511*e^5 - 29947262/279511*e^4 + 208428346/279511*e^3 + 549377249/2236088*e^2 - 567407575/2236088*e - 7960417/279511, 4756387/24596968*e^11 - 2802343/24596968*e^10 - 187252927/24596968*e^9 + 95121031/24596968*e^8 + 636332577/6149242*e^7 - 140120988/3074621*e^6 - 3349807729/6149242*e^5 + 1229695095/6149242*e^4 + 1826566363/2236088*e^3 - 2006818641/24596968*e^2 - 5353737981/24596968*e - 61844251/24596968, 130770/3074621*e^11 + 583053/12298484*e^10 - 42628895/24596968*e^9 - 48358097/24596968*e^8 + 154226471/6149242*e^7 + 166668647/6149242*e^6 - 934225799/6149242*e^5 - 414252946/3074621*e^4 + 192612969/559022*e^3 + 1834247119/12298484*e^2 - 4448778493/24596968*e + 944688845/24596968, 7197265/24596968*e^11 + 316649/12298484*e^10 - 36125293/3074621*e^9 - 31029675/24596968*e^8 + 2012839699/12298484*e^7 + 216951993/12298484*e^6 - 10995029405/12298484*e^5 - 1132507229/12298484*e^4 + 3265638995/2236088*e^3 + 988198564/3074621*e^2 - 4677845347/12298484*e - 97466255/24596968, 99541/559022*e^11 + 94813/1118044*e^10 - 3996939/559022*e^9 - 4030245/1118044*e^8 + 55725543/559022*e^7 + 28203681/559022*e^6 - 305902249/559022*e^5 - 148572781/559022*e^4 + 255983172/279511*e^3 + 530986513/1118044*e^2 - 63716828/279511*e - 18921705/1118044, -1349809/24596968*e^11 - 1444985/24596968*e^10 + 13396059/6149242*e^9 + 15772821/6149242*e^8 - 92097338/3074621*e^7 - 117118949/3074621*e^6 + 496071511/3074621*e^5 + 676126478/3074621*e^4 - 572860941/2236088*e^3 - 9943457451/24596968*e^2 + 50192535/6149242*e + 244209105/3074621, -611836/3074621*e^11 - 339131/24596968*e^10 + 97717811/12298484*e^9 + 20209355/24596968*e^8 - 1350432021/12298484*e^7 - 157500331/12298484*e^6 + 7278545521/12298484*e^5 + 889526223/12298484*e^4 - 1047219169/1118044*e^3 - 5875864615/24596968*e^2 + 773394627/3074621*e + 391635335/24596968, 377981/24596968*e^11 + 253669/6149242*e^10 - 3456129/6149242*e^9 - 47981805/24596968*e^8 + 93261411/12298484*e^7 + 375621353/12298484*e^6 - 605861623/12298484*e^5 - 2136202473/12298484*e^4 + 359430039/2236088*e^3 + 2671689539/12298484*e^2 - 1165212207/12298484*e - 300181605/24596968, 176975/3074621*e^11 + 1990051/24596968*e^10 - 28341103/12298484*e^9 - 78355087/24596968*e^8 + 392761797/12298484*e^7 + 524619043/12298484*e^6 - 2128961479/12298484*e^5 - 2680662965/12298484*e^4 + 306820061/1118044*e^3 + 8055268327/24596968*e^2 + 25343183/6149242*e - 1133685951/24596968, 2428049/24596968*e^11 - 754349/24596968*e^10 - 94405735/24596968*e^9 + 16337015/24596968*e^8 + 158750304/3074621*e^7 - 12949067/6149242*e^6 - 836490856/3074621*e^5 - 83533080/3074621*e^4 + 969231717/2236088*e^3 + 4048307561/24596968*e^2 - 2898693905/24596968*e - 1289202711/24596968, -409214/3074621*e^11 - 268243/12298484*e^10 + 16533775/3074621*e^9 + 11694713/12298484*e^8 - 232868080/3074621*e^7 - 77138735/6149242*e^6 + 1302929978/3074621*e^5 + 360098873/6149242*e^4 - 208703278/279511*e^3 - 1680697927/12298484*e^2 + 758429763/3074621*e + 24911933/12298484, 2480673/24596968*e^11 - 1316503/12298484*e^10 - 24412483/6149242*e^9 + 96924819/24596968*e^8 + 664150369/12298484*e^7 - 621611967/12298484*e^6 - 3512204235/12298484*e^5 + 3067636325/12298484*e^4 + 989825703/2236088*e^3 - 841815880/3074621*e^2 - 2097994859/12298484*e + 799081311/24596968, 328703/2236088*e^11 + 12075/2236088*e^10 - 1630041/279511*e^9 - 193200/279511*e^8 + 45047781/559022*e^7 + 8131111/559022*e^6 - 247633083/559022*e^5 - 55041105/559022*e^4 + 1736650389/2236088*e^3 + 526055829/2236088*e^2 - 140774981/559022*e - 8968793/279511, -755413/12298484*e^11 - 130700/3074621*e^10 + 15242921/6149242*e^9 + 21917129/12298484*e^8 - 212385779/6149242*e^7 - 77784645/3074621*e^6 + 1145420203/6149242*e^5 + 429305744/3074621*e^4 - 311444647/1118044*e^3 - 799478219/3074621*e^2 - 89334798/3074621*e + 407490983/12298484, 2406247/24596968*e^11 - 31297/24596968*e^10 - 95826517/24596968*e^9 - 2422737/24596968*e^8 + 330955775/6149242*e^7 + 7907928/3074621*e^6 - 1797053275/6149242*e^5 - 133064071/6149242*e^4 + 1087409071/2236088*e^3 + 3034349385/24596968*e^2 - 4742946711/24596968*e - 644269675/24596968, -202121/3074621*e^11 - 414229/6149242*e^10 + 16373791/6149242*e^9 + 15846349/6149242*e^8 - 114464061/3074621*e^7 - 205678469/6149242*e^6 + 616886390/3074621*e^5 + 1049054007/6149242*e^4 - 81120479/279511*e^3 - 973675664/3074621*e^2 - 272477961/6149242*e + 176584125/3074621, 87511/6149242*e^11 - 631945/24596968*e^10 - 6554315/12298484*e^9 + 24707249/24596968*e^8 + 76942875/12298484*e^7 - 161911755/12298484*e^6 - 223175615/12298484*e^5 + 716354503/12298484*e^4 - 72962143/1118044*e^3 - 58742945/24596968*e^2 + 758337519/6149242*e - 492105255/24596968, 1401491/24596968*e^11 - 1156517/12298484*e^10 - 27210521/12298484*e^9 + 87273635/24596968*e^8 + 358816609/12298484*e^7 - 570924103/12298484*e^6 - 1742168603/12298484*e^5 + 2845775377/12298484*e^4 + 328052937/2236088*e^3 - 1595821571/6149242*e^2 - 43312807/3074621*e + 1574110895/24596968, -477165/24596968*e^11 - 1198165/24596968*e^10 + 4575551/6149242*e^9 + 11787735/6149242*e^8 - 115531651/12298484*e^7 - 319416855/12298484*e^6 + 481944743/12298484*e^5 + 1703909573/12298484*e^4 + 5785221/2236088*e^3 - 5971960285/24596968*e^2 - 1043141871/12298484*e + 500255125/12298484, -6360931/24596968*e^11 - 282159/12298484*e^10 + 63511913/6149242*e^9 + 32821653/24596968*e^8 - 1755110737/12298484*e^7 - 268528693/12298484*e^6 + 9447932287/12298484*e^5 + 1663157209/12298484*e^4 - 2693515593/2236088*e^3 - 2544906183/6149242*e^2 + 3118777395/12298484*e + 457660125/24596968]; heckeEigenvalues := AssociativeArray(); for i := 1 to #heckeEigenvaluesArray do heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i]; end for; ALEigenvalues := AssociativeArray(); ALEigenvalues[ideal] := -1; ALEigenvalues[ideal] := -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;