/* 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, 2, -15, -1, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [4, 2, w + 2], [4, 2, -1/2*w^3 + 3/2*w^2 + 9/2*w - 10], [9, 3, 1/2*w^3 - 5/2*w^2 - 5/2*w + 17], [9, 3, 3/2*w^3 - 11/2*w^2 - 19/2*w + 28], [11, 11, 1/2*w^3 - 3/2*w^2 - 9/2*w + 11], [11, 11, -w - 3], [25, 5, w^3 - 3*w^2 - 7*w + 15], [29, 29, w + 1], [29, 29, 1/2*w^3 - 3/2*w^2 - 9/2*w + 9], [31, 31, -1/2*w^3 + 5/2*w^2 + 5/2*w - 16], [31, 31, 1/2*w^3 - 3/2*w^2 - 9/2*w + 5], [31, 31, -w + 3], [31, 31, 3/2*w^3 - 11/2*w^2 - 19/2*w + 29], [59, 59, 2*w^2 - w - 13], [59, 59, 9/2*w^3 - 31/2*w^2 - 61/2*w + 85], [61, 61, 2*w^3 - 6*w^2 - 15*w + 31], [61, 61, -3/2*w^3 + 11/2*w^2 + 21/2*w - 34], [71, 71, 3/2*w^3 - 11/2*w^2 - 19/2*w + 32], [71, 71, -1/2*w^3 + 5/2*w^2 + 5/2*w - 13], [79, 79, -3*w^3 + 10*w^2 + 19*w - 51], [79, 79, 15/2*w^3 - 51/2*w^2 - 103/2*w + 139], [101, 101, -2*w^3 + 7*w^2 + 14*w - 37], [101, 101, -1/2*w^3 + 5/2*w^2 + 7/2*w - 16], [109, 109, w^3 - 3*w^2 - 6*w + 19], [109, 109, -w^3 + 4*w^2 + 5*w - 19], [121, 11, -3/2*w^3 + 9/2*w^2 + 21/2*w - 23], [139, 139, -w^3 + 4*w^2 + 7*w - 25], [139, 139, -5/2*w^3 + 17/2*w^2 + 33/2*w - 41], [149, 149, 1/2*w^3 + 1/2*w^2 - 11/2*w - 8], [149, 149, 5/2*w^3 - 19/2*w^2 - 35/2*w + 50], [149, 149, -9/2*w^3 + 31/2*w^2 + 59/2*w - 82], [149, 149, -5/2*w^3 + 19/2*w^2 + 35/2*w - 56], [151, 151, -1/2*w^3 + 3/2*w^2 + 3/2*w - 12], [151, 151, 3/2*w^3 - 9/2*w^2 - 25/2*w + 28], [179, 179, -1/2*w^3 + 3/2*w^2 + 9/2*w - 3], [179, 179, w - 5], [229, 229, -15/2*w^3 + 51/2*w^2 + 105/2*w - 142], [229, 229, 1/2*w^3 - 7/2*w^2 - 7/2*w + 19], [229, 229, -17/2*w^3 + 57/2*w^2 + 119/2*w - 156], [229, 229, -9/2*w^3 + 33/2*w^2 + 55/2*w - 82], [239, 239, -9*w^3 + 31*w^2 + 59*w - 161], [239, 239, w^3 + w^2 - 11*w - 19], [241, 241, 5/2*w^3 - 15/2*w^2 - 37/2*w + 37], [241, 241, -2*w^3 + 6*w^2 + 13*w - 29], [251, 251, -7/2*w^3 + 25/2*w^2 + 45/2*w - 67], [251, 251, 1/2*w^3 - 5/2*w^2 - 13/2*w + 7], [251, 251, -1/2*w^3 + 1/2*w^2 + 13/2*w + 4], [251, 251, -1/2*w^3 + 7/2*w^2 + 3/2*w - 23], [271, 271, -w^3 + 4*w^2 + 5*w - 25], [271, 271, -5/2*w^3 + 17/2*w^2 + 33/2*w - 47], [281, 281, 5/2*w^3 - 15/2*w^2 - 39/2*w + 41], [281, 281, 3/2*w^3 - 7/2*w^2 - 27/2*w + 14], [289, 17, -7/2*w^3 + 25/2*w^2 + 45/2*w - 62], [289, 17, 5/2*w^3 - 15/2*w^2 - 39/2*w + 37], [311, 311, -19/2*w^3 + 65/2*w^2 + 129/2*w - 175], [311, 311, -7/2*w^3 + 25/2*w^2 + 47/2*w - 71], [311, 311, 7/2*w^3 - 25/2*w^2 - 49/2*w + 67], [311, 311, -3/2*w^3 + 11/2*w^2 + 15/2*w - 31], [331, 331, 19/2*w^3 - 65/2*w^2 - 127/2*w + 173], [331, 331, -w^3 - w^2 + 10*w + 15], [349, 349, -5/2*w^3 + 15/2*w^2 + 33/2*w - 35], [349, 349, 3/2*w^3 - 11/2*w^2 - 21/2*w + 36], [361, 19, 2*w^3 - 6*w^2 - 14*w + 29], [361, 19, 2*w^3 - 6*w^2 - 14*w + 31], [379, 379, 1/2*w^3 - 5/2*w^2 - 1/2*w + 20], [379, 379, -1/2*w^3 + 5/2*w^2 + 1/2*w - 9], [401, 401, -7/2*w^3 + 25/2*w^2 + 45/2*w - 69], [401, 401, w^3 - 3*w^2 - 5*w + 19], [409, 409, 3/2*w^3 - 7/2*w^2 - 23/2*w + 13], [409, 409, -11/2*w^3 + 37/2*w^2 + 77/2*w - 100], [409, 409, 7/2*w^3 - 23/2*w^2 - 47/2*w + 58], [409, 409, -w^3 + 3*w^2 + 9*w - 9], [419, 419, 3/2*w^3 - 13/2*w^2 - 17/2*w + 36], [419, 419, -5/2*w^3 + 19/2*w^2 + 31/2*w - 54], [421, 421, -w^3 + 4*w^2 + 5*w - 27], [421, 421, 7/2*w^3 - 23/2*w^2 - 47/2*w + 63], [439, 439, 2*w^3 - 7*w^2 - 14*w + 35], [439, 439, -1/2*w^3 + 5/2*w^2 + 7/2*w - 18], [461, 461, -5/2*w^3 + 17/2*w^2 + 33/2*w - 48], [461, 461, -13/2*w^3 + 45/2*w^2 + 85/2*w - 119], [461, 461, -1/2*w^3 + 3/2*w^2 + 1/2*w - 15], [461, 461, 3/2*w^3 - 11/2*w^2 - 17/2*w + 32], [479, 479, -3*w^3 + 10*w^2 + 19*w - 53], [479, 479, 5/2*w^3 - 17/2*w^2 - 33/2*w + 51], [491, 491, 3*w^2 - 2*w - 23], [491, 491, 13/2*w^3 - 45/2*w^2 - 87/2*w + 120], [499, 499, -3*w^3 + 11*w^2 + 21*w - 63], [499, 499, -5/2*w^3 + 19/2*w^2 + 31/2*w - 50], [499, 499, 11/2*w^3 - 37/2*w^2 - 75/2*w + 101], [499, 499, 9*w^3 - 31*w^2 - 58*w + 159], [509, 509, 3/2*w^3 - 9/2*w^2 - 23/2*w + 29], [509, 509, w^3 - 3*w^2 - 6*w + 21], [521, 521, 2*w^3 - 8*w^2 - 12*w + 43], [521, 521, -3/2*w^3 + 11/2*w^2 + 19/2*w - 36], [521, 521, 2*w^3 - 8*w^2 - 12*w + 47], [521, 521, -7/2*w^3 + 23/2*w^2 + 45/2*w - 58], [541, 541, -1/2*w^3 + 5/2*w^2 + 13/2*w - 6], [541, 541, 9/2*w^3 - 33/2*w^2 - 55/2*w + 80], [541, 541, -15/2*w^3 + 51/2*w^2 + 101/2*w - 134], [541, 541, w^3 - w^2 - 7*w + 1], [571, 571, 13/2*w^3 - 47/2*w^2 - 79/2*w + 116], [571, 571, -5/2*w^3 + 11/2*w^2 + 43/2*w - 21], [599, 599, -3*w^3 + 9*w^2 + 19*w - 47], [599, 599, -15/2*w^3 + 51/2*w^2 + 103/2*w - 137], [599, 599, -w^3 + 2*w^2 + 11*w + 1], [599, 599, 5/2*w^3 - 17/2*w^2 - 35/2*w + 38], [601, 601, -1/2*w^3 + 11/2*w^2 - 5/2*w - 47], [601, 601, -3/2*w^3 + 13/2*w^2 + 17/2*w - 30], [619, 619, -w^3 + 5*w^2 + 5*w - 27], [619, 619, -1/2*w^3 + 1/2*w^2 + 11/2*w - 2], [619, 619, -2*w^3 + 7*w^2 + 12*w - 39], [619, 619, -3*w^3 + 11*w^2 + 19*w - 63], [631, 631, -3/2*w^3 + 13/2*w^2 + 17/2*w - 37], [631, 631, 5/2*w^3 - 19/2*w^2 - 31/2*w + 53], [641, 641, 5*w^3 - 16*w^2 - 35*w + 79], [641, 641, -2*w^3 + 8*w^2 + 12*w - 53], [641, 641, 3/2*w^3 - 11/2*w^2 - 23/2*w + 34], [641, 641, 3/2*w^3 - 11/2*w^2 - 23/2*w + 27], [659, 659, -5/2*w^3 + 19/2*w^2 + 31/2*w - 51], [659, 659, -3/2*w^3 + 13/2*w^2 + 17/2*w - 39], [661, 661, -5/2*w^3 + 17/2*w^2 + 33/2*w - 50], [661, 661, 5*w^3 - 17*w^2 - 30*w + 83], [661, 661, 5/2*w^3 - 17/2*w^2 - 31/2*w + 46], [661, 661, 3/2*w^3 - 5/2*w^2 - 21/2*w + 9], [691, 691, -3/2*w^3 + 13/2*w^2 + 19/2*w - 35], [691, 691, 3*w^3 - 11*w^2 - 20*w + 63], [709, 709, 19/2*w^3 - 65/2*w^2 - 127/2*w + 171], [709, 709, 4*w^3 - 14*w^2 - 28*w + 75], [709, 709, 1/2*w^3 - 5/2*w^2 - 15/2*w + 4], [709, 709, -w^3 + 5*w^2 + 7*w - 31], [739, 739, 11/2*w^3 - 37/2*w^2 - 73/2*w + 95], [739, 739, -3/2*w^3 + 5/2*w^2 + 25/2*w - 5], [739, 739, 27/2*w^3 - 91/2*w^2 - 187/2*w + 247], [739, 739, 4*w^3 - 15*w^2 - 24*w + 73], [751, 751, -5/2*w^3 + 19/2*w^2 + 35/2*w - 49], [751, 751, -2*w^2 + 2*w + 21], [751, 751, -9*w^3 + 31*w^2 + 61*w - 169], [751, 751, 17/2*w^3 - 57/2*w^2 - 117/2*w + 152], [761, 761, 5/2*w^3 - 15/2*w^2 - 33/2*w + 39], [761, 761, -3*w^3 + 9*w^2 + 22*w - 47], [761, 761, 9/2*w^3 - 29/2*w^2 - 61/2*w + 80], [761, 761, 25/2*w^3 - 85/2*w^2 - 169/2*w + 227], [769, 769, 2*w^3 - 8*w^2 - 12*w + 45], [811, 811, 5/2*w^3 - 19/2*w^2 - 27/2*w + 45], [811, 811, 1/2*w^3 - 7/2*w^2 + 1/2*w + 29], [821, 821, 25/2*w^3 - 85/2*w^2 - 173/2*w + 233], [821, 821, 19/2*w^3 - 63/2*w^2 - 135/2*w + 173], [829, 829, -7/2*w^3 + 27/2*w^2 + 43/2*w - 79], [829, 829, 10*w^3 - 34*w^2 - 67*w + 179], [829, 829, -3/2*w^3 + 1/2*w^2 + 27/2*w + 9], [829, 829, 5/2*w^3 - 13/2*w^2 - 41/2*w + 31], [839, 839, -3/2*w^3 + 11/2*w^2 + 25/2*w - 26], [839, 839, 2*w^3 - 7*w^2 - 16*w + 43], [841, 29, 5/2*w^3 - 15/2*w^2 - 35/2*w + 39], [881, 881, -8*w^3 + 27*w^2 + 56*w - 151], [881, 881, -w^3 + 3*w^2 + 4*w - 21], [911, 911, 5/2*w^3 - 19/2*w^2 - 33/2*w + 51], [911, 911, 2*w^3 - 8*w^2 - 13*w + 47], [919, 919, 3/2*w^3 - 9/2*w^2 - 27/2*w + 29], [919, 919, -3*w - 5], [919, 919, 1/2*w^3 - 7/2*w^2 - 5/2*w + 17], [919, 919, -4*w^3 + 14*w^2 + 27*w - 81], [929, 929, 7/2*w^3 - 23/2*w^2 - 49/2*w + 58], [929, 929, 13*w^3 - 44*w^2 - 89*w + 237], [929, 929, 9/2*w^3 - 29/2*w^2 - 59/2*w + 78], [929, 929, -w^3 + 2*w^2 + 7*w - 5], [941, 941, 5/2*w^3 - 19/2*w^2 - 31/2*w + 59], [941, 941, -3/2*w^3 + 13/2*w^2 + 17/2*w - 31], [941, 941, w^3 - 3*w^2 - 10*w + 7], [941, 941, -8*w^3 + 27*w^2 + 56*w - 147], [971, 971, -9/2*w^3 + 29/2*w^2 + 73/2*w - 92], [971, 971, -1/2*w^3 + 5/2*w^2 + 17/2*w - 1], [991, 991, w^3 - 4*w^2 - 3*w + 15], [991, 991, -1/2*w^3 + 1/2*w^2 + 15/2*w + 6], [1019, 1019, 3*w^3 - 9*w^2 - 19*w + 45], [1019, 1019, 3*w^3 - 11*w^2 - 20*w + 53], [1019, 1019, -1/2*w^3 + 1/2*w^2 + 17/2*w + 9], [1019, 1019, -1/2*w^3 + 5/2*w^2 - 3/2*w - 4], [1021, 1021, -3/2*w^3 + 13/2*w^2 + 19/2*w - 37], [1021, 1021, 3*w^3 - 11*w^2 - 20*w + 61], [1049, 1049, w^3 - 4*w^2 - 9*w + 15], [1049, 1049, 5/2*w^3 - 17/2*w^2 - 39/2*w + 54], [1051, 1051, 3/2*w^3 - 11/2*w^2 - 15/2*w + 21], [1051, 1051, -1/2*w^3 + 7/2*w^2 + 7/2*w - 23], [1051, 1051, 9/2*w^3 - 31/2*w^2 - 63/2*w + 83], [1051, 1051, -1/2*w^3 + 1/2*w^2 + 13/2*w + 8], [1061, 1061, 2*w^3 - 5*w^2 - 14*w + 19], [1061, 1061, 9/2*w^3 - 29/2*w^2 - 63/2*w + 72], [1091, 1091, 3/2*w^3 - 5/2*w^2 - 21/2*w + 10], [1091, 1091, 3/2*w^3 - 3/2*w^2 - 19/2*w + 7], [1091, 1091, -13/2*w^3 + 43/2*w^2 + 91/2*w - 116], [1091, 1091, 19/2*w^3 - 63/2*w^2 - 135/2*w + 174], [1109, 1109, -5/2*w^3 + 17/2*w^2 + 33/2*w - 53], [1109, 1109, 4*w^3 - 13*w^2 - 26*w + 67], [1109, 1109, -3/2*w^3 + 11/2*w^2 + 23/2*w - 25], [1109, 1109, 4*w^3 - 13*w^2 - 28*w + 65], [1171, 1171, 1/2*w^3 - 1/2*w^2 + 3/2*w + 12], [1171, 1171, 11/2*w^3 - 35/2*w^2 - 87/2*w + 105], [1181, 1181, 2*w^3 - 8*w^2 - 13*w + 45], [1181, 1181, -5/2*w^3 + 19/2*w^2 + 33/2*w - 53], [1201, 1201, -5/2*w^3 + 15/2*w^2 + 39/2*w - 45], [1201, 1201, -1/2*w^3 + 3/2*w^2 + 13/2*w - 3], [1201, 1201, -w^3 + 3*w^2 + 10*w - 21], [1201, 1201, 3/2*w^3 - 9/2*w^2 - 17/2*w + 29], [1229, 1229, -5*w^3 + 17*w^2 + 35*w - 91], [1229, 1229, 3/2*w^3 - 9/2*w^2 - 25/2*w + 17], [1249, 1249, 5/2*w^3 - 17/2*w^2 - 35/2*w + 40], [1249, 1249, 3/2*w^3 - 3/2*w^2 - 21/2*w + 4], [1249, 1249, w^2 - 13], [1249, 1249, 9*w^3 - 30*w^2 - 63*w + 163], [1289, 1289, 3/2*w^3 - 1/2*w^2 - 23/2*w - 3], [1289, 1289, 11*w^3 - 37*w^2 - 76*w + 201], [1291, 1291, -1/2*w^3 - 7/2*w^2 + 13/2*w + 29], [1291, 1291, 23/2*w^3 - 79/2*w^2 - 155/2*w + 212], [1301, 1301, 11*w^3 - 38*w^2 - 73*w + 201], [1301, 1301, 1/2*w^3 - 5/2*w^2 - 17/2*w + 3], [1319, 1319, 12*w^3 - 40*w^2 - 85*w + 219], [1319, 1319, 3/2*w^3 - 1/2*w^2 - 19/2*w - 1], [1321, 1321, -1/2*w^3 - 1/2*w^2 - 1/2*w - 7], [1321, 1321, -3*w^3 + 11*w^2 + 15*w - 45], [1361, 1361, -3*w^3 + 11*w^2 + 21*w - 57], [1361, 1361, 5/2*w^3 - 15/2*w^2 - 39/2*w + 35], [1381, 1381, -3*w^3 + 9*w^2 + 23*w - 43], [1381, 1381, 2*w^3 - 6*w^2 - 12*w + 27], [1381, 1381, -1/2*w^3 + 3/2*w^2 + 9/2*w - 1], [1381, 1381, w - 7], [1399, 1399, 9/2*w^3 - 33/2*w^2 - 57/2*w + 85], [1399, 1399, -5/2*w^3 + 15/2*w^2 + 41/2*w - 37], [1409, 1409, 3/2*w^3 - 1/2*w^2 - 21/2*w - 1], [1409, 1409, -23/2*w^3 + 77/2*w^2 + 161/2*w - 211], [1409, 1409, 11/2*w^3 - 39/2*w^2 - 71/2*w + 98], [1409, 1409, 1/2*w^3 - 9/2*w^2 - 1/2*w + 37], [1429, 1429, 3/2*w^3 - 5/2*w^2 - 33/2*w - 5], [1429, 1429, 7/2*w^3 - 25/2*w^2 - 37/2*w + 53], [1439, 1439, -7*w^3 + 23*w^2 + 52*w - 135], [1439, 1439, -1/2*w^3 - 1/2*w^2 + 1/2*w - 5], [1451, 1451, 1/2*w^3 + 3/2*w^2 - 13/2*w - 15], [1451, 1451, -13/2*w^3 + 45/2*w^2 + 85/2*w - 120], [1459, 1459, -7/2*w^3 + 27/2*w^2 + 43/2*w - 70], [1459, 1459, 5/2*w^3 - 21/2*w^2 - 29/2*w + 65], [1471, 1471, 5/2*w^3 - 17/2*w^2 - 37/2*w + 43], [1471, 1471, -3*w^3 + 10*w^2 + 21*w - 49], [1481, 1481, -6*w^3 + 21*w^2 + 40*w - 113], [1481, 1481, -16*w^3 + 54*w^2 + 112*w - 299], [1481, 1481, 9*w^3 - 30*w^2 - 63*w + 161], [1481, 1481, 1/2*w^3 - 9/2*w^2 - 3/2*w + 30], [1489, 1489, -8*w^3 + 26*w^2 + 60*w - 151], [1489, 1489, -w^3 + 5*w^2 + 6*w - 35], [1489, 1489, 7/2*w^3 - 25/2*w^2 - 47/2*w + 63], [1489, 1489, -w^3 + w^2 + 3*w - 13], [1499, 1499, 3*w^3 - 10*w^2 - 21*w + 45], [1499, 1499, 9/2*w^3 - 29/2*w^2 - 65/2*w + 75], [1511, 1511, -11/2*w^3 + 35/2*w^2 + 79/2*w - 91], [1511, 1511, -5/2*w^3 + 21/2*w^2 + 33/2*w - 54], [1511, 1511, 7/2*w^3 - 19/2*w^2 - 57/2*w + 42], [1511, 1511, 5/2*w^3 - 15/2*w^2 - 29/2*w + 41], [1531, 1531, -4*w^2 + 2*w + 29], [1531, 1531, 9*w^3 - 31*w^2 - 61*w + 167], [1549, 1549, -1/2*w^3 + 1/2*w^2 + 13/2*w - 5], [1549, 1549, -3/2*w^3 + 11/2*w^2 + 15/2*w - 34], [1559, 1559, 9/2*w^3 - 29/2*w^2 - 63/2*w + 76], [1559, 1559, 2*w^3 - 5*w^2 - 14*w + 23], [1571, 1571, 3*w^3 - 9*w^2 - 20*w + 43], [1571, 1571, 2*w^3 - 7*w^2 - 14*w + 45], [1601, 1601, -27/2*w^3 + 93/2*w^2 + 179/2*w - 247], [1601, 1601, 1/2*w^3 - 1/2*w^2 + 5/2*w + 16], [1609, 1609, -1/2*w^3 + 7/2*w^2 + 1/2*w - 31], [1609, 1609, 3/2*w^3 - 7/2*w^2 - 23/2*w + 25], [1621, 1621, 7/2*w^3 - 25/2*w^2 - 45/2*w + 71], [1621, 1621, -1/2*w^3 + 7/2*w^2 + 3/2*w - 19], [1681, 41, -3*w^3 + 9*w^2 + 21*w - 43], [1681, 41, 3*w^3 - 9*w^2 - 21*w + 47], [1721, 1721, -1/2*w^3 - 3/2*w^2 + 21/2*w + 25], [1721, 1721, -9/2*w^3 + 33/2*w^2 + 49/2*w - 78], [1759, 1759, 4*w^3 - 14*w^2 - 25*w + 75], [1759, 1759, 2*w^3 - 7*w^2 - 12*w + 43], [1831, 1831, -3/2*w^3 + 7/2*w^2 + 29/2*w - 6], [1831, 1831, 15/2*w^3 - 51/2*w^2 - 103/2*w + 136], [1849, 43, -1/2*w^3 + 7/2*w^2 - 3/2*w - 31], [1849, 43, 15/2*w^3 - 51/2*w^2 - 101/2*w + 138], [1871, 1871, 3*w^3 - 9*w^2 - 18*w + 43], [1871, 1871, -7/2*w^3 + 21/2*w^2 + 45/2*w - 51], [1879, 1879, 21/2*w^3 - 71/2*w^2 - 145/2*w + 195], [1879, 1879, -w^3 - w^2 + 8*w + 9], [1889, 1889, 2*w^3 - 4*w^2 - 16*w + 15], [1889, 1889, -6*w^3 + 20*w^2 + 40*w - 105], [1901, 1901, 2*w^2 - 7*w - 29], [1901, 1901, -19/2*w^3 + 65/2*w^2 + 133/2*w - 182], [1901, 1901, 1/2*w^3 - 11/2*w^2 - 7/2*w + 30], [1901, 1901, -1/2*w^3 + 5/2*w^2 + 1/2*w - 24], [1931, 1931, -1/2*w^3 + 9/2*w^2 + 3/2*w - 34], [1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 59], [1931, 1931, -5/2*w^3 + 19/2*w^2 + 35/2*w - 47], [1931, 1931, 6*w^3 - 21*w^2 - 40*w + 109], [1949, 1949, -3/2*w^3 + 15/2*w^2 + 19/2*w - 46], [1949, 1949, -11/2*w^3 + 39/2*w^2 + 75/2*w - 105], [1979, 1979, -7/2*w^3 + 21/2*w^2 + 55/2*w - 51], [1979, 1979, 3/2*w^3 - 5/2*w^2 - 29/2*w + 7], [1979, 1979, 9/2*w^3 - 31/2*w^2 - 55/2*w + 81], [1979, 1979, -2*w^3 + 6*w^2 + 11*w - 27]]; primes := [ideal : I in primesArray]; heckePol := x^10 - x^9 - 30*x^8 + 19*x^7 + 315*x^6 - 119*x^5 - 1379*x^4 + 361*x^3 + 2504*x^2 - 356*x - 1571; K := NumberField(heckePol); heckeEigenvaluesArray := [e, -2107/14912*e^9 - 401/3728*e^8 + 30219/7456*e^7 + 67901/14912*e^6 - 8592/233*e^5 - 750035/14912*e^4 + 840669/7456*e^3 + 2395807/14912*e^2 - 1546725/14912*e - 2196981/14912, -1, -3843/14912*e^9 - 1233/3728*e^8 + 56851/7456*e^7 + 172149/14912*e^6 - 16559/233*e^5 - 1731515/14912*e^4 + 1647717/7456*e^3 + 5235623/14912*e^2 - 3033661/14912*e - 4582221/14912, 4559/14912*e^9 + 307/3728*e^8 - 64163/7456*e^7 - 87457/14912*e^6 + 36095/466*e^5 + 1106343/14912*e^4 - 1767837/7456*e^3 - 3597595/14912*e^2 + 3224865/14912*e + 3327417/14912, -719/14912*e^9 - 569/3728*e^8 + 12207/7456*e^7 + 62873/14912*e^6 - 15845/932*e^5 - 540343/14912*e^4 + 437817/7456*e^3 + 1484179/14912*e^2 - 863873/14912*e - 1292033/14912, 4991/14912*e^9 + 295/3728*e^8 - 70043/7456*e^7 - 90945/14912*e^6 + 19614/233*e^5 + 1158135/14912*e^4 - 1902261/7456*e^3 - 3676891/14912*e^2 + 3399793/14912*e + 3233017/14912, 3115/14912*e^9 + 839/3728*e^8 - 46735/7456*e^7 - 117669/14912*e^6 + 13917/233*e^5 + 1176579/14912*e^4 - 1444177/7456*e^3 - 3469959/14912*e^2 + 2746469/14912*e + 3057213/14912, -27/233*e^9 - 221/932*e^8 + 1703/466*e^7 + 6697/932*e^6 - 33685/932*e^5 - 61645/932*e^4 + 28220/233*e^3 + 175701/932*e^2 - 112933/932*e - 36739/233, -1139/7456*e^9 + 8/233*e^8 + 15749/3728*e^7 + 8273/7456*e^6 - 8865/233*e^5 - 176267/7456*e^4 + 452007/3728*e^3 + 682707/7456*e^2 - 896213/7456*e - 687241/7456, -255/466*e^9 - 127/466*e^8 + 14427/932*e^7 + 3230/233*e^6 - 129723/932*e^5 - 150693/932*e^4 + 391717/932*e^3 + 119710/233*e^2 - 350791/932*e - 427381/932, 9837/14912*e^9 + 1183/3728*e^8 - 140533/7456*e^7 - 237787/14912*e^6 + 160225/932*e^5 + 2753029/14912*e^4 - 3973491/7456*e^3 - 8664457/14912*e^2 + 7313603/14912*e + 7872307/14912, 2649/14912*e^9 + 373/3728*e^8 - 38813/7456*e^7 - 65943/14912*e^6 + 45649/932*e^5 + 721297/14912*e^4 - 1187411/7456*e^3 - 2140461/14912*e^2 + 2295847/14912*e + 1887087/14912, 1369/1864*e^9 + 377/932*e^8 - 19475/932*e^7 - 36157/1864*e^6 + 176183/932*e^5 + 414111/1864*e^4 - 537167/932*e^3 - 1310635/1864*e^2 + 975901/1864*e + 1188743/1864, -971/7456*e^9 - 281/932*e^8 + 14705/3728*e^7 + 71121/7456*e^6 - 17209/466*e^5 - 687987/7456*e^4 + 420235/3728*e^3 + 2134371/7456*e^2 - 801261/7456*e - 1918569/7456, 85/1864*e^9 + 293/932*e^8 - 805/466*e^7 - 15745/1864*e^6 + 4319/233*e^5 + 134509/1864*e^4 - 14544/233*e^3 - 381231/1864*e^2 + 123511/1864*e + 321977/1864, -2057/7456*e^9 - 493/1864*e^8 + 30341/3728*e^7 + 72071/7456*e^6 - 17707/233*e^5 - 732753/7456*e^4 + 892603/3728*e^3 + 2149021/7456*e^2 - 1664967/7456*e - 1817071/7456, -855/932*e^9 - 975/1864*e^8 + 48647/1864*e^7 + 46349/1864*e^6 - 219937/932*e^5 - 132453/466*e^4 + 1337499/1864*e^3 + 1678561/1864*e^2 - 602201/932*e - 1516507/1864, -811/7456*e^9 - 51/466*e^8 + 12113/3728*e^7 + 30409/7456*e^6 - 29043/932*e^5 - 320651/7456*e^4 + 386603/3728*e^3 + 1034859/7456*e^2 - 757253/7456*e - 978729/7456, 1391/1864*e^9 + 881/1864*e^8 - 39989/1864*e^7 - 19561/932*e^6 + 91521/466*e^5 + 434819/1864*e^4 - 1135169/1864*e^3 - 168622/233*e^2 + 1046563/1864*e + 601551/932, 2243/14912*e^9 + 449/3728*e^8 - 30931/7456*e^7 - 81909/14912*e^6 + 8384/233*e^5 + 939899/14912*e^4 - 767109/7456*e^3 - 3124327/14912*e^2 + 1449085/14912*e + 2893325/14912, 1273/7456*e^9 - 469/1864*e^8 - 15217/3728*e^7 + 25457/7456*e^6 + 14265/466*e^5 - 41807/7456*e^4 - 278023/3728*e^3 - 194341/7456*e^2 + 478743/7456*e + 289319/7456, -5053/7456*e^9 - 645/932*e^8 + 75055/3728*e^7 + 184007/7456*e^6 - 88315/466*e^5 - 1844789/7456*e^4 + 2249229/3728*e^3 + 5365509/7456*e^2 - 4195835/7456*e - 4617279/7456, 151/932*e^9 + 35/932*e^8 - 4473/932*e^7 - 568/233*e^6 + 21543/466*e^5 + 27941/932*e^4 - 146941/932*e^3 - 44019/466*e^2 + 145369/932*e + 44591/466, -3877/7456*e^9 - 1711/1864*e^8 + 58893/3728*e^7 + 220387/7456*e^6 - 69989/466*e^5 - 2127549/7456*e^4 + 1770059/3728*e^3 + 6373985/7456*e^2 - 3339179/7456*e - 5608155/7456, -2949/7456*e^9 - 65/233*e^8 + 42275/3728*e^7 + 88455/7456*e^6 - 23997/233*e^5 - 962925/7456*e^4 + 1165193/3728*e^3 + 2934293/7456*e^2 - 2080355/7456*e - 2581215/7456, 1425/3728*e^9 + 581/1864*e^8 - 5247/466*e^7 - 43789/3728*e^6 + 98145/932*e^5 + 443141/3728*e^4 - 309955/932*e^3 - 1231235/3728*e^2 + 1120479/3728*e + 990641/3728, -337/7456*e^9 + 909/1864*e^8 + 1545/3728*e^7 - 84585/7456*e^6 + 1253/466*e^5 + 627479/7456*e^4 - 88721/3728*e^3 - 1597283/7456*e^2 + 275553/7456*e + 1303665/7456, -7143/7456*e^9 - 1685/1864*e^8 + 104719/3728*e^7 + 251089/7456*e^6 - 121389/466*e^5 - 2577615/7456*e^4 + 3018009/3728*e^3 + 7621787/7456*e^2 - 5455593/7456*e - 6579961/7456, 639/7456*e^9 - 309/1864*e^8 - 7183/3728*e^7 + 18063/7456*e^6 + 12343/932*e^5 - 39425/7456*e^4 - 102257/3728*e^3 - 159931/7456*e^2 + 151257/7456*e + 289009/7456, -825/932*e^9 - 113/233*e^8 + 23235/932*e^7 + 22531/932*e^6 - 207797/932*e^5 - 65871/233*e^4 + 623401/932*e^3 + 858899/932*e^2 - 282587/466*e - 393595/466, 1151/1864*e^9 + 1529/1864*e^8 - 34543/1864*e^7 - 25841/932*e^6 + 163607/932*e^5 + 508721/1864*e^4 - 1043127/1864*e^3 - 376947/466*e^2 + 981017/1864*e + 329873/466, -3187/7456*e^9 - 535/932*e^8 + 48181/3728*e^7 + 142793/7456*e^6 - 115211/932*e^5 - 1392115/7456*e^4 + 1495007/3728*e^3 + 4076859/7456*e^2 - 2863853/7456*e - 3456841/7456, 2401/7456*e^9 + 587/1864*e^8 - 35541/3728*e^7 - 83271/7456*e^6 + 83025/932*e^5 + 817281/7456*e^4 - 1037235/3728*e^3 - 2221277/7456*e^2 + 1861079/7456*e + 1699719/7456, 1979/3728*e^9 + 767/932*e^8 - 30289/1864*e^7 - 97589/3728*e^6 + 145881/932*e^5 + 919743/3728*e^4 - 947319/1864*e^3 - 2605519/3728*e^2 + 1804353/3728*e + 2184185/3728, 1179/3728*e^9 - 881/1864*e^8 - 7383/932*e^7 + 27217/3728*e^6 + 14936/233*e^5 - 90253/3728*e^4 - 41970/233*e^3 + 2375/3728*e^2 + 590801/3728*e + 146311/3728, 17737/7456*e^9 + 2957/1864*e^8 - 254533/3728*e^7 - 516519/7456*e^6 + 145084/233*e^5 + 5710993/7456*e^4 - 7137387/3728*e^3 - 17733853/7456*e^2 + 13042311/7456*e + 15775055/7456, -3511/3728*e^9 - 207/233*e^8 + 50727/1864*e^7 + 129565/3728*e^6 - 232211/932*e^5 - 1379699/3728*e^4 + 1427133/1864*e^3 + 4312479/3728*e^2 - 2625045/3728*e - 3889321/3728, 525/1864*e^9 + 631/932*e^8 - 2068/233*e^7 - 37765/1864*e^6 + 20207/233*e^5 + 345493/1864*e^4 - 131019/466*e^3 - 985883/1864*e^2 + 509687/1864*e + 816061/1864, -6699/7456*e^9 + 161/932*e^8 + 91841/3728*e^7 + 49713/7456*e^6 - 50478/233*e^5 - 969187/7456*e^4 + 2419443/3728*e^3 + 3338211/7456*e^2 - 4299277/7456*e - 3131241/7456, -6309/14912*e^9 - 2213/3728*e^8 + 96241/7456*e^7 + 290075/14912*e^6 - 115965/932*e^5 - 2803517/14912*e^4 + 3024815/7456*e^3 + 8214457/14912*e^2 - 5737147/14912*e - 7082451/14912, 555/932*e^9 + 249/932*e^8 - 3913/233*e^7 - 6797/466*e^6 + 140943/932*e^5 + 40886/233*e^4 - 215919/466*e^3 - 270811/466*e^2 + 100680/233*e + 510903/932, 4741/3728*e^9 + 755/932*e^8 - 67857/1864*e^7 - 134163/3728*e^6 + 154091/466*e^5 + 1487397/3728*e^4 - 1879535/1864*e^3 - 4571649/3728*e^2 + 3400115/3728*e + 3978483/3728, -3887/14912*e^9 - 1879/3728*e^8 + 59987/7456*e^7 + 238193/14912*e^6 - 72669/932*e^5 - 2292055/14912*e^4 + 1894253/7456*e^3 + 6984779/14912*e^2 - 3668945/14912*e - 6299257/14912, 7259/7456*e^9 + 1397/1864*e^8 - 105107/3728*e^7 - 229485/7456*e^6 + 60511/233*e^5 + 2479475/7456*e^4 - 3022261/3728*e^3 - 7643183/7456*e^2 + 5663973/7456*e + 6770181/7456, -16597/14912*e^9 - 3843/3728*e^8 + 240725/7456*e^7 + 602275/14912*e^6 - 277063/932*e^5 - 6421197/14912*e^4 + 6883779/7456*e^3 + 20074241/14912*e^2 - 12803547/14912*e - 18075291/14912, 9673/14912*e^9 + 2249/3728*e^8 - 142909/7456*e^7 - 338327/14912*e^6 + 42058/233*e^5 + 3521425/14912*e^4 - 4331763/7456*e^3 - 10725037/14912*e^2 + 8260935/14912*e + 9553055/14912, -12075/14912*e^9 + 83/3728*e^8 + 166723/7456*e^7 + 143965/14912*e^6 - 92133/466*e^5 - 2242499/14912*e^4 + 4435717/7456*e^3 + 7644479/14912*e^2 - 8055381/14912*e - 7095637/14912, 4849/3728*e^9 + 1271/1864*e^8 - 34547/932*e^7 - 125249/3728*e^6 + 314215/932*e^5 + 1449085/3728*e^4 - 242725/233*e^3 - 4626423/3728*e^2 + 3606015/3728*e + 4233085/3728, -8093/7456*e^9 - 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136565/7456*e^4 - 1332015/3728*e^3 - 643875/7456*e^2 + 2108789/7456*e + 714297/7456, 27035/14912*e^9 + 5663/3728*e^8 - 393231/7456*e^7 - 888917/14912*e^6 + 113241/233*e^5 + 9363763/14912*e^4 - 11210449/7456*e^3 - 28008791/14912*e^2 + 20387573/14912*e + 23585069/14912, -30483/14912*e^9 - 3755/3728*e^8 + 439023/7456*e^7 + 740781/14912*e^6 - 253503/466*e^5 - 8556427/14912*e^4 + 12909345/7456*e^3 + 27160639/14912*e^2 - 24779965/14912*e - 24842597/14912, -65107/14912*e^9 - 10767/3728*e^8 + 938047/7456*e^7 + 1872669/14912*e^6 - 1075533/932*e^5 - 20672539/14912*e^4 + 26746353/7456*e^3 + 64202063/14912*e^2 - 49773005/14912*e - 57444293/14912, 41403/7456*e^9 + 6869/1864*e^8 - 593559/3728*e^7 - 1203821/7456*e^6 + 1351789/932*e^5 + 13299723/7456*e^4 - 16585953/3728*e^3 - 41074783/7456*e^2 + 30129821/7456*e + 36252253/7456, 3199/1864*e^9 + 2217/932*e^8 - 47257/932*e^7 - 153815/1864*e^6 + 439273/932*e^5 + 1554013/1864*e^4 - 1362669/932*e^3 - 4808973/1864*e^2 + 2559547/1864*e + 4307413/1864, 15853/14912*e^9 + 5417/3728*e^8 - 231841/7456*e^7 - 762371/14912*e^6 + 266401/932*e^5 + 7732485/14912*e^4 - 6503151/7456*e^3 - 23791185/14912*e^2 + 12090131/14912*e + 20963451/14912, -13477/7456*e^9 - 4085/1864*e^8 + 198569/3728*e^7 + 573563/7456*e^6 - 115037/233*e^5 - 5740205/7456*e^4 + 5669687/3728*e^3 + 16922393/7456*e^2 - 10266859/7456*e - 14311843/7456, 603/1864*e^9 - 154/233*e^8 - 3929/466*e^7 + 24567/1864*e^6 + 69349/932*e^5 - 150455/1864*e^4 - 117175/466*e^3 + 313609/1864*e^2 + 489131/1864*e - 135417/1864, 22393/7456*e^9 + 402/233*e^8 - 317751/3728*e^7 - 614899/7456*e^6 + 358297/466*e^5 + 7043377/7456*e^4 - 8700349/3728*e^3 - 22295673/7456*e^2 + 15822159/7456*e + 19756363/7456, 8203/7456*e^9 + 4115/1864*e^8 - 124687/3728*e^7 - 518709/7456*e^6 + 147305/466*e^5 + 4924307/7456*e^4 - 3653697/3728*e^3 - 14512983/7456*e^2 + 6705941/7456*e + 12432669/7456, -39299/7456*e^9 - 4701/1864*e^8 + 556119/3728*e^7 + 979653/7456*e^6 - 1253905/932*e^5 - 11545507/7456*e^4 + 15305265/3728*e^3 + 37213879/7456*e^2 - 28122453/7456*e - 34132309/7456, 4499/7456*e^9 + 1163/1864*e^8 - 67851/3728*e^7 - 159565/7456*e^6 + 161849/932*e^5 + 1545267/7456*e^4 - 2074901/3728*e^3 - 4234943/7456*e^2 + 3719797/7456*e + 3540701/7456, 39405/14912*e^9 + 8905/3728*e^8 - 574985/7456*e^7 - 1376419/14912*e^6 + 333447/466*e^5 + 14505717/14912*e^4 - 16806071/7456*e^3 - 44524113/14912*e^2 + 31771939/14912*e + 39545899/14912, 5163/14912*e^9 - 3153/3728*e^8 - 56799/7456*e^7 + 215675/14912*e^6 + 12032/233*e^5 - 942269/14912*e^4 - 837537/7456*e^3 + 906905/14912*e^2 + 1442789/14912*e - 488419/14912, 8363/7456*e^9 + 64/233*e^8 - 117493/3728*e^7 - 152137/7456*e^6 + 131469/466*e^5 + 1942035/7456*e^4 - 3168671/3728*e^3 - 6340027/7456*e^2 + 5422781/7456*e + 5969633/7456, -11795/14912*e^9 - 2669/3728*e^8 + 167779/7456*e^7 + 435733/14912*e^6 - 188213/932*e^5 - 4760539/14912*e^4 + 4468197/7456*e^3 + 15311079/14912*e^2 - 7892157/14912*e - 13397149/14912, -6835/14912*e^9 - 1357/3728*e^8 + 98611/7456*e^7 + 223093/14912*e^6 - 112939/932*e^5 - 2415387/14912*e^4 + 2817941/7456*e^3 + 7406087/14912*e^2 - 5713341/14912*e - 6630109/14912, -7431/7456*e^9 - 1211/1864*e^8 + 106775/3728*e^7 + 211785/7456*e^6 - 244065/932*e^5 - 2341863/7456*e^4 + 3021881/3728*e^3 + 7322355/7456*e^2 - 5721953/7456*e - 6773017/7456, 36767/7456*e^9 + 7645/1864*e^8 - 535791/3728*e^7 - 1207225/7456*e^6 + 310349/233*e^5 + 12794039/7456*e^4 - 15593385/3728*e^3 - 38956403/7456*e^2 + 29105537/7456*e + 34574897/7456, -29797/7456*e^9 - 1777/932*e^8 + 422411/3728*e^7 + 734431/7456*e^6 - 953643/932*e^5 - 8603317/7456*e^4 + 11633793/3728*e^3 + 27347613/7456*e^2 - 21119371/7456*e - 24702735/7456, -9329/3728*e^9 - 364/233*e^8 + 132583/1864*e^7 + 272139/3728*e^6 - 149901/233*e^5 - 3125609/3728*e^4 + 3667541/1864*e^3 + 10187713/3728*e^2 - 6860679/3728*e - 9464435/3728, 29687/14912*e^9 + 5667/3728*e^8 - 435075/7456*e^7 - 901113/14912*e^6 + 508271/932*e^5 + 9531967/14912*e^4 - 12963469/7456*e^3 - 28626371/14912*e^2 + 24209801/14912*e + 25316193/14912, -4429/7456*e^9 - 453/1864*e^8 + 60193/3728*e^7 + 111347/7456*e^6 - 31956/233*e^5 - 1353685/7456*e^4 + 1375167/3728*e^3 + 4211169/7456*e^2 - 2050787/7456*e - 3456187/7456, -34787/7456*e^9 - 846/233*e^8 + 502317/3728*e^7 + 1110465/7456*e^6 - 575397/466*e^5 - 12003051/7456*e^4 + 14191599/3728*e^3 + 37176323/7456*e^2 - 25903573/7456*e - 33252297/7456, -15781/7456*e^9 - 4487/1864*e^8 + 235521/3728*e^7 + 626339/7456*e^6 - 556421/932*e^5 - 6241973/7456*e^4 + 7098663/3728*e^3 + 18376097/7456*e^2 - 13219763/7456*e - 15953219/7456, 10351/14912*e^9 - 1459/3728*e^8 - 141031/7456*e^7 + 29879/14912*e^6 + 155381/932*e^5 + 543575/14912*e^4 - 3792241/7456*e^3 - 2221187/14912*e^2 + 6862017/14912*e + 2453681/14912, 3757/932*e^9 + 3207/932*e^8 - 109005/932*e^7 - 63821/466*e^6 + 502313/466*e^5 + 1364611/932*e^4 - 3130617/932*e^3 - 1055604/233*e^2 + 2933839/932*e + 942316/233, -40379/14912*e^9 - 10729/3728*e^8 + 591323/7456*e^7 + 1579261/14912*e^6 - 341871/466*e^5 - 16321939/14912*e^4 + 16934941/7456*e^3 + 50081727/14912*e^2 - 30977381/14912*e - 44886453/14912, 6125/14912*e^9 + 6671/3728*e^8 - 107613/7456*e^7 - 720347/14912*e^6 + 35012/233*e^5 + 6083637/14912*e^4 - 3716267/7456*e^3 - 16449801/14912*e^2 + 6539411/14912*e + 13748419/14912, 77399/14912*e^9 + 4031/3728*e^8 - 1080139/7456*e^7 - 1397769/14912*e^6 + 1204251/932*e^5 + 18348831/14912*e^4 - 29150069/7456*e^3 - 60451795/14912*e^2 + 52958153/14912*e + 55267377/14912, 15319/7456*e^9 + 591/466*e^8 - 223097/3728*e^7 - 410061/7456*e^6 + 129797/233*e^5 + 4501839/7456*e^4 - 6616355/3728*e^3 - 13743911/7456*e^2 + 12405969/7456*e + 12236133/7456, 5391/932*e^9 + 7423/1864*e^8 - 310053/1864*e^7 - 319045/1864*e^6 + 353980/233*e^5 + 1752139/932*e^4 - 8713565/1864*e^3 - 10821213/1864*e^2 + 1991285/466*e + 9566621/1864, 4183/3728*e^9 + 421/932*e^8 - 59563/1864*e^7 - 95329/3728*e^6 + 136001/466*e^5 + 1164199/3728*e^4 - 1710797/1864*e^3 - 3891851/3728*e^2 + 3305889/3728*e + 3689249/3728, -353/3728*e^9 + 157/466*e^8 + 3575/1864*e^7 - 27949/3728*e^6 - 4439/466*e^5 + 210303/3728*e^4 - 16483/1864*e^3 - 642567/3728*e^2 + 270593/3728*e + 630909/3728, -4505/1864*e^9 - 329/233*e^8 + 64593/932*e^7 + 120107/1864*e^6 - 294481/466*e^5 - 1345917/1864*e^4 + 1813711/932*e^3 + 4165057/1864*e^2 - 3343731/1864*e - 3694775/1864, -36589/14912*e^9 - 1579/3728*e^8 + 511285/7456*e^7 + 618507/14912*e^6 - 285565/466*e^5 - 8253845/14912*e^4 + 13862339/7456*e^3 + 27159353/14912*e^2 - 24975187/14912*e - 25086803/14912, 10907/3728*e^9 + 609/466*e^8 - 155537/1864*e^7 - 252001/3728*e^6 + 176705/233*e^5 + 2934227/3728*e^4 - 4350787/1864*e^3 - 9155011/3728*e^2 + 7907661/3728*e + 8213657/3728, -18285/14912*e^9 - 2657/3728*e^8 + 257073/7456*e^7 + 513315/14912*e^6 - 286281/932*e^5 - 5888325/14912*e^4 + 6821247/7456*e^3 + 18609969/14912*e^2 - 12411603/14912*e - 16691035/14912, 22259/7456*e^9 + 1757/1864*e^8 - 308963/3728*e^7 - 484597/7456*e^6 + 341491/466*e^5 + 6184059/7456*e^4 - 8138053/3728*e^3 - 20964775/7456*e^2 + 14685053/7456*e + 19882141/7456, 21639/7456*e^9 + 1845/932*e^8 - 307773/3728*e^7 - 656533/7456*e^6 + 173526/233*e^5 + 7343903/7456*e^4 - 8385655/3728*e^3 - 23168751/7456*e^2 + 15155505/7456*e + 20469677/7456, -15809/7456*e^9 - 577/1864*e^8 + 218453/3728*e^7 + 269471/7456*e^6 - 120431/233*e^5 - 3697449/7456*e^4 + 5739355/3728*e^3 + 12459205/7456*e^2 - 10317807/7456*e - 11594695/7456, 11799/3728*e^9 + 2177/932*e^8 - 168403/1864*e^7 - 372769/3728*e^6 + 380667/466*e^5 + 4113175/3728*e^4 - 4605669/1864*e^3 - 12959963/3728*e^2 + 8302545/3728*e + 11619089/3728]; heckeEigenvalues := AssociativeArray(); for i := 1 to #heckeEigenvaluesArray do heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i]; end for; ALEigenvalues := AssociativeArray(); 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;