/* 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^12 - 3*x^11 - 24*x^10 + 66*x^9 + 208*x^8 - 461*x^7 - 919*x^6 + 1193*x^5 + 2262*x^4 - 532*x^3 - 2421*x^2 - 1391*x - 251; K := NumberField(heckePol); heckeEigenvaluesArray := [183/44*e^11 - 705/44*e^10 - 973/11*e^9 + 15555/44*e^8 + 6828/11*e^7 - 27629/11*e^6 - 95527/44*e^5 + 155785/22*e^4 + 227653/44*e^3 - 282383/44*e^2 - 306457/44*e - 74949/44, e, -155/88*e^11 + 145/22*e^10 + 1653/44*e^9 - 6351/44*e^8 - 2903/11*e^7 + 88993/88*e^6 + 39953/44*e^5 - 244941/88*e^4 - 181201/88*e^3 + 212635/88*e^2 + 29015/11*e + 57083/88, 71/11*e^11 - 260/11*e^10 - 6137/44*e^9 + 5705/11*e^8 + 44203/44*e^7 - 80209/22*e^6 - 156867/44*e^5 + 443457/44*e^4 + 356481/44*e^3 - 96308/11*e^2 - 110595/11*e - 110795/44, -1, 889/88*e^11 - 799/22*e^10 - 9663/44*e^9 + 35005/44*e^8 + 17569/11*e^7 - 490539/88*e^6 - 250875/44*e^5 + 1347591/88*e^4 + 1122851/88*e^3 - 1154121/88*e^2 - 169076/11*e - 340673/88, -53/88*e^11 + 135/44*e^10 + 533/44*e^9 - 779/11*e^8 - 882/11*e^7 + 47877/88*e^6 + 3536/11*e^5 - 151825/88*e^4 - 101435/88*e^3 + 162229/88*e^2 + 91115/44*e + 48337/88, 25/22*e^11 - 45/11*e^10 - 284/11*e^9 + 1013/11*e^8 + 2265/11*e^7 - 14881/22*e^6 - 9364/11*e^5 + 43737/22*e^4 + 47503/22*e^3 - 40121/22*e^2 - 29499/11*e - 16919/22, 289/88*e^11 - 259/22*e^10 - 3089/44*e^9 + 11221/44*e^8 + 10807/22*e^7 - 154075/88*e^6 - 71701/44*e^5 + 409971/88*e^4 + 296983/88*e^3 - 337473/88*e^2 - 43727/11*e - 80917/88, 551/88*e^11 - 1049/44*e^10 - 1472/11*e^9 + 11563/22*e^8 + 41697/44*e^7 - 328067/88*e^6 - 147203/44*e^5 + 921705/88*e^4 + 697299/88*e^3 - 827403/88*e^2 - 460591/44*e - 229101/88, 543/88*e^11 - 995/44*e^10 - 2943/22*e^9 + 5471/11*e^8 + 42697/44*e^7 - 308991/88*e^6 - 153355/44*e^5 + 859985/88*e^4 + 704091/88*e^3 - 754983/88*e^2 - 437301/44*e - 218861/88, -1591/88*e^11 + 1455/22*e^10 + 17181/44*e^9 - 63817/44*e^8 - 30892/11*e^7 + 896389/88*e^6 + 436993/44*e^5 - 2474885/88*e^4 - 1976697/88*e^3 + 2148951/88*e^2 + 611635/22*e + 607591/88, -371/44*e^11 + 681/22*e^10 + 2003/11*e^9 - 7474/11*e^8 - 14416/11*e^7 + 210311/44*e^6 + 102385/22*e^5 - 582185/44*e^4 - 467429/44*e^3 + 506997/44*e^2 + 291811/22*e + 146695/44, 377/22*e^11 - 1355/22*e^10 - 8191/22*e^9 + 29669/22*e^8 + 59497/22*e^7 - 103861/11*e^6 - 105966/11*e^5 + 569999/22*e^4 + 236618/11*e^3 - 487513/22*e^2 - 569607/22*e - 71561/11, -251/8*e^11 + 455/4*e^10 + 2719/4*e^9 - 4985/2*e^8 - 4915*e^7 + 139807/8*e^6 + 34915/2*e^5 - 384691/8*e^4 - 314045/8*e^3 + 331099/8*e^2 + 191651/4*e + 96143/8, -317/88*e^11 + 597/44*e^10 + 1691/22*e^9 - 3276/11*e^8 - 23801/44*e^7 + 184365/88*e^6 + 82421/44*e^5 - 510667/88*e^4 - 378525/88*e^3 + 447745/88*e^2 + 245071/44*e + 120827/88, 633/44*e^11 - 617/11*e^10 - 3342/11*e^9 + 13608/11*e^8 + 46253/22*e^7 - 386547/44*e^6 - 79500/11*e^5 + 1090047/44*e^4 + 759527/44*e^3 - 993165/44*e^2 - 522263/22*e - 250791/44, 1213/44*e^11 - 2201/22*e^10 - 6577/11*e^9 + 24140/11*e^8 + 95347/22*e^7 - 678357/44*e^6 - 340299/22*e^5 + 1872619/44*e^4 + 1539169/44*e^3 - 1619853/44*e^2 - 942257/22*e - 473903/44, 9/8*e^11 - 7/4*e^10 - 113/4*e^9 + 32*e^8 + 247*e^7 - 1105/8*e^6 - 932*e^5 - 483/8*e^4 + 10423/8*e^3 + 6863/8*e^2 + 173/4*e - 349/8, -747/88*e^11 + 362/11*e^10 + 7851/44*e^9 - 31797/44*e^8 - 26831/22*e^7 + 448093/88*e^6 + 179497/44*e^5 - 1248573/88*e^4 - 832053/88*e^3 + 1121467/88*e^2 + 283553/22*e + 263567/88, 37/11*e^11 - 425/44*e^10 - 849/11*e^9 + 9027/44*e^8 + 13323/22*e^7 - 59415/44*e^6 - 97371/44*e^5 + 143713/44*e^4 + 45180/11*e^3 - 21954/11*e^2 - 141923/44*e - 9245/11, -17/4*e^11 + 17*e^10 + 181/2*e^9 - 759/2*e^8 - 642*e^7 + 11015/4*e^6 + 4691/2*e^5 - 32107/4*e^4 - 24107/4*e^3 + 30557/4*e^2 + 8533*e + 8569/4, 1741/88*e^11 - 1645/22*e^10 - 18687/44*e^9 + 72579/44*e^8 + 33360/11*e^7 - 1030775/88*e^6 - 475467/44*e^5 + 2900063/88*e^4 + 2247899/88*e^3 - 2604485/88*e^2 - 733847/22*e - 732029/88, -615/88*e^11 + 1041/44*e^10 + 3359/22*e^9 - 11229/22*e^8 - 48855/44*e^7 + 305643/88*e^6 + 168541/44*e^5 - 797045/88*e^4 - 679791/88*e^3 + 618547/88*e^2 + 359635/44*e + 175457/88, 3021/88*e^11 - 1360/11*e^10 - 32735/44*e^9 + 118993/44*e^8 + 59129/11*e^7 - 1663155/88*e^6 - 835369/44*e^5 + 4551091/88*e^4 + 3706843/88*e^3 - 3882485/88*e^2 - 558009/11*e - 1110005/88, 181/8*e^11 - 325/4*e^10 - 981/2*e^9 + 1776*e^8 + 14181/4*e^7 - 99157/8*e^6 - 50053/4*e^5 + 270643/8*e^4 + 221413/8*e^3 - 229537/8*e^2 - 132799/4*e - 66475/8, 157/88*e^11 - 287/44*e^10 - 1659/44*e^9 + 1554/11*e^8 + 5659/22*e^7 - 85325/88*e^6 - 17937/22*e^5 + 227173/88*e^4 + 142719/88*e^3 - 190293/88*e^2 - 84631/44*e - 32693/88, 727/88*e^11 - 673/22*e^10 - 7901/44*e^9 + 29737/44*e^8 + 14442/11*e^7 - 423261/88*e^6 - 211685/44*e^5 + 1192701/88*e^4 + 1000657/88*e^3 - 1063463/88*e^2 - 316915/22*e - 325967/88, 325/22*e^11 - 2483/44*e^10 - 6911/22*e^9 + 54645/44*e^8 + 24198/11*e^7 - 386455/44*e^6 - 335403/44*e^5 + 1081535/44*e^4 + 196355/11*e^3 - 484921/22*e^2 - 1044085/44*e - 63196/11, -323/88*e^11 + 577/44*e^10 + 3521/44*e^9 - 3161/11*e^8 - 12873/22*e^7 + 177299/88*e^6 + 46301/22*e^5 - 487371/88*e^4 - 417145/88*e^3 + 415611/88*e^2 + 252413/44*e + 131939/88, 491/88*e^11 - 875/44*e^10 - 5257/44*e^9 + 4737/11*e^8 + 9222/11*e^7 - 260039/88*e^6 - 30667/11*e^5 + 691499/88*e^4 + 507185/88*e^3 - 568647/88*e^2 - 297741/44*e - 137671/88, 2419/44*e^11 - 4429/22*e^10 - 13061/11*e^9 + 48574/11*e^8 + 187917/22*e^7 - 1364987/44*e^6 - 665389/22*e^5 + 3769861/44*e^4 + 3017731/44*e^3 - 3271703/44*e^2 - 1871761/22*e - 935337/44, 182/11*e^11 - 664/11*e^10 - 7871/22*e^9 + 14557/11*e^8 + 56741/22*e^7 - 102164/11*e^6 - 201203/22*e^5 + 563259/22*e^4 + 454441/22*e^3 - 243493/11*e^2 - 279388/11*e - 139275/22, -3609/88*e^11 + 3335/22*e^10 + 38899/44*e^9 - 146557/44*e^8 - 69783/11*e^7 + 2065979/88*e^6 + 989319/44*e^5 - 5739023/88*e^4 - 4537707/88*e^3 + 5037609/88*e^2 + 714579/11*e + 1423129/88, 915/22*e^11 - 3349/22*e^10 - 19779/22*e^9 + 36748/11*e^8 + 142533/22*e^7 - 258404/11*e^6 - 252947/11*e^5 + 714729/11*e^4 + 1148451/22*e^3 - 1243791/22*e^2 - 711632/11*e - 177368/11, -1717/88*e^11 + 3205/44*e^10 + 9225/22*e^9 - 17623/11*e^8 - 131765/44*e^7 + 995613/88*e^6 + 466137/44*e^5 - 2775403/88*e^4 - 2160805/88*e^3 + 2452961/88*e^2 + 1384547/44*e + 692003/88, -3837/88*e^11 + 7087/44*e^10 + 41343/44*e^9 - 77821/22*e^8 - 74120/11*e^7 + 2192085/88*e^6 + 524919/22*e^5 - 6080649/88*e^4 - 4811943/88*e^3 + 5323561/88*e^2 + 3030249/44*e + 1513449/88, 86/11*e^11 - 639/22*e^10 - 3639/22*e^9 + 13905/22*e^8 + 25035/22*e^7 - 96315/22*e^6 - 41158/11*e^5 + 130287/11*e^4 + 177317/22*e^3 - 111057/11*e^2 - 224089/22*e - 51607/22, 127/4*e^11 - 116*e^10 - 687*e^9 + 5091/2*e^8 + 4961*e^7 - 71585/4*e^6 - 17663*e^5 + 197903/4*e^4 + 160601/4*e^3 - 171797/4*e^2 - 49648*e - 49851/4, 1333/44*e^11 - 2417/22*e^10 - 7230/11*e^9 + 26503/11*e^8 + 104877/22*e^7 - 744365/44*e^6 - 374497/22*e^5 + 2052311/44*e^4 + 1691609/44*e^3 - 1769877/44*e^2 - 1031963/22*e - 519439/44, 145/22*e^11 - 305/11*e^10 - 1502/11*e^9 + 6806/11*e^8 + 10090/11*e^7 - 98753/22*e^6 - 34674/11*e^5 + 288527/22*e^4 + 182651/22*e^3 - 279861/22*e^2 - 140094/11*e - 65447/22, 2477/88*e^11 - 4617/44*e^10 - 13291/22*e^9 + 25357/11*e^8 + 189203/44*e^7 - 1429445/88*e^6 - 664413/44*e^5 + 3971107/88*e^4 + 3052001/88*e^3 - 3495645/88*e^2 - 1946503/44*e - 960407/88, 9*e^11 - 32*e^10 - 391/2*e^9 + 698*e^8 + 2833/2*e^7 - 4851*e^6 - 9981/2*e^5 + 26273/2*e^4 + 21755/2*e^3 - 10966*e^2 - 12765*e - 6367/2, 2451/44*e^11 - 2284/11*e^10 - 13164/11*e^9 + 100411/22*e^8 + 187811/22*e^7 - 1416673/44*e^6 - 331165/11*e^5 + 3942711/44*e^4 + 3056167/44*e^3 - 3478531/44*e^2 - 976317/11*e - 968905/44, -2869/88*e^11 + 5173/44*e^10 + 31179/44*e^9 - 56701/22*e^8 - 113403/22*e^7 + 1591353/88*e^6 + 202867/11*e^5 - 4381897/88*e^4 - 3651311/88*e^3 + 3767765/88*e^2 + 2210441/44*e + 1114677/88, -3691/88*e^11 + 1700/11*e^10 + 39893/44*e^9 - 149503/44*e^8 - 71978/11*e^7 + 2109565/88*e^6 + 1029287/44*e^5 - 5866269/88*e^4 - 4742957/88*e^3 + 5142211/88*e^2 + 744231/11*e + 1502899/88, 4909/88*e^11 - 9021/44*e^10 - 13238/11*e^9 + 49492/11*e^8 + 380247/44*e^7 - 2784285/88*e^6 - 1345127/44*e^5 + 7704423/88*e^4 + 6122121/88*e^3 - 6716065/88*e^2 - 3821639/44*e - 1903815/88, 67/22*e^11 - 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6756535/88*e^2 - 3872527/44*e - 1926247/88, 2879/88*e^11 - 2689/22*e^10 - 31187/44*e^9 + 118843/44*e^8 + 113449/22*e^7 - 1692341/88*e^6 - 829947/44*e^5 + 4773405/88*e^4 + 3962305/88*e^3 - 4262639/88*e^2 - 637019/11*e - 1322859/88, 3457/88*e^11 - 6161/44*e^10 - 37651/44*e^9 + 33707/11*e^8 + 68626/11*e^7 - 1885981/88*e^6 - 244682/11*e^5 + 5165425/88*e^4 + 4332971/88*e^3 - 4403821/88*e^2 - 2573271/44*e - 1282821/88, -89/2*e^11 + 163*e^10 + 953*e^9 - 3557*e^8 - 6726*e^7 + 49515/2*e^6 + 23004*e^5 - 134799/2*e^4 - 100965/2*e^3 + 115015/2*e^2 + 62226*e + 29913/2, 2843/44*e^11 - 2749/11*e^10 - 30287/22*e^9 + 121581/22*e^8 + 106789/11*e^7 - 1734605/44*e^6 - 755199/22*e^5 + 4920705/44*e^4 + 3645005/44*e^3 - 4498123/44*e^2 - 1232674/11*e - 1213551/44, 7475/44*e^11 - 13763/22*e^10 - 161329/44*e^9 + 151141/11*e^8 + 1160001/44*e^7 - 4257777/44*e^6 - 4117477/44*e^5 + 5904933/22*e^4 + 2354624/11*e^3 - 10329679/44*e^2 - 5900999/22*e - 737534/11, 631/8*e^11 - 1147/4*e^10 - 6807/4*e^9 + 6273*e^8 + 24391/2*e^7 - 350843/8*e^6 - 85385/2*e^5 + 961379/8*e^4 + 759969/8*e^3 - 824915/8*e^2 - 464933/4*e - 229151/8, 5685/88*e^11 - 5023/22*e^10 - 61869/44*e^9 + 219057/44*e^8 + 224899/22*e^7 - 3043287/88*e^6 - 1589333/44*e^5 + 8235703/88*e^4 + 6906563/88*e^3 - 6863253/88*e^2 - 1004460/11*e - 2010385/88, 3361/44*e^11 - 5931/22*e^10 - 73593/44*e^9 + 64890/11*e^8 + 541933/44*e^7 - 1814391/44*e^6 - 1957429/44*e^5 + 1239442/11*e^4 + 2173011/22*e^3 - 4176873/44*e^2 - 2547275/22*e - 654677/22, 7009/44*e^11 - 12647/22*e^10 - 151933/44*e^9 + 138428/11*e^8 + 1098785/44*e^7 - 3875339/44*e^6 - 3892629/44*e^5 + 2657789/11*e^4 + 4342457/22*e^3 - 9105601/44*e^2 - 5255369/22*e - 1311501/22, -7267/88*e^11 + 12865/44*e^10 + 39561/22*e^9 - 140429/22*e^8 - 575899/44*e^7 + 3910807/88*e^6 + 2040837/44*e^5 - 10627249/88*e^4 - 8920931/88*e^3 + 8928999/88*e^2 + 5227435/44*e + 2610845/88, -2735/88*e^11 + 4439/44*e^10 + 30711/44*e^9 - 24075/11*e^8 - 117631/22*e^7 + 1323211/88*e^6 + 436071/22*e^5 - 3491131/88*e^4 - 3675713/88*e^3 + 2681131/88*e^2 + 1892477/44*e + 1023479/88, -2323/88*e^11 + 3627/44*e^10 + 13115/22*e^9 - 19516/11*e^8 - 201985/44*e^7 + 1055907/88*e^6 + 742227/44*e^5 - 2702037/88*e^4 - 2992535/88*e^3 + 1926451/88*e^2 + 1425917/44*e + 778313/88, -147/88*e^11 + 239/22*e^10 + 947/44*e^9 - 10389/44*e^8 + 899/22*e^7 + 144585/88*e^6 - 41785/44*e^5 - 406829/88*e^4 + 175623/88*e^3 + 426875/88*e^2 + 10833/22*e - 50001/88, 1229/88*e^11 - 1149/22*e^10 - 13147/44*e^9 + 50445/44*e^8 + 23224/11*e^7 - 709975/88*e^6 - 321967/44*e^5 + 1969131/88*e^4 + 1462951/88*e^3 - 1738557/88*e^2 - 233374/11*e - 444861/88, -2347/88*e^11 + 4163/44*e^10 + 6328/11*e^9 - 22598/11*e^8 - 180439/44*e^7 + 1246323/88*e^6 + 616389/44*e^5 - 3335337/88*e^4 - 2601283/88*e^3 + 2751395/88*e^2 + 1514201/44*e + 727325/88, 1849/88*e^11 - 3271/44*e^10 - 10193/22*e^9 + 35961/22*e^8 + 152533/44*e^7 - 1014269/88*e^6 - 567315/44*e^5 + 2808403/88*e^4 + 2599265/88*e^3 - 2402229/88*e^2 - 1542705/44*e - 817007/88, -1763/88*e^11 + 3103/44*e^10 + 4823/11*e^9 - 16954/11*e^8 - 141767/44*e^7 + 945723/88*e^6 + 508445/44*e^5 - 2571713/88*e^4 - 2225459/88*e^3 + 2150427/88*e^2 + 1284225/44*e + 647373/88, 3895/44*e^11 - 3588/11*e^10 - 20984/11*e^9 + 157491/22*e^8 + 150379/11*e^7 - 2215337/44*e^6 - 530734/11*e^5 + 6132207/44*e^4 + 4832001/44*e^3 - 5353617/44*e^2 - 1512318/11*e - 1498831/44, -343/11*e^11 + 2529/22*e^10 + 7492/11*e^9 - 55967/22*e^8 - 55325/11*e^7 + 399477/22*e^6 + 411375/22*e^5 - 1130387/22*e^4 - 490156/11*e^3 + 505427/11*e^2 + 1237569/22*e + 161697/11, -2465/44*e^11 + 2378/11*e^10 + 26029/22*e^9 - 104581/22*e^8 - 89868/11*e^7 + 1477303/44*e^6 + 611205/22*e^5 - 4129723/44*e^4 - 2859063/44*e^3 + 3712945/44*e^2 + 969039/11*e + 925093/44, -3445/88*e^11 + 6663/44*e^10 + 9115/11*e^9 - 73407/22*e^8 - 253245/44*e^7 + 2081569/88*e^6 + 872005/44*e^5 - 5852723/88*e^4 - 4132421/88*e^3 + 5302373/88*e^2 + 2809233/44*e + 1356539/88, -189/44*e^11 + 213/11*e^10 + 1015/11*e^9 - 9831/22*e^8 - 15117/22*e^7 + 150783/44*e^6 + 32132/11*e^5 - 474449/44*e^4 - 399241/44*e^3 + 492733/44*e^2 + 154395/11*e + 168847/44, 4395/88*e^11 - 1909/11*e^10 - 48275/44*e^9 + 166685/44*e^8 + 178485/22*e^7 - 2319621/88*e^6 - 1287325/44*e^5 + 6286029/88*e^4 + 5615125/88*e^3 - 5209795/88*e^2 - 1601817/22*e - 1642423/88, 6227/88*e^11 - 5821/22*e^10 - 66685/44*e^9 + 255677/44*e^8 + 118183/11*e^7 - 3601777/88*e^6 - 1652113/44*e^5 + 10004185/88*e^4 + 7594629/88*e^3 - 8818947/88*e^2 - 2438111/22*e - 2398675/88, -661/8*e^11 + 621/2*e^10 + 7087/4*e^9 - 27337/4*e^8 - 12605*e^7 + 386647/8*e^6 + 177843/4*e^5 - 1080699/8*e^4 - 828503/8*e^3 + 961277/8*e^2 + 134086*e + 265685/8, -373/8*e^11 + 339/2*e^10 + 4023/4*e^9 - 14827/4*e^8 - 7205*e^7 + 207167/8*e^6 + 100819/4*e^5 - 566863/8*e^4 - 447939/8*e^3 + 484941/8*e^2 + 136657/2*e + 134501/8, -7259/88*e^11 + 13383/44*e^10 + 39197/22*e^9 - 73556/11*e^8 - 564755/44*e^7 + 4151859/88*e^6 + 2012691/44*e^5 - 11551525/88*e^4 - 9253763/88*e^3 + 10156559/88*e^2 + 5813897/44*e + 2905789/88, -1115/11*e^11 + 3992/11*e^10 + 48503/22*e^9 - 87361/11*e^8 - 352871/22*e^7 + 610952/11*e^6 + 1257415/22*e^5 - 3345231/22*e^4 - 2795755/22*e^3 + 1422914/11*e^2 + 1670419/11*e + 841389/22, 2285/22*e^11 - 4157/11*e^10 - 24785/11*e^9 + 91266/11*e^8 + 179829/11*e^7 - 1284373/22*e^6 - 643706/11*e^5 + 3554649/22*e^4 + 2925379/22*e^3 - 3088213/22*e^2 - 1796842/11*e - 902945/22, -4133/88*e^11 + 7325/44*e^10 + 11270/11*e^9 - 40026/11*e^8 - 329539/44*e^7 + 2233981/88*e^6 + 1177855/44*e^5 - 6088015/88*e^4 - 5197649/88*e^3 + 5122993/88*e^2 + 3054659/44*e + 1550911/88, 1325/11*e^11 - 4781/11*e^10 - 57381/22*e^9 + 104584/11*e^8 + 413993/22*e^7 - 731009/11*e^6 - 1460567/22*e^5 + 4002885/22*e^4 + 3246003/22*e^3 - 1710272/11*e^2 - 1962423/11*e - 975509/22, 2039/44*e^11 - 1812/11*e^10 - 11105/11*e^9 + 79227/22*e^8 + 161937/22*e^7 - 1106073/44*e^6 - 288466/11*e^5 + 3018823/44*e^4 + 2545799/44*e^3 - 2554803/44*e^2 - 751639/11*e - 753593/44, -805/88*e^11 + 2021/44*e^10 + 7497/44*e^9 - 11299/11*e^8 - 19587/22*e^7 + 659841/88*e^6 + 47763/22*e^5 - 1964113/88*e^4 - 681963/88*e^3 + 2025737/88*e^2 + 793923/44*e + 316093/88, -4957/22*e^11 + 8872/11*e^10 + 53877/11*e^9 - 388147/22*e^8 - 391484/11*e^7 + 2712511/22*e^6 + 1392057/11*e^5 - 3709291/11*e^4 - 3088870/11*e^3 + 6304641/22*e^2 + 7378115/22*e + 1853759/22, -1768/11*e^11 + 6444/11*e^10 + 38196/11*e^9 - 141183/11*e^8 - 274705/11*e^7 + 989727/11*e^6 + 969413/11*e^5 - 2723643/11*e^4 - 2179513/11*e^3 + 2349992/11*e^2 + 2680607/11*e + 666665/11, -11371/88*e^11 + 20481/44*e^10 + 30850/11*e^9 - 224207/22*e^8 - 894719/44*e^7 + 6277911/88*e^6 + 3181263/44*e^5 - 17221885/88*e^4 - 14215779/88*e^3 + 14726235/88*e^2 + 8578111/44*e + 4309733/88, 805/88*e^11 - 1647/44*e^10 - 2042/11*e^9 + 18055/22*e^8 + 51703/44*e^7 - 508217/88*e^6 - 154453/44*e^5 + 1422011/88*e^4 + 722465/88*e^3 - 1319185/88*e^2 - 567521/44*e - 232999/88, 1049/11*e^11 - 7357/22*e^10 - 45841/22*e^9 + 160477/22*e^8 + 335535/22*e^7 - 1115303/22*e^6 - 596978/11*e^5 + 1509634/11*e^4 + 2589857/22*e^3 - 1256132/11*e^2 - 2980093/22*e - 747405/22, -3873/88*e^11 + 3313/22*e^10 + 42683/44*e^9 - 144291/44*e^8 - 79254/11*e^7 + 1998747/88*e^6 + 1142615/44*e^5 - 5370875/88*e^4 - 4902687/88*e^3 + 4370217/88*e^2 + 1361013/22*e + 1401921/88, 91/4*e^11 - 145/2*e^10 - 504*e^9 + 1549*e^8 + 3740*e^7 - 41343/4*e^6 - 25963/2*e^5 + 103625/4*e^4 + 98877/4*e^3 - 72661/4*e^2 - 45991/2*e - 22915/4, -189/44*e^11 + 151/22*e^10 + 2305/22*e^9 - 1324/11*e^8 - 9599/11*e^7 + 19509/44*e^6 + 33243/11*e^5 + 32739/44*e^4 - 141907/44*e^3 - 173735/44*e^2 - 51757/22*e - 25039/44, 2193/22*e^11 - 8161/22*e^10 - 47203/22*e^9 + 179475/22*e^8 + 338119/22*e^7 - 633529/11*e^6 - 600153/11*e^5 + 3529311/22*e^4 + 1389626/11*e^3 - 3111425/22*e^2 - 3539891/22*e - 442879/11, -13843/88*e^11 + 25331/44*e^10 + 149439/44*e^9 - 138869/11*e^8 - 537043/22*e^7 + 7801215/88*e^6 + 1897695/22*e^5 - 21532399/88*e^4 - 17169725/88*e^3 + 18683415/88*e^2 + 10639085/44*e + 5292659/88, -6703/88*e^11 + 12391/44*e^10 + 72007/44*e^9 - 135869/22*e^8 - 128234/11*e^7 + 3817595/88*e^6 + 897789/22*e^5 - 10551095/88*e^4 - 8158065/88*e^3 + 9204391/88*e^2 + 5145367/44*e + 2545515/88, 3287/88*e^11 - 6141/44*e^10 - 34963/44*e^9 + 33581/11*e^8 + 60997/11*e^7 - 1878871/88*e^6 - 207080/11*e^5 + 5164899/88*e^4 + 3713505/88*e^3 - 4505183/88*e^2 - 2385341/44*e - 1137403/88, 4155/44*e^11 - 7853/22*e^10 - 44409/22*e^9 + 86410/11*e^8 + 157031/11*e^7 - 2443839/44*e^6 - 550004/11*e^5 + 6831703/44*e^4 + 5128657/44*e^3 - 6092995/44*e^2 - 3349327/22*e - 1644059/44, 1149/44*e^11 - 1022/11*e^10 - 12577/22*e^9 + 44801/22*e^8 + 46388/11*e^7 - 628247/44*e^6 - 338057/22*e^5 + 1724875/44*e^4 + 1527439/44*e^3 - 1460825/44*e^2 - 454028/11*e - 476045/44, -1473/11*e^11 + 5316/11*e^10 + 63865/22*e^9 - 232777/22*e^8 - 461939/22*e^7 + 814800/11*e^6 + 1636851/22*e^5 - 2236307/11*e^4 - 1826728/11*e^3 + 1917185/11*e^2 + 4424479/22*e + 1103831/22, -10061/88*e^11 + 18321/44*e^10 + 54543/22*e^9 - 100558/11*e^8 - 790971/44*e^7 + 5660533/88*e^6 + 2830329/44*e^5 - 15666107/88*e^4 - 12877697/88*e^3 + 13606749/88*e^2 + 7927275/44*e + 3996999/88, 8245/44*e^11 - 7558/11*e^10 - 44504/11*e^9 + 331663/22*e^8 + 639967/22*e^7 - 4662863/44*e^6 - 1132530/11*e^5 + 12893113/44*e^4 + 10280533/44*e^3 - 11222857/44*e^2 - 3194122/11*e - 3176791/44, -2913/22*e^11 + 20989/44*e^10 + 31597/11*e^9 - 459471/44*e^8 - 457649/22*e^7 + 3215673/44*e^6 + 3246939/44*e^5 - 8820015/44*e^4 - 3619565/22*e^3 + 3773925/22*e^2 + 8738727/44*e + 1092259/22, -1845/88*e^11 + 3607/44*e^10 + 19659/44*e^9 - 40001/22*e^8 - 34785/11*e^7 + 1147709/88*e^6 + 250001/22*e^5 - 3285193/88*e^4 - 2483487/88*e^3 + 3037569/88*e^2 + 1712021/44*e + 863257/88, 3565/44*e^11 - 3401/11*e^10 - 76049/44*e^9 + 149923/22*e^8 + 536341/44*e^7 - 2126149/44*e^6 - 1880991/44*e^5 + 2986227/22*e^4 + 2220503/22*e^3 - 5371481/44*e^2 - 1472586/11*e - 724649/22, 2345/22*e^11 - 4342/11*e^10 - 25295/11*e^9 + 95499/11*e^8 + 363809/22*e^7 - 1348617/22*e^6 - 647957/11*e^5 + 3756651/22*e^4 + 1495712/11*e^3 - 1654922/11*e^2 - 1890634/11*e - 472839/11]; 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;