/* 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![-14, 0, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [2, 2, -w - 4], [5, 5, -w + 3], [5, 5, w + 3], [7, 7, -2*w - 7], [9, 3, 3], [11, 11, w + 5], [11, 11, -w + 5], [13, 13, -w - 1], [13, 13, -w + 1], [31, 31, 2*w - 5], [31, 31, -2*w - 5], [43, 43, 7*w + 27], [43, 43, 3*w + 13], [47, 47, 2*w - 3], [47, 47, -2*w - 3], [61, 61, 7*w + 25], [61, 61, -5*w - 17], [67, 67, -w - 9], [67, 67, w - 9], [101, 101, 3*w - 5], [101, 101, -3*w - 5], [103, 103, 4*w - 11], [103, 103, -4*w - 11], [107, 107, -w - 11], [107, 107, w - 11], [113, 113, 2*w - 13], [113, 113, -2*w - 13], [137, 137, 4*w + 19], [137, 137, 16*w + 61], [157, 157, 13*w + 47], [157, 157, -7*w - 23], [163, 163, -3*w - 17], [163, 163, 3*w - 17], [167, 167, -8*w - 27], [167, 167, 12*w + 43], [173, 173, 11*w + 39], [173, 173, -9*w - 31], [179, 179, 17*w + 65], [179, 179, 5*w + 23], [181, 181, -5*w - 13], [181, 181, 5*w - 13], [193, 193, 12*w + 47], [193, 193, 8*w + 33], [199, 199, -4*w - 5], [199, 199, 4*w - 5], [211, 211, -w - 15], [211, 211, w - 15], [223, 223, -4*w - 1], [223, 223, 4*w - 1], [229, 229, -5*w - 11], [229, 229, 5*w - 11], [233, 233, 2*w - 17], [233, 233, -2*w - 17], [269, 269, 5*w - 9], [269, 269, -5*w - 9], [271, 271, -8*w - 25], [271, 271, 20*w + 73], [281, 281, 14*w + 55], [281, 281, 10*w + 41], [289, 17, -17], [293, 293, 19*w + 69], [293, 293, -9*w - 29], [311, 311, 18*w + 65], [311, 311, -10*w - 33], [331, 331, 15*w + 59], [331, 331, 11*w + 45], [337, 337, 6*w + 29], [337, 337, 26*w + 99], [347, 347, -w - 19], [347, 347, w - 19], [349, 349, -5*w - 1], [349, 349, 5*w - 1], [361, 19, -19], [367, 367, 8*w - 23], [367, 367, -8*w - 23], [379, 379, -5*w - 27], [379, 379, 5*w - 27], [383, 383, 6*w - 11], [383, 383, -6*w - 11], [397, 397, 7*w - 17], [397, 397, -7*w - 17], [401, 401, 4*w - 25], [401, 401, -4*w - 25], [439, 439, -10*w - 31], [439, 439, 26*w + 95], [443, 443, 17*w + 67], [443, 443, 13*w + 53], [449, 449, 10*w + 43], [449, 449, 22*w + 85], [457, 457, 6*w - 31], [457, 457, -6*w - 31], [461, 461, -7*w - 15], [461, 461, 7*w - 15], [479, 479, 6*w - 5], [479, 479, -6*w - 5], [491, 491, -5*w - 29], [491, 491, 5*w - 29], [499, 499, 3*w - 25], [499, 499, -3*w - 25], [503, 503, -6*w - 1], [503, 503, 6*w - 1], [509, 509, -9*w - 25], [509, 509, 9*w - 25], [529, 23, -23], [547, 547, 29*w + 111], [547, 547, 9*w + 41], [569, 569, 2*w - 25], [569, 569, -2*w - 25], [571, 571, 19*w + 75], [571, 571, 15*w + 61], [607, 607, -8*w - 17], [607, 607, 8*w - 17], [617, 617, 4*w - 29], [617, 617, -4*w - 29], [641, 641, 20*w + 79], [641, 641, 16*w + 65], [647, 647, -12*w - 37], [647, 647, 32*w + 117], [659, 659, 13*w + 55], [659, 659, 25*w + 97], [661, 661, -7*w - 5], [661, 661, 7*w - 5], [673, 673, 2*w - 27], [673, 673, -2*w - 27], [677, 677, 7*w - 3], [677, 677, -7*w - 3], [683, 683, -7*w - 37], [683, 683, 7*w - 37], [719, 719, -14*w - 45], [719, 719, 30*w + 109], [727, 727, 8*w - 13], [727, 727, -8*w - 13], [733, 733, -11*w - 31], [733, 733, 11*w - 31], [739, 739, 5*w - 33], [739, 739, -5*w - 33], [773, 773, -9*w - 19], [773, 773, 9*w - 19], [797, 797, -17*w - 57], [797, 797, 27*w + 97], [809, 809, 38*w + 145], [809, 809, 10*w + 47], [827, 827, -w - 29], [827, 827, w - 29], [829, 829, 25*w + 89], [829, 829, -19*w - 65], [839, 839, -20*w - 69], [839, 839, 24*w + 85], [841, 29, -29], [853, 853, 11*w - 29], [853, 853, -11*w - 29], [883, 883, 13*w + 57], [883, 883, 33*w + 127], [887, 887, -8*w - 3], [887, 887, 8*w - 3], [907, 907, 11*w + 51], [907, 907, 39*w + 149], [941, 941, 37*w + 135], [941, 941, -15*w - 47], [947, 947, -w - 31], [947, 947, w - 31], [953, 953, 8*w - 43], [953, 953, -8*w - 43], [977, 977, 34*w + 131], [977, 977, 14*w + 61], [983, 983, 36*w + 131], [983, 983, -16*w - 51], [997, 997, -13*w - 37], [997, 997, 13*w - 37], [1009, 1009, 12*w + 55], [1009, 1009, 40*w + 153], [1013, 1013, 9*w - 11], [1013, 1013, -9*w - 11], [1019, 1019, -5*w - 37], [1019, 1019, 5*w - 37], [1021, 1021, 35*w + 127], [1021, 1021, -17*w - 55], [1033, 1033, 2*w - 33], [1033, 1033, -2*w - 33], [1039, 1039, 10*w - 19], [1039, 1039, -10*w - 19], [1051, 1051, 25*w + 99], [1051, 1051, 21*w + 85], [1063, 1063, -14*w + 41], [1063, 1063, 14*w + 41], [1069, 1069, -11*w - 25], [1069, 1069, 11*w - 25], [1109, 1109, -9*w - 5], [1109, 1109, 9*w - 5], [1129, 1129, -8*w - 45], [1129, 1129, 8*w - 45], [1151, 1151, -22*w - 75], [1151, 1151, 30*w + 107], [1163, 1163, 7*w - 43], [1163, 1163, -7*w - 43], [1171, 1171, -5*w - 39], [1171, 1171, 5*w - 39], [1181, 1181, 27*w + 95], [1181, 1181, -25*w - 87], [1187, 1187, 19*w + 79], [1187, 1187, 31*w + 121], [1201, 1201, 10*w - 51], [1201, 1201, -10*w - 51], [1223, 1223, 14*w - 39], [1223, 1223, -14*w - 39], [1231, 1231, 10*w - 13], [1231, 1231, -10*w - 13], [1237, 1237, 43*w + 157], [1237, 1237, -17*w - 53], [1277, 1277, -13*w - 33], [1277, 1277, 13*w - 33], [1279, 1279, -10*w - 11], [1279, 1279, 10*w - 11], [1283, 1283, 37*w + 143], [1283, 1283, 17*w + 73], [1289, 1289, 32*w + 125], [1289, 1289, 20*w + 83], [1297, 1297, -4*w - 39], [1297, 1297, 4*w - 39], [1301, 1301, -15*w - 43], [1301, 1301, 15*w - 43], [1319, 1319, 10*w - 9], [1319, 1319, -10*w - 9], [1369, 37, -37], [1399, 1399, -10*w - 1], [1399, 1399, 10*w - 1], [1409, 1409, -10*w - 53], [1409, 1409, 10*w - 53], [1447, 1447, 38*w + 137], [1447, 1447, -22*w - 73], [1451, 1451, 29*w + 115], [1451, 1451, 25*w + 101], [1481, 1481, 14*w + 65], [1481, 1481, 50*w + 191], [1487, 1487, 12*w - 23], [1487, 1487, -12*w - 23], [1499, 1499, 5*w - 43], [1499, 1499, -5*w - 43], [1511, 1511, -18*w - 55], [1511, 1511, 50*w + 183], [1523, 1523, 7*w - 47], [1523, 1523, -7*w - 47], [1543, 1543, 34*w + 121], [1543, 1543, -26*w - 89], [1559, 1559, -16*w - 45], [1559, 1559, 16*w - 45], [1567, 1567, -28*w - 97], [1567, 1567, 32*w + 113], [1579, 1579, 45*w + 173], [1579, 1579, 17*w + 75], [1613, 1613, -11*w - 9], [1613, 1613, 11*w - 9], [1619, 1619, 35*w + 137], [1619, 1619, 23*w + 95], [1637, 1637, -13*w - 27], [1637, 1637, 13*w - 27], [1667, 1667, -w - 41], [1667, 1667, w - 41], [1669, 1669, 11*w - 5], [1669, 1669, -11*w - 5], [1681, 41, -41], [1693, 1693, -11*w - 1], [1693, 1693, 11*w - 1], [1723, 1723, 3*w - 43], [1723, 1723, -3*w - 43], [1741, 1741, 13*w - 25], [1741, 1741, -13*w - 25], [1747, 1747, 21*w + 89], [1747, 1747, 41*w + 159], [1783, 1783, -14*w - 31], [1783, 1783, 14*w - 31], [1787, 1787, 11*w - 59], [1787, 1787, -11*w - 59], [1801, 1801, 4*w - 45], [1801, 1801, -4*w - 45], [1823, 1823, -24*w - 79], [1823, 1823, 44*w + 159], [1847, 1847, -12*w - 13], [1847, 1847, 12*w - 13], [1861, 1861, 43*w + 155], [1861, 1861, -25*w - 83], [1873, 1873, 42*w + 163], [1873, 1873, 22*w + 93], [1879, 1879, -20*w - 61], [1879, 1879, 56*w + 205], [1913, 1913, -8*w - 53], [1913, 1913, 8*w - 53], [1949, 1949, 55*w + 201], [1949, 1949, -21*w - 65], [1951, 1951, 40*w + 143], [1951, 1951, -28*w - 95], [1973, 1973, 39*w + 139], [1973, 1973, -29*w - 99], [2003, 2003, 23*w + 97], [2003, 2003, 43*w + 167], [2011, 2011, -w - 45], [2011, 2011, w - 45], [2017, 2017, -14*w - 69], [2017, 2017, 14*w - 69], [2027, 2027, 11*w - 61], [2027, 2027, -11*w - 61], [2029, 2029, -19*w - 55], [2029, 2029, 19*w - 55], [2063, 2063, -16*w - 39], [2063, 2063, 16*w - 39], [2081, 2081, -10*w - 59], [2081, 2081, 10*w - 59], [2083, 2083, -3*w - 47], [2083, 2083, 3*w - 47], [2129, 2129, -8*w - 55], [2129, 2129, 8*w - 55], [2137, 2137, 44*w + 171], [2137, 2137, 24*w + 101], [2141, 2141, 13*w - 15], [2141, 2141, -13*w - 15], [2153, 2153, 2*w - 47], [2153, 2153, -2*w - 47], [2179, 2179, 67*w + 255], [2179, 2179, 15*w + 73], [2239, 2239, 50*w + 181], [2239, 2239, -26*w - 85], [2251, 2251, 5*w - 51], [2251, 2251, -5*w - 51], [2287, 2287, -22*w - 67], [2287, 2287, 62*w + 227], [2297, 2297, 14*w - 71], [2297, 2297, -14*w - 71], [2309, 2309, 15*w - 29], [2309, 2309, -15*w - 29], [2339, 2339, -7*w - 55], [2339, 2339, 7*w - 55], [2341, 2341, 13*w - 5], [2341, 2341, -13*w - 5], [2347, 2347, 9*w - 59], [2347, 2347, -9*w - 59], [2351, 2351, 20*w - 57], [2351, 2351, -20*w - 57], [2357, 2357, 13*w - 3], [2357, 2357, -13*w - 3], [2377, 2377, -4*w - 51], [2377, 2377, 4*w - 51], [2383, 2383, -14*w - 19], [2383, 2383, 14*w - 19], [2399, 2399, -30*w - 101], [2399, 2399, 46*w + 165], [2417, 2417, 26*w + 109], [2417, 2417, 46*w + 179], [2459, 2459, 5*w - 53], [2459, 2459, -5*w - 53], [2473, 2473, -12*w - 67], [2473, 2473, 12*w - 67], [2477, 2477, 43*w + 153], [2477, 2477, -33*w - 113], [2521, 2521, 6*w - 55], [2521, 2521, -6*w - 55], [2531, 2531, -11*w - 65], [2531, 2531, 11*w - 65], [2551, 2551, 70*w + 257], [2551, 2551, -22*w - 65], [2621, 2621, -15*w - 23], [2621, 2621, 15*w - 23], [2633, 2633, 58*w + 223], [2633, 2633, 22*w + 97], [2657, 2657, -16*w - 79], [2657, 2657, 16*w - 79], [2663, 2663, 14*w - 9], [2663, 2663, -14*w - 9], [2677, 2677, -17*w - 37], [2677, 2677, 17*w - 37], [2683, 2683, -3*w - 53], [2683, 2683, 3*w - 53], [2687, 2687, 18*w - 43], [2687, 2687, -18*w - 43], [2689, 2689, 70*w + 267], [2689, 2689, 18*w + 85], [2693, 2693, -21*w - 59], [2693, 2693, 21*w - 59], [2699, 2699, 25*w + 107], [2699, 2699, 53*w + 205], [2713, 2713, 28*w + 117], [2713, 2713, 48*w + 187], [2719, 2719, -14*w - 5], [2719, 2719, 14*w - 5], [2731, 2731, 39*w + 155], [2731, 2731, 35*w + 141], [2749, 2749, -29*w - 95], [2749, 2749, 55*w + 199], [2753, 2753, 2*w - 53], [2753, 2753, -2*w - 53], [2789, 2789, -15*w - 19], [2789, 2789, 15*w - 19], [2791, 2791, 20*w - 53], [2791, 2791, -20*w - 53], [2801, 2801, -4*w - 55], [2801, 2801, 4*w - 55], [2809, 53, -53], [2843, 2843, 17*w - 83], [2843, 2843, -17*w - 83], [2851, 2851, 65*w + 249], [2851, 2851, 21*w + 95], [2857, 2857, 26*w + 111], [2857, 2857, 54*w + 209], [2861, 2861, 15*w - 17], [2861, 2861, -15*w - 17], [2887, 2887, -32*w - 107], [2887, 2887, 52*w + 187], [2903, 2903, -26*w - 81], [2903, 2903, 66*w + 241], [2917, 2917, 23*w + 67], [2917, 2917, -23*w + 67], [2957, 2957, 17*w - 33], [2957, 2957, -17*w - 33], [2963, 2963, 13*w - 73], [2963, 2963, -13*w - 73], [2969, 2969, 2*w - 55], [2969, 2969, -2*w - 55], [2999, 2999, 20*w - 51], [2999, 2999, -20*w - 51], [3011, 3011, -w - 55], [3011, 3011, w - 55], [3019, 3019, 55*w + 213], [3019, 3019, 27*w + 115], [3023, 3023, 76*w + 279], [3023, 3023, -24*w - 71], [3037, 3037, -37*w - 127], [3037, 3037, 47*w + 167], [3049, 3049, 20*w + 93], [3049, 3049, 72*w + 275], [3067, 3067, 11*w - 69], [3067, 3067, -11*w - 69], [3079, 3079, -40*w - 139], [3079, 3079, 44*w + 155], [3089, 3089, 10*w - 67], [3089, 3089, -10*w - 67], [3137, 3137, 34*w + 139], [3137, 3137, 46*w + 181], [3167, 3167, -18*w - 37], [3167, 3167, 18*w - 37], [3181, 3181, 23*w - 65], [3181, 3181, -23*w - 65], [3187, 3187, 31*w + 129], [3187, 3187, 51*w + 199], [3191, 3191, -30*w - 97], [3191, 3191, 62*w + 225], [3203, 3203, 23*w + 103], [3203, 3203, 67*w + 257], [3217, 3217, 6*w - 61], [3217, 3217, -6*w - 61], [3253, 3253, -31*w - 101], [3253, 3253, 61*w + 221], [3257, 3257, -4*w - 59], [3257, 3257, 4*w - 59], [3259, 3259, 13*w - 75], [3259, 3259, -13*w - 75], [3299, 3299, 47*w + 185], [3299, 3299, 35*w + 143], [3313, 3313, 12*w - 73], [3313, 3313, -12*w - 73], [3329, 3329, 8*w - 65], [3329, 3329, -8*w - 65], [3347, 3347, -11*w - 71], [3347, 3347, 11*w - 71], [3359, 3359, 16*w - 15], [3359, 3359, -16*w - 15], [3361, 3361, -10*w - 69], [3361, 3361, 10*w - 69], [3371, 3371, 5*w - 61], [3371, 3371, -5*w - 61], [3373, 3373, 19*w - 41], [3373, 3373, -19*w - 41], [3391, 3391, -20*w - 47], [3391, 3391, 20*w - 47], [3407, 3407, 72*w + 263], [3407, 3407, -28*w - 87], [3461, 3461, -35*w - 117], [3461, 3461, 57*w + 205], [3463, 3463, -16*w - 11], [3463, 3463, 16*w - 11], [3467, 3467, -w - 59], [3467, 3467, w - 59], [3481, 59, -59], [3517, 3517, -17*w - 23], [3517, 3517, 17*w - 23], [3527, 3527, 22*w - 57], [3527, 3527, -22*w - 57], [3529, 3529, 58*w + 225], [3529, 3529, 30*w + 127], [3533, 3533, -19*w - 39], [3533, 3533, 19*w - 39], [3539, 3539, -7*w - 65], [3539, 3539, 7*w - 65], [3541, 3541, -37*w - 125], [3541, 3541, 55*w + 197], [3559, 3559, 16*w - 5], [3559, 3559, -16*w - 5], [3571, 3571, 25*w + 111], [3571, 3571, 69*w + 265], [3583, 3583, -16*w - 1], [3583, 3583, 16*w - 1], [3593, 3593, 8*w - 67], [3593, 3593, -8*w - 67], [3631, 3631, 52*w + 185], [3631, 3631, -40*w - 137], [3671, 3671, 50*w + 177], [3671, 3671, -42*w - 145], [3691, 3691, 45*w + 179], [3691, 3691, 41*w + 165], [3697, 3697, 54*w + 211], [3697, 3697, 34*w + 141], [3701, 3701, 47*w + 165], [3701, 3701, -45*w - 157], [3709, 3709, -25*w - 71], [3709, 3709, 25*w - 71], [3727, 3727, 68*w + 247], [3727, 3727, -32*w - 103], [3739, 3739, 15*w - 83], [3739, 3739, -15*w - 83], [3761, 3761, 26*w + 115], [3761, 3761, 70*w + 269], [3797, 3797, 67*w + 243], [3797, 3797, -33*w - 107], [3803, 3803, 7*w - 67], [3803, 3803, -7*w - 67], [3821, 3821, -17*w - 15], [3821, 3821, 17*w - 15], [3833, 3833, 82*w + 313], [3833, 3833, 22*w + 103], [3851, 3851, 65*w + 251], [3851, 3851, 29*w + 125], [3853, 3853, 79*w + 289], [3853, 3853, -29*w - 89], [3863, 3863, 66*w + 239], [3863, 3863, -34*w - 111], [3877, 3877, -17*w - 13], [3877, 3877, 17*w - 13], [3889, 3889, 32*w + 135], [3889, 3889, 60*w + 233], [3907, 3907, -9*w - 71], [3907, 3907, 9*w - 71], [3911, 3911, 18*w - 25], [3911, 3911, -18*w - 25], [3919, 3919, -20*w - 41], [3919, 3919, 20*w - 41], [3929, 3929, -10*w - 73], [3929, 3929, 10*w - 73], [3931, 3931, 11*w - 75], [3931, 3931, -11*w - 75], [3967, 3967, -22*w - 53], [3967, 3967, 22*w - 53], [3989, 3989, -25*w - 69], [3989, 3989, 25*w - 69], [4001, 4001, 4*w - 65], [4001, 4001, -4*w - 65], [4007, 4007, 18*w - 23], [4007, 4007, -18*w - 23], [4019, 4019, 77*w + 295], [4019, 4019, 25*w + 113], [4021, 4021, -17*w - 5], [4021, 4021, 17*w - 5], [4027, 4027, 89*w + 339], [4027, 4027, 21*w + 101], [4057, 4057, 36*w + 149], [4057, 4057, 56*w + 219], [4079, 4079, 20*w - 39], [4079, 4079, -20*w - 39], [4093, 4093, -19*w - 31], [4093, 4093, 19*w - 31], [4099, 4099, -3*w - 65], [4099, 4099, 3*w - 65], [4133, 4133, -39*w - 131], [4133, 4133, 61*w + 219], [4139, 4139, -5*w - 67], [4139, 4139, 5*w - 67], [4153, 4153, 28*w + 123], [4153, 4153, 72*w + 277], [4157, 4157, 23*w - 57], [4157, 4157, -23*w - 57], [4201, 4201, -20*w - 99], [4201, 4201, 20*w - 99], [4211, 4211, -w - 65], [4211, 4211, w - 65], [4231, 4231, 20*w - 37], [4231, 4231, -20*w - 37], [4243, 4243, 57*w + 223], [4243, 4243, 37*w + 153], [4261, 4261, -25*w - 67], [4261, 4261, 25*w - 67], [4337, 4337, -16*w - 89], [4337, 4337, 16*w - 89], [4357, 4357, -47*w - 163], [4357, 4357, 53*w + 187], [4363, 4363, 3*w - 67], [4363, 4363, -3*w - 67], [4373, 4373, 51*w + 179], [4373, 4373, -49*w - 171], [4423, 4423, -26*w - 71], [4423, 4423, 26*w - 71], [4481, 4481, 14*w - 85], [4481, 4481, -14*w - 85], [4493, 4493, 21*w - 41], [4493, 4493, -21*w - 41], [4523, 4523, -13*w - 83], [4523, 4523, 13*w - 83], [4547, 4547, -11*w - 79], [4547, 4547, 11*w - 79], [4549, 4549, -29*w - 85], [4549, 4549, 95*w + 349], [4561, 4561, 74*w + 285], [4561, 4561, 30*w + 131], [4567, 4567, 22*w - 47], [4567, 4567, -22*w - 47], [4583, 4583, -24*w - 59], [4583, 4583, 24*w - 59], [4591, 4591, -38*w - 125], [4591, 4591, 70*w + 253], [4597, 4597, -23*w - 53], [4597, 4597, 23*w - 53], [4603, 4603, -17*w - 93], [4603, 4603, 17*w - 93], [4637, 4637, 83*w + 303], [4637, 4637, -33*w - 103], [4639, 4639, 20*w - 31], [4639, 4639, -20*w - 31], [4643, 4643, -7*w - 73], [4643, 4643, 7*w - 73], [4649, 4649, 80*w + 307], [4649, 4649, 28*w + 125], [4657, 4657, 36*w + 151], [4657, 4657, 64*w + 249], [4673, 4673, 22*w - 107], [4673, 4673, -22*w - 107], [4679, 4679, 94*w + 345], [4679, 4679, -30*w - 89], [4691, 4691, 5*w - 71], [4691, 4691, -5*w - 71], [4703, 4703, 26*w - 69], [4703, 4703, -26*w - 69], [4729, 4729, 8*w - 75], [4729, 4729, -8*w - 75], [4751, 4751, -22*w - 45], [4751, 4751, 22*w - 45], [4759, 4759, -20*w - 29], [4759, 4759, 20*w - 29], [4817, 4817, -4*w - 71], [4817, 4817, 4*w - 71], [4861, 4861, 65*w + 233], [4861, 4861, -43*w - 145], [4871, 4871, -20*w - 27], [4871, 4871, 20*w - 27], [4877, 4877, -27*w - 73], [4877, 4877, 27*w - 73], [4903, 4903, -44*w - 149], [4903, 4903, 64*w + 229], [4919, 4919, 80*w + 291], [4919, 4919, -36*w - 115], [4933, 4933, -19*w - 11], [4933, 4933, 19*w - 11], [4937, 4937, 56*w + 221], [4937, 4937, 44*w + 179], [4973, 4973, 19*w - 9], [4973, 4973, -19*w - 9], [4993, 4993, 52*w + 207], [4993, 4993, 48*w + 193], [5009, 5009, 20*w - 103], [5009, 5009, -20*w - 103], [5039, 5039, -24*w - 55], [5039, 5039, 24*w - 55], [5041, 71, -71], [5051, 5051, 71*w + 275], [5051, 5051, 35*w + 149], [5087, 5087, -38*w - 123], [5087, 5087, 78*w + 283], [5101, 5101, 55*w + 193], [5101, 5101, -53*w - 185], [5107, 5107, 9*w - 79], [5107, 5107, -9*w - 79], [5147, 5147, -19*w - 101], [5147, 5147, 19*w - 101], [5153, 5153, 28*w + 127], [5153, 5153, 88*w + 337], [5197, 5197, -23*w - 47], [5197, 5197, 23*w - 47], [5209, 5209, 12*w - 85], [5209, 5209, -12*w - 85], [5233, 5233, 62*w + 243], [5233, 5233, 42*w + 173], [5273, 5273, 2*w - 73], [5273, 5273, -2*w - 73], [5309, 5309, 75*w + 271], [5309, 5309, -41*w - 135], [5329, 73, -73], [5333, 5333, -21*w - 29], [5333, 5333, 21*w - 29], [5351, 5351, -28*w - 75], [5351, 5351, 28*w - 75], [5381, 5381, 23*w - 45], [5381, 5381, -23*w - 45], [5387, 5387, 89*w + 341], [5387, 5387, 29*w + 131], [5407, 5407, -22*w - 37], [5407, 5407, 22*w - 37], [5419, 5419, 95*w + 363], [5419, 5419, 27*w + 125], [5431, 5431, 20*w - 13], [5431, 5431, -20*w - 13], [5437, 5437, 73*w + 263], [5437, 5437, -43*w - 143], [5441, 5441, -16*w - 95], [5441, 5441, 16*w - 95], [5443, 5443, 43*w + 177], [5443, 5443, 63*w + 247], [5477, 5477, 87*w + 317], [5477, 5477, -37*w - 117], [5479, 5479, 20*w - 11], [5479, 5479, -20*w - 11], [5483, 5483, 37*w + 157], [5483, 5483, 73*w + 283], [5501, 5501, 25*w - 57], [5501, 5501, -25*w - 57], [5519, 5519, -20*w - 9], [5519, 5519, 20*w - 9], [5531, 5531, -11*w - 85], [5531, 5531, 11*w - 85], [5557, 5557, 23*w - 43], [5557, 5557, -23*w - 43], [5569, 5569, 2*w - 75], [5569, 5569, -2*w - 75], [5591, 5591, -20*w - 3], [5591, 5591, 20*w - 3], [5647, 5647, -28*w - 73], [5647, 5647, 28*w - 73], [5651, 5651, 79*w + 305], [5651, 5651, 35*w + 151], [5657, 5657, 64*w + 251], [5657, 5657, 44*w + 181], [5669, 5669, -39*w - 125], [5669, 5669, 85*w + 309], [5701, 5701, 97*w + 355], [5701, 5701, -35*w - 107], [5711, 5711, 30*w - 83], [5711, 5711, -30*w - 83], [5717, 5717, 27*w - 67], [5717, 5717, -27*w - 67], [5737, 5737, 6*w - 79], [5737, 5737, -6*w - 79], [5743, 5743, -26*w - 61], [5743, 5743, 26*w - 61], [5779, 5779, 33*w + 145], [5779, 5779, 85*w + 327], [5813, 5813, -21*w - 19], [5813, 5813, 21*w - 19], [5849, 5849, 20*w - 107], [5849, 5849, -20*w - 107], [5867, 5867, 31*w + 139], [5867, 5867, 91*w + 349], [5869, 5869, 61*w + 215], [5869, 5869, -55*w - 191], [5879, 5879, -56*w - 195], [5879, 5879, 60*w + 211], [5881, 5881, 36*w + 155], [5881, 5881, 80*w + 309], [5923, 5923, 103*w + 393], [5923, 5923, 27*w + 127], [5927, 5927, 82*w + 297], [5927, 5927, -42*w - 137], [5981, 5981, -27*w - 65], [5981, 5981, 27*w - 65], [5987, 5987, 49*w + 199], [5987, 5987, 61*w + 241], [6037, 6037, -23*w - 37], [6037, 6037, 23*w - 37], [6043, 6043, 57*w + 227], [6043, 6043, 53*w + 213], [6047, 6047, -22*w - 27], [6047, 6047, 22*w - 27], [6053, 6053, -21*w - 11], [6053, 6053, 21*w - 11], [6073, 6073, 18*w - 103], [6073, 6073, -18*w - 103], [6079, 6079, -44*w - 145], [6079, 6079, 80*w + 289], [6091, 6091, -9*w - 85], [6091, 6091, 9*w - 85], [6113, 6113, 92*w + 353], [6113, 6113, 32*w + 143], [6151, 6151, 22*w - 25], [6151, 6151, -22*w - 25], [6173, 6173, -21*w - 1], [6173, 6173, 21*w - 1], [6203, 6203, -7*w - 83], [6203, 6203, 7*w - 83], [6211, 6211, 5*w - 81], [6211, 6211, -5*w - 81], [6217, 6217, -16*w - 99], [6217, 6217, 16*w - 99], [6221, 6221, -33*w - 95], [6221, 6221, 33*w - 95], [6229, 6229, 31*w - 85], [6229, 6229, -31*w - 85], [6241, 79, -79], [6247, 6247, -22*w - 23], [6247, 6247, 22*w - 23], [6263, 6263, -36*w - 109], [6263, 6263, 104*w + 381], [6271, 6271, 92*w + 335], [6271, 6271, -40*w - 127], [6277, 6277, -47*w - 157], [6277, 6277, 77*w + 277], [6317, 6317, -23*w - 33], [6317, 6317, 23*w - 33], [6323, 6323, 67*w + 263], [6323, 6323, 47*w + 193], [6329, 6329, -8*w - 85], [6329, 6329, 8*w - 85], [6337, 6337, 4*w - 81], [6337, 6337, -4*w - 81], [6353, 6353, 82*w + 317], [6353, 6353, 38*w + 163], [6359, 6359, 30*w - 79], [6359, 6359, -30*w - 79], [6373, 6373, 91*w + 331], [6373, 6373, -41*w - 131], [6379, 6379, 25*w - 123], [6379, 6379, -25*w - 123], [6389, 6389, 75*w + 269], [6389, 6389, -49*w - 165], [6397, 6397, 103*w + 377], [6397, 6397, -37*w - 113], [6427, 6427, 99*w + 379], [6427, 6427, 31*w + 141], [6449, 6449, 22*w - 115], [6449, 6449, -22*w - 115], [6451, 6451, 29*w + 135], [6451, 6451, 105*w + 401], [6491, 6491, 59*w + 235], [6491, 6491, 55*w + 221], [6521, 6521, -10*w - 89], [6521, 6521, 10*w - 89], [6547, 6547, -w - 81], [6547, 6547, w - 81], [6551, 6551, -22*w - 15], [6551, 6551, 22*w - 15], [6553, 6553, 48*w + 197], [6553, 6553, 68*w + 267], [6563, 6563, 17*w - 103], [6563, 6563, -17*w - 103], [6577, 6577, 24*w - 121], [6577, 6577, -24*w - 121], [6599, 6599, 70*w + 249], [6599, 6599, -54*w - 185], [6607, 6607, 22*w - 13], [6607, 6607, -22*w - 13], [6619, 6619, 73*w + 285], [6619, 6619, 45*w + 187], [6653, 6653, -39*w - 121], [6653, 6653, 101*w + 369], [6659, 6659, -13*w - 95], [6659, 6659, 13*w - 95], [6673, 6673, -8*w - 87], [6673, 6673, 8*w - 87], [6689, 6689, 32*w + 145], [6689, 6689, 100*w + 383], [6709, 6709, -59*w - 205], [6709, 6709, 65*w + 229], [6719, 6719, -60*w - 209], [6719, 6719, 64*w + 225], [6733, 6733, -29*w - 71], [6733, 6733, 29*w - 71], [6763, 6763, -3*w - 83], [6763, 6763, 3*w - 83], [6781, 6781, 23*w - 25], [6781, 6781, -23*w - 25], [6823, 6823, 86*w + 311], [6823, 6823, -46*w - 151], [6827, 6827, -19*w - 109], [6827, 6827, 19*w - 109], [6833, 6833, 2*w - 83], [6833, 6833, -2*w - 83], [6841, 6841, 84*w + 325], [6841, 6841, 40*w + 171], [6857, 6857, 46*w + 191], [6857, 6857, 74*w + 289], [6863, 6863, 26*w - 51], [6863, 6863, -26*w - 51], [6883, 6883, -7*w - 87], [6883, 6883, 7*w - 87], [6889, 83, -83], [6899, 6899, 65*w + 257], [6899, 6899, 53*w + 215], [6949, 6949, 35*w - 101], [6949, 6949, -35*w - 101], [6991, 6991, -38*w - 115], [6991, 6991, 110*w + 403], [7001, 7001, 4*w - 85], [7001, 7001, -4*w - 85], [7013, 7013, -29*w - 69], [7013, 7013, 29*w - 69], [7043, 7043, -13*w - 97], [7043, 7043, 13*w - 97], [7057, 7057, 14*w - 99], [7057, 7057, -14*w - 99], [7069, 7069, -25*w - 41], [7069, 7069, 25*w - 41], [7103, 7103, -24*w - 31], [7103, 7103, 24*w - 31], [7121, 7121, 80*w + 311], [7121, 7121, 44*w + 185], [7159, 7159, 34*w - 95], [7159, 7159, -34*w - 95], [7177, 7177, -26*w - 129], [7177, 7177, 26*w - 129], [7193, 7193, 62*w + 247], [7193, 7193, 58*w + 233], [7211, 7211, -w - 85], [7211, 7211, w - 85], [7213, 7213, -31*w - 79], [7213, 7213, 31*w - 79], [7219, 7219, -5*w - 87], [7219, 7219, 5*w - 87], [7229, 7229, -25*w - 39], [7229, 7229, 25*w - 39], [7237, 7237, 23*w - 13], [7237, 7237, -23*w - 13], [7331, 7331, -11*w - 95], [7331, 7331, 11*w - 95], [7349, 7349, 35*w - 99], [7349, 7349, -35*w - 99], [7393, 7393, 12*w - 97], [7393, 7393, -12*w - 97], [7417, 7417, -6*w - 89], [7417, 7417, 6*w - 89], [7457, 7457, 14*w - 101], [7457, 7457, -14*w - 101], [7459, 7459, 15*w - 103], [7459, 7459, -15*w - 103], [7499, 7499, 35*w + 157], [7499, 7499, 103*w + 395], [7517, 7517, -47*w - 153], [7517, 7517, 93*w + 337], [7529, 7529, 40*w + 173], [7529, 7529, 92*w + 355], [7547, 7547, 29*w + 139], [7547, 7547, 121*w + 461], [7549, 7549, 29*w - 65], [7549, 7549, -29*w - 65], [7559, 7559, -30*w - 71], [7559, 7559, 30*w - 71], [7561, 7561, 24*w - 125], [7561, 7561, -24*w - 125], [7573, 7573, -61*w - 211], [7573, 7573, 71*w + 251], [7591, 7591, -62*w - 215], [7591, 7591, 70*w + 247], [7603, 7603, 87*w + 337], [7603, 7603, 43*w + 183], [7607, 7607, 92*w + 333], [7607, 7607, -48*w - 157], [7621, 7621, 67*w + 235], [7621, 7621, -65*w - 227], [7673, 7673, 38*w + 167], [7673, 7673, 98*w + 377], [7681, 7681, 64*w + 255], [7681, 7681, 60*w + 241], [7703, 7703, 24*w - 19], [7703, 7703, -24*w - 19], [7717, 7717, 37*w + 107], [7717, 7717, -127*w - 467], [7723, 7723, 23*w - 123], [7723, 7723, -23*w - 123], [7727, 7727, -28*w - 57], [7727, 7727, 28*w - 57], [7741, 7741, -35*w - 97], [7741, 7741, 35*w - 97], [7753, 7753, -8*w - 93], [7753, 7753, 8*w - 93], [7759, 7759, -40*w - 121], [7759, 7759, 116*w + 425], [7789, 7789, 25*w - 31], [7789, 7789, -25*w - 31], [7793, 7793, 28*w - 137], [7793, 7793, -28*w - 137], [7829, 7829, -31*w - 75], [7829, 7829, 31*w - 75], [7841, 7841, 110*w + 421], [7841, 7841, 34*w + 155], [7853, 7853, -51*w - 169], [7853, 7853, 89*w + 321], [7883, 7883, 83*w + 323], [7883, 7883, 47*w + 197], [7901, 7901, -45*w - 143], [7901, 7901, 103*w + 375], [7907, 7907, -w - 89], [7907, 7907, w - 89], [7921, 89, -89], [7927, 7927, 88*w + 317], [7927, 7927, -52*w - 173], [7951, 7951, 28*w - 55], [7951, 7951, -28*w - 55], [7963, 7963, -7*w - 93], [7963, 7963, 7*w - 93], [8009, 8009, 10*w - 97], [8009, 8009, -10*w - 97], [8017, 8017, 74*w + 291], [8017, 8017, 54*w + 221], [8039, 8039, -24*w - 5], [8039, 8039, 24*w - 5], [8053, 8053, -29*w - 61], [8053, 8053, 29*w - 61], [8059, 8059, 37*w + 165], [8059, 8059, 105*w + 403], [8069, 8069, -39*w - 115], [8069, 8069, 125*w + 459], [8089, 8089, -20*w - 117], [8089, 8089, 20*w - 117], [8111, 8111, -30*w - 67], [8111, 8111, 30*w - 67], [8167, 8167, -28*w - 53], [8167, 8167, 28*w - 53], [8171, 8171, 19*w - 115], [8171, 8171, -19*w - 115], [8219, 8219, 23*w - 125], [8219, 8219, -23*w - 125], [8221, 8221, -25*w - 23], [8221, 8221, 25*w - 23], [8231, 8231, 100*w + 363], [8231, 8231, -48*w - 155], [8233, 8233, -18*w - 113], [8233, 8233, 18*w - 113], [8237, 8237, -57*w - 193], [8237, 8237, 83*w + 297], [8243, 8243, -13*w - 103], [8243, 8243, 13*w - 103], [8263, 8263, -34*w - 89], [8263, 8263, 34*w - 89], [8287, 8287, 82*w + 293], [8287, 8287, -58*w - 197], [8293, 8293, -29*w - 59], [8293, 8293, 29*w - 59], [8297, 8297, 16*w - 109], [8297, 8297, -16*w - 109], [8353, 8353, -22*w - 123], [8353, 8353, 22*w - 123], [8369, 8369, 80*w + 313], [8369, 8369, 52*w + 215], [8387, 8387, 71*w + 281], [8387, 8387, 59*w + 239], [8389, 8389, -25*w - 19], [8389, 8389, 25*w - 19], [8431, 8431, 98*w + 355], [8431, 8431, -50*w - 163], [8443, 8443, 67*w + 267], [8443, 8443, 63*w + 253], [8447, 8447, -62*w - 213], [8447, 8447, 78*w + 277], [8461, 8461, -25*w - 17], [8461, 8461, 25*w - 17], [8467, 8467, 21*w - 121], [8467, 8467, -21*w - 121], [8501, 8501, 35*w - 93], [8501, 8501, -35*w - 93], [8513, 8513, 8*w - 97], [8513, 8513, -8*w - 97], [8521, 8521, -6*w - 95], [8521, 8521, 6*w - 95], [8537, 8537, 56*w + 229], [8537, 8537, 76*w + 299], [8543, 8543, 74*w + 261], [8543, 8543, -66*w - 229], [8563, 8563, -27*w - 137], [8563, 8563, 27*w - 137], [8573, 8573, 71*w + 249], [8573, 8573, -69*w - 241], [8581, 8581, -25*w - 13], [8581, 8581, 25*w - 13], [8599, 8599, 110*w + 401], [8599, 8599, -46*w - 145], [8623, 8623, -26*w - 29], [8623, 8623, 26*w - 29], [8629, 8629, 25*w - 11], [8629, 8629, -25*w - 11], [8669, 8669, 25*w - 9], [8669, 8669, -25*w - 9], [8681, 8681, 50*w + 209], [8681, 8681, 86*w + 335], [8689, 8689, -18*w - 115], [8689, 8689, 18*w - 115], [8693, 8693, -31*w - 69], [8693, 8693, 31*w - 69], [8731, 8731, 15*w - 109], [8731, 8731, -15*w - 109], [8737, 8737, -16*w - 111], [8737, 8737, 16*w - 111], [8741, 8741, 25*w - 3], [8741, 8741, -25*w - 3], [8747, 8747, 131*w + 499], [8747, 8747, 31*w + 149], [8761, 8761, -26*w - 135], [8761, 8761, 26*w - 135], [8779, 8779, 33*w + 155], [8779, 8779, 125*w + 477], [8783, 8783, 94*w + 339], [8783, 8783, -54*w - 179], [8803, 8803, 77*w + 303], [8803, 8803, 57*w + 233], [8837, 8837, 27*w - 37], [8837, 8837, -27*w - 37], [8839, 8839, 26*w - 25], [8839, 8839, -26*w - 25], [8849, 8849, 22*w - 125], [8849, 8849, -22*w - 125], [8861, 8861, 93*w + 335], [8861, 8861, -55*w - 183], [8893, 8893, -41*w - 121], [8893, 8893, 131*w + 481], [8929, 8929, 40*w + 177], [8929, 8929, 108*w + 415], [8951, 8951, -28*w - 45], [8951, 8951, 28*w - 45], [8969, 8969, 2*w - 95], [8969, 8969, -2*w - 95], [8971, 8971, 69*w + 275], [8971, 8971, 65*w + 261], [9007, 9007, 32*w - 73], [9007, 9007, -32*w - 73], [9011, 9011, -w - 95], [9011, 9011, w - 95], [9029, 9029, 119*w + 435], [9029, 9029, -45*w - 139], [9041, 9041, 20*w - 121], [9041, 9041, -20*w - 121], [9059, 9059, -5*w - 97], [9059, 9059, 5*w - 97], [9067, 9067, -9*w - 101], [9067, 9067, 9*w - 101], [9103, 9103, -26*w - 19], [9103, 9103, 26*w - 19], [9127, 9127, 28*w - 43], [9127, 9127, -28*w - 43], [9133, 9133, 89*w + 319], [9133, 9133, -59*w - 199], [9137, 9137, -14*w - 109], [9137, 9137, 14*w - 109], [9173, 9173, -29*w - 51], [9173, 9173, 29*w - 51], [9209, 9209, -10*w - 103], [9209, 9209, 10*w - 103], [9227, 9227, 41*w + 181], [9227, 9227, 109*w + 419], [9239, 9239, -26*w - 15], [9239, 9239, 26*w - 15], [9241, 9241, 70*w + 279], [9241, 9241, 66*w + 265], [9283, 9283, 3*w - 97], [9283, 9283, -3*w - 97], [9341, 9341, -63*w - 215], [9341, 9341, 85*w + 303], [9343, 9343, 26*w - 11], [9343, 9343, -26*w - 11], [9377, 9377, 104*w + 401], [9377, 9377, 44*w + 191], [9397, 9397, -53*w - 173], [9397, 9397, 103*w + 373], [9403, 9403, 133*w + 507], [9403, 9403, 33*w + 157], [9409, 97, -97], [9413, 9413, 39*w - 109], [9413, 9413, -39*w - 109], [9419, 9419, 35*w + 163], [9419, 9419, 127*w + 485], [9421, 9421, -65*w - 223], [9421, 9421, 83*w + 295], [9433, 9433, -12*w - 107], [9433, 9433, 12*w - 107], [9439, 9439, 26*w - 5], [9439, 9439, -26*w - 5], [9463, 9463, -26*w - 1], [9463, 9463, 26*w - 1], [9473, 9473, -28*w - 143], [9473, 9473, 28*w - 143], [9511, 9511, -68*w - 235], [9511, 9511, 80*w + 283], [9521, 9521, 50*w + 211], [9521, 9521, 94*w + 365], [9533, 9533, 79*w + 279], [9533, 9533, -69*w - 239], [9551, 9551, -70*w - 243], [9551, 9551, 78*w + 275], [9587, 9587, -19*w - 121], [9587, 9587, 19*w - 121], [9601, 9601, -30*w - 149], [9601, 9601, 30*w - 149], [9619, 9619, 15*w - 113], [9619, 9619, -15*w - 113], [9623, 9623, 34*w - 81], [9623, 9623, -34*w - 81], [9631, 9631, -40*w - 113], [9631, 9631, 40*w - 113], [9643, 9643, 17*w - 117], [9643, 9643, -17*w - 117], [9677, 9677, 27*w - 23], [9677, 9677, -27*w - 23], [9679, 9679, 100*w + 361], [9679, 9679, -56*w - 185], [9689, 9689, -32*w - 155], [9689, 9689, 32*w - 155], [9697, 9697, -6*w - 101], [9697, 9697, 6*w - 101], [9719, 9719, 114*w + 415], [9719, 9719, -50*w - 159], [9733, 9733, 31*w - 61], [9733, 9733, -31*w - 61], [9739, 9739, 57*w + 235], [9739, 9739, 85*w + 333], [9743, 9743, 126*w + 461], [9743, 9743, -46*w - 141], [9749, 9749, 29*w - 45], [9749, 9749, -29*w - 45], [9769, 9769, 48*w + 205], [9769, 9769, 100*w + 387], [9787, 9787, -w - 99], [9787, 9787, w - 99], [9791, 9791, 30*w - 53], [9791, 9791, -30*w - 53], [9811, 9811, 95*w + 369], [9811, 9811, 51*w + 215], [9851, 9851, 5*w - 101], [9851, 9851, -5*w - 101], [9857, 9857, 26*w - 139], [9857, 9857, -26*w - 139], [9887, 9887, 28*w - 33], [9887, 9887, -28*w - 33], [9901, 9901, -47*w - 145], [9901, 9901, 125*w + 457], [9907, 9907, 61*w + 249], [9907, 9907, 81*w + 319], [9923, 9923, 7*w - 103], [9923, 9923, -7*w - 103], [9967, 9967, -52*w - 167], [9967, 9967, 112*w + 407], [9973, 9973, -31*w - 59], [9973, 9973, 31*w - 59]]; primes := [ideal : I in primesArray]; heckePol := x; K := Rationals(); e := 1; heckeEigenvaluesArray := [0, -2, -2, -4, -2, 2, 2, -2, -2, 0, 0, -6, -6, -8, -8, -2, -2, -10, -10, 6, 6, -4, -4, 2, 2, 2, 2, 10, 10, -18, -18, -2, -2, -20, -20, -18, -18, 6, 6, -2, -2, -2, -2, -4, -4, 22, 22, 0, 0, 14, 14, -18, -18, -10, -10, 8, 8, -18, -18, -30, 14, 14, -28, -28, -14, -14, -14, -14, 18, 18, -10, -10, -34, -8, -8, 2, 2, 0, 0, 6, 6, 30, 30, 36, 36, -6, -6, -34, -34, -6, -6, -10, -10, 0, 0, 10, 10, 22, 22, 20, 20, 14, 14, -30, 38, 38, 26, 26, -38, -38, -16, -16, -2, -2, 30, 30, 12, 12, 6, 6, -34, -34, -2, -2, 22, 22, 42, 42, 24, 24, -12, -12, 6, 6, -18, -18, 54, 54, -18, -18, -6, -6, -22, -22, 14, 14, -36, -36, -22, -26, -26, -34, -34, 36, 36, -38, -38, 38, 38, 14, 14, 58, 58, 30, 30, 20, 20, 54, 54, -34, -34, -34, -34, -6, -6, -42, -42, -34, -34, 40, 40, -30, -30, -52, -52, 46, 46, -18, -18, -38, -38, 64, 64, -54, -54, 14, 14, -26, -26, -34, -34, 50, 50, 12, 12, -40, -40, -10, -10, -42, -42, 64, 64, 14, 14, 14, 14, -34, -34, 62, 62, 12, 12, 26, -12, -12, 30, 30, 28, 28, 26, 26, -2, -2, -8, -8, -6, -6, 12, 12, 54, 54, -20, -20, 52, 52, -64, -64, -22, -22, 38, 38, -74, -74, -42, -42, -2, -2, 70, 70, -46, 22, 22, 50, 50, -2, -2, -50, -50, -76, -76, 10, 10, -18, -18, 32, 32, -12, -12, -34, -34, -2, -2, 4, 4, -66, -66, -66, -66, 64, 64, 14, 14, 6, 6, 26, 26, -66, -66, 50, 50, 14, 14, -56, -56, 30, 30, 86, 86, -46, -46, -22, -22, -42, -42, -54, -54, 30, 30, -64, -64, -70, -70, 56, 56, 74, 74, -42, -42, -2, -2, -2, -2, 18, 18, -24, -24, -82, -82, -22, -22, 24, 24, 48, 48, 30, 30, -14, -14, -34, -34, 94, 94, -70, -70, -58, -58, 52, 52, -58, -58, -6, -6, -78, -78, -36, -36, -58, -58, 82, 82, -32, -32, -62, -62, -42, -42, -46, -46, 10, 10, -80, -80, 42, 42, 54, 54, 30, 30, -66, -66, 60, 60, 30, 30, -70, -94, -94, -50, -50, 62, 62, -98, -98, -52, -52, -12, -12, -90, -90, -18, -18, 14, 14, 30, 30, 36, 36, 30, 30, -62, -62, -72, -72, -34, -34, -2, -2, 74, 74, 76, 76, 34, 34, -14, -14, 48, 48, -18, -18, 38, 38, 36, 36, 86, 86, 34, 34, -58, -58, -2, -2, -70, -70, -42, -42, 2, 2, -2, -2, -10, -10, -16, -16, 82, 82, 98, 98, -10, -10, -48, -48, -104, -104, -18, -18, -100, -100, 58, 58, 78, -2, -2, 44, 44, -34, -34, 6, 6, -34, -34, -18, -18, -116, -116, -58, -58, 64, 64, 58, 58, 24, 24, -44, -44, -22, -22, -2, -2, -50, -50, -10, -10, -104, -104, 82, 82, -78, -78, -90, -90, -6, -6, -90, -90, -114, -114, 114, 114, 94, 94, -12, -12, -26, -26, -66, -66, -58, -58, 76, 76, -56, -56, 90, 90, 74, 74, 64, 64, 30, 30, 34, 34, 12, 12, 30, 30, -106, -106, -102, -102, 30, 30, -104, -104, -34, -34, -74, -74, -18, -18, 42, 42, -18, -18, -34, -34, -82, -82, 30, 30, 44, 44, 62, 62, 118, 118, -2, -2, -98, -98, 26, 26, -42, -42, 12, 12, 2, 2, 94, 94, -78, -78, -2, -2, 78, 78, -34, -34, 132, 132, 12, 12, 8, 8, 62, 62, -14, -14, 70, 70, 112, 112, -114, -114, 10, 10, -14, -14, -2, -2, -132, -132, 62, 62, -16, -16, 90, 90, 8, 8, -60, -60, -30, -30, 110, 110, -52, -52, -34, -34, -4, -4, 68, 68, -98, -98, -34, -34, -26, -26, -46, -46, 62, 62, 88, 88, 2, 98, 98, -32, -32, 30, 30, 94, 94, 106, 106, 94, 94, -66, -66, 30, 30, -14, -14, -6, -6, 70, 70, 50, 54, 54, -20, -20, 94, 94, -78, -78, 80, 80, 90, 90, -92, -92, -66, -66, -34, -34, 14, 14, 70, 70, -68, -68, 26, 26, 14, 14, 104, 104, -54, -54, -98, -98, 114, 114, -12, -12, -8, -8, 94, 94, 74, 74, -106, -106, -10, -10, 8, 8, -66, -66, -50, -50, -8, -8, -26, -26, 30, 30, 42, 42, -54, -54, -82, -82, -12, -12, 110, 110, -74, -74, 92, 92, -10, -10, 150, 150, 118, 118, 82, 82, -112, -112, -18, -18, 10, 10, -48, -48, -78, -78, -66, -66, -132, -132, -114, -114, -102, -102, 134, 134, 90, 90, -146, -146, -74, -74, -94, 140, 140, 116, 116, 48, 48, 38, 38, 38, 38, 22, 22, -54, -54, 94, 94, -30, -30, 52, 52, 94, 94, 50, 50, 78, 78, 110, 110, 18, 18, 130, 130, -82, -82, -102, -102, -114, -114, 86, 86, -44, -44, -34, -34, 14, 14, -98, -98, 60, 60, 152, 152, 58, 58, -42, -42, -50, -50, -130, -130, 34, 34, 22, 22, -80, -80, 14, 14, 98, 98, -106, -106, -4, -4, -110, -110, 30, 30, -50, -50, 78, 78, 24, 24, 70, 70, -130, -146, -146, 94, 94, -56, -56, 26, 26, -66, -66, 102, 102, -66, -66, 142, 142, -144, -144, -78, -78, 52, 52, -38, -38, 74, 74, -38, -38, 30, 30, 22, 22, 22, 22, -26, -26, -162, -162, 118, 118, 146, 146, 26, 26, -34, -34, 62, 62, -166, -166, -98, -98, 78, 78, 26, 26, -26, -26, -4, -4, -38, -38, 22, 22, 92, 92, 142, 142, 68, 68, -74, -74, -134, -134, 62, 62, -44, -44, -82, -82, -126, -126, -24, -24, 102, 102, -114, -114, -56, -56, -50, -50, -14, -14, 134, 134, 98, 98, 150, 150, -54, -54, 78, 78, -26, -26, -174, -108, -108, 56, 56, -150, -150, -70, -70, 62, 62, 76, 76, -130, -130, 58, 58, 158, 158, 122, 122, -120, -120, -132, -132, 90, 90, 162, 162, 142, 142, -4, -4, 94, 94, 102, 102, -114, -114, -148, -148, -80, -80, -34, -34, 138, 138, -66, -66, 66, 66, -66, -66, -90, -90, -136, -136, 74, 74, 96, 96, 70, 70, 38, 38, 94, 94, -162, -162, 122, 122, 110, 110, 96, 96, -74, -74, 102, 102, 158, 158, -140, -140, -104, -104, -114, -114, -50, -50, -102, -102, -98, -98, -146, -146, 10, 10, -2, -2, -130, -130, -126, -126, -66, -66, -126, -126, -24, -24, 22, 22, -66, -66, -20, -20, -98, -98, -58, -58, 38, 38, -34, -34, 180, 180, -18, -18, 50, 50, 40, 40, 78, 78, 30, 30, -66, -66, 166, 166, -78, -78, -56, -56, 44, 44, -154, -154, -174, -174, -10, -10, -114, -114, -30, -30, -44, -44, 14, 14, 110, 110, 6, 6, -64, -64, -30, -30, 38, 38, -6, -6, -190, -66, -66, 10, 10, -10, -10, 122, 122, -144, -144, 132, 132, 66, 66, -116, -116, 114, 114, -186, -186, -8, -8, -34, -34, 2, 2, 70, 70, -60, -60, 96, 96, -118, -118, 30, 30, -8, -8, -86, -86, 98, 98, -108, -108, -82, -82, 186, 186, -120, -120, 6, 6, 14, 14, -6, -6, -48, -48, 78, 78, -14, -14, 30, 30, 32, 32, 70, 70, 158, 158, -114, -114, -8, -8, -74, -74]; 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;