/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([-2, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 4, 2*w]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [5, 5, w^2 - w - 7],\ [11, 11, -w^2 + w + 1],\ [17, 17, -w^2 + w + 3],\ [25, 5, -w^2 - w - 1],\ [27, 3, 3],\ [29, 29, -w^2 + 3*w - 1],\ [37, 37, 3*w^2 - 5*w - 13],\ [41, 41, 2*w - 1],\ [53, 53, 5*w^2 - 9*w - 21],\ [53, 53, 3*w^2 - 5*w - 15],\ [53, 53, w^2 - 3*w - 7],\ [59, 59, w^2 - 3*w - 5],\ [61, 61, 2*w^2 - 4*w - 9],\ [61, 61, 2*w - 7],\ [61, 61, 2*w - 5],\ [67, 67, -w^2 + w - 1],\ [71, 71, -2*w - 5],\ [71, 71, 3*w^2 - 3*w - 19],\ [79, 79, 2*w - 3],\ [83, 83, 2*w^2 - 5],\ [83, 83, w^2 - w - 9],\ [83, 83, -2*w^2 + 4*w + 11],\ [97, 97, 4*w + 3],\ [101, 101, -6*w^2 + 8*w + 35],\ [103, 103, 2*w^2 - 2*w - 7],\ [109, 109, -3*w^2 + 3*w + 17],\ [113, 113, w^2 + 3*w - 1],\ [121, 11, -5*w^2 + 7*w + 25],\ [127, 127, -2*w^2 + 19],\ [127, 127, 2*w^2 - 2*w - 15],\ [127, 127, 3*w^2 - 3*w - 13],\ [137, 137, -4*w^2 + 8*w + 13],\ [139, 139, -2*w^2 + 2*w + 3],\ [151, 151, w^2 + w - 5],\ [157, 157, 2*w^2 - 2*w - 5],\ [163, 163, -w^2 + 3*w - 3],\ [167, 167, 3*w^2 - 5*w - 11],\ [191, 191, -w^2 - w - 3],\ [193, 193, w^2 - 5*w + 7],\ [199, 199, 4*w^2 - 4*w - 25],\ [211, 211, -4*w^2 + 6*w + 25],\ [223, 223, w^2 + 5*w + 7],\ [227, 227, 4*w - 1],\ [229, 229, w^2 - 5*w - 5],\ [241, 241, w^2 + w - 7],\ [257, 257, 2*w^2 - 9],\ [263, 263, 2*w^2 + 2*w - 5],\ [271, 271, w^2 - 3*w - 11],\ [277, 277, 2*w^2 - 6*w - 7],\ [281, 281, w^2 - w - 11],\ [283, 283, 4*w^2 - 6*w - 17],\ [289, 17, 3*w^2 - 5*w - 9],\ [293, 293, 2*w^2 - 8*w - 5],\ [307, 307, 3*w^2 - 7*w - 11],\ [311, 311, 3*w^2 - w - 13],\ [317, 317, 5*w^2 - 9*w - 19],\ [317, 317, -2*w^2 + 6*w + 15],\ [317, 317, w^2 - 7*w - 1],\ [331, 331, w^2 + 3*w - 3],\ [337, 337, 4*w - 11],\ [343, 7, -7],\ [347, 347, -3*w^2 + w + 27],\ [353, 353, -3*w^2 + 9*w + 7],\ [359, 359, -7*w^2 + 11*w + 39],\ [367, 367, 5*w^2 - 9*w - 23],\ [373, 373, 6*w + 5],\ [379, 379, -4*w^2 + 8*w + 17],\ [379, 379, -w^2 - 7*w - 1],\ [379, 379, -5*w^2 + 7*w + 23],\ [397, 397, 7*w^2 - 11*w - 37],\ [397, 397, 3*w^2 - 5*w - 21],\ [397, 397, -3*w^2 - w + 3],\ [401, 401, -12*w^2 + 16*w + 69],\ [419, 419, -10*w^2 + 12*w + 59],\ [419, 419, 2*w^2 - 6*w - 9],\ [419, 419, -5*w^2 + 5*w + 31],\ [431, 431, 5*w^2 - 13*w - 11],\ [433, 433, 2*w^2 - 2*w - 17],\ [439, 439, 2*w^2 - 11],\ [439, 439, w^2 + w - 15],\ [439, 439, -w^2 - 5*w + 1],\ [443, 443, -2*w^2 - 2*w + 25],\ [449, 449, -w^2 + 3*w - 5],\ [457, 457, 2*w^2 - 17],\ [463, 463, 7*w^2 - 13*w - 29],\ [467, 467, -2*w^2 - 4*w + 3],\ [487, 487, 2*w^2 - 6*w - 13],\ [487, 487, -6*w^2 + 8*w + 37],\ [487, 487, -3*w^2 + w + 7],\ [491, 491, -4*w^2 + 8*w + 7],\ [503, 503, -3*w^2 + 3*w + 5],\ [509, 509, 6*w^2 - 10*w - 31],\ [521, 521, -5*w^2 + 5*w + 29],\ [521, 521, 6*w^2 - 6*w - 41],\ [521, 521, 4*w^2 - 6*w - 15],\ [523, 523, -6*w^2 + 10*w + 33],\ [541, 541, 6*w^2 - 10*w - 25],\ [541, 541, 3*w^2 - 3*w - 7],\ [541, 541, -w^2 - w - 5],\ [557, 557, -3*w^2 + 3*w + 23],\ [563, 563, 5*w^2 - 11*w - 17],\ [571, 571, 8*w + 5],\ [571, 571, 2*w^2 - 4*w - 17],\ [571, 571, 6*w^2 - 12*w - 23],\ [577, 577, -5*w^2 + 9*w + 25],\ [577, 577, 4*w^2 - 8*w - 19],\ [577, 577, -10*w^2 + 16*w + 49],\ [587, 587, 8*w^2 - 16*w - 27],\ [587, 587, 2*w^2 - 15],\ [587, 587, 4*w - 9],\ [601, 601, -13*w^2 + 19*w + 71],\ [607, 607, -3*w^2 - 9*w - 1],\ [607, 607, 3*w^2 - 7*w - 15],\ [607, 607, 2*w^2 + 6*w + 7],\ [613, 613, -5*w^2 + 11*w + 9],\ [619, 619, -w^2 - 9*w - 5],\ [631, 631, -w^2 + w - 5],\ [631, 631, w^2 - 7*w - 13],\ [631, 631, -11*w^2 + 15*w + 57],\ [647, 647, w^2 - w - 13],\ [653, 653, 4*w^2 - 6*w - 27],\ [653, 653, 4*w - 7],\ [653, 653, -6*w + 1],\ [673, 673, -7*w^2 + 7*w + 45],\ [677, 677, 2*w^2 + 3],\ [683, 683, -3*w^2 + 11*w + 7],\ [691, 691, -2*w - 9],\ [719, 719, -10*w^2 + 12*w + 55],\ [751, 751, 4*w^2 - 6*w - 13],\ [751, 751, -4*w^2 + 12*w + 9],\ [751, 751, 4*w^2 - 2*w - 19],\ [761, 761, 11*w^2 - 21*w - 41],\ [769, 769, -2*w^2 + 4*w - 3],\ [797, 797, 15*w^2 - 19*w - 85],\ [809, 809, 2*w - 11],\ [811, 811, 4*w^2 + 2*w - 11],\ [811, 811, -4*w^2 + 2*w + 31],\ [811, 811, 3*w^2 + w - 11],\ [821, 821, 4*w^2 + 1],\ [827, 827, -2*w^2 + 2*w - 3],\ [829, 829, -w^2 - 5*w - 9],\ [839, 839, -4*w^2 + 3],\ [841, 29, w^2 - 5*w - 15],\ [853, 853, w^2 - 7*w - 11],\ [859, 859, -w^2 + 7*w + 9],\ [877, 877, 6*w^2 - 8*w - 27],\ [883, 883, 3*w^2 - w - 17],\ [887, 887, -10*w^2 + 14*w + 59],\ [887, 887, -4*w - 11],\ [887, 887, w^2 + 3*w - 7],\ [907, 907, -15*w^2 + 19*w + 83],\ [929, 929, -8*w - 7],\ [929, 929, -8*w^2 + 10*w + 39],\ [929, 929, -5*w^2 + 7*w + 33],\ [937, 937, -2*w^2 + 6*w - 5],\ [941, 941, -4*w^2 + 4*w + 5],\ [947, 947, 3*w^2 - 5*w - 23],\ [947, 947, 4*w^2 + 4*w + 3],\ [947, 947, w^2 + 3*w - 21],\ [953, 953, 2*w^2 - 8*w - 9],\ [953, 953, -w^2 + 7*w - 3],\ [953, 953, 7*w^2 - 9*w - 33],\ [977, 977, -2*w^2 + 10*w + 7],\ [977, 977, -w^2 - 9*w - 1],\ [977, 977, 2*w^2 + 4*w - 5],\ [983, 983, 9*w^2 - 19*w - 27],\ [997, 997, -w^2 + 9*w - 17]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 1, 2, 4, 6, -2, -4, -6, 2, -2, -10, -10, -10, -4, 10, -2, -6, -4, 8, 8, 0, -12, -4, -4, -10, 6, 8, -18, -14, 14, 16, 0, 16, 10, 12, -8, -2, 12, 8, -16, 22, -8, -12, 0, -4, -26, -14, 6, -24, 16, 18, 30, 28, -10, -14, 20, 24, -6, -22, -2, -20, -26, -8, 20, -30, 8, 16, 2, -28, 28, 20, 14, 26, -6, 18, 12, 28, 36, 16, 18, -8, 24, -40, 36, 6, 30, -16, 28, 8, 40, -40, 12, -8, -22, 10, 42, 42, -44, 30, -38, -22, 10, -12, 20, -4, -28, 2, 22, 38, 12, -12, 20, -38, -32, 0, -32, 34, 12, -8, 24, 8, -40, -18, 26, -6, 34, 6, 12, -12, 16, 16, -48, -32, -34, 2, -2, 42, 36, 52, -20, 54, -36, 26, 40, -34, 22, -36, -18, -44, 56, 24, 24, -20, 6, 34, 6, 42, -18, 12, 52, -52, 46, -6, -34, -10, 18, 38, -24, -26] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, w])] = 1 AL_eigenvalues[ZF.ideal([2, 2, w + 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]