/* 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([3, 6, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7, 7, -w^3 + 5*w - 2]) primes_array = [ [3, 3, w],\ [3, 3, w - 1],\ [7, 7, w + 1],\ [7, 7, -w^3 + 5*w - 2],\ [13, 13, -w^3 + 5*w + 1],\ [16, 2, 2],\ [29, 29, w^3 + w^2 - 5*w - 1],\ [31, 31, -w^3 + 4*w - 1],\ [41, 41, w^3 - 6*w + 1],\ [43, 43, w^3 + w^2 - 6*w - 1],\ [47, 47, -w^3 + 2*w^2 + 5*w - 11],\ [49, 7, w^2 + w - 1],\ [59, 59, w^3 - w^2 - 6*w + 4],\ [59, 59, w^2 - w - 4],\ [67, 67, 2*w^3 + w^2 - 9*w - 2],\ [71, 71, -3*w^3 - w^2 + 16*w + 5],\ [71, 71, 2*w - 1],\ [73, 73, w^3 - 6*w + 4],\ [83, 83, w^3 - w^2 - 3*w + 4],\ [103, 103, w^3 + w^2 - 4*w - 5],\ [103, 103, 2*w^3 + w^2 - 10*w - 1],\ [107, 107, 2*w^3 + w^2 - 9*w - 5],\ [107, 107, 2*w^2 + w - 11],\ [109, 109, w^2 + 2*w - 4],\ [113, 113, -w^3 - 2*w^2 + 5*w + 8],\ [127, 127, -w^3 + 4*w - 5],\ [127, 127, -2*w^3 + 3*w^2 + 11*w - 19],\ [131, 131, w^2 - w - 5],\ [131, 131, 2*w^3 - 3*w^2 - 12*w + 17],\ [137, 137, w^3 - w^2 - 7*w + 8],\ [149, 149, w^3 + 2*w^2 - 6*w - 8],\ [163, 163, w^3 - 7*w - 1],\ [167, 167, w^2 + 2*w - 7],\ [173, 173, 2*w^2 - w - 5],\ [173, 173, w^2 - w - 7],\ [173, 173, 2*w^2 + w - 5],\ [179, 179, 2*w^2 - 7],\ [191, 191, -2*w^3 + 11*w - 4],\ [191, 191, 2*w^3 - 11*w - 1],\ [199, 199, -2*w^3 + w^2 + 11*w - 5],\ [199, 199, w^3 + 2*w^2 - 6*w - 4],\ [211, 211, 2*w^2 + 2*w - 5],\ [227, 227, 3*w^3 - 5*w^2 - 16*w + 29],\ [229, 229, w^3 - 2*w^2 - 6*w + 8],\ [233, 233, 2*w^3 + w^2 - 9*w + 2],\ [241, 241, 2*w^3 - w^2 - 11*w + 11],\ [241, 241, w^3 + 2*w^2 - 6*w - 5],\ [251, 251, -w^3 - 2*w^2 + 3*w + 7],\ [257, 257, -3*w^2 + 4*w + 4],\ [263, 263, w^3 - 2*w^2 - 5*w + 7],\ [269, 269, w^3 + 2*w^2 - 5*w - 5],\ [271, 271, w^3 - 4*w - 4],\ [271, 271, 4*w^3 - 5*w^2 - 22*w + 28],\ [277, 277, -w^3 + 3*w - 4],\ [277, 277, 2*w^3 - 2*w^2 - 11*w + 10],\ [283, 283, -2*w^3 + 8*w + 1],\ [283, 283, 2*w^3 + w^2 - 12*w - 8],\ [293, 293, 2*w^3 - w^2 - 9*w + 7],\ [293, 293, 2*w^3 - 9*w + 2],\ [307, 307, w^2 + 3*w - 8],\ [307, 307, -2*w^3 + 10*w - 7],\ [313, 313, -w^3 + w^2 + w - 2],\ [317, 317, -2*w^3 + w^2 + 10*w - 4],\ [331, 331, -2*w^3 - 2*w^2 + 9*w - 1],\ [331, 331, 3*w^2 - w - 13],\ [331, 331, -w^3 + 7*w - 2],\ [331, 331, w^2 - 2*w - 4],\ [337, 337, -3*w^3 - 3*w^2 + 16*w + 13],\ [347, 347, 3*w^3 + 2*w^2 - 17*w - 11],\ [349, 349, 3*w - 1],\ [349, 349, 2*w^3 - 4*w^2 - 12*w + 19],\ [353, 353, -w^3 + w^2 + 6*w - 2],\ [353, 353, w^3 + 3*w^2 - 3*w - 8],\ [359, 359, 2*w^2 + w - 4],\ [367, 367, -w^3 + w^2 + 5*w - 1],\ [379, 379, -w^3 + 2*w - 2],\ [383, 383, w - 5],\ [389, 389, 4*w^3 + 3*w^2 - 19*w - 10],\ [397, 397, w^3 + 3*w^2 - 2*w - 10],\ [401, 401, -w^3 + w^2 + 7*w - 5],\ [409, 409, w^3 - 2*w^2 - 5*w + 14],\ [409, 409, -2*w^3 - 3*w^2 + 11*w + 11],\ [419, 419, w^3 + w^2 - 8*w - 4],\ [421, 421, -2*w^3 + w^2 + 7*w - 5],\ [421, 421, -w^3 - w^2 + 7*w + 5],\ [431, 431, w^3 + w^2 - 2*w - 5],\ [449, 449, -2*w^3 + 2*w^2 + 9*w - 7],\ [449, 449, -w^3 + w^2 + 6*w + 1],\ [457, 457, 3*w^3 - w^2 - 16*w + 10],\ [457, 457, 2*w^3 + 3*w^2 - 8*w - 7],\ [461, 461, 3*w^3 - 2*w^2 - 15*w + 13],\ [461, 461, 4*w^2 + w - 19],\ [467, 467, -2*w^3 - 3*w^2 + 10*w + 5],\ [479, 479, 2*w^3 + w^2 - 10*w - 7],\ [479, 479, w^3 + 2*w^2 - 6*w - 10],\ [479, 479, 3*w^3 + 3*w^2 - 14*w - 8],\ [479, 479, 2*w^3 - 2*w^2 - 9*w + 13],\ [491, 491, w^2 + 3*w - 2],\ [491, 491, 2*w^2 + 3*w - 7],\ [499, 499, -2*w^3 - 2*w^2 + 10*w + 11],\ [499, 499, w^3 + w^2 - 3*w - 7],\ [503, 503, w^3 - w^2 - 6*w + 1],\ [509, 509, -3*w^3 + 2*w^2 + 16*w - 11],\ [523, 523, 2*w^2 + 2*w - 11],\ [529, 23, 3*w^3 + w^2 - 13*w + 2],\ [529, 23, 4*w^3 - 3*w^2 - 21*w + 22],\ [541, 541, -3*w^3 + 16*w - 5],\ [563, 563, 3*w^3 - 17*w + 1],\ [563, 563, 3*w^3 + 3*w^2 - 15*w - 5],\ [571, 571, w^3 + 2*w^2 - 7*w - 7],\ [577, 577, 5*w^3 + 2*w^2 - 26*w - 4],\ [577, 577, 3*w^3 + 3*w^2 - 15*w - 10],\ [587, 587, -w^3 + w^2 + 5*w - 10],\ [587, 587, -w^3 + 8*w - 5],\ [599, 599, 2*w^3 + w^2 - 14*w + 4],\ [599, 599, -2*w^2 + 13],\ [607, 607, -2*w^3 - w^2 + 11*w - 1],\ [617, 617, -3*w^3 - 2*w^2 + 17*w + 10],\ [617, 617, 2*w^3 - w^2 - 8*w + 5],\ [625, 5, -5],\ [643, 643, 2*w^3 + 2*w^2 - 8*w - 7],\ [659, 659, 2*w^3 - w^2 - 12*w + 7],\ [661, 661, w^3 + 3*w^2 - 4*w - 11],\ [683, 683, w^3 - 8*w - 1],\ [701, 701, -w^3 + 2*w^2 + w + 2],\ [709, 709, -w^3 + 2*w^2 + 4*w - 4],\ [709, 709, 3*w^3 - w^2 - 14*w + 10],\ [727, 727, w^3 - 4*w - 5],\ [733, 733, 2*w^2 - w - 11],\ [739, 739, 5*w^3 - 4*w^2 - 26*w + 29],\ [761, 761, 2*w^3 - w^2 - 7*w + 7],\ [761, 761, 2*w^3 + 2*w^2 - 10*w - 1],\ [769, 769, w^3 + w^2 - 5*w - 8],\ [773, 773, -2*w^3 - 3*w^2 + 11*w + 14],\ [797, 797, -2*w^3 - 3*w^2 + 5*w + 8],\ [797, 797, 2*w^3 + w^2 - 12*w + 2],\ [809, 809, 3*w^3 - 14*w + 1],\ [811, 811, -3*w^3 - w^2 + 13*w - 1],\ [821, 821, -3*w - 4],\ [821, 821, 5*w^3 - 4*w^2 - 26*w + 26],\ [823, 823, -3*w^3 - 2*w^2 + 10*w + 5],\ [823, 823, w^3 - 2*w^2 - 8*w + 7],\ [829, 829, w^3 + 2*w^2 - 2*w - 8],\ [853, 853, -4*w^3 + 5*w^2 + 23*w - 29],\ [853, 853, 4*w^3 - 21*w + 1],\ [863, 863, w^3 + 3*w^2 - 7*w - 11],\ [863, 863, 4*w^3 - w^2 - 21*w + 11],\ [877, 877, w^3 + 3*w^2 - 4*w - 10],\ [877, 877, w^3 + 3*w^2 - 8*w - 1],\ [881, 881, -w^3 + w^2 + 3*w - 7],\ [883, 883, 3*w^2 - 11],\ [883, 883, -w^3 + w^2 + 9*w - 11],\ [887, 887, -3*w^3 + w^2 + 13*w - 10],\ [907, 907, w^3 + 3*w^2 - 4*w - 8],\ [907, 907, 3*w^3 + 4*w^2 - 11*w - 10],\ [911, 911, -3*w^3 + 14*w - 4],\ [911, 911, 2*w^3 + 3*w^2 - 9*w - 7],\ [929, 929, 3*w^3 + w^2 - 16*w + 1],\ [947, 947, 2*w^3 + 3*w^2 - 8*w - 11],\ [947, 947, -2*w^3 + 2*w^2 + 13*w - 8],\ [971, 971, 3*w^3 + 4*w^2 - 12*w - 8],\ [983, 983, w^3 - 4*w^2 - 6*w + 14],\ [991, 991, w^3 - 2*w^2 - 8*w + 11],\ [997, 997, -6*w^3 - 5*w^2 + 29*w + 16]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, 2, -1, 1, -4, 6, -2, 9, 10, -3, 4, 3, 12, -5, 9, 12, -8, -3, -4, -5, -6, -18, -11, 12, 2, -10, 9, -12, 3, 0, 13, -9, -15, -24, -12, 6, -21, -6, 10, -16, -5, 3, 10, 6, 22, 8, 21, 0, 0, 24, 8, 16, -4, -2, 28, -4, 12, -30, -4, 16, -25, 0, 31, 17, -8, 8, -22, 27, 10, 22, -18, 36, 15, 19, 32, 21, 30, 2, 6, 11, 14, -9, -2, 8, 9, 6, -24, -2, -22, -27, -3, 42, 0, 6, 6, 12, 39, 24, 5, -16, 12, 24, -4, 40, -26, -38, 36, 24, 2, -2, 38, 30, 30, 12, -21, 40, -12, -15, 32, -4, 6, 5, -30, 6, 1, 37, 5, 41, 19, -3, 0, -25, -12, -6, 27, -39, -17, 6, -42, 23, 31, -4, -26, 46, 33, 6, -52, -2, 18, -34, -2, 12, 53, -52, 42, 57, -54, -45, -51, -36, 0, 40, -7] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7, 7, -w^3 + 5*w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]