/* 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([-89, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, 3]) primes_array = [ [3, 3, w + 1],\ [4, 2, 2],\ [7, 7, w + 3],\ [11, 11, w + 3],\ [11, 11, w + 7],\ [17, 17, w + 8],\ [23, 23, w + 4],\ [23, 23, w + 18],\ [25, 5, 5],\ [29, 29, w + 1],\ [29, 29, w + 27],\ [31, 31, w + 13],\ [31, 31, w + 17],\ [43, 43, -w - 11],\ [43, 43, w - 12],\ [47, 47, -w - 6],\ [47, 47, w - 7],\ [59, 59, -w - 5],\ [59, 59, w - 6],\ [61, 61, w + 16],\ [61, 61, w + 44],\ [67, 67, -w - 12],\ [67, 67, w - 13],\ [71, 71, w + 29],\ [71, 71, w + 41],\ [73, 73, w + 24],\ [73, 73, w + 48],\ [83, 83, -w - 2],\ [83, 83, w - 3],\ [89, 89, -w],\ [89, 89, w - 1],\ [97, 97, w + 19],\ [97, 97, w + 77],\ [101, 101, 2*w - 17],\ [101, 101, -2*w - 15],\ [107, 107, w + 50],\ [107, 107, w + 56],\ [113, 113, w + 36],\ [113, 113, w + 76],\ [127, 127, 2*w - 23],\ [127, 127, 2*w + 21],\ [139, 139, w + 22],\ [139, 139, w + 116],\ [151, 151, -w - 15],\ [151, 151, w - 16],\ [169, 13, -13],\ [181, 181, w + 75],\ [181, 181, w + 105],\ [197, 197, w + 47],\ [197, 197, w + 149],\ [199, 199, w + 38],\ [199, 199, w + 160],\ [233, 233, w + 51],\ [233, 233, w + 181],\ [241, 241, w + 28],\ [241, 241, w + 212],\ [251, 251, -3*w - 22],\ [251, 251, 3*w - 25],\ [257, 257, 2*w - 11],\ [257, 257, -2*w - 9],\ [283, 283, w + 45],\ [283, 283, w + 237],\ [293, 293, 2*w - 9],\ [293, 293, -2*w - 7],\ [313, 313, w + 138],\ [313, 313, w + 174],\ [317, 317, w + 127],\ [317, 317, w + 189],\ [331, 331, -w - 20],\ [331, 331, w - 21],\ [347, 347, w + 62],\ [347, 347, w + 284],\ [353, 353, 2*w - 3],\ [353, 353, -2*w - 1],\ [361, 19, -19],\ [367, 367, w + 34],\ [367, 367, w + 332],\ [373, 373, -w - 21],\ [373, 373, w - 22],\ [383, 383, -3*w - 19],\ [383, 383, 3*w - 22],\ [397, 397, w + 170],\ [397, 397, w + 226],\ [401, 401, w + 96],\ [401, 401, w + 304],\ [421, 421, -5*w - 49],\ [421, 421, 5*w - 54],\ [431, 431, w + 69],\ [431, 431, w + 361],\ [439, 439, w + 37],\ [439, 439, w + 401],\ [449, 449, w + 114],\ [449, 449, w + 334],\ [457, 457, 3*w - 37],\ [457, 457, -3*w - 34],\ [461, 461, 3*w - 20],\ [461, 461, -3*w - 17],\ [463, 463, -w - 23],\ [463, 463, w - 24],\ [467, 467, -4*w - 29],\ [467, 467, 4*w - 33],\ [509, 509, -6*w - 49],\ [509, 509, 6*w - 55],\ [563, 563, 3*w - 17],\ [563, 563, -3*w - 14],\ [587, 587, 4*w - 31],\ [587, 587, -4*w - 27],\ [593, 593, -3*w - 13],\ [593, 593, 3*w - 16],\ [601, 601, w + 43],\ [601, 601, w + 557],\ [607, 607, w + 137],\ [607, 607, w + 469],\ [613, 613, -w - 26],\ [613, 613, w - 27],\ [617, 617, w + 119],\ [617, 617, w + 497],\ [619, 619, w + 66],\ [619, 619, w + 552],\ [631, 631, -6*w - 59],\ [631, 631, 6*w - 65],\ [641, 641, w + 84],\ [641, 641, w + 556],\ [643, 643, w + 141],\ [643, 643, w + 501],\ [647, 647, 3*w - 14],\ [647, 647, -3*w - 11],\ [653, 653, w + 264],\ [653, 653, w + 388],\ [683, 683, w + 270],\ [683, 683, w + 412],\ [691, 691, w + 46],\ [691, 691, w + 644],\ [739, 739, -5*w - 52],\ [739, 739, 5*w - 57],\ [743, 743, w + 297],\ [743, 743, w + 445],\ [757, 757, -3*w - 38],\ [757, 757, 3*w - 41],\ [761, 761, 3*w - 8],\ [761, 761, -3*w - 5],\ [773, 773, -3*w - 4],\ [773, 773, 3*w - 7],\ [787, 787, w + 49],\ [787, 787, w + 737],\ [797, 797, -3*w - 1],\ [797, 797, 3*w - 4],\ [809, 809, w + 302],\ [809, 809, w + 506],\ [811, 811, w + 243],\ [811, 811, w + 567],\ [821, 821, w + 95],\ [821, 821, w + 725],\ [827, 827, w + 242],\ [827, 827, w + 584],\ [853, 853, w + 399],\ [853, 853, w + 453],\ [883, 883, -7*w - 69],\ [883, 883, 7*w - 76],\ [911, 911, w + 254],\ [911, 911, w + 656],\ [919, 919, 3*w - 43],\ [919, 919, -3*w - 40],\ [947, 947, w + 102],\ [947, 947, w + 844],\ [967, 967, -w - 32],\ [967, 967, w - 33],\ [971, 971, -5*w - 33],\ [971, 971, 5*w - 38],\ [997, 997, w + 55],\ [997, 997, w + 941]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 3, 0, 4, -4, 0, -8, 8, -10, 2, -2, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, -4, -4, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20, 20, 2, -2, 16, 16, 0, 0, -24, -24, 26, 0, 0, -26, 26, 0, 0, -22, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34, -34, -36, -36, 4, -4, 0, 0, 38, 0, 0, -22, -22, 0, 0, 0, 0, -34, 34, -26, -26, 32, -32, 0, 0, -2, 2, -6, -6, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -38, -38, 26, -26, 0, 0, 16, 16, 46, -46, 0, 0, 0, 0, -50, 50, -52, 52, 0, 0, 52, 52, 40, -40, 54, 54, 0, 0, 0, 0, 0, 0, 0, 0, -38, 38, 0, 0, -22, 22, 44, -44, 0, 0, -12, -12, 16, -16, 48, 48, 20, -20, -40, -40, 0, 0, 0, 0] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w + 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]