/* 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([-35, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([14, 14, w - 7]) primes_array = [ [2, 2, w + 1],\ [5, 5, w],\ [7, 7, w],\ [9, 3, 3],\ [13, 13, w + 3],\ [13, 13, w + 10],\ [17, 17, w + 1],\ [17, 17, w + 16],\ [19, 19, w + 4],\ [19, 19, -w + 4],\ [23, 23, w + 9],\ [23, 23, w + 14],\ [29, 29, -w - 8],\ [29, 29, w - 8],\ [31, 31, -w - 2],\ [31, 31, w - 2],\ [43, 43, w + 11],\ [43, 43, w + 32],\ [59, 59, 2*w - 9],\ [59, 59, -2*w - 9],\ [67, 67, w + 13],\ [67, 67, w + 54],\ [73, 73, w + 20],\ [73, 73, w + 53],\ [97, 97, w + 36],\ [97, 97, w + 61],\ [107, 107, w + 28],\ [107, 107, w + 79],\ [109, 109, -w - 12],\ [109, 109, w - 12],\ [121, 11, -11],\ [127, 127, w + 17],\ [127, 127, w + 110],\ [131, 131, 2*w - 3],\ [131, 131, -2*w - 3],\ [139, 139, 2*w - 1],\ [139, 139, -2*w - 1],\ [149, 149, 2*w - 17],\ [149, 149, -2*w - 17],\ [157, 157, w + 52],\ [157, 157, w + 105],\ [163, 163, w + 19],\ [163, 163, w + 144],\ [173, 173, w + 30],\ [173, 173, w + 143],\ [199, 199, -5*w - 26],\ [199, 199, 5*w - 26],\ [251, 251, 3*w - 8],\ [251, 251, -3*w - 8],\ [257, 257, w + 99],\ [257, 257, w + 158],\ [263, 263, w + 78],\ [263, 263, w + 185],\ [271, 271, -4*w - 17],\ [271, 271, 4*w - 17],\ [281, 281, -5*w - 34],\ [281, 281, 5*w - 34],\ [293, 293, w + 62],\ [293, 293, w + 231],\ [311, 311, 3*w - 2],\ [311, 311, -3*w - 2],\ [313, 313, w + 40],\ [313, 313, w + 273],\ [347, 347, w + 27],\ [347, 347, w + 320],\ [353, 353, w + 68],\ [353, 353, w + 285],\ [389, 389, 2*w - 23],\ [389, 389, -2*w - 23],\ [397, 397, w + 157],\ [397, 397, w + 240],\ [401, 401, -4*w - 31],\ [401, 401, 4*w - 31],\ [419, 419, -7*w - 36],\ [419, 419, 7*w - 36],\ [421, 421, -6*w - 41],\ [421, 421, 6*w - 41],\ [433, 433, w + 86],\ [433, 433, w + 347],\ [439, 439, 4*w - 11],\ [439, 439, -4*w - 11],\ [443, 443, w + 56],\ [443, 443, w + 387],\ [449, 449, -w - 22],\ [449, 449, w - 22],\ [463, 463, w + 31],\ [463, 463, w + 432],\ [479, 479, -4*w - 9],\ [479, 479, 4*w - 9],\ [487, 487, w + 106],\ [487, 487, w + 381],\ [541, 541, -w - 24],\ [541, 541, w - 24],\ [547, 547, w + 242],\ [547, 547, w + 305],\ [569, 569, 5*w - 38],\ [569, 569, -5*w - 38],\ [577, 577, w + 261],\ [577, 577, w + 316],\ [593, 593, w + 88],\ [593, 593, w + 505],\ [619, 619, -5*w - 16],\ [619, 619, 5*w - 16],\ [641, 641, -w - 26],\ [641, 641, w - 26],\ [677, 677, w + 94],\ [677, 677, w + 583],\ [683, 683, w + 214],\ [683, 683, w + 469],\ [691, 691, -7*w - 32],\ [691, 691, 7*w - 32],\ [701, 701, 2*w - 29],\ [701, 701, -2*w - 29],\ [709, 709, -3*w - 32],\ [709, 709, 3*w - 32],\ [719, 719, -9*w - 46],\ [719, 719, 9*w - 46],\ [733, 733, w + 167],\ [733, 733, w + 566],\ [743, 743, w + 39],\ [743, 743, w + 704],\ [773, 773, w + 219],\ [773, 773, w + 554],\ [797, 797, w + 340],\ [797, 797, w + 457],\ [809, 809, 4*w - 37],\ [809, 809, -4*w - 37],\ [811, 811, -5*w - 8],\ [811, 811, 5*w - 8],\ [821, 821, 2*w - 31],\ [821, 821, -2*w - 31],\ [823, 823, w + 41],\ [823, 823, w + 782],\ [827, 827, w + 375],\ [827, 827, w + 452],\ [839, 839, -5*w - 6],\ [839, 839, 5*w - 6],\ [853, 853, w + 366],\ [853, 853, w + 487],\ [857, 857, w + 245],\ [857, 857, w + 612],\ [859, 859, 5*w - 4],\ [859, 859, -5*w - 4],\ [863, 863, w + 335],\ [863, 863, w + 528],\ [883, 883, w + 370],\ [883, 883, w + 513],\ [907, 907, w + 43],\ [907, 907, w + 864],\ [937, 937, w + 413],\ [937, 937, w + 524],\ [947, 947, w + 300],\ [947, 947, w + 647],\ [967, 967, w + 204],\ [967, 967, w + 763],\ [971, 971, 6*w - 17],\ [971, 971, -6*w - 17],\ [997, 997, w + 114],\ [997, 997, w + 883]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 0, 1, -2, -4, -4, 6, 6, 2, 2, 0, 0, -6, -6, -4, -4, 8, 8, -6, -6, -4, -4, 2, 2, -10, -10, 12, 12, 2, 2, -22, -16, -16, 18, 18, 14, 14, -18, -18, -4, -4, -16, -16, -12, -12, 20, 20, -18, -18, 18, 18, 0, 0, -16, -16, -6, -6, 24, 24, -24, -24, -10, -10, -24, -24, 18, 18, 18, 18, 20, 20, -18, -18, 6, 6, -10, -10, -34, -34, 8, 8, -12, -12, 18, 18, 32, 32, -36, -36, -16, -16, 38, 38, 8, 8, 6, 6, 2, 2, -6, -6, 26, 26, -18, -18, -12, -12, -12, -12, -46, -46, 18, 18, -46, -46, 12, 12, -40, -40, 24, 24, 24, 24, -12, -12, 6, 6, 2, 2, 6, 6, -40, -40, -36, -36, 12, 12, 44, 44, -18, -18, 14, 14, -24, -24, 20, 20, 44, 44, 2, 2, 24, 24, 32, 32, -6, -6, 8, 8] 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])] = 1 AL_eigenvalues[ZF.ideal([7, 7, w])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]