/* 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([-1, -4, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([37, 37, -2*w^2 + 5]) primes_array = [ [2, 2, w + 1],\ [4, 2, -w^2 + w + 3],\ [7, 7, w^2 - 2],\ [13, 13, -w^2 + 2*w + 2],\ [23, 23, -2*w + 1],\ [27, 3, 3],\ [29, 29, -2*w + 3],\ [31, 31, -2*w^2 + 2*w + 3],\ [37, 37, 4*w^2 - 2*w - 13],\ [37, 37, -2*w^2 + 5],\ [37, 37, 2*w^2 - w - 10],\ [41, 41, w^2 - 2*w - 4],\ [47, 47, w - 4],\ [49, 7, 2*w^2 - w - 4],\ [53, 53, 2*w^2 - 2*w - 7],\ [53, 53, 3*w^2 - 2*w - 8],\ [53, 53, 2*w + 5],\ [59, 59, 2*w^2 - 2*w - 9],\ [67, 67, 2*w^2 - 3],\ [73, 73, 2*w^2 + w - 8],\ [79, 79, -2*w^2 - 2*w + 5],\ [89, 89, w^2 + 2*w - 4],\ [101, 101, 3*w^2 - 8],\ [107, 107, 3*w^2 + 2*w - 8],\ [109, 109, w^2 + 2*w - 6],\ [113, 113, 2*w^2 - 3*w - 6],\ [125, 5, -5],\ [127, 127, 4*w - 1],\ [131, 131, 4*w^2 - 3*w - 10],\ [137, 137, 3*w^2 - 2*w - 6],\ [139, 139, -w^2 - 2*w + 10],\ [157, 157, 4*w^2 - 4*w - 11],\ [163, 163, 2*w^2 - 4*w - 5],\ [169, 13, 2*w^2 - 3*w - 10],\ [173, 173, 3*w^2 - 2*w - 4],\ [173, 173, 2*w^2 - 3*w - 8],\ [173, 173, 2*w^2 + 2*w - 7],\ [179, 179, 4*w^2 - 2*w - 11],\ [191, 191, w - 6],\ [193, 193, -w - 6],\ [193, 193, 2*w^2 + 2*w - 11],\ [193, 193, 2*w^2 - w - 12],\ [197, 197, 3*w^2 - 2*w - 16],\ [199, 199, 4*w^2 + w - 10],\ [211, 211, 5*w + 4],\ [223, 223, -2*w + 7],\ [227, 227, -2*w^2 + w - 2],\ [229, 229, 3*w^2 - 4],\ [229, 229, 4*w - 3],\ [239, 239, -2*w - 7],\ [241, 241, -w^2 + 4*w - 6],\ [241, 241, w^2 - 4*w - 6],\ [241, 241, -w^2 + 4*w + 8],\ [251, 251, -3*w - 8],\ [257, 257, -w^2 - 4],\ [263, 263, 3*w^2 + 2*w - 10],\ [269, 269, 4*w^2 - 4*w - 5],\ [281, 281, 2*w^2 - 4*w - 7],\ [283, 283, 4*w^2 - 3*w - 8],\ [313, 313, 4*w^2 - w - 10],\ [317, 317, 5*w - 2],\ [331, 331, -2*w^2 - 2*w + 15],\ [347, 347, -4*w^2 + 4*w + 13],\ [347, 347, 4*w^2 + 2*w - 13],\ [347, 347, 3*w^2 - 4*w - 10],\ [349, 349, 2*w^2 - 4*w - 11],\ [353, 353, w^2 + 4*w - 4],\ [359, 359, 2*w^2 - 5*w - 6],\ [359, 359, 2*w^2 - 4*w - 9],\ [359, 359, 6*w - 1],\ [379, 379, 5*w^2 - 14],\ [383, 383, 5*w^2 - 2*w - 14],\ [383, 383, 4*w^2 + w - 8],\ [383, 383, 3*w^2 + 2*w - 14],\ [389, 389, 4*w^2 - 4*w - 19],\ [419, 419, 2*w^2 + 3*w - 8],\ [439, 439, 4*w^2 - 2*w - 7],\ [439, 439, 4*w^2 + w - 22],\ [439, 439, 9*w^2 - 4*w - 30],\ [443, 443, 2*w^2 + 3*w - 12],\ [443, 443, 3*w^2 - 4*w - 12],\ [443, 443, 3*w^2 - 4*w - 14],\ [449, 449, -6*w^2 + 5*w + 14],\ [449, 449, -2*w^2 - 5*w - 6],\ [449, 449, 4*w^2 - w - 8],\ [461, 461, 5*w^2 - 4*w - 22],\ [461, 461, 5*w - 4],\ [461, 461, 4*w^2 - 2*w - 5],\ [479, 479, w - 8],\ [487, 487, 2*w^2 + 3*w - 10],\ [499, 499, 6*w^2 + 2*w - 15],\ [503, 503, 4*w^2 - 7],\ [503, 503, 4*w^2 + w - 6],\ [503, 503, w^2 + 2*w - 12],\ [509, 509, 4*w^2 - 2*w - 21],\ [509, 509, 2*w^2 - w - 14],\ [509, 509, 6*w^2 - 29],\ [521, 521, 4*w^2 - w - 6],\ [523, 523, 2*w^2 - 5*w - 8],\ [529, 23, 4*w^2 + 2*w - 15],\ [541, 541, 6*w^2 - w - 18],\ [541, 541, 4*w^2 - 5],\ [541, 541, -w^2 + 2*w - 6],\ [547, 547, -4*w^2 + 5*w + 12],\ [563, 563, 4*w^2 - 3*w - 22],\ [571, 571, 4*w^2 + 3*w - 12],\ [577, 577, 2*w - 9],\ [593, 593, 2*w^2 - 7*w + 8],\ [593, 593, 2*w^2 + 4*w - 15],\ [593, 593, -2*w - 9],\ [599, 599, w^2 + 8*w + 6],\ [601, 601, -w^2 - 6],\ [607, 607, 6*w^2 - 4*w - 15],\ [607, 607, 4*w^2 + 2*w - 17],\ [607, 607, 6*w^2 - 7*w - 8],\ [613, 613, -3*w + 10],\ [617, 617, -7*w - 6],\ [617, 617, 2*w^2 + 4*w - 7],\ [617, 617, 7*w^2 - 4*w - 20],\ [619, 619, 3*w^2 - 6*w - 8],\ [619, 619, 5*w^2 - 2*w - 12],\ [619, 619, 3*w^2 + 4*w - 8],\ [643, 643, -5*w^2 + 12],\ [643, 643, 2*w^2 - 2*w - 15],\ [643, 643, 6*w^2 - 6*w - 17],\ [647, 647, w^2 - 2*w - 12],\ [653, 653, 2*w^2 - 4*w + 5],\ [659, 659, 5*w^2 - 4*w - 8],\ [677, 677, 6*w^2 - 2*w - 17],\ [691, 691, 6*w^2 - 5*w - 20],\ [691, 691, 6*w^2 - 3*w - 16],\ [691, 691, -4*w^2 - 3*w + 22],\ [709, 709, -8*w^2 + 6*w + 21],\ [719, 719, w^2 - 4*w - 14],\ [727, 727, 2*w^2 - 15],\ [739, 739, -4*w^2 + 5*w + 20],\ [761, 761, 5*w^2 - 6*w - 14],\ [773, 773, 10*w^2 - 5*w - 32],\ [797, 797, 6*w^2 - 5*w - 12],\ [809, 809, 2*w^2 + 5*w - 6],\ [811, 811, 6*w - 5],\ [823, 823, 5*w^2 - 2*w - 10],\ [827, 827, -2*w^2 - 4*w + 13],\ [829, 829, 4*w^2 + 4*w - 11],\ [839, 839, -6*w^2 - 2*w + 21],\ [841, 29, 2*w^2 + 3*w - 18],\ [853, 853, -2*w^2 - 5],\ [857, 857, -2*w^2 + 2*w - 5],\ [877, 877, 2*w^2 + 4*w - 11],\ [881, 881, 6*w - 7],\ [887, 887, 3*w^2 - 6*w - 10],\ [907, 907, 4*w^2 - 5*w - 18],\ [907, 907, 3*w^2 + 4*w - 10],\ [907, 907, 7*w^2 - 6*w - 22],\ [929, 929, 4*w^2 - 7*w - 10],\ [937, 937, -8*w - 7],\ [947, 947, 5*w^2 - 2*w - 8],\ [961, 31, 7*w^2 - 8*w - 10],\ [967, 967, 2*w^2 - 6*w - 13],\ [967, 967, 7*w^2 + 2*w - 24],\ [967, 967, 6*w^2 - 5*w - 26],\ [977, 977, 2*w^2 - 6*w - 11],\ [977, 977, 6*w^2 + 6*w - 5],\ [977, 977, -w^2 - 2*w - 8],\ [983, 983, 2*w^2 + 6*w - 5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [2, 2, 0, 1, 2, -7, 1, -1, 10, 1, -4, -9, -12, 2, 9, 9, -3, -4, 2, -6, -4, 8, -12, 20, 4, -10, 6, 8, 6, 17, 22, 13, -3, 12, 9, 6, 6, 21, 0, -15, -26, -6, -13, 4, -21, -8, 22, 16, -15, 0, 14, 22, -10, -30, -7, 16, 12, -22, -7, 8, -22, -9, -18, -3, 16, 22, -19, -24, 2, 11, -26, -14, -7, -21, -18, 28, 6, 23, -28, 6, 9, -10, 36, -12, 4, 7, -39, -10, 19, -18, -29, 25, 31, 14, 40, -6, 24, -38, 4, 17, 2, -20, -3, 4, -9, -22, 4, -39, 16, -6, 4, -37, 10, 20, 12, 6, 12, -18, -42, 29, 24, 4, 32, 19, 11, 18, 29, -45, 6, -3, -3, 13, 26, 24, 28, -20, -16, -6, -56, -33, 22, 25, 12, 20, 23, 10, -29, 42, -12, 20, -47, 27, -58, 7, -5, -11, -15, 12, 34, 16, -12, 58, -54, 46, 52] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([37, 37, -2*w^2 + 5])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]