/* 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, -5, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([3, 3, w + 1]) primes_array = [ [3, 3, w + 1],\ [5, 5, w - 1],\ [8, 2, 2],\ [9, 3, -w^2 + w + 4],\ [11, 11, -w^2 + 3],\ [11, 11, -w^2 - w + 1],\ [13, 13, w + 3],\ [17, 17, -w^2 + 2],\ [25, 5, w^2 + w - 4],\ [37, 37, w^2 + w - 5],\ [41, 41, 2*w^2 + w - 6],\ [43, 43, w^2 - 3*w - 2],\ [43, 43, -w + 4],\ [71, 71, w^2 - 8],\ [73, 73, 3*w + 5],\ [73, 73, w^2 - 2*w - 5],\ [73, 73, w^2 - 2*w - 7],\ [79, 79, 2*w^2 + w - 9],\ [83, 83, 3*w^2 - 2*w - 13],\ [89, 89, -w^2 - 2*w + 9],\ [101, 101, -w - 5],\ [103, 103, 2*w^2 - 2*w - 9],\ [103, 103, 2*w^2 - w - 13],\ [103, 103, 2*w^2 - w - 5],\ [107, 107, w^2 - 2*w - 10],\ [109, 109, 2*w^2 - 13],\ [113, 113, -w^2 - 2*w - 3],\ [127, 127, -3*w^2 - w + 10],\ [137, 137, 2*w^2 + 2*w - 7],\ [139, 139, 2*w^2 - 3],\ [149, 149, -3*w^2 + 11],\ [149, 149, 3*w^2 - w - 11],\ [149, 149, w^2 + 2*w - 6],\ [157, 157, -3*w^2 + 3*w + 11],\ [163, 163, w^2 + 3*w - 3],\ [167, 167, 2*w^2 - 3*w - 7],\ [169, 13, -w^2 + 3*w - 4],\ [173, 173, -w^2 + 5*w - 1],\ [179, 179, -3*w - 8],\ [191, 191, -w^2 + w - 3],\ [193, 193, -w^2 - 3],\ [197, 197, -3*w^2 + 2*w + 9],\ [199, 199, w^2 - 3*w - 6],\ [211, 211, 2*w^2 - w - 14],\ [211, 211, -4*w - 5],\ [211, 211, -2*w - 7],\ [223, 223, 3*w^2 - 10],\ [239, 239, w^2 - 2*w - 11],\ [257, 257, 2*w^2 + 3*w - 6],\ [271, 271, -w^2 + 2*w - 4],\ [277, 277, 4*w^2 - 3*w - 17],\ [277, 277, w^2 + 2*w - 12],\ [277, 277, 4*w - 3],\ [281, 281, 4*w^2 + w - 14],\ [283, 283, w^2 + 3*w - 5],\ [289, 17, 3*w^2 - w - 9],\ [293, 293, -3*w^2 - 2*w + 12],\ [307, 307, w - 7],\ [311, 311, 4*w^2 - 15],\ [311, 311, 2*w^2 - 3*w - 10],\ [311, 311, w^2 + w - 11],\ [313, 313, -2*w^2 - 2*w + 17],\ [317, 317, 3*w^2 - 3*w - 13],\ [317, 317, 2*w^2 - 3*w - 12],\ [317, 317, 2*w^2 + 2*w - 11],\ [331, 331, w^2 + 3*w - 6],\ [337, 337, 4*w^2 - w - 15],\ [343, 7, -7],\ [353, 353, 3*w^2 - w - 8],\ [353, 353, 2*w^2 - 4*w - 7],\ [353, 353, 2*w^2 + 3*w - 7],\ [359, 359, w^2 - 4*w - 6],\ [367, 367, 3*w^2 - 2*w - 4],\ [367, 367, 2*w^2 - 15],\ [367, 367, 3*w^2 + w - 7],\ [373, 373, w^2 + 3*w - 8],\ [373, 373, -3*w^2 + 3*w + 17],\ [373, 373, 3*w^2 - 3*w - 14],\ [383, 383, 4*w^2 - 3*w - 12],\ [389, 389, 3*w^2 + 3*w - 10],\ [409, 409, w^2 + 4*w - 13],\ [409, 409, -5*w^2 + 3*w + 18],\ [409, 409, w^2 + 4*w - 4],\ [419, 419, 3*w^2 + w - 6],\ [421, 421, 3*w^2 - 7],\ [431, 431, -4*w^2 - w + 13],\ [433, 433, -w^2 + 2*w - 5],\ [439, 439, 3*w^2 - w - 6],\ [449, 449, 3*w^2 - w - 5],\ [457, 457, 3*w^2 - 4],\ [457, 457, 2*w^2 - 5*w - 6],\ [457, 457, -w^2 - w - 5],\ [461, 461, -3*w^2 - 5*w + 6],\ [463, 463, 3*w^2 + 2*w - 14],\ [467, 467, 3*w^2 + 2*w - 18],\ [479, 479, 3*w^2 + w - 21],\ [499, 499, w^2 - 5*w - 13],\ [509, 509, 4*w^2 + 3*w - 9],\ [509, 509, 3*w^2 - w - 20],\ [509, 509, 2*w^2 + 5*w - 4],\ [521, 521, w^2 + 7*w + 5],\ [523, 523, 3*w^2 + 2*w - 17],\ [523, 523, 3*w^2 - 4*w - 20],\ [523, 523, 3*w^2 - 5*w - 9],\ [541, 541, 2*w - 9],\ [547, 547, -4*w^2 + 5*w + 13],\ [557, 557, -2*w - 9],\ [563, 563, 3*w^2 - 4*w - 12],\ [569, 569, -w^2 - 2*w - 6],\ [577, 577, -3*w - 10],\ [587, 587, w^2 - 12],\ [613, 613, -5*w + 8],\ [631, 631, 7*w^2 - 5*w - 28],\ [641, 641, -4*w^2 + 7*w + 9],\ [643, 643, -5*w^2 + 5*w + 18],\ [643, 643, 6*w^2 - 5*w - 19],\ [643, 643, w^2 - 5*w - 7],\ [647, 647, w^2 - 2*w - 13],\ [653, 653, 3*w^2 + 2*w - 23],\ [659, 659, 5*w - 6],\ [661, 661, w^2 + 4*w - 11],\ [661, 661, w^2 + 4*w - 7],\ [661, 661, -6*w^2 + 4*w + 21],\ [677, 677, w^2 + 3*w - 15],\ [677, 677, 3*w^2 - 5*w - 10],\ [677, 677, 2*w^2 + 3*w - 13],\ [683, 683, 2*w^2 + 3*w - 12],\ [683, 683, 2*w^2 + 5*w - 5],\ [683, 683, w - 9],\ [691, 691, 5*w^2 - 6*w - 10],\ [701, 701, w^2 + 5*w - 15],\ [709, 709, 4*w^2 - w - 12],\ [709, 709, w^2 - 5*w - 8],\ [709, 709, w^2 + 4*w - 8],\ [719, 719, 4*w^2 + w - 11],\ [719, 719, -w^2 + w - 6],\ [719, 719, 4*w^2 - 2*w - 11],\ [727, 727, -w^2 - 6],\ [751, 751, w^2 - 5*w - 10],\ [757, 757, 5*w^2 - 18],\ [769, 769, w^2 + 6*w - 3],\ [773, 773, 3*w^2 - 4*w - 18],\ [787, 787, 3*w^2 + w - 22],\ [809, 809, 3*w - 11],\ [821, 821, 3*w^2 + 4*w - 10],\ [823, 823, 5*w^2 - 3*w - 16],\ [823, 823, 3*w^2 - 4*w - 17],\ [823, 823, 2*w^2 - w - 17],\ [827, 827, 4*w^2 - 11],\ [829, 829, 2*w^2 - 5*w - 9],\ [839, 839, -w^2 - 4*w + 17],\ [853, 853, 5*w^2 - 4*w - 14],\ [857, 857, 2*w^2 - 6*w - 7],\ [859, 859, -3*w^2 + 5*w - 3],\ [863, 863, -3*w - 11],\ [877, 877, 6*w^2 - 3*w - 22],\ [911, 911, 6*w^2 - 23],\ [919, 919, 2*w^2 + 4*w - 9],\ [929, 929, 4*w^2 - 2*w - 5],\ [941, 941, 5*w^2 + 2*w - 23],\ [967, 967, 6*w^2 - 5*w - 24],\ [971, 971, 6*w^2 - 5*w - 18],\ [971, 971, 4*w^2 - 4*w - 21],\ [971, 971, w^2 - 3*w - 15],\ [983, 983, -3*w^2 + 4*w - 3],\ [991, 991, 6*w - 5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -3, 3, -1, -6, -6, -5, 3, -7, -2, 3, 2, 4, 0, 10, 1, -1, 10, 0, -15, -9, -8, 2, 4, -6, 1, -3, -2, 3, 20, 3, -6, -9, -17, -14, -18, -11, 21, -12, -24, 17, -21, -14, 22, 14, -14, -10, 24, -27, -10, 5, 23, -1, -18, -16, -11, -9, -14, 30, 24, 12, -5, -9, -30, 15, -2, 2, 2, 9, -18, 21, -12, 4, -28, 16, 5, -2, 13, 6, -21, 23, 17, 26, 0, -10, -18, -2, -14, -9, -10, -14, -2, 18, 2, -12, 36, -40, -6, -30, 6, 30, -34, -34, 38, 43, 38, 21, -24, 33, -34, -24, 29, 14, 39, -14, 28, 38, 12, 6, -18, 31, 5, 10, -18, -9, 33, 24, -12, -12, 10, -39, -19, 46, -35, 0, -6, -6, 14, -46, -43, -41, -27, -8, -30, -33, -14, 8, -2, 48, 19, 12, -26, 3, 4, 36, 23, 18, -38, -57, -30, -22, 30, -12, -54, -36, -2] 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]