/* 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, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([25, 5, w^2 - 6]) primes_array = [ [5, 5, w + 1],\ [5, 5, w - 1],\ [7, 7, -w + 2],\ [8, 2, 2],\ [11, 11, -w^2 + 2*w + 2],\ [17, 17, -w - 3],\ [17, 17, -w^2 + 2*w + 1],\ [17, 17, -w^2 + w + 4],\ [23, 23, -w^2 + 3],\ [27, 3, -3],\ [29, 29, w^2 - w - 8],\ [29, 29, w^2 - w - 3],\ [29, 29, w^2 - w - 1],\ [31, 31, w^2 - 2],\ [37, 37, 2*w - 5],\ [43, 43, w^2 - 2*w - 5],\ [47, 47, w^2 - 3*w - 2],\ [49, 7, w^2 + w - 4],\ [53, 53, w^2 - 2*w - 6],\ [71, 71, w - 5],\ [79, 79, w^2 - 10],\ [83, 83, -2*w^2 + 3*w + 7],\ [89, 89, 2*w^2 - w - 9],\ [97, 97, 3*w^2 - 4*w - 15],\ [107, 107, w^2 - 2*w - 10],\ [121, 11, w^2 - 5*w + 3],\ [127, 127, 2*w^2 - 3*w - 13],\ [131, 131, 3*w + 4],\ [137, 137, 2*w^2 - 3*w - 12],\ [139, 139, 2*w^2 - 3*w - 6],\ [149, 149, w^2 + w - 9],\ [151, 151, 2*w^2 - 11],\ [157, 157, w^2 + w - 8],\ [163, 163, 2*w^2 + w - 4],\ [173, 173, 3*w - 4],\ [179, 179, -w^2 + 2*w - 3],\ [193, 193, 3*w - 5],\ [197, 197, -w^2 + 3*w - 4],\ [197, 197, w^2 - 3*w - 7],\ [199, 199, 2*w^2 - w - 7],\ [211, 211, w^2 + 2*w - 5],\ [223, 223, 2*w^2 - 3*w - 3],\ [227, 227, w^2 - 2*w - 11],\ [227, 227, 2*w^2 + w - 9],\ [227, 227, 2*w^2 - 5],\ [229, 229, 2*w^2 - 13],\ [233, 233, 4*w - 3],\ [241, 241, 3*w^2 - w - 18],\ [257, 257, 2*w^2 + 2*w - 7],\ [269, 269, w^2 - w - 11],\ [271, 271, 2*w^2 - 2*w - 3],\ [277, 277, 2*w^2 - 4*w - 9],\ [277, 277, 2*w^2 - w - 5],\ [277, 277, w^2 + 2*w - 6],\ [281, 281, w^2 + 4*w - 3],\ [293, 293, 2*w^2 - 3*w - 17],\ [311, 311, w^2 - 12],\ [311, 311, 2*w^2 - 5*w - 6],\ [311, 311, 3*w^2 - 6*w - 10],\ [313, 313, -w^2 + 2*w - 4],\ [337, 337, -w^2 - 2*w - 4],\ [337, 337, w^2 + 2*w - 7],\ [337, 337, w^2 + 2*w - 12],\ [347, 347, -w^2 + 6*w - 6],\ [349, 349, -w - 7],\ [353, 353, 2*w^2 - 19],\ [359, 359, 2*w - 9],\ [383, 383, w^2 + 2*w - 16],\ [383, 383, w^2 + 3*w - 16],\ [383, 383, w^2 + 3*w - 5],\ [389, 389, -3*w^2 + 6*w + 5],\ [397, 397, 3*w^2 - 2*w - 13],\ [397, 397, 2*w^2 - 2*w - 17],\ [397, 397, w^2 + 2*w - 11],\ [401, 401, 3*w - 11],\ [401, 401, w^2 + w - 14],\ [401, 401, w - 8],\ [409, 409, -w^2 - w - 4],\ [409, 409, w^2 - 4*w - 6],\ [409, 409, 3*w^2 - 5*w - 14],\ [421, 421, w^2 + 2*w - 10],\ [433, 433, 4*w^2 - 3*w - 20],\ [439, 439, w^2 - 4*w - 9],\ [443, 443, 3*w^2 - 16],\ [457, 457, w^2 - 4*w - 8],\ [461, 461, 4*w - 7],\ [487, 487, w^2 - 5*w - 13],\ [491, 491, 4*w^2 - 6*w - 19],\ [491, 491, 4*w^2 - 4*w - 19],\ [491, 491, 3*w^2 + w - 8],\ [503, 503, -5*w - 3],\ [509, 509, 2*w^2 + w - 12],\ [523, 523, w^2 - 5*w - 4],\ [523, 523, 2*w^2 - 6*w - 5],\ [523, 523, 2*w^2 - 3*w - 18],\ [529, 23, 3*w^2 - 5*w - 7],\ [541, 541, -w^2 - 2*w - 5],\ [557, 557, 3*w^2 - w - 11],\ [563, 563, 3*w^2 - 5*w - 21],\ [571, 571, 3*w^2 - 17],\ [587, 587, -5*w - 7],\ [599, 599, w^2 + 3*w - 7],\ [607, 607, 3*w^2 - 5*w - 6],\ [613, 613, 4*w^2 - 3*w - 19],\ [617, 617, 2*w^2 + w - 14],\ [631, 631, w^2 - 5*w - 5],\ [631, 631, 4*w^2 - 8*w - 13],\ [631, 631, 2*w^2 + w - 22],\ [641, 641, -w^2 - 5],\ [647, 647, 4*w^2 - w - 17],\ [647, 647, 2*w^2 - 5*w - 9],\ [647, 647, 5*w^2 - 6*w - 23],\ [653, 653, 3*w^2 - 5*w - 5],\ [659, 659, w^2 - 5*w - 12],\ [661, 661, w^2 - 6*w - 3],\ [661, 661, 3*w^2 - 5*w - 4],\ [661, 661, 3*w^2 + w - 6],\ [683, 683, 3*w^2 + w - 5],\ [691, 691, 2*w^2 + 2*w - 21],\ [691, 691, 3*w^2 - 5*w - 17],\ [691, 691, 3*w^2 + 2*w - 12],\ [701, 701, 3*w^2 - 4*w - 8],\ [709, 709, 3*w^2 - 7*w - 9],\ [719, 719, -2*w^2 - w - 3],\ [727, 727, w^2 - 14],\ [733, 733, -3*w - 10],\ [739, 739, 2*w^2 + 3*w - 8],\ [739, 739, 5*w - 6],\ [739, 739, 2*w^2 - w - 19],\ [743, 743, 4*w^2 - 5*w - 16],\ [743, 743, 5*w^2 - 3*w - 25],\ [743, 743, 2*w^2 - 5*w - 10],\ [761, 761, w^2 + 4*w - 6],\ [773, 773, -5*w^2 + 7*w + 25],\ [787, 787, 3*w^2 - 20],\ [797, 797, 3*w^2 + w - 15],\ [809, 809, 4*w^2 - 3*w - 18],\ [821, 821, 2*w^2 - 5*w - 11],\ [821, 821, 2*w^2 + 2*w - 11],\ [821, 821, 3*w^2 - 4*w - 6],\ [827, 827, 5*w - 7],\ [853, 853, -w^2 + w - 6],\ [859, 859, w^2 + 3*w - 12],\ [863, 863, 3*w^2 - 3*w - 8],\ [863, 863, w^2 + 3*w - 11],\ [863, 863, w^2 - 5*w - 9],\ [881, 881, w^2 + 4*w - 18],\ [881, 881, w^2 - 5*w - 17],\ [881, 881, 4*w^2 - 4*w - 17],\ [883, 883, 5*w - 8],\ [883, 883, 3*w^2 - 3*w - 4],\ [883, 883, 4*w^2 - 6*w - 27],\ [887, 887, w^2 - w - 14],\ [887, 887, 3*w^2 - w - 26],\ [887, 887, 2*w^2 - 5*w - 14],\ [911, 911, 2*w^2 + 4*w - 7],\ [919, 919, 3*w^2 - 3*w - 7],\ [929, 929, 3*w^2 - w - 5],\ [941, 941, 5*w^2 - 24],\ [947, 947, 3*w^2 - w - 6],\ [947, 947, 3*w^2 + 2*w - 13],\ [947, 947, 3*w^2 - 5*w - 26],\ [961, 31, 4*w^2 - 5*w - 15],\ [967, 967, -5*w - 13],\ [967, 967, 4*w^2 - 21],\ [967, 967, 3*w^2 - 2*w - 7],\ [971, 971, w^2 + w - 16]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 1, -5, 1, 0, -1, -2, 4, 6, -1, -4, -6, -7, -4, 3, -8, -10, -5, 0, 12, 12, -1, -12, 13, -2, -12, 7, 4, -16, 1, -18, 0, -10, -4, -6, 3, 19, -6, 16, 7, 6, 4, 11, -11, -12, -24, -11, -1, -23, -13, 19, 13, 10, -18, -20, -31, 4, -7, -25, 16, -22, -14, 12, -9, 9, 10, -11, -6, -12, 0, -6, 25, 12, -2, 18, 25, -1, -5, -5, -18, -26, 26, -15, 6, -17, 37, 0, -15, -12, 7, 0, 4, 38, 22, -20, -34, -10, 33, -27, -31, 39, -25, 4, 42, 22, -34, -31, 34, -24, 19, -2, 22, 4, 50, 13, 31, 21, 20, 14, -33, -28, 22, -27, -37, 26, 31, -17, 46, -38, 48, 8, 17, 18, 51, 46, 17, -40, -28, 0, 11, -19, 35, 40, -35, -36, -6, -6, -39, -6, 13, -14, -44, -16, 37, 9, -30, 8, 43, -24, -32, -30, -24, 46, -46, 44, 17, -9] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, w + 1])] = -1 AL_eigenvalues[ZF.ideal([5, 5, w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]