/* 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([-10, -10, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7, 7, w + 3]) primes_array = [ [2, 2, -w - 2],\ [5, 5, -w^2 + 2*w + 5],\ [7, 7, w + 3],\ [11, 11, -2*w^2 + 5*w + 9],\ [13, 13, -w^2 + w + 7],\ [13, 13, w - 3],\ [17, 17, -w^2 + 2*w + 7],\ [17, 17, -2*w^2 + 5*w + 7],\ [17, 17, -w^2 + 3*w + 3],\ [19, 19, -w + 1],\ [27, 3, -3],\ [31, 31, w^2 - 2*w - 9],\ [37, 37, w^2 - 7],\ [41, 41, w^2 - w - 11],\ [47, 47, w^2 - 3],\ [49, 7, w^2 - 3*w - 1],\ [59, 59, w^2 - 4*w + 1],\ [67, 67, w^2 - 3*w - 7],\ [71, 71, 4*w + 9],\ [73, 73, -4*w^2 + 8*w + 23],\ [83, 83, 2*w^2 - 4*w - 13],\ [89, 89, -w^2 + 11],\ [97, 97, 2*w^2 - w - 13],\ [109, 109, 2*w^2 - 5*w - 11],\ [121, 11, -3*w^2 + 5*w + 29],\ [137, 137, 3*w^2 - 3*w - 23],\ [149, 149, 3*w^2 - 5*w - 19],\ [151, 151, 2*w^2 - 3*w - 11],\ [157, 157, w^2 - 2*w - 13],\ [157, 157, 4*w^2 - 7*w - 27],\ [157, 157, 2*w^2 - 2*w - 13],\ [163, 163, 2*w^2 - 13],\ [167, 167, w^2 - 4*w - 3],\ [173, 173, 2*w - 3],\ [173, 173, -5*w^2 + 7*w + 47],\ [173, 173, -2*w^2 + 6*w + 3],\ [181, 181, w^2 - 4*w - 1],\ [181, 181, -2*w^2 + 3*w + 21],\ [181, 181, 2*w^2 - 2*w - 21],\ [193, 193, 3*w^2 - 9*w - 7],\ [197, 197, 5*w^2 - 11*w - 23],\ [211, 211, w^2 - 4*w - 9],\ [211, 211, -7*w^2 + 16*w + 31],\ [211, 211, -5*w^2 + 10*w + 29],\ [223, 223, 3*w^2 - 5*w - 23],\ [227, 227, w^2 + w - 7],\ [229, 229, 4*w^2 - 11*w - 11],\ [239, 239, -2*w^2 - 5*w + 1],\ [241, 241, 3*w^2 - 4*w - 21],\ [251, 251, 2*w^2 - w - 11],\ [251, 251, 2*w^2 - 2*w - 11],\ [251, 251, w^2 - 3*w + 1],\ [263, 263, -2*w^2 + 5*w + 13],\ [263, 263, w^2 - 4*w - 13],\ [263, 263, w - 7],\ [271, 271, 5*w + 9],\ [281, 281, -2*w^2 - 6*w - 1],\ [283, 283, -w - 7],\ [283, 283, -5*w^2 + 10*w + 27],\ [283, 283, -2*w^2 - w + 7],\ [293, 293, -w^2 + 4*w + 17],\ [307, 307, 3*w^2 - 5*w - 27],\ [317, 317, 3*w^2 - 7*w - 17],\ [331, 331, -w^2 + w - 1],\ [349, 349, 2*w^2 - w - 9],\ [353, 353, -5*w^2 + 9*w + 33],\ [359, 359, 3*w - 1],\ [361, 19, w^2 + w - 9],\ [379, 379, 4*w^2 - 8*w - 19],\ [383, 383, 2*w^2 - 7],\ [397, 397, 3*w^2 - 2*w - 27],\ [401, 401, 8*w^2 - 18*w - 39],\ [409, 409, -4*w^2 + 3*w + 29],\ [421, 421, w^2 - 6*w - 19],\ [431, 431, -2*w^2 - 2*w + 9],\ [439, 439, w^2 + w - 11],\ [439, 439, w^2 - 5*w - 11],\ [439, 439, 3*w^2 - 4*w - 19],\ [443, 443, 4*w^2 - 6*w - 27],\ [443, 443, 5*w^2 - 14*w - 13],\ [443, 443, w^2 - 5*w + 3],\ [449, 449, -2*w - 9],\ [457, 457, -7*w^2 + 15*w + 37],\ [461, 461, -w^2 - 2*w + 21],\ [463, 463, w^2 + 3*w - 3],\ [479, 479, 2*w^2 - 5*w - 21],\ [487, 487, 2*w^2 - 7*w - 3],\ [499, 499, -w^2 - 5*w - 9],\ [509, 509, -4*w^2 + 5*w + 29],\ [523, 523, -2*w^2 + 27],\ [523, 523, -8*w^2 + 14*w + 53],\ [523, 523, -4*w + 13],\ [541, 541, 2*w^2 - 7*w + 1],\ [547, 547, -6*w^2 + 9*w + 43],\ [547, 547, 2*w^2 - 5*w - 17],\ [547, 547, 2*w^2 - 3*w - 23],\ [557, 557, 3*w - 7],\ [571, 571, 3*w^2 - 4*w - 31],\ [571, 571, w^2 + 6*w + 11],\ [571, 571, 3*w^2 + 2*w - 11],\ [577, 577, -2*w^2 - 3*w + 7],\ [587, 587, -5*w + 17],\ [593, 593, -2*w^2 + 23],\ [607, 607, -w^2 + 7*w - 13],\ [607, 607, -w^2 - 7*w - 13],\ [607, 607, -w^2 - 3],\ [613, 613, 3*w^2 - 4*w - 17],\ [617, 617, w^2 + 2*w - 7],\ [619, 619, -4*w^2 + 10*w + 21],\ [631, 631, w^2 - 5*w - 1],\ [643, 643, -3*w^2 + w + 17],\ [647, 647, 3*w^2 + w - 13],\ [647, 647, -9*w^2 + 12*w + 83],\ [647, 647, 2*w^2 - 17],\ [653, 653, -4*w^2 + 9*w + 23],\ [653, 653, -6*w^2 + 17*w + 17],\ [653, 653, -3*w^2 + w + 33],\ [661, 661, -6*w^2 + 11*w + 39],\ [673, 673, 3*w^2 - 6*w - 23],\ [673, 673, w^2 - 5*w + 7],\ [673, 673, w^2 + 9*w + 13],\ [683, 683, 2*w^2 + w - 13],\ [691, 691, 3*w^2 - 6*w - 29],\ [709, 709, -w^2 + 7*w + 21],\ [733, 733, w^2 - 17],\ [739, 739, -5*w^2 + 9*w + 29],\ [743, 743, 7*w + 13],\ [757, 757, -3*w + 13],\ [757, 757, 4*w + 13],\ [757, 757, -w^2 + w - 3],\ [761, 761, -4*w^2 + 7*w + 21],\ [769, 769, -2*w^2 + 8*w + 9],\ [773, 773, -4*w^2 + 7*w + 17],\ [787, 787, -w^2 + 2*w - 3],\ [809, 809, -5*w^2 + 10*w + 31],\ [809, 809, -2*w^2 - 7*w - 9],\ [809, 809, 4*w^2 - 7*w - 31],\ [811, 811, 2*w - 11],\ [821, 821, 3*w^2 - 3*w - 11],\ [827, 827, 7*w^2 - 15*w - 33],\ [839, 839, 2*w^2 - 8*w + 1],\ [853, 853, -9*w^2 + 16*w + 57],\ [859, 859, -5*w + 19],\ [859, 859, -w^2 + 7*w - 11],\ [859, 859, 4*w^2 - 7*w - 19],\ [863, 863, -4*w^2 + 5*w + 27],\ [877, 877, -4*w^2 + 8*w + 27],\ [887, 887, 2*w^2 - 6*w - 17],\ [887, 887, 3*w^2 + 4*w - 3],\ [887, 887, -3*w^2 + 37],\ [919, 919, -2*w^2 - 6*w + 1],\ [919, 919, -w^2 + 4*w + 19],\ [919, 919, 4*w^2 - 8*w - 41],\ [929, 929, 3*w^2 - 7*w - 21],\ [941, 941, 9*w^2 - 20*w - 41],\ [947, 947, -3*w^2 + 5*w + 33],\ [953, 953, w^2 - 2*w - 17],\ [953, 953, 7*w^2 - 18*w - 23],\ [953, 953, -6*w - 17],\ [961, 31, -3*w^2 + 8*w + 19],\ [967, 967, 3*w^2 - 3*w - 13],\ [971, 971, -2*w^2 - 8*w - 11],\ [971, 971, -2*w^2 + 10*w - 11],\ [971, 971, -2*w - 11],\ [977, 977, -2*w^2 - w + 27],\ [983, 983, w^2 - w - 17]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, -1, 0, -5, 3, -5, -6, 3, 2, 8, 10, -1, -7, 2, 9, -4, 8, -12, 3, -18, -13, 7, -7, -15, -14, 5, 22, 23, 2, 9, -18, -16, 21, -11, -22, 7, -18, 13, -22, 2, 20, -2, -10, -4, -8, -3, -20, 27, 16, -10, 0, 16, 2, -16, -28, -10, 16, -6, 18, 15, 22, -33, 4, -22, 3, -18, 2, 2, -26, -10, 5, -10, 29, 12, -26, -10, -10, -28, -26, -40, -3, -17, -23, -24, -14, -18, -38, 2, -12, -34, 4, 35, 2, -44, -46, 21, 18, -34, 38, 2, 24, -43, -34, 26, 6, -11, 15, 26, 46, 6, 18, -10, -2, 3, 6, 11, 3, 22, -35, -23, -42, 34, 41, -11, 30, 18, 13, -3, -34, 11, -14, 7, 0, -9, 45, 29, -2, -3, -18, 20, -19, 22, 58, -14, -24, -49, -26, -4, -16, 56, -8, 4, 29, 37, -4, -34, 37, 29, 39, 58, 48, -26, 14, -19, 36] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7, 7, w + 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]