/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 9, w^2 - w - 3]) primes_array = [ [2, 2, -w - 1],\ [3, 3, w^2 - 2*w - 2],\ [7, 7, -w + 2],\ [9, 3, w^2 - 2],\ [11, 11, -w^2 + 2*w + 4],\ [29, 29, -2*w + 1],\ [37, 37, 2*w^2 - 4*w - 3],\ [37, 37, -w^2 + 3*w + 3],\ [37, 37, 2*w^2 - w - 8],\ [41, 41, w^2 - 4*w + 2],\ [43, 43, -2*w^2 + 2*w + 7],\ [43, 43, -2*w^2 + 3*w + 6],\ [43, 43, -w^2 + 6],\ [49, 7, w^2 + w - 3],\ [53, 53, 2*w^2 - 5*w - 4],\ [59, 59, 2*w - 3],\ [61, 61, -w - 4],\ [67, 67, -2*w^2 - w + 2],\ [73, 73, 2*w^2 - 3*w - 12],\ [83, 83, -2*w - 5],\ [89, 89, -w^2 + 2*w - 2],\ [97, 97, -2*w + 7],\ [97, 97, -2*w^2 + 3],\ [97, 97, 2*w^2 - 2*w - 5],\ [101, 101, w^2 - 3*w - 9],\ [101, 101, 2*w^2 - 4*w - 9],\ [103, 103, w^2 - 3*w + 3],\ [109, 109, -w^2 + 4*w + 8],\ [113, 113, 3*w^2 - 3*w - 11],\ [121, 11, w^2 - 4*w - 4],\ [125, 5, -5],\ [127, 127, 4*w^2 - 7*w - 14],\ [139, 139, 3*w^2 - 4*w - 10],\ [149, 149, w - 6],\ [151, 151, -w^2 - w + 9],\ [163, 163, -w^2 - w - 3],\ [167, 167, -3*w^2 - 2*w + 6],\ [173, 173, w^2 + w - 7],\ [179, 179, -3*w^2 + 6*w + 10],\ [179, 179, -2*w^2 + 6*w - 3],\ [179, 179, -3*w^2 + 2*w + 20],\ [191, 191, 3*w - 4],\ [199, 199, w^2 + 2*w - 4],\ [223, 223, -w - 6],\ [223, 223, 3*w - 10],\ [223, 223, -7*w^2 + 14*w + 18],\ [229, 229, -3*w^2 + 10*w - 2],\ [233, 233, 2*w^2 - 9],\ [233, 233, 2*w^2 - 5*w - 8],\ [233, 233, 3*w^2 - 5*w - 5],\ [241, 241, -w^2 + 5*w + 9],\ [257, 257, -3*w^2 + 10],\ [263, 263, 2*w^2 - 5*w - 10],\ [269, 269, w^2 - 7*w + 11],\ [271, 271, -7*w^2 + 11*w + 25],\ [277, 277, -6*w^2 + 9*w + 22],\ [283, 283, -5*w^2 + 11*w + 7],\ [283, 283, w^2 - 2*w - 10],\ [283, 283, -3*w^2 + w + 7],\ [293, 293, 6*w + 11],\ [311, 311, -w^2 + 5*w + 7],\ [313, 313, 4*w - 3],\ [331, 331, -3*w^2 + 9*w + 5],\ [337, 337, 4*w^2 - 7*w - 20],\ [347, 347, 3*w^2 - w - 13],\ [349, 349, 3*w^2 - 3*w - 7],\ [353, 353, -3*w^2 + 7*w + 9],\ [379, 379, 2*w - 9],\ [379, 379, -4*w + 9],\ [379, 379, -4*w^2 + 11*w + 6],\ [383, 383, 4*w^2 - 8*w - 13],\ [383, 383, 2*w^2 + w - 8],\ [383, 383, 3*w^2 - 3*w - 5],\ [389, 389, 3*w^2 - 2*w - 6],\ [397, 397, -6*w^2 + 13*w + 10],\ [401, 401, w^2 - w - 11],\ [409, 409, -5*w^2 + 5*w + 19],\ [409, 409, -2*w^2 - 5*w + 2],\ [409, 409, -3*w^2 - w + 9],\ [419, 419, w^2 - 12],\ [431, 431, 3*w^2 + 5*w - 3],\ [433, 433, w^2 + 2*w - 10],\ [439, 439, 4*w - 5],\ [443, 443, 4*w^2 - 7*w - 8],\ [457, 457, w^2 + 7*w + 5],\ [461, 461, 4*w^2 - 4*w - 13],\ [463, 463, 2*w^2 - 5*w - 16],\ [467, 467, 2*w^2 + 2*w - 21],\ [479, 479, 2*w^2 - 6*w - 9],\ [487, 487, w^2 + 3*w - 15],\ [503, 503, -3*w^2 + 10*w - 6],\ [509, 509, 4*w^2 - 5*w - 12],\ [509, 509, 5*w^2 - 7*w - 17],\ [509, 509, 3*w^2 - w - 15],\ [523, 523, 3*w^2 - 8*w - 8],\ [547, 547, 5*w^2 - 6*w - 18],\ [557, 557, -w^2 - 2*w + 16],\ [557, 557, -2*w^2 + 5*w - 4],\ [557, 557, 8*w^2 - 13*w - 30],\ [571, 571, -6*w^2 + 11*w + 20],\ [577, 577, -6*w^2 + 12*w + 17],\ [593, 593, w^2 + 4*w - 4],\ [593, 593, 6*w^2 - 4*w - 25],\ [593, 593, -2*w^2 - 3*w + 24],\ [599, 599, 4*w^2 - 6*w - 9],\ [613, 613, 4*w^2 - 8*w - 15],\ [617, 617, -5*w + 12],\ [641, 641, 5*w - 4],\ [647, 647, 2*w^2 + w - 16],\ [653, 653, 3*w^2 - 7*w - 13],\ [653, 653, 3*w^2 - 9*w - 7],\ [653, 653, w^2 - 2*w - 12],\ [659, 659, -6*w^2 + 6*w + 23],\ [661, 661, -w^2 + 2*w - 6],\ [673, 673, -2*w^2 + 7*w + 14],\ [683, 683, 4*w^2 - 4*w - 11],\ [683, 683, -2*w^2 - 3*w + 6],\ [683, 683, -5*w^2 - 2*w + 12],\ [691, 691, -5*w^2 - 4*w + 4],\ [691, 691, 6*w^2 - 4*w - 21],\ [691, 691, 4*w^2 - 5*w - 10],\ [709, 709, 8*w + 11],\ [719, 719, -2*w - 9],\ [733, 733, -w^2 + 4*w - 8],\ [739, 739, 4*w^2 - w - 16],\ [751, 751, -w^2 - 6],\ [757, 757, w^2 - 7*w - 7],\ [761, 761, 2*w^2 + w - 14],\ [761, 761, -10*w^2 + 16*w + 35],\ [761, 761, 5*w^2 - 2*w - 34],\ [769, 769, -4*w^2 - w + 12],\ [773, 773, 4*w^2 - w - 8],\ [797, 797, -3*w^2 + 22],\ [809, 809, w^2 + 7*w + 11],\ [809, 809, 4*w^2 - 8*w - 19],\ [809, 809, 5*w^2 - 7*w - 29],\ [811, 811, 3*w^2 + w - 11],\ [821, 821, 5*w^2 - 9*w - 21],\ [821, 821, -9*w^2 + 14*w + 32],\ [821, 821, -11*w^2 + 20*w + 34],\ [823, 823, 5*w^2 - 7*w - 15],\ [827, 827, w^2 + w - 15],\ [827, 827, 2*w^2 - 8*w - 7],\ [827, 827, 2*w^2 - 7*w - 12],\ [839, 839, 2*w^2 + 2*w - 9],\ [839, 839, 5*w - 6],\ [839, 839, w^2 - w - 13],\ [841, 29, -2*w^2 + w - 4],\ [853, 853, 3*w^2 - 14],\ [853, 853, 2*w^2 - w - 18],\ [853, 853, 2*w^2 - 2*w - 17],\ [859, 859, -3*w^2 + 11*w - 9],\ [863, 863, -w^2 + 7*w - 5],\ [877, 877, -3*w - 10],\ [881, 881, w^2 + 10*w + 12],\ [883, 883, 6*w^2 - 7*w - 22],\ [887, 887, 6*w^2 - 8*w - 21],\ [887, 887, -9*w^2 + 19*w + 21],\ [887, 887, -6*w^2 + 11*w + 14],\ [907, 907, 4*w^2 - 14*w + 9],\ [911, 911, 4*w^2 - 4*w - 7],\ [919, 919, w^2 + 4*w - 6],\ [937, 937, -4*w^2 + 2*w + 7],\ [941, 941, 4*w^2 - 3*w - 6],\ [947, 947, 2*w^2 - 4*w - 17],\ [953, 953, 2*w^2 + 6*w - 3],\ [971, 971, -3*w^2 - w + 29],\ [983, 983, -5*w^2 + 14*w + 8],\ [991, 991, 2*w^2 + 4*w - 29],\ [991, 991, -6*w^2 + w + 16],\ [991, 991, 3*w^2 - 8*w - 12]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, 2, 4, 6, -6, -10, -4, 2, -6, -4, -10, -4, 2, -6, 0, 8, 8, 2, 0, 6, -10, 8, 14, 0, -6, 8, 14, -18, 2, -18, -16, -4, 12, -10, -4, -12, -6, -12, -6, 0, 18, 20, 8, -16, 20, 8, 12, -24, 18, -10, 0, -24, 6, 8, 26, 14, 14, -28, 30, 12, 14, 32, 20, -12, 26, -18, -4, 20, -28, -18, -24, -24, 6, 2, 24, 2, -22, 14, -18, -30, -16, 20, 24, 26, 12, 8, 12, 12, -4, -6, 6, 18, 18, -4, -28, -18, 6, -24, -4, -10, 18, -42, 6, 24, 38, -6, -30, -6, 24, -6, 6, 12, 38, -10, -12, 18, 36, -40, 8, 20, -46, 6, 14, 26, 32, -10, 6, -6, -48, -34, -6, 0, 42, 6, -6, 38, -18, -36, -54, -4, 36, 48, -24, 0, 54, 24, -16, -10, -40, -10, 44, 36, -10, -30, 20, 0, 0, 42, -22, 24, -28, 2, -18, 0, -24, -12, 18, -10, -52, 2] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]