/* 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([-30, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([30, 30, w]) primes_array = [ [2, 2, w],\ [3, 3, w],\ [5, 5, -w + 5],\ [7, 7, w + 3],\ [7, 7, w + 4],\ [13, 13, w + 2],\ [13, 13, w + 11],\ [17, 17, w + 8],\ [17, 17, w + 9],\ [19, 19, w + 7],\ [19, 19, -w + 7],\ [29, 29, -w - 1],\ [29, 29, w - 1],\ [37, 37, w + 17],\ [37, 37, w + 20],\ [71, 71, 2*w - 7],\ [71, 71, -2*w - 7],\ [83, 83, w + 14],\ [83, 83, w + 69],\ [101, 101, -7*w + 37],\ [101, 101, -3*w + 13],\ [103, 103, w + 37],\ [103, 103, w + 66],\ [107, 107, w + 43],\ [107, 107, w + 64],\ [113, 113, w + 16],\ [113, 113, w + 97],\ [121, 11, -11],\ [127, 127, w + 41],\ [127, 127, w + 86],\ [137, 137, w + 21],\ [137, 137, w + 116],\ [139, 139, -w - 13],\ [139, 139, w - 13],\ [149, 149, 3*w - 11],\ [149, 149, -3*w - 11],\ [157, 157, w + 40],\ [157, 157, w + 117],\ [191, 191, -4*w - 17],\ [191, 191, 4*w - 17],\ [211, 211, -5*w + 31],\ [211, 211, -7*w + 41],\ [223, 223, w + 91],\ [223, 223, w + 132],\ [227, 227, w + 22],\ [227, 227, w + 205],\ [233, 233, w + 27],\ [233, 233, w + 206],\ [239, 239, 6*w - 29],\ [239, 239, 8*w - 41],\ [241, 241, 2*w - 19],\ [241, 241, -2*w - 19],\ [257, 257, w + 95],\ [257, 257, w + 162],\ [269, 269, -3*w - 1],\ [269, 269, 3*w - 1],\ [277, 277, w + 108],\ [277, 277, w + 169],\ [311, 311, -4*w - 13],\ [311, 311, 4*w - 13],\ [331, 331, -w - 19],\ [331, 331, w - 19],\ [347, 347, w + 77],\ [347, 347, w + 270],\ [353, 353, w + 33],\ [353, 353, w + 320],\ [359, 359, 4*w - 11],\ [359, 359, -4*w - 11],\ [367, 367, w + 146],\ [367, 367, w + 221],\ [373, 373, w + 75],\ [373, 373, w + 298],\ [379, 379, -7*w + 43],\ [379, 379, -9*w + 53],\ [389, 389, 5*w - 19],\ [389, 389, -5*w - 19],\ [397, 397, w + 53],\ [397, 397, w + 344],\ [409, 409, 2*w - 23],\ [409, 409, -2*w - 23],\ [431, 431, 4*w - 7],\ [431, 431, -4*w - 7],\ [443, 443, w + 159],\ [443, 443, w + 284],\ [461, 461, 5*w - 17],\ [461, 461, -5*w - 17],\ [463, 463, w + 131],\ [463, 463, w + 332],\ [467, 467, w + 214],\ [467, 467, w + 253],\ [479, 479, -4*w - 1],\ [479, 479, 4*w - 1],\ [487, 487, w + 70],\ [487, 487, w + 417],\ [499, 499, -w - 23],\ [499, 499, w - 23],\ [509, 509, -7*w + 31],\ [509, 509, -15*w + 79],\ [529, 23, -23],\ [563, 563, w + 34],\ [563, 563, w + 529],\ [571, 571, -3*w - 29],\ [571, 571, 3*w - 29],\ [587, 587, w + 183],\ [587, 587, w + 404],\ [593, 593, w + 246],\ [593, 593, w + 347],\ [599, 599, 10*w - 49],\ [599, 599, 12*w - 61],\ [601, 601, -16*w + 91],\ [601, 601, 6*w - 41],\ [607, 607, w + 89],\ [607, 607, w + 518],\ [613, 613, w + 231],\ [613, 613, w + 382],\ [617, 617, w + 257],\ [617, 617, w + 360],\ [619, 619, -5*w - 37],\ [619, 619, 5*w - 37],\ [683, 683, w + 264],\ [683, 683, w + 419],\ [691, 691, 3*w - 31],\ [691, 691, -3*w - 31],\ [701, 701, 5*w - 7],\ [701, 701, -5*w - 7],\ [719, 719, -6*w - 19],\ [719, 719, 6*w - 19],\ [727, 727, w + 311],\ [727, 727, w + 416],\ [733, 733, w + 105],\ [733, 733, w + 628],\ [739, 739, -7*w + 47],\ [739, 739, 17*w - 97],\ [757, 757, w + 73],\ [757, 757, w + 684],\ [769, 769, 6*w - 43],\ [769, 769, -6*w - 43],\ [811, 811, -w - 29],\ [811, 811, w - 29],\ [821, 821, 15*w - 77],\ [821, 821, 11*w - 53],\ [823, 823, w + 186],\ [823, 823, w + 637],\ [827, 827, w + 388],\ [827, 827, w + 439],\ [839, 839, 12*w - 59],\ [839, 839, 14*w - 71],\ [853, 853, w + 258],\ [853, 853, w + 595],\ [857, 857, w + 51],\ [857, 857, w + 806],\ [859, 859, -11*w + 67],\ [859, 859, -13*w + 77],\ [877, 877, w + 192],\ [877, 877, w + 685],\ [911, 911, -6*w - 13],\ [911, 911, 6*w - 13],\ [941, 941, 7*w - 23],\ [941, 941, -7*w - 23],\ [947, 947, w + 127],\ [947, 947, w + 820],\ [953, 953, w + 44],\ [953, 953, w + 909],\ [961, 31, -31],\ [967, 967, w + 442],\ [967, 967, w + 525],\ [977, 977, w + 185],\ [977, 977, w + 792],\ [997, 997, w + 100],\ [997, 997, w + 897]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 1, -1, -4, -4, 2, 2, 6, 6, -4, -4, -6, -6, 2, 2, 0, 0, 12, 12, 18, 18, -4, -4, -12, -12, -18, -18, -22, 20, 20, 6, 6, -4, -4, -6, -6, 2, 2, -24, -24, 20, 20, 20, 20, -12, -12, -18, -18, 24, 24, 2, 2, -18, -18, -6, -6, 2, 2, 0, 0, -28, -28, 12, 12, 6, 6, -24, -24, -28, -28, 26, 26, -4, -4, -6, -6, -22, -22, 26, 26, 0, 0, 12, 12, -30, -30, -4, -4, -36, -36, -24, -24, -28, -28, -4, -4, -6, -6, -46, -12, -12, 20, 20, -12, -12, 30, 30, -24, -24, -22, -22, -4, -4, 2, 2, 30, 30, 44, 44, -12, -12, 44, 44, -6, -6, 0, 0, -28, -28, -22, -22, -52, -52, 2, 2, 2, 2, -4, -4, 18, 18, 20, 20, 12, 12, 24, 24, -46, -46, -18, -18, -4, -4, 2, 2, -48, -48, 18, 18, 36, 36, 6, 6, 2, -4, -4, -42, -42, 26, 26] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, w])] = 1 AL_eigenvalues[ZF.ideal([3, 3, w])] = -1 AL_eigenvalues[ZF.ideal([5, 5, -w + 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]