/* 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([-51, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([34, 34, w + 17]) primes_array = [ [2, 2, -w + 7],\ [3, 3, w],\ [5, 5, w + 1],\ [5, 5, w + 4],\ [7, 7, w + 3],\ [7, 7, w + 4],\ [13, 13, w - 8],\ [13, 13, w + 8],\ [17, 17, w],\ [29, 29, w + 14],\ [29, 29, w + 15],\ [31, 31, w + 12],\ [31, 31, w + 19],\ [41, 41, w + 16],\ [41, 41, w + 25],\ [47, 47, -w - 2],\ [47, 47, w - 2],\ [59, 59, 3*w - 20],\ [59, 59, 10*w - 71],\ [79, 79, w + 29],\ [79, 79, w + 50],\ [83, 83, 2*w - 11],\ [83, 83, -2*w - 11],\ [113, 113, w + 27],\ [113, 113, w + 86],\ [121, 11, -11],\ [139, 139, w + 32],\ [139, 139, w + 107],\ [157, 157, 2*w - 19],\ [157, 157, -2*w - 19],\ [163, 163, w + 41],\ [163, 163, w + 122],\ [173, 173, w + 33],\ [173, 173, w + 140],\ [179, 179, 2*w - 5],\ [179, 179, -2*w - 5],\ [191, 191, 25*w - 178],\ [191, 191, 4*w - 25],\ [197, 197, w + 53],\ [197, 197, w + 144],\ [199, 199, w + 38],\ [199, 199, w + 161],\ [211, 211, w + 85],\ [211, 211, w + 126],\ [229, 229, 11*w - 80],\ [229, 229, -10*w + 73],\ [233, 233, w + 98],\ [233, 233, w + 135],\ [239, 239, 8*w - 55],\ [239, 239, 15*w - 106],\ [251, 251, 5*w - 32],\ [251, 251, 26*w - 185],\ [263, 263, 3*w - 14],\ [263, 263, -3*w - 14],\ [269, 269, w + 68],\ [269, 269, w + 201],\ [283, 283, w + 30],\ [283, 283, w + 253],\ [317, 317, w + 67],\ [317, 317, w + 250],\ [349, 349, -w - 20],\ [349, 349, w - 20],\ [359, 359, -3*w - 10],\ [359, 359, 3*w - 10],\ [361, 19, -19],\ [367, 367, w + 61],\ [367, 367, w + 306],\ [373, 373, 29*w - 208],\ [373, 373, -6*w + 47],\ [379, 379, w + 52],\ [379, 379, w + 327],\ [383, 383, 28*w - 199],\ [383, 383, 7*w - 46],\ [401, 401, w + 177],\ [401, 401, w + 224],\ [409, 409, -4*w - 35],\ [409, 409, 4*w - 35],\ [421, 421, 2*w - 25],\ [421, 421, -2*w - 25],\ [433, 433, -w - 22],\ [433, 433, w - 22],\ [439, 439, w + 200],\ [439, 439, w + 239],\ [443, 443, -3*w - 4],\ [443, 443, 3*w - 4],\ [449, 449, w + 167],\ [449, 449, w + 282],\ [457, 457, 27*w - 194],\ [457, 457, -8*w + 61],\ [467, 467, 41*w - 292],\ [467, 467, 6*w - 37],\ [487, 487, w + 138],\ [487, 487, w + 349],\ [491, 491, -5*w - 28],\ [491, 491, 5*w - 28],\ [499, 499, w + 71],\ [499, 499, w + 428],\ [521, 521, w + 234],\ [521, 521, w + 287],\ [529, 23, -23],\ [547, 547, w + 208],\ [547, 547, w + 339],\ [563, 563, 7*w - 44],\ [563, 563, 42*w - 299],\ [571, 571, w + 42],\ [571, 571, w + 529],\ [577, 577, -12*w + 89],\ [577, 577, 23*w - 166],\ [587, 587, 14*w - 97],\ [587, 587, 21*w - 148],\ [599, 599, -5*w - 26],\ [599, 599, 5*w - 26],\ [607, 607, w + 281],\ [607, 607, w + 326],\ [613, 613, -14*w + 103],\ [613, 613, 21*w - 152],\ [617, 617, w + 56],\ [617, 617, w + 561],\ [619, 619, w + 79],\ [619, 619, w + 540],\ [641, 641, w + 95],\ [641, 641, w + 546],\ [643, 643, w + 242],\ [643, 643, w + 401],\ [647, 647, -4*w - 13],\ [647, 647, 4*w - 13],\ [653, 653, w + 63],\ [653, 653, w + 590],\ [659, 659, 15*w - 104],\ [659, 659, 22*w - 155],\ [661, 661, -5*w - 44],\ [661, 661, 5*w - 44],\ [677, 677, w + 205],\ [677, 677, w + 472],\ [691, 691, w + 310],\ [691, 691, w + 381],\ [733, 733, -w - 28],\ [733, 733, w - 28],\ [751, 751, w + 48],\ [751, 751, w + 703],\ [757, 757, 2*w - 31],\ [757, 757, -2*w - 31],\ [769, 769, -9*w + 70],\ [769, 769, 40*w - 287],\ [787, 787, w + 89],\ [787, 787, w + 698],\ [809, 809, w + 64],\ [809, 809, w + 745],\ [811, 811, w + 217],\ [811, 811, w + 594],\ [821, 821, w + 351],\ [821, 821, w + 470],\ [823, 823, w + 91],\ [823, 823, w + 732],\ [829, 829, -10*w + 77],\ [829, 829, 39*w - 280],\ [857, 857, w + 395],\ [857, 857, w + 462],\ [863, 863, 57*w - 406],\ [863, 863, 8*w - 49],\ [881, 881, w + 160],\ [881, 881, w + 721],\ [907, 907, w + 80],\ [907, 907, w + 827],\ [929, 929, w + 75],\ [929, 929, w + 854],\ [937, 937, 37*w - 266],\ [937, 937, -12*w + 91],\ [941, 941, w + 115],\ [941, 941, w + 826],\ [971, 971, 14*w - 95],\ [971, 971, 35*w - 248],\ [991, 991, w + 359],\ [991, 991, w + 632]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -2, 0, 0, -4, -4, 2, 2, -1, 0, 0, -4, -4, 6, 6, 0, 0, 0, 0, 8, 8, 0, 0, -6, -6, 14, 2, 2, 14, 14, 2, 2, 24, 24, 12, 12, -24, -24, -12, -12, -16, -16, -10, -10, 14, 14, 18, 18, 24, 24, -24, -24, 24, 24, -24, -24, 14, 14, -12, -12, 26, 26, 24, 24, -22, -16, -16, -22, -22, 14, 14, -24, -24, 30, 30, -10, -10, 2, 2, 2, 2, 8, 8, -24, -24, -18, -18, 26, 26, 12, 12, 8, 8, -12, -12, 14, 14, -18, -18, -46, 2, 2, -24, -24, 26, 26, 14, 14, 12, 12, -24, -24, 20, 20, 14, 14, -30, -30, 26, 26, -18, -18, 14, 14, -48, -48, 24, 24, -12, -12, -46, -46, -12, -12, -10, -10, -22, -22, 8, 8, -10, -10, 14, 14, -46, -46, 30, 30, 38, 38, 36, 36, -16, -16, -10, -10, -18, -18, 48, 48, 18, 18, -58, -58, -18, -18, -58, -58, -36, -36, -24, -24, -16, -16] 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 + 7])] = -1 AL_eigenvalues[ZF.ideal([17, 17, w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]