/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([45, 15, -3*w + 24]) primes_array = [ [3, 3, w],\ [3, 3, w + 2],\ [4, 2, 2],\ [5, 5, -w + 8],\ [7, 7, w + 1],\ [7, 7, w + 5],\ [13, 13, w + 3],\ [13, 13, w + 9],\ [17, 17, w],\ [17, 17, w + 16],\ [31, 31, -w - 4],\ [31, 31, w - 5],\ [41, 41, 3*w - 22],\ [47, 47, w + 19],\ [47, 47, w + 27],\ [53, 53, w + 14],\ [53, 53, w + 38],\ [59, 59, -w - 10],\ [59, 59, w - 11],\ [61, 61, 2*w - 13],\ [61, 61, -2*w - 11],\ [67, 67, w + 32],\ [67, 67, w + 34],\ [97, 97, w + 18],\ [97, 97, w + 78],\ [121, 11, -11],\ [131, 131, -w - 13],\ [131, 131, w - 14],\ [137, 137, w + 21],\ [137, 137, w + 115],\ [139, 139, 9*w - 70],\ [139, 139, 3*w - 26],\ [157, 157, w + 65],\ [157, 157, w + 91],\ [167, 167, w + 23],\ [167, 167, w + 143],\ [193, 193, w + 82],\ [193, 193, w + 110],\ [227, 227, w + 40],\ [227, 227, w + 186],\ [233, 233, w + 55],\ [233, 233, w + 177],\ [241, 241, 3*w - 28],\ [241, 241, -3*w - 25],\ [251, 251, -3*w - 13],\ [251, 251, 3*w - 16],\ [257, 257, w + 62],\ [257, 257, w + 194],\ [263, 263, w + 43],\ [263, 263, w + 219],\ [269, 269, -4*w - 31],\ [269, 269, 4*w - 35],\ [271, 271, 6*w - 49],\ [271, 271, 9*w - 71],\ [293, 293, w + 30],\ [293, 293, w + 262],\ [313, 313, w + 121],\ [313, 313, w + 191],\ [317, 317, w + 141],\ [317, 317, w + 175],\ [347, 347, w + 72],\ [347, 347, w + 274],\ [349, 349, 11*w - 82],\ [349, 349, -7*w + 50],\ [359, 359, 5*w - 43],\ [359, 359, 14*w - 109],\ [361, 19, -19],\ [379, 379, 4*w - 23],\ [379, 379, -4*w - 19],\ [383, 383, w + 155],\ [383, 383, w + 227],\ [389, 389, -3*w - 7],\ [389, 389, 3*w - 10],\ [397, 397, w + 77],\ [397, 397, w + 319],\ [401, 401, -6*w + 41],\ [401, 401, 15*w - 113],\ [409, 409, 3*w - 31],\ [409, 409, -3*w - 28],\ [419, 419, 3*w - 8],\ [419, 419, -3*w - 5],\ [431, 431, -3*w - 4],\ [431, 431, 3*w - 7],\ [449, 449, 3*w - 5],\ [449, 449, -3*w - 2],\ [457, 457, w + 172],\ [457, 457, w + 284],\ [461, 461, 3*w - 2],\ [461, 461, 3*w - 1],\ [463, 463, w + 127],\ [463, 463, w + 335],\ [491, 491, -9*w + 65],\ [491, 491, 12*w - 89],\ [503, 503, w + 39],\ [503, 503, w + 463],\ [529, 23, -23],\ [541, 541, 9*w - 73],\ [541, 541, 12*w - 95],\ [547, 547, w + 160],\ [547, 547, w + 386],\ [557, 557, w + 41],\ [557, 557, w + 515],\ [563, 563, w + 123],\ [563, 563, w + 439],\ [569, 569, 16*w - 125],\ [569, 569, 7*w - 59],\ [577, 577, w + 266],\ [577, 577, w + 310],\ [587, 587, w + 64],\ [587, 587, w + 522],\ [593, 593, w + 263],\ [593, 593, w + 329],\ [599, 599, -w - 25],\ [599, 599, w - 26],\ [619, 619, -7*w - 40],\ [619, 619, 7*w - 47],\ [631, 631, -5*w - 23],\ [631, 631, 5*w - 28],\ [643, 643, w + 44],\ [643, 643, w + 598],\ [653, 653, w + 276],\ [653, 653, w + 376],\ [661, 661, -3*w - 32],\ [661, 661, 3*w - 35],\ [673, 673, w + 45],\ [673, 673, w + 627],\ [683, 683, w + 94],\ [683, 683, w + 588],\ [701, 701, 4*w - 41],\ [701, 701, -4*w - 37],\ [727, 727, w + 217],\ [727, 727, w + 509],\ [739, 739, 4*w - 11],\ [739, 739, -4*w - 7],\ [757, 757, w + 218],\ [757, 757, w + 538],\ [761, 761, -w - 28],\ [761, 761, w - 29],\ [769, 769, 17*w - 127],\ [769, 769, -10*w + 71],\ [773, 773, w + 100],\ [773, 773, w + 672],\ [811, 811, -4*w - 1],\ [811, 811, 4*w - 5],\ [821, 821, 6*w - 35],\ [821, 821, -6*w - 29],\ [823, 823, w + 118],\ [823, 823, w + 704],\ [827, 827, w + 235],\ [827, 827, w + 591],\ [829, 829, 13*w - 95],\ [829, 829, 14*w - 103],\ [841, 29, -29],\ [859, 859, 6*w - 55],\ [859, 859, -6*w - 49],\ [881, 881, -5*w - 44],\ [881, 881, 5*w - 49],\ [883, 883, w + 321],\ [883, 883, w + 561],\ [887, 887, w + 236],\ [887, 887, w + 650],\ [911, 911, 7*w + 55],\ [911, 911, 7*w - 62],\ [937, 937, w + 53],\ [937, 937, w + 883],\ [941, 941, -w - 31],\ [941, 941, w - 32],\ [967, 967, w + 226],\ [967, 967, w + 740],\ [977, 977, w + 460],\ [977, 977, w + 516],\ [997, 997, w + 122],\ [997, 997, w + 874]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 1, -3, 1, 0, 0, 2, 2, -2, -2, 0, 0, 10, -8, -8, 10, 10, -4, -4, -2, -2, -12, -12, -2, -2, -6, -12, -12, 6, 6, -4, -4, -14, -14, 0, 0, -2, -2, 20, 20, 6, 6, -14, -14, 12, 12, -18, -18, -16, -16, 14, 14, 16, 16, -6, -6, -26, -26, 2, 2, 28, 28, -2, -2, -24, -24, -22, -20, -20, 24, 24, 6, 6, 2, 2, 18, 18, 26, 26, 4, 4, 0, 0, 2, 2, -10, -10, -18, -18, -24, -24, 28, 28, 32, 32, -46, 30, 30, 20, 20, 18, 18, -12, -12, -6, -6, -2, -2, 12, 12, -34, -34, -8, -8, -4, -4, -8, -8, 36, 36, -46, -46, 22, 22, 30, 30, -36, -36, -2, -2, 16, 16, -44, -44, 26, 26, -6, -6, 2, 2, -6, -6, 12, 12, 54, 54, -32, -32, 28, 28, 30, 30, -54, -20, -20, -46, -46, -44, -44, -48, -48, 32, 32, 54, 54, -50, -50, -32, -32, -2, -2, -54, -54] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w])] = -1 AL_eigenvalues[ZF.ideal([3, 3, w + 2])] = -1 AL_eigenvalues[ZF.ideal([5, 5, -w + 8])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]