/* 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([-57, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([1, 1, 1]) primes_array = [ [3, 3, w],\ [3, 3, w + 2],\ [4, 2, 2],\ [5, 5, w + 1],\ [5, 5, w + 3],\ [11, 11, w + 1],\ [11, 11, w + 9],\ [17, 17, w + 2],\ [17, 17, w + 14],\ [19, 19, w],\ [19, 19, w + 18],\ [37, 37, -w - 4],\ [37, 37, w - 5],\ [43, 43, w + 16],\ [43, 43, w + 26],\ [49, 7, -7],\ [53, 53, -w - 10],\ [53, 53, w - 11],\ [61, 61, w + 15],\ [61, 61, w + 45],\ [71, 71, w + 33],\ [71, 71, w + 37],\ [83, 83, w + 17],\ [83, 83, w + 65],\ [97, 97, w + 30],\ [97, 97, w + 66],\ [103, 103, w + 34],\ [103, 103, w + 68],\ [149, 149, w + 61],\ [149, 149, w + 87],\ [151, 151, w + 28],\ [151, 151, w + 122],\ [167, 167, w + 39],\ [167, 167, w + 127],\ [169, 13, -13],\ [173, 173, 3*w - 20],\ [173, 173, -3*w - 17],\ [181, 181, w + 24],\ [181, 181, w + 156],\ [193, 193, 2*w - 7],\ [193, 193, -2*w - 5],\ [229, 229, 2*w - 1],\ [233, 233, w + 27],\ [233, 233, w + 205],\ [241, 241, -3*w - 26],\ [241, 241, 3*w - 29],\ [271, 271, w + 29],\ [271, 271, w + 241],\ [277, 277, w + 50],\ [277, 277, w + 226],\ [293, 293, w + 112],\ [293, 293, w + 180],\ [307, 307, w + 132],\ [307, 307, w + 174],\ [311, 311, w + 88],\ [311, 311, w + 222],\ [337, 337, w + 71],\ [337, 337, w + 265],\ [347, 347, 2*w - 25],\ [347, 347, -2*w - 23],\ [359, 359, 3*w - 14],\ [359, 359, -3*w - 11],\ [367, 367, w + 43],\ [367, 367, w + 323],\ [373, 373, w + 64],\ [373, 373, w + 308],\ [383, 383, -3*w - 10],\ [383, 383, 3*w - 13],\ [397, 397, w + 82],\ [397, 397, w + 314],\ [401, 401, w + 35],\ [401, 401, w + 365],\ [409, 409, w + 67],\ [409, 409, w + 341],\ [421, 421, w + 46],\ [421, 421, w + 374],\ [431, 431, w + 119],\ [431, 431, w + 311],\ [433, 433, w + 175],\ [433, 433, w + 257],\ [439, 439, 5*w - 34],\ [439, 439, -5*w - 29],\ [443, 443, -3*w - 7],\ [443, 443, 3*w - 10],\ [449, 449, -w - 22],\ [449, 449, w - 23],\ [457, 457, w + 208],\ [457, 457, w + 248],\ [461, 461, 5*w - 46],\ [461, 461, -5*w - 41],\ [463, 463, w + 186],\ [463, 463, w + 276],\ [467, 467, w + 94],\ [467, 467, w + 372],\ [491, 491, w + 145],\ [491, 491, w + 345],\ [503, 503, 3*w - 5],\ [503, 503, -3*w - 2],\ [509, 509, -3*w - 1],\ [509, 509, 3*w - 4],\ [529, 23, -23],\ [541, 541, 3*w - 34],\ [541, 541, -3*w - 31],\ [557, 557, w + 158],\ [557, 557, w + 398],\ [569, 569, w + 262],\ [569, 569, w + 306],\ [587, 587, w + 223],\ [587, 587, w + 363],\ [593, 593, -w - 25],\ [593, 593, w - 26],\ [607, 607, -3*w - 32],\ [607, 607, 3*w - 35],\ [617, 617, 6*w - 41],\ [617, 617, -6*w - 35],\ [619, 619, -5*w - 26],\ [619, 619, 5*w - 31],\ [631, 631, w + 144],\ [631, 631, w + 486],\ [641, 641, w + 44],\ [641, 641, w + 596],\ [643, 643, 7*w + 43],\ [643, 643, 7*w - 50],\ [661, 661, w + 77],\ [661, 661, w + 583],\ [673, 673, w + 58],\ [673, 673, w + 614],\ [683, 683, w + 101],\ [683, 683, w + 581],\ [691, 691, -4*w - 13],\ [691, 691, 4*w - 17],\ [701, 701, w + 196],\ [701, 701, w + 504],\ [733, 733, w + 47],\ [733, 733, w + 685],\ [743, 743, w + 136],\ [743, 743, w + 606],\ [751, 751, w + 318],\ [751, 751, w + 432],\ [757, 757, w + 353],\ [757, 757, w + 403],\ [769, 769, w + 209],\ [769, 769, w + 559],\ [787, 787, w + 84],\ [787, 787, w + 702],\ [821, 821, w + 354],\ [821, 821, w + 466],\ [841, 29, -29],\ [859, 859, w + 97],\ [859, 859, w + 761],\ [863, 863, w + 264],\ [863, 863, w + 598],\ [883, 883, w + 250],\ [883, 883, w + 632],\ [907, 907, -4*w - 1],\ [907, 907, 4*w - 5],\ [911, 911, w + 261],\ [911, 911, w + 649],\ [919, 919, w + 203],\ [919, 919, w + 715],\ [941, 941, w + 356],\ [941, 941, w + 584],\ [953, 953, w + 177],\ [953, 953, w + 775],\ [961, 31, -31],\ [967, 967, 3*w - 40],\ [967, 967, -3*w - 37],\ [971, 971, w + 54],\ [971, 971, w + 916],\ [977, 977, -7*w - 58],\ [977, 977, 7*w - 65],\ [991, 991, w + 459],\ [991, 991, w + 531],\ [997, 997, w + 385],\ [997, 997, w + 611]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 1, -1, 3, 3, 3, 3, -3, -3, -1, -1, 2, 2, -1, -1, 14, 6, 6, 5, 5, -15, -15, -9, -9, -7, -7, 11, 11, -21, -21, -7, -7, 3, 3, 26, 6, 6, -7, -7, 14, 14, 14, 9, 9, -10, -10, -25, -25, 17, 17, 9, 9, 17, 17, 15, 15, -13, -13, -12, -12, -24, -24, 17, 17, -19, -19, -24, -24, 23, 23, 27, 27, 35, 35, 17, 17, 15, 15, -19, -19, 20, 20, 36, 36, -30, -30, 23, 23, -18, -18, -1, -1, 27, 27, -15, -15, -24, -24, 6, 6, 26, -10, -10, -3, -3, 45, 45, -27, -27, 6, 6, 32, 32, 42, 42, 20, 20, -43, -43, -45, -45, 44, 44, -13, -13, -19, -19, 9, 9, 8, 8, 33, 33, 11, 11, -39, -39, 5, 5, -13, -13, 5, 5, 23, 23, 3, 3, 38, 5, 5, 9, 9, 29, 29, -52, -52, -15, -15, -25, -25, -45, -45, -39, -39, 62, -28, -28, 33, 33, 18, 18, -25, -25, -37, -37] 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]