/* 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([-26, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([26, 26, w]) primes_array = [ [2, 2, w],\ [5, 5, w + 1],\ [5, 5, w + 4],\ [9, 3, 3],\ [11, 11, w + 2],\ [11, 11, w + 9],\ [13, 13, w],\ [17, 17, w + 3],\ [17, 17, -w + 3],\ [19, 19, w + 8],\ [19, 19, w + 11],\ [23, 23, -w - 7],\ [23, 23, w - 7],\ [37, 37, w + 10],\ [37, 37, w + 27],\ [49, 7, -7],\ [59, 59, w + 12],\ [59, 59, w + 47],\ [67, 67, w + 19],\ [67, 67, w + 48],\ [79, 79, 2*w - 5],\ [79, 79, -2*w - 5],\ [83, 83, w + 21],\ [83, 83, w + 62],\ [103, 103, 2*w - 1],\ [103, 103, -2*w - 1],\ [109, 109, w + 35],\ [109, 109, w + 74],\ [113, 113, 3*w - 11],\ [113, 113, -3*w - 11],\ [127, 127, 4*w + 17],\ [127, 127, -4*w + 17],\ [149, 149, w + 18],\ [149, 149, w + 131],\ [163, 163, w + 29],\ [163, 163, w + 134],\ [191, 191, 4*w - 15],\ [191, 191, -4*w - 15],\ [197, 197, w + 82],\ [197, 197, w + 115],\ [199, 199, -w - 15],\ [199, 199, w - 15],\ [227, 227, w + 88],\ [227, 227, w + 139],\ [229, 229, w + 22],\ [229, 229, w + 207],\ [233, 233, -3*w - 1],\ [233, 233, 3*w - 1],\ [257, 257, 2*w - 19],\ [257, 257, -2*w - 19],\ [263, 263, -w - 17],\ [263, 263, w - 17],\ [293, 293, w + 57],\ [293, 293, w + 236],\ [307, 307, w + 124],\ [307, 307, w + 183],\ [311, 311, 5*w - 31],\ [311, 311, -5*w - 31],\ [313, 313, -4*w - 27],\ [313, 313, 4*w - 27],\ [317, 317, w + 126],\ [317, 317, w + 191],\ [331, 331, w + 41],\ [331, 331, w + 290],\ [337, 337, 2*w - 21],\ [337, 337, -2*w - 21],\ [349, 349, w + 153],\ [349, 349, w + 196],\ [367, 367, 4*w - 7],\ [367, 367, -4*w - 7],\ [379, 379, w + 28],\ [379, 379, w + 351],\ [397, 397, w + 87],\ [397, 397, w + 310],\ [421, 421, w + 187],\ [421, 421, w + 234],\ [433, 433, 6*w - 37],\ [433, 433, -6*w - 37],\ [439, 439, -8*w - 35],\ [439, 439, 8*w - 35],\ [461, 461, w + 165],\ [461, 461, w + 296],\ [499, 499, w + 32],\ [499, 499, w + 467],\ [503, 503, -w - 23],\ [503, 503, w - 23],\ [509, 509, w + 75],\ [509, 509, w + 434],\ [521, 521, 2*w - 25],\ [521, 521, -2*w - 25],\ [541, 541, w + 244],\ [541, 541, w + 297],\ [557, 557, w + 103],\ [557, 557, w + 454],\ [569, 569, 5*w - 9],\ [569, 569, -5*w - 9],\ [587, 587, w + 253],\ [587, 587, w + 334],\ [599, 599, -w - 25],\ [599, 599, w - 25],\ [601, 601, 5*w - 7],\ [601, 601, -5*w - 7],\ [607, 607, -3*w - 29],\ [607, 607, 3*w - 29],\ [613, 613, w + 168],\ [613, 613, w + 445],\ [619, 619, w + 176],\ [619, 619, w + 443],\ [641, 641, -5*w - 3],\ [641, 641, 5*w - 3],\ [643, 643, w + 266],\ [643, 643, w + 377],\ [647, 647, 6*w - 17],\ [647, 647, -6*w - 17],\ [661, 661, w + 150],\ [661, 661, w + 511],\ [673, 673, 4*w - 33],\ [673, 673, -4*w - 33],\ [683, 683, w + 241],\ [683, 683, w + 442],\ [691, 691, w + 59],\ [691, 691, w + 632],\ [709, 709, w + 38],\ [709, 709, w + 671],\ [719, 719, -5*w - 37],\ [719, 719, 5*w - 37],\ [727, 727, 3*w - 31],\ [727, 727, -3*w - 31],\ [733, 733, w + 284],\ [733, 733, w + 449],\ [739, 739, w + 61],\ [739, 739, w + 678],\ [751, 751, -10*w + 43],\ [751, 751, 10*w + 43],\ [773, 773, w + 355],\ [773, 773, w + 418],\ [787, 787, w + 40],\ [787, 787, w + 747],\ [809, 809, -4*w - 35],\ [809, 809, 4*w - 35],\ [811, 811, w + 358],\ [811, 811, w + 453],\ [821, 821, w + 125],\ [821, 821, w + 696],\ [823, 823, 8*w - 29],\ [823, 823, -8*w - 29],\ [827, 827, w + 175],\ [827, 827, w + 652],\ [841, 29, -29],\ [853, 853, w + 97],\ [853, 853, w + 756],\ [857, 857, 2*w - 31],\ [857, 857, -2*w - 31],\ [877, 877, w + 405],\ [877, 877, w + 472],\ [881, 881, 9*w - 35],\ [881, 881, -9*w - 35],\ [887, 887, -6*w - 7],\ [887, 887, 6*w - 7],\ [911, 911, 6*w - 5],\ [911, 911, -6*w - 5],\ [919, 919, 9*w - 55],\ [919, 919, -9*w - 55],\ [937, 937, 11*w + 47],\ [937, 937, -11*w + 47],\ [941, 941, w + 329],\ [941, 941, w + 612],\ [947, 947, w + 69],\ [947, 947, w + 878],\ [953, 953, 4*w - 37],\ [953, 953, -4*w - 37],\ [961, 31, -31],\ [991, 991, -3*w - 35],\ [991, 991, 3*w - 35]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -1, -1, 3, -2, -2, -1, -3, -3, 6, 6, -4, -4, 3, 3, -13, -10, -10, -2, -2, -4, -4, 0, 0, -8, -8, 19, 19, 2, 2, 16, 16, -18, -18, -4, -4, 10, 10, 9, 9, -10, -10, -24, -24, -15, -15, -11, -11, -15, -15, 12, 12, 7, 7, 14, 14, 18, 18, -1, -1, -18, -18, -4, -4, 23, 23, 7, 7, -10, -10, 16, 16, -22, -22, -5, -5, 7, 7, -22, -22, -21, -21, -32, -32, -14, -14, 34, 34, 39, 39, 17, 17, 33, 33, 31, 31, -28, -28, -2, -2, -35, -35, 6, 6, 26, 26, 4, 4, -2, -2, 14, 14, -38, -38, -10, -10, 37, 37, -44, -44, -8, -8, 38, 38, -22, -22, -14, -14, -43, -43, 12, 12, 24, 24, 11, 11, 32, 32, -9, -9, -28, -28, -25, -25, 54, 54, 30, 30, -54, 49, 49, 46, 46, -39, -39, 21, 21, -8, -8, -54, -54, 24, 24, -42, -42, 25, 25, -18, -18, 23, 23, -46, -30, -30] 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([13, 13, w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]