/* 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([-68, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([4, 2, 2]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [3, 3, -4*w + 35],\ [7, 7, w + 3],\ [11, 11, w + 1],\ [11, 11, w + 9],\ [13, 13, w + 6],\ [17, 17, -2*w + 17],\ [17, 17, -2*w - 15],\ [19, 19, w + 5],\ [19, 19, w + 13],\ [25, 5, -5],\ [31, 31, w + 2],\ [31, 31, w + 28],\ [43, 43, -38*w + 333],\ [43, 43, 6*w - 53],\ [71, 71, w + 14],\ [71, 71, w + 56],\ [73, 73, w + 22],\ [73, 73, w + 50],\ [79, 79, 30*w - 263],\ [79, 79, -14*w + 123],\ [97, 97, w + 25],\ [97, 97, w + 71],\ [101, 101, -54*w + 473],\ [101, 101, 10*w - 87],\ [127, 127, -2*w + 21],\ [127, 127, -2*w - 19],\ [131, 131, 4*w + 29],\ [131, 131, -4*w + 33],\ [137, 137, w + 18],\ [137, 137, w + 118],\ [149, 149, w + 35],\ [149, 149, w + 113],\ [173, 173, 2*w - 11],\ [173, 173, -2*w - 9],\ [197, 197, w + 21],\ [197, 197, w + 175],\ [211, 211, 2*w - 23],\ [211, 211, -2*w - 21],\ [223, 223, w + 37],\ [223, 223, w + 185],\ [229, 229, w + 80],\ [229, 229, w + 148],\ [239, 239, w + 44],\ [239, 239, w + 194],\ [241, 241, w + 76],\ [241, 241, w + 164],\ [251, 251, 4*w - 31],\ [251, 251, 4*w + 27],\ [257, 257, 2*w - 5],\ [257, 257, -2*w - 3],\ [269, 269, 2*w - 3],\ [269, 269, -2*w - 1],\ [271, 271, w + 87],\ [271, 271, w + 183],\ [277, 277, -4*w - 35],\ [277, 277, -4*w + 39],\ [281, 281, w + 111],\ [281, 281, w + 169],\ [307, 307, w + 102],\ [307, 307, w + 204],\ [311, 311, -16*w - 123],\ [311, 311, 16*w - 139],\ [317, 317, w + 26],\ [317, 317, w + 290],\ [337, 337, -32*w + 281],\ [337, 337, 56*w - 491],\ [349, 349, w + 46],\ [349, 349, w + 302],\ [359, 359, w + 107],\ [359, 359, w + 251],\ [373, 373, 12*w + 95],\ [373, 373, 12*w - 107],\ [397, 397, w + 49],\ [397, 397, w + 347],\ [401, 401, w + 29],\ [401, 401, w + 371],\ [409, 409, w + 176],\ [409, 409, w + 232],\ [419, 419, 12*w - 103],\ [419, 419, -12*w - 91],\ [431, 431, w + 30],\ [431, 431, w + 400],\ [449, 449, w + 60],\ [449, 449, w + 388],\ [467, 467, 4*w - 27],\ [467, 467, -4*w - 23],\ [503, 503, 24*w - 209],\ [503, 503, -112*w + 981],\ [521, 521, 6*w - 47],\ [521, 521, -6*w - 41],\ [529, 23, -23],\ [547, 547, -14*w - 111],\ [547, 547, 14*w - 125],\ [557, 557, w + 238],\ [557, 557, w + 318],\ [563, 563, -4*w - 21],\ [563, 563, 4*w - 25],\ [571, 571, 10*w - 91],\ [571, 571, -10*w - 81],\ [577, 577, w + 235],\ [577, 577, w + 341],\ [617, 617, w + 230],\ [617, 617, w + 386],\ [619, 619, w + 61],\ [619, 619, w + 557],\ [643, 643, w + 124],\ [643, 643, w + 518],\ [647, 647, 8*w + 57],\ [647, 647, -8*w + 65],\ [661, 661, w + 295],\ [661, 661, w + 365],\ [673, 673, 8*w - 75],\ [673, 673, -8*w - 67],\ [677, 677, 86*w - 753],\ [677, 677, 42*w - 367],\ [683, 683, w + 242],\ [683, 683, w + 440],\ [691, 691, w + 153],\ [691, 691, w + 537],\ [719, 719, 120*w - 1051],\ [719, 719, 32*w - 279],\ [733, 733, w + 143],\ [733, 733, w + 589],\ [743, 743, w + 308],\ [743, 743, w + 434],\ [751, 751, 2*w - 33],\ [751, 751, -2*w - 31],\ [757, 757, 4*w - 45],\ [757, 757, -4*w - 41],\ [769, 769, w + 323],\ [769, 769, w + 445],\ [787, 787, w + 312],\ [787, 787, w + 474],\ [797, 797, -18*w - 137],\ [797, 797, 18*w - 155],\ [811, 811, w + 353],\ [811, 811, w + 457],\ [821, 821, w + 289],\ [821, 821, w + 531],\ [823, 823, 22*w - 195],\ [823, 823, -22*w - 173],\ [827, 827, w + 41],\ [827, 827, w + 785],\ [841, 29, -29],\ [853, 853, w + 170],\ [853, 853, w + 682],\ [857, 857, -6*w - 37],\ [857, 857, 6*w - 43],\ [863, 863, w + 83],\ [863, 863, w + 779],\ [881, 881, 94*w - 823],\ [881, 881, 50*w - 437],\ [883, 883, 2*w - 35],\ [883, 883, -2*w - 33],\ [887, 887, 8*w - 63],\ [887, 887, 8*w + 55],\ [907, 907, 6*w - 61],\ [907, 907, -6*w - 55],\ [919, 919, -10*w - 83],\ [919, 919, 10*w - 93],\ [947, 947, w + 285],\ [947, 947, w + 661],\ [971, 971, -4*w - 9],\ [971, 971, 4*w - 13],\ [977, 977, w + 207],\ [977, 977, w + 769],\ [991, 991, -18*w - 143],\ [991, 991, 18*w - 161]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -1, -3, -5, 0, 0, 2, -3, -3, 2, 2, 7, -8, -8, -11, -11, -9, -9, -2, -2, 10, 10, 8, 8, 12, 12, -2, -2, 15, 15, -18, -18, -6, -6, 6, 6, 15, 15, -13, -13, -7, -7, -5, -5, 15, 15, 10, 10, -12, -12, -21, -21, 0, 0, -1, -1, -16, -16, -30, -30, -14, -14, -30, -30, 6, 6, 5, 5, 1, 1, 0, 0, 16, 16, -22, -22, -6, -6, 14, 14, 27, 27, 33, 33, 0, 0, -36, -36, 6, 6, 27, 27, 34, 17, 17, 33, 33, 21, 21, 13, 13, -46, -46, 36, 36, -40, -40, 40, 40, -30, -30, 22, 22, -17, -17, 18, 18, 30, 30, 20, 20, -12, -12, 19, 19, -33, -33, 4, 4, 38, 38, 4, 4, 32, 32, -42, -42, 16, 16, 15, 15, 38, 38, -30, -30, 10, -19, -19, -18, -18, 33, 33, 15, 15, 17, 17, 24, 24, 53, 53, -52, -52, -36, -36, -9, -9, 24, 24, 10, 10] 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([2, 2, w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]