/* 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([-46, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([1, 1, 1]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [5, 5, w + 2],\ [9, 3, 3],\ [11, 11, 2*w + 13],\ [11, 11, -2*w + 15],\ [13, 13, w + 4],\ [13, 13, w + 8],\ [17, 17, w + 3],\ [17, 17, w + 13],\ [23, 23, w],\ [23, 23, w + 22],\ [37, 37, w + 18],\ [41, 41, -2*w + 13],\ [41, 41, -2*w - 11],\ [43, 43, w + 11],\ [43, 43, w + 31],\ [49, 7, -7],\ [71, 71, -2*w + 17],\ [71, 71, -2*w - 15],\ [97, 97, w + 15],\ [97, 97, w + 81],\ [101, 101, 4*w + 27],\ [101, 101, 4*w - 31],\ [103, 103, w + 29],\ [103, 103, w + 73],\ [113, 113, w + 16],\ [113, 113, w + 96],\ [139, 139, 2*w - 19],\ [139, 139, -2*w - 17],\ [149, 149, 2*w - 7],\ [149, 149, -2*w - 5],\ [151, 151, -8*w - 49],\ [151, 151, -8*w + 57],\ [163, 163, w + 57],\ [163, 163, w + 105],\ [167, 167, w + 19],\ [167, 167, w + 147],\ [181, 181, 2*w - 3],\ [181, 181, -2*w - 1],\ [193, 193, w + 62],\ [193, 193, w + 130],\ [211, 211, -4*w - 21],\ [211, 211, 4*w - 25],\ [227, 227, w + 85],\ [227, 227, w + 141],\ [229, 229, 14*w + 87],\ [229, 229, -14*w + 101],\ [257, 257, w + 75],\ [257, 257, w + 181],\ [269, 269, -10*w - 61],\ [269, 269, -10*w + 71],\ [271, 271, 6*w + 41],\ [271, 271, 6*w - 47],\ [277, 277, w + 24],\ [277, 277, w + 252],\ [283, 283, w + 121],\ [283, 283, w + 161],\ [313, 313, w + 50],\ [313, 313, w + 262],\ [347, 347, w + 134],\ [347, 347, w + 212],\ [349, 349, -4*w - 31],\ [349, 349, 4*w - 35],\ [353, 353, w + 106],\ [353, 353, w + 246],\ [359, 359, -8*w + 55],\ [359, 359, -8*w - 47],\ [361, 19, -19],\ [379, 379, -4*w - 17],\ [379, 379, 4*w - 21],\ [383, 383, w + 28],\ [383, 383, w + 354],\ [419, 419, -12*w - 73],\ [419, 419, -12*w + 85],\ [457, 457, w + 100],\ [457, 457, w + 356],\ [463, 463, w + 206],\ [463, 463, w + 256],\ [467, 467, w + 61],\ [467, 467, w + 405],\ [487, 487, w + 197],\ [487, 487, w + 289],\ [491, 491, 2*w - 27],\ [491, 491, -2*w - 25],\ [503, 503, w + 210],\ [503, 503, w + 292],\ [509, 509, -6*w - 31],\ [509, 509, 6*w - 37],\ [521, 521, 8*w + 55],\ [521, 521, 8*w - 63],\ [523, 523, w + 102],\ [523, 523, w + 420],\ [547, 547, w + 66],\ [547, 547, w + 480],\ [557, 557, w + 221],\ [557, 557, w + 335],\ [563, 563, w + 111],\ [563, 563, w + 451],\ [571, 571, 4*w - 15],\ [571, 571, -4*w - 11],\ [577, 577, w + 230],\ [577, 577, w + 346],\ [587, 587, w + 219],\ [587, 587, w + 367],\ [599, 599, 2*w - 29],\ [599, 599, -2*w - 27],\ [601, 601, -14*w - 85],\ [601, 601, -14*w + 99],\ [607, 607, w + 35],\ [607, 607, w + 571],\ [619, 619, -4*w - 9],\ [619, 619, 4*w - 13],\ [641, 641, 6*w - 35],\ [641, 641, -6*w - 29],\ [643, 643, w + 36],\ [643, 643, w + 606],\ [647, 647, w + 119],\ [647, 647, w + 527],\ [653, 653, w + 231],\ [653, 653, w + 421],\ [659, 659, 4*w - 11],\ [659, 659, -4*w - 7],\ [683, 683, w + 311],\ [683, 683, w + 371],\ [691, 691, -4*w - 5],\ [691, 691, 4*w - 9],\ [719, 719, 24*w + 149],\ [719, 719, -24*w + 173],\ [727, 727, w + 307],\ [727, 727, w + 419],\ [739, 739, 4*w - 3],\ [739, 739, 4*w - 1],\ [751, 751, -8*w - 43],\ [751, 751, -8*w + 51],\ [757, 757, w + 39],\ [757, 757, w + 717],\ [761, 761, 8*w - 65],\ [761, 761, 8*w + 57],\ [797, 797, w + 40],\ [797, 797, w + 756],\ [811, 811, -20*w - 123],\ [811, 811, -20*w + 143],\ [821, 821, -20*w + 149],\ [821, 821, -20*w - 129],\ [827, 827, w + 260],\ [827, 827, w + 566],\ [839, 839, 2*w - 33],\ [839, 839, -2*w - 31],\ [841, 29, -29],\ [853, 853, w + 330],\ [853, 853, w + 522],\ [857, 857, w + 241],\ [857, 857, w + 615],\ [881, 881, -6*w - 25],\ [881, 881, 6*w - 31],\ [883, 883, w + 387],\ [883, 883, w + 495],\ [907, 907, w + 170],\ [907, 907, w + 736],\ [929, 929, -16*w - 105],\ [929, 929, -16*w + 121],\ [941, 941, -4*w - 39],\ [941, 941, 4*w - 43],\ [947, 947, w + 144],\ [947, 947, w + 802],\ [961, 31, -31],\ [967, 967, w + 44],\ [967, 967, w + 922],\ [971, 971, 2*w - 35],\ [971, 971, -2*w - 33],\ [977, 977, w + 225],\ [977, 977, w + 751],\ [997, 997, w + 282],\ [997, 997, w + 714]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^4 + 7*x^2 + 4 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e, 0, e^2 + 3, -e^2 - 3, -e^2 - 3, e^3 + 5*e, -e^3 - 5*e, -2*e, 2*e, -e^3 - 9*e, e^3 + 9*e, 0, -3*e^2 - 11, -3*e^2 - 11, 2*e, -2*e, e^2 + 11, -e^2 + 1, -e^2 + 1, -3*e^3 - 21*e, 3*e^3 + 21*e, -e^2 - 7, -e^2 - 7, -2*e^3 - 8*e, 2*e^3 + 8*e, 2*e^3 + 16*e, -2*e^3 - 16*e, -4*e^2 - 20, -4*e^2 - 20, e^2 + 11, e^2 + 11, -12, -12, e^3 + e, -e^3 - e, -3*e^3 - 19*e, 3*e^3 + 19*e, 3*e^2 + 5, 3*e^2 + 5, -e^3 - 15*e, e^3 + 15*e, e^2 - 9, e^2 - 9, 4*e^3 + 30*e, -4*e^3 - 30*e, -e^2 - 1, -e^2 - 1, -e^3 - e, e^3 + e, 6*e^2 + 18, 6*e^2 + 18, 7*e^2 + 33, 7*e^2 + 33, 5*e^3 + 37*e, -5*e^3 - 37*e, 8*e^3 + 46*e, -8*e^3 - 46*e, -4*e^3 - 24*e, 4*e^3 + 24*e, 3*e^3 + 15*e, -3*e^3 - 15*e, 6*e^2 + 14, 6*e^2 + 14, 7*e^3 + 41*e, -7*e^3 - 41*e, -e^2 + 25, -e^2 + 25, -10*e^2 - 34, e^2 - 9, e^2 - 9, -7*e^3 - 31*e, 7*e^3 + 31*e, e^2 - 21, e^2 - 21, 4*e, -4*e, 6*e^3 + 52*e, -6*e^3 - 52*e, -4*e^3 - 34*e, 4*e^3 + 34*e, 4*e^3 + 26*e, -4*e^3 - 26*e, -4*e^2 - 4, -4*e^2 - 4, -4*e^3 - 30*e, 4*e^3 + 30*e, 3*e^2 - 1, 3*e^2 - 1, -5*e^2 - 3, -5*e^2 - 3, -2*e^3 - 8*e, 2*e^3 + 8*e, 8*e^3 + 58*e, -8*e^3 - 58*e, 5*e^3 + 25*e, -5*e^3 - 25*e, 3*e^3 + 27*e, -3*e^3 - 27*e, 9*e^2 + 35, 9*e^2 + 35, 10*e^3 + 60*e, -10*e^3 - 60*e, 3*e^3 + 7*e, -3*e^3 - 7*e, 3*e^2 + 13, 3*e^2 + 13, 2*e^2 - 10, 2*e^2 - 10, 10*e^3 + 52*e, -10*e^3 - 52*e, -13*e^2 - 35, -13*e^2 - 35, -7*e^2 - 5, -7*e^2 - 5, 3*e^3 + 3*e, -3*e^3 - 3*e, 11*e^3 + 63*e, -11*e^3 - 63*e, -e^3 + 5*e, e^3 - 5*e, 5*e^2 + 47, 5*e^2 + 47, 5*e^3 + 21*e, -5*e^3 - 21*e, -4*e^2 - 28, -4*e^2 - 28, e^2 - 5, e^2 - 5, 11*e^3 + 63*e, -11*e^3 - 63*e, -9*e^2 - 47, -9*e^2 - 47, e^2 + 19, e^2 + 19, -3*e^3 - 9*e, 3*e^3 + 9*e, 7*e^2 - 1, 7*e^2 - 1, -6*e^3 - 40*e, 6*e^3 + 40*e, -3*e^2 - 21, -3*e^2 - 21, 17*e^2 + 57, 17*e^2 + 57, -e^3 + 3*e, e^3 - 3*e, -8*e^2 - 48, -8*e^2 - 48, 12*e^2 + 22, 3*e^3 + 17*e, -3*e^3 - 17*e, 11*e^3 + 53*e, -11*e^3 - 53*e, 6*e^2 + 58, 6*e^2 + 58, 10*e^3 + 48*e, -10*e^3 - 48*e, -7*e^3 - 35*e, 7*e^3 + 35*e, -4*e^2 + 34, -4*e^2 + 34, 6*e^2 + 30, 6*e^2 + 30, 8*e^3 + 50*e, -8*e^3 - 50*e, 10*e^2 + 66, 4*e^3 + 30*e, -4*e^3 - 30*e, 8*e^2 + 44, 8*e^2 + 44, 10*e^3 + 42*e, -10*e^3 - 42*e, -e^3 - 11*e, e^3 + 11*e] 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]