/* 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, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([32, 8, 92*w - 624]) primes_array = [ [2, 2, 23*w - 156],\ [3, 3, -w - 7],\ [3, 3, w - 7],\ [5, 5, -9*w + 61],\ [5, 5, -9*w - 61],\ [7, 7, 4*w - 27],\ [7, 7, 4*w + 27],\ [23, 23, 78*w - 529],\ [37, 37, -w - 3],\ [37, 37, w - 3],\ [41, 41, -2*w + 15],\ [41, 41, 2*w + 15],\ [53, 53, -3*w - 19],\ [53, 53, 3*w - 19],\ [59, 59, 11*w - 75],\ [59, 59, -11*w - 75],\ [61, 61, -5*w + 33],\ [61, 61, 5*w + 33],\ [73, 73, -24*w - 163],\ [73, 73, -24*w + 163],\ [79, 79, 50*w + 339],\ [79, 79, 50*w - 339],\ [103, 103, 2*w - 9],\ [103, 103, -2*w - 9],\ [109, 109, 73*w - 495],\ [109, 109, -395*w + 2679],\ [121, 11, -11],\ [131, 131, 65*w + 441],\ [131, 131, 65*w - 441],\ [139, 139, -129*w + 875],\ [139, 139, -285*w + 1933],\ [149, 149, 15*w - 101],\ [149, 149, 15*w + 101],\ [157, 157, -349*w + 2367],\ [157, 157, 119*w - 807],\ [163, 163, 21*w - 143],\ [163, 163, -21*w - 143],\ [169, 13, -13],\ [179, 179, -w - 15],\ [179, 179, w - 15],\ [181, 181, 35*w + 237],\ [181, 181, 35*w - 237],\ [191, 191, 30*w - 203],\ [191, 191, -30*w - 203],\ [193, 193, -6*w + 43],\ [193, 193, 6*w + 43],\ [199, 199, -280*w + 1899],\ [199, 199, 188*w - 1275],\ [211, 211, 3*w - 25],\ [211, 211, -3*w - 25],\ [229, 229, 7*w - 45],\ [229, 229, -7*w - 45],\ [233, 233, 26*w - 177],\ [233, 233, -26*w - 177],\ [257, 257, 2*w - 21],\ [257, 257, -2*w - 21],\ [263, 263, 18*w + 121],\ [263, 263, -18*w + 121],\ [289, 17, -17],\ [293, 293, 3*w - 11],\ [293, 293, -3*w - 11],\ [307, 307, 93*w + 631],\ [307, 307, 93*w - 631],\ [331, 331, 75*w - 509],\ [331, 331, 75*w + 509],\ [347, 347, 7*w + 51],\ [347, 347, -7*w + 51],\ [353, 353, 4*w - 33],\ [353, 353, -4*w - 33],\ [359, 359, -48*w - 325],\ [359, 359, 48*w - 325],\ [361, 19, -19],\ [367, 367, -14*w + 93],\ [367, 367, 14*w + 93],\ [373, 373, 43*w - 291],\ [373, 373, -43*w - 291],\ [383, 383, -12*w + 79],\ [383, 383, 12*w + 79],\ [389, 389, 3*w - 5],\ [389, 389, -3*w - 5],\ [409, 409, 36*w - 245],\ [409, 409, -36*w - 245],\ [421, 421, 5*w - 27],\ [421, 421, -5*w - 27],\ [431, 431, 6*w - 35],\ [431, 431, -6*w - 35],\ [443, 443, 49*w + 333],\ [443, 443, -49*w + 333],\ [449, 449, -80*w - 543],\ [449, 449, -80*w + 543],\ [479, 479, 132*w - 895],\ [479, 479, 132*w + 895],\ [491, 491, -25*w + 171],\ [491, 491, 25*w + 171],\ [499, 499, 9*w + 65],\ [499, 499, -9*w + 65],\ [503, 503, 252*w - 1709],\ [503, 503, -528*w + 3581],\ [547, 547, 3*w - 31],\ [547, 547, -3*w - 31],\ [557, 557, 321*w - 2177],\ [557, 557, -459*w + 3113],\ [577, 577, -162*w + 1099],\ [577, 577, -162*w - 1099],\ [587, 587, 103*w - 699],\ [587, 587, 103*w + 699],\ [593, 593, -226*w + 1533],\ [593, 593, -694*w + 4707],\ [601, 601, -12*w + 85],\ [601, 601, 12*w + 85],\ [613, 613, 127*w - 861],\ [613, 613, 127*w + 861],\ [631, 631, 10*w - 63],\ [631, 631, -10*w - 63],\ [661, 661, -29*w + 195],\ [661, 661, 29*w + 195],\ [673, 673, 144*w - 977],\ [673, 673, 144*w + 977],\ [677, 677, 201*w - 1363],\ [677, 677, -891*w + 6043],\ [683, 683, -w - 27],\ [683, 683, w - 27],\ [691, 691, -27*w - 185],\ [691, 691, 27*w - 185],\ [701, 701, -9*w - 55],\ [701, 701, 9*w - 55],\ [709, 709, -5*w - 21],\ [709, 709, 5*w - 21],\ [727, 727, 4*w - 3],\ [727, 727, -4*w - 3],\ [733, 733, -7*w - 39],\ [733, 733, 7*w - 39],\ [739, 739, -21*w + 145],\ [739, 739, 21*w + 145],\ [743, 743, 18*w + 119],\ [743, 743, -18*w + 119],\ [751, 751, 16*w - 105],\ [751, 751, -16*w - 105],\ [757, 757, -89*w - 603],\ [757, 757, -89*w + 603],\ [761, 761, -740*w + 5019],\ [761, 761, -272*w + 1845],\ [773, 773, 27*w + 181],\ [773, 773, -27*w + 181],\ [797, 797, -39*w + 263],\ [797, 797, -39*w - 263],\ [809, 809, 64*w + 435],\ [809, 809, -64*w + 435],\ [811, 811, -3*w - 35],\ [811, 811, 3*w - 35],\ [839, 839, 270*w - 1831],\ [839, 839, -822*w + 5575],\ [841, 29, -29],\ [857, 857, 32*w + 219],\ [857, 857, -32*w + 219],\ [859, 859, -405*w + 2747],\ [859, 859, -561*w + 3805],\ [883, 883, -231*w + 1567],\ [883, 883, -1011*w + 6857],\ [911, 911, -54*w + 365],\ [911, 911, -54*w - 365],\ [919, 919, 8*w - 45],\ [919, 919, -8*w - 45],\ [929, 929, 40*w - 273],\ [929, 929, 40*w + 273],\ [941, 941, 15*w - 97],\ [941, 941, -15*w - 97],\ [947, 947, -23*w + 159],\ [947, 947, 23*w + 159],\ [961, 31, -31],\ [983, 983, 168*w + 1139],\ [983, 983, 168*w - 1139]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 10, 10, -14, -14, 0, 0, 10, 10, -6, -6, 0, 0, 0, 0, -6, -6, -22, 0, 0, 0, 0, -14, -14, -22, -22, 0, 0, 10, 0, 0, 18, 18, 0, 0, -14, -14, 0, 0, 0, 0, -30, -30, 26, 26, 2, 2, 0, 0, -30, 34, 34, 0, 0, 0, 0, 0, 0, 34, 34, 0, 0, -38, 0, 0, -14, -14, 0, 0, 34, 34, -6, -6, -30, -30, 0, 0, 0, 0, -14, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -38, -38, 2, 2, 0, 0, -46, -46, 10, 10, 34, 34, 0, 0, 50, 50, -46, -46, 2, 2, 0, 0, 0, 0, 10, 10, -30, -30, 0, 0, -54, -54, 0, 0, 0, 0, 0, 0, 18, 18, -38, -38, 34, 34, -22, -22, 10, 10, 0, 0, 0, 0, 42, 58, 58, 0, 0, 0, 0, 0, 0, 0, 0, -46, -46, 58, 58, 0, 0, -62, 0, 0] 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, 23*w - 156])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]