/* 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([-67, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([6, 6, 5*w + 41]) primes_array = [ [2, 2, -27*w + 221],\ [3, 3, -w + 8],\ [3, 3, -w - 8],\ [7, 7, -11*w + 90],\ [7, 7, -11*w - 90],\ [11, 11, 6*w - 49],\ [11, 11, 6*w + 49],\ [17, 17, 4*w + 33],\ [17, 17, -4*w + 33],\ [25, 5, -5],\ [29, 29, -70*w + 573],\ [29, 29, 151*w - 1236],\ [31, 31, -w - 6],\ [31, 31, w - 6],\ [37, 37, -21*w - 172],\ [37, 37, -21*w + 172],\ [43, 43, 2*w - 15],\ [43, 43, 2*w + 15],\ [67, 67, -w],\ [73, 73, -3*w - 26],\ [73, 73, -3*w + 26],\ [79, 79, 92*w - 753],\ [79, 79, 313*w - 2562],\ [89, 89, -5*w - 42],\ [89, 89, -5*w + 42],\ [139, 139, 10*w + 81],\ [139, 139, 10*w - 81],\ [149, 149, 19*w - 156],\ [149, 149, -19*w - 156],\ [157, 157, -102*w + 835],\ [157, 157, 561*w - 4592],\ [169, 13, -13],\ [173, 173, 2*w - 21],\ [173, 173, -2*w - 21],\ [179, 179, 87*w - 712],\ [179, 179, 87*w + 712],\ [181, 181, 3*w - 28],\ [181, 181, 3*w + 28],\ [191, 191, 15*w - 122],\ [191, 191, 15*w + 122],\ [193, 193, 36*w + 295],\ [193, 193, -36*w + 295],\ [239, 239, 12*w + 97],\ [239, 239, 12*w - 97],\ [241, 241, -183*w + 1498],\ [241, 241, 480*w - 3929],\ [251, 251, 45*w + 368],\ [251, 251, 45*w - 368],\ [257, 257, -w - 18],\ [257, 257, w - 18],\ [269, 269, 41*w + 336],\ [269, 269, -41*w + 336],\ [271, 271, 40*w - 327],\ [271, 271, -40*w - 327],\ [277, 277, 426*w - 3487],\ [277, 277, -237*w + 1940],\ [293, 293, -998*w + 8169],\ [293, 293, 107*w - 876],\ [311, 311, 804*w - 6581],\ [311, 311, 141*w - 1154],\ [317, 317, -7*w + 60],\ [317, 317, -7*w - 60],\ [331, 331, 254*w - 2079],\ [331, 331, 475*w - 3888],\ [347, 347, -3*w - 16],\ [347, 347, 3*w - 16],\ [349, 349, -9*w - 76],\ [349, 349, -9*w + 76],\ [361, 19, -19],\ [367, 367, 7*w + 54],\ [367, 367, 7*w - 54],\ [379, 379, 5*w + 36],\ [379, 379, 5*w - 36],\ [383, 383, 168*w - 1375],\ [383, 383, 831*w - 6802],\ [389, 389, 34*w - 279],\ [389, 389, -34*w - 279],\ [397, 397, -6*w - 53],\ [397, 397, -6*w + 53],\ [421, 421, -3*w - 32],\ [421, 421, 3*w - 32],\ [443, 443, -27*w - 220],\ [443, 443, -27*w + 220],\ [449, 449, -4*w - 39],\ [449, 449, 4*w - 39],\ [457, 457, 51*w + 418],\ [457, 457, -51*w + 418],\ [461, 461, 2*w - 27],\ [461, 461, -2*w - 27],\ [463, 463, 136*w + 1113],\ [463, 463, 136*w - 1113],\ [487, 487, 32*w + 261],\ [487, 487, -32*w + 261],\ [499, 499, -62*w - 507],\ [499, 499, 62*w - 507],\ [503, 503, -3*w - 10],\ [503, 503, 3*w - 10],\ [509, 509, -w - 24],\ [509, 509, w - 24],\ [529, 23, -23],\ [547, 547, 47*w + 384],\ [547, 547, -47*w + 384],\ [557, 557, 14*w - 117],\ [557, 557, 14*w + 117],\ [563, 563, 6*w + 43],\ [563, 563, 6*w - 43],\ [569, 569, -56*w - 459],\ [569, 569, 56*w - 459],\ [587, 587, -3*w - 4],\ [587, 587, 3*w - 4],\ [599, 599, 3*w - 2],\ [599, 599, -3*w - 2],\ [601, 601, 117*w - 958],\ [601, 601, 117*w + 958],\ [613, 613, 6*w - 55],\ [613, 613, -6*w - 55],\ [617, 617, -269*w + 2202],\ [617, 617, 836*w - 6843],\ [631, 631, -4*w - 21],\ [631, 631, 4*w - 21],\ [647, 647, 21*w - 170],\ [647, 647, 21*w + 170],\ [683, 683, 18*w + 145],\ [683, 683, 18*w - 145],\ [709, 709, 30*w - 247],\ [709, 709, 30*w + 247],\ [727, 727, 416*w - 3405],\ [727, 727, 637*w - 5214],\ [739, 739, 158*w - 1293],\ [739, 739, 158*w + 1293],\ [761, 761, -100*w - 819],\ [761, 761, -100*w + 819],\ [773, 773, 122*w + 999],\ [773, 773, 122*w - 999],\ [787, 787, -1322*w + 10821],\ [787, 787, -217*w + 1776],\ [797, 797, 674*w - 5517],\ [797, 797, -431*w + 3528],\ [811, 811, 14*w - 111],\ [811, 811, 14*w + 111],\ [821, 821, 2*w - 33],\ [821, 821, -2*w - 33],\ [829, 829, -66*w - 541],\ [829, 829, 66*w - 541],\ [853, 853, -171*w - 1400],\ [853, 853, 171*w - 1400],\ [877, 877, 54*w - 443],\ [877, 877, -54*w - 443],\ [881, 881, 1300*w - 10641],\ [881, 881, -247*w + 2022],\ [883, 883, 31*w + 252],\ [883, 883, 31*w - 252],\ [919, 919, 13*w + 102],\ [919, 919, 13*w - 102],\ [953, 953, 4*w - 45],\ [953, 953, -4*w - 45],\ [977, 977, -71*w - 582],\ [977, 977, 71*w - 582],\ [983, 983, 36*w - 293],\ [983, 983, 36*w + 293],\ [991, 991, -4*w - 9],\ [991, 991, 4*w - 9],\ [997, 997, 3*w - 40],\ [997, 997, -3*w - 40]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 1, 1, -2, -3, 5, 1, 0, -2, -6, 6, -3, -7, 10, -2, 3, -2, -2, 5, 2, 2, -6, 3, -14, -4, 16, -12, -6, -11, -4, -14, -6, -13, 6, -6, -4, 18, -13, -15, -16, -6, -25, 25, 6, -7, 7, 6, 24, -18, 23, -30, -31, 12, 17, 18, -1, 18, -16, 3, -18, -22, -24, 17, -13, -7, 7, 31, 28, 7, -3, -32, 19, -31, 10, 20, -8, -27, 21, 8, -18, -7, 2, -34, 18, 10, -34, 16, -6, -24, 8, -7, -12, -2, -40, -14, 16, -12, 36, -35, -16, -2, -34, -16, 14, 12, -30, -5, -15, 16, -24, 20, -35, 34, 22, -9, 46, -12, -12, 4, -21, 22, -31, 38, -6, 45, -30, 32, -7, 0, -26, -40, -12, 35, -42, 1, -4, 46, 38, 8, -25, -20, 30, -6, 2, 6, -26, 6, 23, -40, 18, -4, -20, 26, -8, 38, -7, -8, 40, 35, 36, -5, 36, 14, 16] 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, -27*w + 221])] = 1 AL_eigenvalues[ZF.ideal([3, 3, -w + 8])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]