/* 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([-3, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([19, 19, -w^2 - w + 4]) primes_array = [ [3, 3, w],\ [3, 3, w + 1],\ [3, 3, w + 2],\ [8, 2, 2],\ [11, 11, -w^2 + 5],\ [13, 13, w^2 - w - 7],\ [17, 17, -w^2 + w + 4],\ [19, 19, -w^2 - w + 4],\ [29, 29, 2*w^2 - 2*w - 11],\ [31, 31, w^2 - 2*w - 4],\ [37, 37, -2*w^2 + 3*w + 7],\ [41, 41, w^2 - 2],\ [59, 59, 2*w^2 - 13],\ [61, 61, w^2 + w - 10],\ [67, 67, 2*w^2 - w - 11],\ [73, 73, -w^2 - 1],\ [83, 83, w^2 - w - 10],\ [89, 89, -w^2 + 4*w - 2],\ [97, 97, w^2 - 2*w - 7],\ [97, 97, -w^2 - 4*w - 5],\ [97, 97, 2*w^2 + w - 8],\ [101, 101, -4*w^2 + 2*w + 25],\ [103, 103, w^2 + w - 7],\ [107, 107, -3*w - 4],\ [109, 109, 5*w^2 - 3*w - 31],\ [121, 11, 2*w^2 - 3*w - 4],\ [125, 5, -5],\ [137, 137, -5*w^2 + 3*w + 34],\ [139, 139, w^2 + 2*w - 4],\ [151, 151, 3*w^2 - 23],\ [151, 151, w^2 - 3*w - 5],\ [151, 151, 3*w^2 - 3*w - 17],\ [157, 157, 4*w^2 - 9*w - 8],\ [157, 157, w^2 + 3*w - 2],\ [157, 157, 2*w^2 - w - 2],\ [167, 167, 2*w^2 + w - 11],\ [167, 167, -w^2 + 11],\ [167, 167, -3*w^2 + 19],\ [169, 13, w^2 - 4*w - 4],\ [173, 173, 2*w^2 - 3*w - 10],\ [179, 179, -3*w + 7],\ [191, 191, -w^2 + 5*w - 5],\ [193, 193, -w^2 + w - 2],\ [199, 199, 3*w - 2],\ [211, 211, w^2 - 3*w - 11],\ [223, 223, 3*w^2 - 20],\ [223, 223, w^2 - 5*w - 4],\ [223, 223, 2*w^2 - w - 8],\ [229, 229, 4*w^2 - 3*w - 26],\ [229, 229, 2*w^2 + w - 20],\ [229, 229, 2*w^2 - 2*w - 5],\ [239, 239, -6*w^2 + 3*w + 38],\ [241, 241, -w^2 + 4*w - 5],\ [257, 257, -2*w^2 + 5*w - 1],\ [263, 263, -2*w^2 - w + 17],\ [269, 269, -w^2 - w + 13],\ [269, 269, 3*w - 4],\ [269, 269, -4*w^2 + w + 31],\ [271, 271, 2*w^2 - 7],\ [271, 271, 3*w - 5],\ [271, 271, w^2 - 3*w - 8],\ [289, 17, 2*w^2 + w - 5],\ [307, 307, 2*w^2 - w - 5],\ [311, 311, 3*w^2 - 3*w - 19],\ [311, 311, -7*w^2 + 13*w + 19],\ [311, 311, w^2 - 2*w - 13],\ [313, 313, w^2 + 2*w - 7],\ [317, 317, -5*w^2 + w + 35],\ [331, 331, -w^2 + 3*w - 4],\ [337, 337, 3*w^2 - 3*w - 13],\ [343, 7, -7],\ [347, 347, 2*w^2 - 3*w - 13],\ [349, 349, 3*w^2 - 3*w - 20],\ [359, 359, -w^2 + 5*w - 2],\ [361, 19, -2*w^2 + 7*w - 1],\ [389, 389, -2*w^2 + w - 1],\ [397, 397, w^2 - 6*w + 10],\ [401, 401, 6*w^2 - 3*w - 44],\ [419, 419, -3*w^2 + 6*w + 10],\ [419, 419, 4*w^2 - 2*w - 31],\ [419, 419, -4*w^2 + 4*w + 19],\ [421, 421, 6*w^2 - 12*w - 13],\ [431, 431, 4*w^2 - 7*w - 10],\ [433, 433, w^2 - 4*w - 7],\ [443, 443, 2*w^2 + 4*w - 5],\ [443, 443, 5*w^2 - 11*w - 11],\ [443, 443, 3*w^2 - 14],\ [449, 449, -2*w^2 + 2*w - 1],\ [457, 457, w^2 - 6*w - 5],\ [457, 457, w^2 + 3*w - 5],\ [457, 457, 6*w^2 - 3*w - 37],\ [463, 463, w^2 + 5*w - 1],\ [467, 467, w^2 - w - 13],\ [479, 479, 5*w^2 - 9*w - 16],\ [487, 487, -6*w - 5],\ [499, 499, 3*w^2 - 3*w - 4],\ [499, 499, 3*w^2 + 3*w - 1],\ [499, 499, w^2 - 5*w + 8],\ [503, 503, 4*w^2 - 5*w - 16],\ [509, 509, 2*w^2 - 5*w - 8],\ [521, 521, 4*w^2 - w - 22],\ [523, 523, w^2 - 5*w - 16],\ [547, 547, 5*w^2 - 2*w - 38],\ [547, 547, 8*w^2 - 3*w - 58],\ [547, 547, 4*w^2 - 29],\ [557, 557, 7*w^2 - 4*w - 43],\ [557, 557, 3*w - 11],\ [557, 557, 2*w^2 - 4*w - 11],\ [569, 569, 5*w^2 - 4*w - 32],\ [569, 569, 3*w^2 - 3*w - 11],\ [569, 569, w^2 + 2*w - 16],\ [571, 571, w^2 - 4*w - 10],\ [593, 593, 2*w^2 - 6*w - 7],\ [601, 601, -w^2 - 3*w + 14],\ [607, 607, 3*w^2 + 3*w - 7],\ [619, 619, 3*w^2 - 6*w - 11],\ [631, 631, -w^2 - w - 5],\ [641, 641, 3*w^2 - 3*w - 5],\ [647, 647, -w^2 + 6*w - 1],\ [653, 653, -5*w^2 + 4*w + 35],\ [661, 661, 3*w^2 - 3*w - 10],\ [673, 673, w^2 + 4*w - 4],\ [677, 677, 5*w^2 - 6*w - 25],\ [677, 677, w^2 - 14],\ [677, 677, 4*w^2 - 3*w - 20],\ [691, 691, 5*w^2 - 2*w - 29],\ [701, 701, 5*w^2 - 10*w - 14],\ [719, 719, -3*w - 11],\ [727, 727, -2*w^2 + 9*w - 8],\ [733, 733, -w^2 - 4*w - 8],\ [739, 739, w^2 + 3*w - 8],\ [743, 743, 2*w^2 - 4*w - 17],\ [757, 757, -w^2 + w - 5],\ [769, 769, 3*w^2 - 3*w - 7],\ [769, 769, -w^2 - 3*w - 7],\ [769, 769, 5*w^2 - 3*w - 28],\ [773, 773, 7*w^2 - 6*w - 38],\ [787, 787, 2*w^2 - w - 20],\ [797, 797, -5*w^2 + 14*w - 1],\ [821, 821, -w^2 + 6*w - 4],\ [823, 823, 7*w^2 - 6*w - 41],\ [839, 839, 4*w^2 - 6*w - 11],\ [841, 29, 5*w^2 - 4*w - 26],\ [857, 857, 3*w^2 - 11],\ [863, 863, 2*w^2 + 2*w - 17],\ [881, 881, 5*w^2 - 5*w - 29],\ [883, 883, -4*w^2 + 8*w + 13],\ [907, 907, 4*w^2 - 9*w - 11],\ [911, 911, 2*w^2 + 3*w - 10],\ [947, 947, 2*w^2 + 5*w - 5],\ [953, 953, 2*w^2 - 5*w - 11],\ [961, 31, w^2 - 5*w - 13],\ [967, 967, 2*w^2 - 3*w - 22],\ [967, 967, 5*w^2 - 9*w - 10],\ [967, 967, 3*w^2 - 10],\ [977, 977, 5*w^2 - 37],\ [983, 983, 7*w^2 - 5*w - 40],\ [997, 997, -7*w^2 + 5*w + 49]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 2, 1, 0, -3, -1, 6, -1, -9, 4, 4, 3, -6, 4, -10, -2, -12, 6, -2, 8, -5, -3, -11, 0, -2, -14, -9, 6, -13, -5, 2, 1, -7, -10, -4, -12, 6, 6, -4, -3, 3, 12, 16, 13, -4, 4, -2, 8, -10, 10, -2, -9, 7, 21, -9, 18, -30, 6, 16, 10, -16, -20, 20, -6, -24, 0, -22, -6, -14, 20, -16, -18, 10, -27, 25, 30, -14, -39, -15, 36, 30, -28, 24, -34, 0, -6, -27, -18, 32, 5, 2, -4, 6, 12, -23, -7, -4, 14, -21, 42, 30, -11, -26, -8, 5, -3, 24, 30, 24, -15, 6, 20, 0, -40, -40, -44, -13, -6, -18, 39, -4, 22, -27, 27, -12, 10, 15, -36, 8, -34, -22, -12, 22, 14, -5, 28, 18, -37, 0, 18, -16, -9, 32, 42, -36, 30, 31, 26, 15, -36, 48, -44, -23, 40, -13, 18, -54, 28] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([19, 19, -w^2 - w + 4])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]