/* 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([-5, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, -w^2 + 2*w + 4]) primes_array = [ [5, 5, w],\ [8, 2, 2],\ [11, 11, -w^2 + 2*w + 4],\ [11, 11, -w + 2],\ [11, 11, w - 1],\ [13, 13, -w^2 + w + 4],\ [17, 17, -w^2 + w + 8],\ [17, 17, -w^2 + w + 3],\ [19, 19, -w^2 + 6],\ [23, 23, -w^2 + 3],\ [25, 5, w^2 - 7],\ [27, 3, -3],\ [31, 31, w^2 - 2*w - 8],\ [37, 37, w^2 - 2*w - 6],\ [41, 41, -w - 4],\ [41, 41, w^2 - 2*w - 7],\ [47, 47, 2*w^2 - 3*w - 7],\ [53, 53, -w^2 + w + 9],\ [61, 61, 3*w^2 - 2*w - 17],\ [67, 67, 2*w - 1],\ [73, 73, 2*w^2 - 2*w - 9],\ [89, 89, 2*w^2 - 3*w - 11],\ [97, 97, 2*w^2 - w - 9],\ [97, 97, w^2 - 3*w - 6],\ [97, 97, 2*w - 3],\ [101, 101, 3*w^2 - 4*w - 13],\ [107, 107, 2*w^2 - 3*w - 14],\ [113, 113, 2*w^2 - 3*w - 12],\ [127, 127, -w^2 + w - 1],\ [127, 127, 2*w^2 - 2*w - 7],\ [127, 127, w^2 + 3*w - 1],\ [131, 131, w^2 - 3*w - 8],\ [137, 137, 2*w^2 - w - 8],\ [139, 139, 4*w^2 - 5*w - 19],\ [149, 149, w^2 + w - 7],\ [151, 151, w^2 - 4*w - 6],\ [157, 157, w^2 + w - 9],\ [163, 163, w^2 + w - 8],\ [169, 13, 2*w^2 - w - 7],\ [173, 173, w^2 - 5*w - 3],\ [179, 179, -w - 6],\ [191, 191, w^2 + 2*w - 4],\ [197, 197, 3*w - 1],\ [229, 229, 3*w^2 - 4*w - 18],\ [233, 233, -w^2 + w - 2],\ [233, 233, -3*w^2 + 4*w + 11],\ [233, 233, 3*w^2 - w - 14],\ [239, 239, 3*w^2 - 5*w - 14],\ [241, 241, w^2 - 4*w - 11],\ [257, 257, -2*w^2 + 2*w + 17],\ [263, 263, 3*w^2 - 3*w - 23],\ [269, 269, w^2 - 2*w - 12],\ [277, 277, w^2 - 4*w - 9],\ [281, 281, 4*w^2 - 2*w - 21],\ [283, 283, 3*w^2 - 3*w - 13],\ [293, 293, 3*w^2 - 4*w - 9],\ [331, 331, w^2 + 3*w - 3],\ [337, 337, w^2 + 2*w - 6],\ [343, 7, -7],\ [361, 19, w^2 - 5*w - 1],\ [367, 367, w^2 - 5*w - 8],\ [373, 373, w^2 + 2*w - 16],\ [373, 373, 2*w^2 + w - 11],\ [373, 373, 3*w^2 - 2*w - 13],\ [379, 379, -w^2 + w - 3],\ [383, 383, 2*w^2 - 6*w - 9],\ [401, 401, w^2 + 2*w - 7],\ [419, 419, 3*w^2 - 6*w - 13],\ [421, 421, 4*w^2 - 5*w - 26],\ [431, 431, 4*w - 1],\ [439, 439, w^2 - 5*w - 9],\ [439, 439, w^2 - 2*w - 13],\ [439, 439, 4*w^2 - 7*w - 17],\ [443, 443, 3*w^2 - 3*w - 8],\ [443, 443, w^2 - 13],\ [443, 443, 3*w^2 - w - 12],\ [449, 449, 4*w^2 - 6*w - 13],\ [457, 457, w^2 + 2*w - 11],\ [461, 461, -w - 8],\ [461, 461, -w^2 + 5*w - 1],\ [461, 461, 2*w^2 + w - 12],\ [463, 463, 3*w^2 + w - 9],\ [487, 487, 5*w^2 - 3*w - 27],\ [499, 499, 4*w^2 - w - 24],\ [499, 499, w^2 - 5*w - 11],\ [499, 499, 5*w^2 - 4*w - 27],\ [503, 503, 3*w^2 - 5*w - 22],\ [503, 503, 3*w^2 - 5*w - 17],\ [503, 503, 5*w^2 - 8*w - 22],\ [509, 509, -w^2 - 4],\ [529, 23, 4*w^2 - 5*w - 16],\ [541, 541, 2*w^2 + w - 17],\ [547, 547, -w^2 + 2*w - 4],\ [547, 547, 3*w^2 - 6*w - 14],\ [547, 547, 2*w^2 - 5*w - 17],\ [557, 557, 5*w^2 - 2*w - 31],\ [563, 563, 3*w^2 - 5*w - 18],\ [571, 571, -w^2 + w - 4],\ [571, 571, w^2 - 6*w - 2],\ [571, 571, 3*w^2 + w - 8],\ [577, 577, 2*w^2 - w - 19],\ [587, 587, 2*w^2 - 5*w - 13],\ [593, 593, 2*w^2 + w - 16],\ [599, 599, 3*w^2 - 19],\ [599, 599, 3*w^2 - 5*w - 19],\ [599, 599, 4*w^2 - w - 18],\ [607, 607, 4*w^2 - 2*w - 19],\ [617, 617, 4*w^2 - 3*w - 19],\ [619, 619, 4*w^2 - 7*w - 18],\ [643, 643, 3*w^2 + w - 7],\ [643, 643, 2*w^2 - 2*w - 19],\ [643, 643, 5*w^2 - 8*w - 16],\ [653, 653, 3*w^2 - w - 9],\ [653, 653, 2*w^2 - 6*w - 11],\ [653, 653, 3*w^2 - w - 7],\ [659, 659, w^2 - 2*w - 14],\ [661, 661, 5*w^2 - 6*w - 31],\ [661, 661, w^2 - 14],\ [661, 661, w - 9],\ [673, 673, -2*w^2 + 4*w - 1],\ [673, 673, 4*w^2 - w - 26],\ [673, 673, 6*w^2 - 5*w - 33],\ [677, 677, 3*w^2 - 8],\ [719, 719, 6*w^2 - 7*w - 29],\ [719, 719, 4*w^2 - 6*w - 29],\ [719, 719, 4*w^2 - 5*w - 14],\ [727, 727, 4*w^2 - 4*w - 31],\ [743, 743, w^2 - w - 14],\ [757, 757, 5*w^2 - 8*w - 23],\ [761, 761, w^2 - 6*w - 11],\ [761, 761, 4*w - 7],\ [761, 761, 4*w^2 - 3*w - 18],\ [773, 773, -5*w^2 + 10*w + 18],\ [787, 787, 5*w^2 - 7*w - 19],\ [797, 797, 4*w^2 - 5*w - 12],\ [797, 797, 3*w^2 + w - 16],\ [797, 797, 3*w^2 - 6*w - 16],\ [811, 811, w^2 + 3*w - 7],\ [821, 821, 4*w^2 - 6*w - 23],\ [829, 829, 2*w^2 + 2*w - 11],\ [829, 829, 2*w^2 - 7*w - 11],\ [829, 829, 5*w^2 - 5*w - 24],\ [853, 853, 2*w^2 - 6*w - 19],\ [857, 857, w^2 + 4*w - 4],\ [877, 877, -w^2 - w - 6],\ [881, 881, -4*w^2 + 4*w + 9],\ [883, 883, 2*w^2 - 6*w - 13],\ [907, 907, 3*w^2 - 6*w - 17],\ [911, 911, w^2 + 3*w - 8],\ [919, 919, 4*w^2 - 8*w - 17],\ [937, 937, 4*w^2 - 6*w - 27],\ [941, 941, 4*w^2 - 2*w - 17],\ [947, 947, 3*w^2 - 8*w - 13],\ [961, 31, 6*w^2 - 7*w - 39],\ [967, 967, 5*w - 2],\ [971, 971, 5*w^2 - 9*w - 21],\ [977, 977, 3*w^2 + w - 17],\ [983, 983, 2*w - 11],\ [991, 991, 6*w^2 - 7*w - 38],\ [991, 991, w^2 + 3*w - 9],\ [991, 991, w^2 + 3*w - 13],\ [997, 997, 4*w^2 - w - 16],\ [997, 997, 5*w - 12],\ [997, 997, 3*w^2 - 2*w - 26]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^2 - 32 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, -3, -1, e, -1/2*e, 0, -2, -e, -1/2*e, e, 0, -4, 0, -6, -10, -6, -2*e, -6, 1/2*e, e, 3/2*e, 2, 1/2*e, 2, 0, -e, 12, 14, -8, 1/2*e, -e, -12, -3*e, 3*e, 3/2*e, 8, 0, 3/2*e, -1/2*e, 5/2*e, 4, -5/2*e, 1/2*e, 10, 6, -2*e, 4*e, 24, -10, -18, -16, 10, 14, 3/2*e, -3/2*e, -1/2*e, -3/2*e, -3*e, -32, 3/2*e, 8, -22, 3*e, -11/2*e, 12, -16, 11/2*e, 4, 34, 7/2*e, 16, -32, -16, -1/2*e, -4, 13/2*e, 11/2*e, -5*e, -2, 3*e, -6*e, -3/2*e, 0, -6*e, -20, -3*e, 0, 16, 8, -2, -15/2*e, -2*e, -4, -36, -44, e, 44, -20, -1/2*e, -3*e, 18, 12, -7/2*e, 2*e, 32, 5/2*e, 13/2*e, -e, 20, -15/2*e, 4, 0, 6*e, 18, -2*e, -20, -22, -42, -22, -14, -15/2*e, -15/2*e, -e, -1/2*e, -16, 2*e, 24, 16, 50, 50, -4*e, -13/2*e, 34, 5*e, 5/2*e, 19/2*e, 22, 0, 22, 8*e, -50, -7/2*e, 26, -8*e, -50, 5*e, 20, -20, 3/2*e, 16, -22, -5*e, -20, 2, 17/2*e, -44, -8*e, -40, 8, -6*e, 3/2*e, 2*e, -4*e, 38] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, -w^2 + 2*w + 4])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]