/* 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([1, 5, 2, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([25, 25, -w^3 + w^2 + 3*w - 2]) primes_array = [ [3, 3, -w^4 + w^3 + 4*w^2 - 2*w - 2],\ [5, 5, w^2 - w - 2],\ [19, 19, w^4 - 2*w^3 - 4*w^2 + 5*w + 4],\ [23, 23, -w^3 + w^2 + 3*w - 1],\ [29, 29, 2*w^4 - 3*w^3 - 8*w^2 + 7*w + 4],\ [32, 2, 2],\ [37, 37, w^3 - 2*w^2 - 2*w + 2],\ [41, 41, -2*w^4 + 3*w^3 + 9*w^2 - 8*w - 6],\ [43, 43, -2*w^4 + 3*w^3 + 8*w^2 - 8*w - 6],\ [47, 47, w^4 - 2*w^3 - 5*w^2 + 6*w + 5],\ [53, 53, -w^4 + w^3 + 4*w^2 - w - 4],\ [61, 61, w^2 - 2*w - 3],\ [67, 67, w^4 - w^3 - 4*w^2 + 3*w],\ [67, 67, -w^4 + w^3 + 5*w^2 - 2*w - 2],\ [71, 71, w^4 - w^3 - 4*w^2 + 5],\ [71, 71, w^4 - 2*w^3 - 3*w^2 + 5*w + 3],\ [71, 71, 2*w^4 - 2*w^3 - 8*w^2 + 5*w + 4],\ [73, 73, -2*w^4 + 2*w^3 + 9*w^2 - 5*w - 6],\ [81, 3, -2*w^4 + 3*w^3 + 10*w^2 - 9*w - 10],\ [97, 97, -2*w^4 + 3*w^3 + 7*w^2 - 5*w - 4],\ [101, 101, -w^4 + 2*w^3 + 2*w^2 - 4*w + 2],\ [103, 103, -w^4 + w^3 + 3*w^2 - 2],\ [103, 103, -2*w^4 + 2*w^3 + 10*w^2 - 5*w - 7],\ [107, 107, 3*w^4 - 4*w^3 - 12*w^2 + 10*w + 5],\ [107, 107, -w^4 + 6*w^2 + w - 4],\ [107, 107, w^4 - 2*w^3 - 5*w^2 + 8*w + 3],\ [109, 109, 3*w^4 - 3*w^3 - 13*w^2 + 6*w + 8],\ [127, 127, -w^4 + 6*w^2 + 2*w - 5],\ [131, 131, -2*w^4 + 3*w^3 + 7*w^2 - 7*w - 5],\ [137, 137, w^4 - w^3 - 3*w^2 - 2],\ [137, 137, 3*w^4 - 5*w^3 - 12*w^2 + 12*w + 9],\ [151, 151, 2*w^4 - 2*w^3 - 8*w^2 + 3*w + 6],\ [151, 151, 2*w^4 - 4*w^3 - 8*w^2 + 11*w + 6],\ [157, 157, -w^4 + 2*w^3 + 2*w^2 - 5*w],\ [167, 167, -w^4 + 6*w^2 - w - 5],\ [167, 167, w^4 - w^3 - 6*w^2 + 3*w + 4],\ [167, 167, w^4 - 5*w^2 - 3*w + 3],\ [169, 13, -w^3 + 4*w - 1],\ [173, 173, w^4 - 2*w^3 - 5*w^2 + 7*w + 4],\ [181, 181, 2*w^4 - 4*w^3 - 5*w^2 + 6*w + 6],\ [181, 181, w^3 - 2*w^2 - 3*w + 3],\ [193, 193, -w^4 + w^3 + 4*w^2 - 3*w + 1],\ [197, 197, 2*w^4 - 3*w^3 - 9*w^2 + 7*w + 5],\ [211, 211, 2*w^4 - 3*w^3 - 8*w^2 + 6*w + 5],\ [229, 229, 2*w^2 - 2*w - 5],\ [239, 239, w^2 - 2*w - 4],\ [257, 257, -w^3 + 4*w - 2],\ [257, 257, w^4 - 2*w^3 - 6*w^2 + 7*w + 7],\ [263, 263, -2*w^4 + 4*w^3 + 7*w^2 - 10*w - 7],\ [271, 271, -w^4 + 2*w^3 + 5*w^2 - 8*w - 6],\ [271, 271, 2*w^4 - 2*w^3 - 9*w^2 + 4*w + 3],\ [271, 271, -w^3 + 2*w^2 + 3*w - 2],\ [277, 277, -w^4 + 3*w^3 + 3*w^2 - 7*w - 3],\ [277, 277, 2*w^4 - 2*w^3 - 7*w^2 + 3*w + 2],\ [277, 277, -2*w^4 + 4*w^3 + 7*w^2 - 12*w - 5],\ [281, 281, -w^4 + 3*w^3 + 4*w^2 - 9*w - 5],\ [281, 281, -3*w^4 + 4*w^3 + 12*w^2 - 8*w - 7],\ [281, 281, -2*w^4 + 3*w^3 + 8*w^2 - 6*w - 4],\ [289, 17, 3*w^4 - 5*w^3 - 13*w^2 + 14*w + 9],\ [331, 331, -w^4 + 2*w^3 + 2*w^2 - 3*w + 2],\ [337, 337, 2*w^4 - w^3 - 9*w^2 + w + 2],\ [337, 337, -w^4 + 2*w^3 + 3*w^2 - 4*w + 2],\ [337, 337, -3*w^4 + 3*w^3 + 13*w^2 - 7*w - 8],\ [347, 347, -w^4 + 2*w^3 + w^2 - 2*w + 2],\ [347, 347, 3*w^4 - 4*w^3 - 11*w^2 + 9*w + 4],\ [349, 349, 3*w^4 - 5*w^3 - 12*w^2 + 12*w + 7],\ [353, 353, w^4 - w^3 - 5*w^2 + 3*w],\ [353, 353, 2*w^2 - w - 5],\ [359, 359, 2*w^4 - 2*w^3 - 9*w^2 + 6*w + 5],\ [373, 373, w^3 - 2*w - 3],\ [373, 373, -3*w^4 + 5*w^3 + 11*w^2 - 12*w - 8],\ [379, 379, -3*w^4 + 5*w^3 + 13*w^2 - 14*w - 14],\ [383, 383, w^4 - 7*w^2 + 2*w + 2],\ [389, 389, w^4 - 3*w^2 - 5*w],\ [389, 389, w^4 - w^3 - 3*w^2 + 2*w - 3],\ [389, 389, 2*w^3 - 2*w^2 - 6*w + 1],\ [397, 397, -w^3 + 4*w^2 + w - 6],\ [419, 419, 2*w^4 - 3*w^3 - 10*w^2 + 10*w + 8],\ [439, 439, -2*w^4 + 3*w^3 + 9*w^2 - 8*w - 4],\ [439, 439, 2*w^4 - 3*w^3 - 7*w^2 + 8*w + 5],\ [443, 443, w^4 + w^3 - 7*w^2 - 4*w + 4],\ [449, 449, -2*w^4 + 2*w^3 + 7*w^2 - 3*w - 3],\ [457, 457, 4*w^4 - 6*w^3 - 15*w^2 + 13*w + 9],\ [461, 461, 3*w^4 - 5*w^3 - 11*w^2 + 11*w + 6],\ [463, 463, -w^4 + 4*w^2 + 3*w - 2],\ [467, 467, 3*w^4 - 5*w^3 - 11*w^2 + 13*w + 7],\ [467, 467, 2*w^4 - 2*w^3 - 9*w^2 + 6*w + 4],\ [479, 479, -3*w^4 + 3*w^3 + 12*w^2 - 4*w - 7],\ [487, 487, w^4 - w^3 - 7*w^2 + 3*w + 11],\ [503, 503, 2*w^4 - 4*w^3 - 7*w^2 + 13*w + 1],\ [509, 509, w^4 - 3*w^3 - 4*w^2 + 8*w + 5],\ [521, 521, -w^4 + 2*w^3 + 2*w^2 - 7*w + 2],\ [523, 523, 2*w^4 - 3*w^3 - 6*w^2 + 6*w],\ [523, 523, -3*w^4 + 4*w^3 + 15*w^2 - 12*w - 11],\ [523, 523, -w^4 + 2*w^3 + 4*w^2 - 8*w - 4],\ [547, 547, w^3 - 3*w^2 - w + 7],\ [557, 557, -w^4 + 4*w^3 + 4*w^2 - 14*w - 6],\ [557, 557, w^4 - 2*w^3 - 6*w^2 + 8*w + 7],\ [563, 563, -w^4 + w^3 + 6*w^2 - 4*w - 10],\ [563, 563, w^4 - w^3 - 4*w^2 + 4*w - 1],\ [569, 569, -3*w^4 + 6*w^3 + 10*w^2 - 14*w - 6],\ [569, 569, -w^4 + w^3 + 5*w^2 - 4],\ [571, 571, 5*w^4 - 8*w^3 - 19*w^2 + 20*w + 12],\ [571, 571, -3*w^4 + 6*w^3 + 12*w^2 - 19*w - 7],\ [587, 587, -2*w^4 + 2*w^3 + 7*w^2 - 5*w],\ [599, 599, -2*w^4 + 3*w^3 + 9*w^2 - 10*w - 7],\ [601, 601, -2*w^4 + 3*w^3 + 8*w^2 - 5*w - 5],\ [607, 607, w^4 - 3*w^3 - 3*w^2 + 6*w],\ [607, 607, -3*w^4 + 5*w^3 + 14*w^2 - 13*w - 10],\ [619, 619, w^4 - w^3 - 2*w^2 - 2],\ [619, 619, 3*w^4 - 3*w^3 - 13*w^2 + 4*w + 7],\ [619, 619, -w^4 + 4*w^3 + 3*w^2 - 13*w - 6],\ [625, 5, -w^4 + 4*w^3 + 3*w^2 - 11*w - 2],\ [641, 641, -3*w^4 + 5*w^3 + 14*w^2 - 16*w - 14],\ [643, 643, -5*w^4 + 7*w^3 + 19*w^2 - 18*w - 7],\ [659, 659, -3*w^4 + 6*w^3 + 12*w^2 - 19*w - 9],\ [661, 661, 2*w^3 - 2*w^2 - 5*w + 1],\ [673, 673, w^4 - 2*w^3 - 3*w^2 + 3*w - 1],\ [677, 677, w^4 - 4*w^2 - 2*w + 3],\ [677, 677, -2*w^4 + 3*w^3 + 11*w^2 - 9*w - 14],\ [677, 677, -2*w^4 + 5*w^3 + 8*w^2 - 17*w - 7],\ [691, 691, 3*w^4 - 4*w^3 - 14*w^2 + 13*w + 6],\ [709, 709, w^4 - 2*w^3 - 5*w^2 + 5*w + 8],\ [719, 719, w^4 - w^3 - 3*w^2 + 2*w - 4],\ [727, 727, -3*w^4 + 4*w^3 + 11*w^2 - 8*w - 5],\ [733, 733, w^4 + w^3 - 7*w^2 - 5*w + 6],\ [733, 733, -4*w^4 + 6*w^3 + 15*w^2 - 14*w - 8],\ [739, 739, 3*w^4 - 3*w^3 - 13*w^2 + 7*w + 7],\ [739, 739, -3*w^4 + 4*w^3 + 11*w^2 - 11*w - 2],\ [757, 757, w^2 - 4*w + 1],\ [757, 757, -2*w^4 + 3*w^3 + 8*w^2 - 5*w - 3],\ [773, 773, -5*w^4 + 8*w^3 + 20*w^2 - 19*w - 14],\ [811, 811, -2*w^4 + 2*w^3 + 10*w^2 - 8*w - 7],\ [811, 811, 2*w^4 - 10*w^2 - 3*w + 6],\ [811, 811, 3*w^4 - 3*w^3 - 14*w^2 + 9*w + 10],\ [821, 821, w^4 - 3*w^3 + 3*w - 2],\ [823, 823, 2*w^4 - 4*w^3 - 9*w^2 + 13*w + 8],\ [827, 827, -3*w^4 + 5*w^3 + 11*w^2 - 13*w - 1],\ [839, 839, 3*w^4 - 5*w^3 - 13*w^2 + 13*w + 7],\ [841, 29, -2*w^3 + 3*w^2 + 3*w - 3],\ [841, 29, -4*w^4 + 6*w^3 + 14*w^2 - 13*w - 5],\ [853, 853, -w^4 + 4*w^2 + 5*w - 1],\ [857, 857, -w^4 + 4*w^3 + 2*w^2 - 11*w - 4],\ [863, 863, w^4 - 4*w^3 - w^2 + 11*w],\ [877, 877, -4*w^4 + 4*w^3 + 17*w^2 - 8*w - 7],\ [881, 881, -4*w^4 + 6*w^3 + 17*w^2 - 17*w - 15],\ [881, 881, -2*w^3 + 3*w^2 + 5*w - 4],\ [907, 907, -3*w^4 + 6*w^3 + 13*w^2 - 18*w - 12],\ [907, 907, -w^4 + 5*w^2 + 4*w - 6],\ [919, 919, 3*w^4 - 3*w^3 - 13*w^2 + 7*w + 5],\ [919, 919, w^4 - 4*w^3 - 3*w^2 + 13*w + 1],\ [919, 919, -4*w^4 + 7*w^3 + 17*w^2 - 20*w - 13],\ [929, 929, -w^3 + 5*w - 3],\ [941, 941, 4*w^4 - 6*w^3 - 15*w^2 + 16*w + 9],\ [947, 947, 3*w^4 - 6*w^3 - 9*w^2 + 16*w + 3],\ [953, 953, -w^4 + 2*w^3 + 6*w^2 - 8*w - 6],\ [953, 953, 3*w^4 - 3*w^3 - 12*w^2 + 8*w + 6],\ [961, 31, -2*w^4 + 4*w^3 + 9*w^2 - 14*w - 5],\ [967, 967, -2*w^3 + 5*w + 4],\ [983, 983, 2*w^3 - 7*w - 6],\ [997, 997, 4*w^4 - 5*w^3 - 15*w^2 + 12*w + 6],\ [997, 997, 4*w^4 - 5*w^3 - 16*w^2 + 13*w + 8]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 0, -5, -6, 0, -3, 2, -12, 4, -3, 9, -8, -13, 2, -3, -12, 12, 1, -13, -2, -3, 4, 19, 3, -12, 3, 10, 7, -12, -18, -12, -2, -7, -23, 3, -3, 3, -5, 6, -7, -7, -14, -18, 13, 20, 15, -27, 27, -9, 28, -17, 2, 8, -7, -28, -12, 12, 18, 5, 28, -32, -8, 22, -12, -12, -10, 24, 6, 30, -26, 31, 20, 6, 30, 0, 0, -2, 15, -20, 20, -24, -30, 13, 3, 11, 33, -18, -30, 38, 6, -15, -42, -44, 16, -11, -13, -33, -12, -36, -21, -30, 0, -28, 23, 12, -15, 37, 8, -22, -10, -10, -25, 41, 33, -4, 0, -13, -31, -18, -18, 33, 47, -10, 0, -23, -34, 41, -20, -25, -2, 8, 51, -28, -22, 28, 3, 46, 18, 30, -28, 37, -44, -12, 21, -2, -48, 48, 28, -43, -20, 40, 40, 0, -48, 33, -9, -6, 38, -13, -21, 28, 2] 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]