# Stored data for newform 684.3.y.h, downloaded from the LMFDB on 25 April 2024.
{"label": "684.3.y.h", "space_label": "684.3.y", "level": 684, "weight": 3, "hecke_orbit": 8, "hecke_orbit_code": 31526846709367468, "dim": 8, "is_polredabs": true, "trace_hash": 1518466659999362056, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [1028196, -79092, 93288, 8736, 6304, 242, 87, -1, 1]], [7, [6940, -498, -158, 6, 1]]], "qexp_display": "q+\\beta _{5}q^{5}+(-2+\\beta _{1})q^{7}+(1-\\beta _{1}-\\beta _{4}+\\cdots)q^{11}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "y", "char_is_real": false, "Nk2": 6156, "analytic_conductor": 18.637650082244306, "hecke_ring_index": 9, "level_radical": 114, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.167", "prec": 17}, "analytic_rank_proved": true, "char_values": [684, 6, [343, 533, 325], [6, 6, 5]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [145, 217], "field_disc": 908364866584464, "field_disc_factorization": [[2, 4], [3, 4], [19, 2], [139, 2], [317, 2]], "field_poly": [4971, -3528, 4294, -1582, 917, -154, 56, -4, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.665", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "245.340", "prec": 24}, {"__RealLiteral__": 0, "data": "54.788", "prec": 20}, {"__RealLiteral__": 0, "data": "12640.693", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 1, -12], "traces": [0, 8, 0, 0, 0, 1, 0, -12, 0, 0, 0, 10, 0, 9, 0, 0, 0, -23, 0, -33, 0, 0, 0, 31, 0, -73, 0, 0, 0, 105, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -18, 0, -41, 0, 0, 0, -107, 0, 312, 0, 0, 0, -39, 0, 70, 0, 0, 0, -348, 0, -45, 0, 0, 0, 0, 0, -432, 0, 0, 0, 243, 0, 16, 0, 0, 0, -544, 0, 75, 0, 0, 0, 82, 0, 109, 0, 0, 0, 213, 0, 222, 0, 0, 0, 385, 0, 144, 0, 0, 0, 301, 0, 0, 0, 0, 0, 0, 0, -369, 0, 0, 0, 0, 0, 982, 0, 0, 0, 308, 0, -82, 0, 0, 0, -886, 0, -297, 0, 0, 0, -446, 0, -446, 0, 0, 0, 106, 0, -522, 0, 0, 0, 528, 0, 0, 0, 0, 0, -263, 0, 0, 0, 0, 0, 414, 0, 111, 0, 0, 0, -190, 0, 390, 0, 0, 0, 699, 0, 83, 0, 0, 0, -393, 0, -478, 0, 0, 0, 0, 0, -1047, 0, 0, 0, 888, 0, -362, 0, 0, 0, -908, 0, -45, 0, 0, 0, -212, 0, -143, 0, 0, 0, -420, 0, 927, 0, 0, 0, 487, 0, 993, 0, 0, 0, 701, 0, 0, 0, 0, 0, 0, 0, 531, 0, 0, 0, 0, 0, -672, 0, 0, 0, -194, 0, 358, 0, 0, 0, 280, 0, -492, 0, 0, 0, -135, 0, 585, 0, 0, 0, 40, 0, 406, 0, 0, 0, -738, 0, 0, 0, 0, 0, -191, 0, 0, 0, 0, 0, -357, 0, -71, 0, 0, 0, -447, 0, 360, 0, 0, 0, -564, 0, 256, 0, 0, 0, -612, 0, 647, 0, 0, 0, 0, 0, 951, 0, 0, 0, 741, 0, -102, 0, 0, 0, 182, 0, -186, 0, 0, 0, 1048, 0, -162, 0, 0, 0, 1737, 0, -696, 0, 0, 0, -617, 0, -2994, 0, 0, 0, -862, 0, 0, 0, 0, 0, 0, 0, 762, 0, 0, 0, 0, 0, -1956, 0, 0, 0, 712, 0, 184, 0, 0, 0, 478, 0, 1719, 0, 0, 0, -41, 0, 551, 0, 0, 0, -1903, 0, 43, 0, 0, 0, -3822, 0, 0, 0, 0, 0, -1011, 0, 0, 0, 0, 0, 2505, 0, 1556, 0, 0, 0, -611, 0, -1610, 0, 0, 0, 2709, 0, -1385, 0, 0, 0, 1590, 0, -444, 0, 0, 0, 0, 0, 528, 0, 0, 0, 2022, 0, -992, 0, 0, 0, -128, 0, 885, 0, 0, 0, 564, 0, -1060, 0, 0, 0, -693, 0, 1011, 0, 0, 0, 763, 0, 711, 0, 0, 0, -1298, 0, 0, 0, 0, 0, 0, 0, 873, 0, 0, 0, 0, 0, -1646, 0, 0, 0, -755, 0, -320, 0, 0, 0, 2494, 0, -690, 0, 0, 0, 260, 0, 3547, 0, 0, 0, -833, 0, 1032, 0, 0, 0, -3069, 0, 0, 0, 0, 0, -863, 0, 0, 0, 0, 0, 234, 0, -1086, 0, 0, 0, -941, 0, 82, 0, 0, 0, 1431, 0, -228, 0, 0, 0, -528, 0, 4, 0, 0, 0, 0, 0, -249, 0, 0, 0, 594, 0, 23, 0, 0, 0, 486, 0, -1740, 0, 0, 0, 1770, 0, -1265, 0, 0, 0, 1773, 0, -225, 0, 0, 0, -465, 0, -2742, 0, 0, 0, -1865, 0, 0, 0, 0, 0, 0, 0, 3450, 0, 0, 0, 0, 0, 202, 0, 0, 0, 834, 0, -462, 0, 0, 0, -1732, 0, 3642, 0, 0, 0, -791, 0, 1332, 0, 0, 0, -2690, 0, 686, 0, 0, 0, -3273, 0, 0, 0, 0, 0, -1977, 0, 0, 0, 0, 0, -2895, 0, 1629, 0, 0, 0, -1160, 0, -1272, 0, 0, 0, 4980, 0, -918, 0, 0, 0, 546, 0, -597, 0, 0, 0, 0, 0, -693, 0, 0, 0, 4986, 0, -2618, 0, 0, 0, -2000, 0, -195, 0, 0, 0, -356, 0, -1031, 0, 0, 0, 1413, 0, 3195, 0, 0, 0, 3626, 0, 921, 0, 0, 0, 1622, 0, 0, 0, 0, 0, 0, 0, 2178, 0, 0, 0, 0, 0, -2858, 0, 0, 0, -219, 0, 1912, 0, 0, 0, -1786, 0, -1467, 0, 0, 0, -587, 0, -276, 0, 0, 0, -64, 0, -707, 0, 0, 0, -1080, 0, 0, 0, 0, 0, -3251, 0, 0, 0, 0, 0, 2394, 0, 727, 0, 0, 0, -763, 0, 1456, 0, 0, 0, 1083, 0, -1134, 0, 0, 0, -2277, 0, -377, 0, 0, 0, 0, 0, -2079, 0, 0, 0, 7098, 0, -927, 0, 0, 0, -2738, 0, 1098, 0, 0, 0, 2958, 0, -117, 0, 0, 0, 1551, 0, -1308, 0, 0, 0, 3051, 0, 612, 0, 0, 0, 737, 0, 0, 0, 0, 0, 0, 0, 1551, 0, 0, 0, 0, 0, -1226, 0, 0, 0, 1535, 0, 536, 0, 0, 0, -326, 0, -2985, 0, 0, 0, -3958, 0, -447, 0, 0, 0, -1289, 0, -1155, 0, 0, 0, -2352, 0, 0, 0, 0, 0, -1761, 0, 0, 0, 0, 0, 2511, 0, -577, 0, 0, 0, -4172, 0, 2768, 0, 0, 0, -726, 0, 2371, 0, 0, 0, -1506, 0, -2832, 0, 0, 0, 0, 0, -5889, 0, 0, 0, 5022, 0, -39, 0, 0, 0, -10388, 0, 4551, 0, 0, 0, 2254, 0, 696, 0, 0, 0, -1899, 0, 4338, 0, 0, 0, 6829, 0, 1854, 0, 0, 0, 1242, 0, 0, 0, 0, 0, 0, 0, -2904, 0, 0, 0, 0, 0, 2818, 0, 0, 0, 2996, 0, 1824, 0, 0, 0, 2178, 0, 894, 0, 0, 0, -1262, 0, 615, 0, 0, 0, -704, 0, -3434, 0, 0, 0, -3525, 0, 0, 0, 0, 0, -2651, 0, 0, 0, 0, 0, 7134, 0, -1910, 0, 0, 0, -4342, 0, 2312, 0, 0, 0, 4443, 0, -699, 0, 0, 0, -4206, 0, -1546, 0, 0, 0, 0, 0, -4116, 0, 0, 0, 1491, 0, -818, 0, 0, 0, -6130, 0, -453, 0, 0, 0, 2702, 0, -2121, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 4, -1, 6, 0]], "char_orbit_index": 25, "prim_orbit_index": 4, "minimal_twist": "76.3.h.a", "char_is_minimal": true, "conrey_index": 145, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -2, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 1, 6, 0, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-6, -1, 5, -2, 2, -1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, 1, 0, -3, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -15, 4, 0, 3, -3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [20, 0, -10, -2, 4, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 4, -2, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [12, -1, -12, 9, -9, 4, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [16, 0, -32, -2, 1, -4, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 1, 1, -2, 4, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, 12, 5, -5, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -22, 7, 0, -1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [41, -3, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -8, 2, 1, -2, 1, 1, 4], [0, 0, 0, 0, 0, 0, 0, 0], [18, 5, -18, -6, 6, 0, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-31, 1, -31, -2, -2, -2, 4, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -12, -4, 0, -3, 3, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [30, 4, -60, 6, -3, 10, -5, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-74, -2, 37, 4, -8, -2, -2, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [20, 0, 20, 1, 1, -3, 6, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, -3, -3, -1, 1, 12, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-72, 0, 0, 0, -3, 0, 10, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, -4, 6, -1, -1, -7, 14, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [7, -2, 0, 0, -10, 0, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 28, 5, 0, -3, 3, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [32, 10, -16, -2, 4, 1, 1, -5], [0, 0, 0, 0, 0, 0, 0, 0], [32, -4, -16, 2, -4, 10, 10, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [68, 3, -48, -3, 1, -13, 12, 4], [0, 0, 0, 0, 0, 0, 0, 0], [13, 4, 13, 2, 2, 8, -16, 4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}