# Stored data for newform 80.3.p.c, downloaded from the LMFDB on 18 April 2024.
{"label": "80.3.p.c", "space_label": "80.3.p", "level": 80, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9008230097223760, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 1965837898126186097, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [8, -4, 1]], [7, [8, 4, 1]]], "qexp_display": "q+(2-2i)q^{3}-5iq^{5}+(-2-2i)q^{7}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "p", "char_is_real": false, "Nk2": 720, "analytic_conductor": 2.179842114882375, "hecke_ring_index": 1, "level_radical": 10, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.248", "prec": 17}, "analytic_rank_proved": true, "char_values": [80, 4, [31, 21, 17], [4, 4, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5], "conrey_indexes": [17, 33], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.951", "prec": 17}, {"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "11.407", "prec": 20}, {"__RealLiteral__": 0, "data": "0.147", "prec": 17}, {"__RealLiteral__": 0, "data": "92.036", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "2.2.3.c4", "trace_display": [0, 4, 0, -4], "traces": [0, 2, 0, 4, 0, 0, 0, -4, 0, 0, 0, 16, 0, 6, 0, -20, 0, 14, 0, 0, 0, -16, 0, 4, 0, -50, 0, 40, 0, 0, 0, -104, 0, 32, 0, -20, 0, -6, 0, 0, 0, -16, 0, 84, 0, 10, 0, 36, 0, 0, 0, 56, 0, 106, 0, 0, 0, 80, 0, 0, 0, -96, 0, 4, 0, -30, 0, -124, 0, 0, 0, 56, 0, -94, 0, -100, 0, -32, 0, 0, 0, 142, 0, -36, 0, 70, 0, 160, 0, 0, 0, -24, 0, -208, 0, 200, 0, -126, 0, 0, 0, 124, 0, -236, 0, 0, 0, -284, 0, 0, 0, -24, 0, 46, 0, -20, 0, 6, 0, 0, 0, -114, 0, -32, 0, 0, 0, 236, 0, 0, 0, 256, 0, 80, 0, 200, 0, -126, 0, 0, 0, 144, 0, 48, 0, 400, 0, -164, 0, 0, 0, -104, 0, -14, 0, 0, 0, 54, 0, 0, 0, -16, 0, 164, 0, -160, 0, -124, 0, 0, 0, -40, 0, -214, 0, 100, 0, 80, 0, 0, 0, 4, 0, -192, 0, -30, 0, 112, 0, 0, 0, -424, 0, -114, 0, -120, 0, -6, 0, 0, 0, -496, 0, 160, 0, 0, 0, 4, 0, 0, 0, 656, 0, 112, 0, -420, 0, 208, 0, 0, 0, 84, 0, -276, 0, 0, 0, -4, 0, 0, 0, -128, 0, 366, 0, 180, 0, 0, 0, 0, 0, 464, 0, -76, 0, -410, 0, 120, 0, 0, 0, 96, 0, 32, 0, 0, 0, -626, 0, 0, 0, -80, 0, 524, 0, -530, 0, 320, 0, 0, 0, -504, 0, -48, 0, -400, 0, 534, 0, 0, 0, 624, 0, 524, 0, 400, 0, 32, 0, 0, 0, -504, 0, 486, 0, 200, 0, 320, 0, 0, 0, -336, 0, 248, 0, 0, 0, 36, 0, 0, 0, 776, 0, 366, 0, -20, 0, -426, 0, 0, 0, -1136, 0, -280, 0, -150, 0, -40, 0, 0, 0, -464, 0, 6, 0, -620, 0, 834, 0, 0, 0, -832, 0, -360, 0, -80, 0, -404, 0, 0, 0, 240, 0, -894, 0, 0, 0, -112, 0, 0, 0, -78, 0, -228, 0, 470, 0, 236, 0, 0, 0, -424, 0, -214, 0, 500, 0, 240, 0, 0, 0, 944, 0, 684, 0, -160, 0, 84, 0, 0, 0, 56, 0, 512, 0, 0, 0, -646, 0, 0, 0, 1284, 0, -312, 0, 0, 0, -48, 0, 0, 0, -504, 0, 80, 0, 180, 0, -560, 0, 0, 0, -416, 0, -36, 0, -350, 0, 192, 0, 0, 0, 1576, 0, -734, 0, 800, 0, 80, 0, 0, 0, 82, 0, -756, 0, 800, 0, -600, 0, 0, 0, -128, 0, -208, 0, 0, 0, -786, 0, 0, 0, 1244, 0, -556, 0, 1040, 0, 76, 0, 0, 0, 216, 0, 672, 0, 0, 0, 106, 0, 0, 0, -36, 0, -32, 0, -630, 0, -1044, 0, 0, 0, 656, 0, -560, 0, 80, 0, -112, 0, 0, 0, -496, 0, 84, 0, 0, 0, 604, 0, 0, 0, 376, 0, -800, 0, 1180, 0, 288, 0, 0, 0, -516, 0, -516, 0, 400, 0, -728, 0, 0, 0, -40, 0, -48, 0, -1420, 0, 880, 0, 0, 0, -676, 0, 8, 0, -100, 0, 1116, 0, 0, 0, -1600, 0, 0, 0, 0, 0, -6, 0, 0, 0, 448, 0, 84, 0, -230, 0, -284, 0, 0, 0, -784, 0, -848, 0, -100, 0, -946, 0, 0, 0, 144, 0, 848, 0, 30, 0, 396, 0, 0, 0, -24, 0, -94, 0, -280, 0, 480, 0, 0, 0, -656, 0, 124, 0, 0, 0, -924, 0, 0, 0, 216, 0, 1446, 0, 160, 0, 654, 0, 0, 0, 160, 0, 320, 0, 1250, 0, 640, 0, 0, 0, 1096, 0, 1312, 0, 1180, 0, -246, 0, 0, 0, -1136, 0, 684, 0, -1680, 0, 236, 0, 0, 0, 832, 0, 906, 0, 0, 0, -94, 0, 0, 0, 1024, 0, 168, 0, -400, 0, 160, 0, 0, 0, -768, 0, 386, 0, -1000, 0, 314, 0, 0, 0, -16, 0, -876, 0, -630, 0, 480, 0, 0, 0, -2064, 0, 32, 0, -1400, 0, -112, 0, 0, 0, -256, 0, 120, 0, 0, 0, -248, 0, 0, 0, 0, 0, -208, 0, -240, 0, -480, 0, 0, 0, 944, 0, 928, 0, 0, 0, 1116, 0, 0, 0, 1176, 0, -1654, 0, -820, 0, -992, 0, 0, 0, 480, 0, 764, 0, -1500, 0, -36, 0, 0, 0, 1176, 0, 192, 0, 0, 0, 1974, 0, 0, 0, -316, 0, -40, 0, 70, 0, 120, 0, 0, 0, -2504, 0, 486, 0, 2600, 0, 48, 0, 0, 0, 448, 0, -1600, 0, 270, 0, -524, 0, 0, 0, -184, 0, -288, 0, -2120, 0, 534, 0, 0, 0, -160, 0, -752, 0, 0, 0, 40, 0, 0, 0, 416, 0, -1008, 0, -820, 0, 1680, 0, 0, 0, -3136, 0, 1124, 0, -800, 0, -1524, 0, 0, 0, 2136, 0, 574, 0, -620, 0, -2080, 0, 0, 0, -1518, 0, 1248, 0, 1510, 0, 228, 0, 0, 0, -24, 0, 2246, 0, 0, 0, 834, 0, 0, 0, 128, 0, 484, 0, 1070, 0, -764, 0, 0, 0, -744, 0, 126, 0, 500, 0, -906, 0, 0, 0, 1424, 0, -236, 0, 400, 0, 2316, 0, 0, 0, 1136, 0, -720, 0, 2200, 0, -48, 0, 0, 0, 1484, 0, -672, 0, 0, 0, -284, 0, 0, 0, -2344, 0, -288, 0, 960, 0, -512, 0, 0, 0, 144, 0, 168, 0, 150, 0, -236, 0, 0, 0, 1640, 0, 1552, 0, 560, 0, -466, 0, 0, 0, -156, 0, -32, 0, -800, 0, -124, 0, 0, 0, -1704, 0, -2034, 0, 0, 0, 1280, 0, 0, 0, 3486, 0, 284, 0, 570, 0, -1004, 0, 0, 0, -1984, 0, -560, 0, 0, 0, -1566, 0, 0, 0, 20, 0, -2116, 0, -30, 0, -288, 0, 0, 0, 136, 0, -928, 0, 1200, 0, -1546, 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, 5, 3, -1, 4, 0]], "char_orbit_index": 16, "prim_orbit_index": 3, "minimal_twist": "10.3.c.a", "char_is_minimal": false, "conrey_index": 17, "id": 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], [1, 0], [0, 0], [2, -2], [0, 0], [0, -5], [0, 0], [-2, -2], [0, 0], [0, 1], [0, 0], [8, 0], [0, 0], [3, -3], [0, 0], [-10, -10], [0, 0], [7, 7], [0, 0], [0, 20], [0, 0], [-8, 0], [0, 0], [2, -2], [0, 0], [-25, 0], [0, 0], [20, 20], [0, 0], [0, 40], [0, 0], [-52, 0], [0, 0], [16, -16], [0, 0], [-10, 10], [0, 0], [-3, -3], [0, 0], [0, -12], [0, 0], [-8, 0], [0, 0], [42, -42], [0, 0], [5, 0], [0, 0], [18, 18], [0, 0], [0, -41], [0, 0], [28, 0], [0, 0], [53, -53], [0, 0], [0, -40], [0, 0], [40, 40], [0, 0], [0, 20], [0, 0], [-48, 0], [0, 0], [2, -2], [0, 0], [-15, -15], [0, 0], [-62, -62], [0, 0], [0, -8], [0, 0], [28, 0], [0, 0], [-47, 47], [0, 0], [-50, 50], [0, 0], [-16, -16], [0, 0], [0, 0], [0, 0], [71, 0], [0, 0], [-18, 18], [0, 0], [35, -35], [0, 0], [80, 80], [0, 0], [0, 80], [0, 0], [-12, 0], [0, 0], [-104, 104], [0, 0], [100, 0], [0, 0], [-63, -63], [0, 0], [0, 8], [0, 0]]}