# Stored data for newform 177.4.d.b, downloaded from the LMFDB on 25 April 2024. {"label": "177.4.d.b", "space_label": "177.4.d", "level": 177, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503805852909745, "dim": 4, "is_polredabs": true, "nf_label": "4.0.31329.1", "trace_hash": 1928575881388296514, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]], [5, [99856, 0, 691, 0, 1]]], "qexp_display": "q+(-2-\\beta _{2}-\\beta _{3})q^{3}-8q^{4}+(4\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 177, "char_orbit_label": "d", "char_is_real": true, "Nk2": 2832, "analytic_conductor": 10.443338071016088, "hecke_ring_index": 6, "level_radical": 177, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.758", "prec": 17}, "analytic_rank_proved": true, "char_values": [177, 2, [119, 61], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [3, 59], "conrey_indexes": [176], "field_disc": 31329, "field_disc_factorization": [[3, 2], [59, 2]], "field_poly": [225, -15, -14, -1, 1], "hecke_ring_index_factorization": [[2, 1], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.476", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "113.687", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5220.373", "prec": 27}], "related_objects": [], "self_twist_discs": [-59], "cm_discs": [-59], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.1.d2", "trace_display": [0, -7, 0, -58], "traces": [0, 4, 0, -7, -32, 0, 0, -58, 0, 5, 0, 0, 56, 0, 0, -191, 256, 0, 0, -238, 0, 367, 0, 0, 0, -882, 0, -448, 464, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, -448, 1062, 0, 472, 0, 0, 0, 0, 0, -911, 0, 0, 1528, 0, 0, -1931, -2048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3402, 1904, 0, 0, 1670, 0, 1433, 0, 0, -2936, -944, 0, 637, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7056, 0, 0, 0, 0, 911, 0, 0, 3584, 0, 0, 0, -3712, 0, 0, 0, 0, 0, 0, 0, 0, -5324, 0, -5483, 0, 0, 0, -1642, 0, 0, 0, 0, 0, -4514, 0, -1298, 0, 0, 0, -7840, 0, 0, 0, 0, 320, 12082, 0, -9558, 0, 0, 0, 0, 0, 3304, 0, 0, 0, 0, 0, -749, 0, 0, 0, -16192, 0, 0, 0, 0, 0, 8788, 0, 8995, 0, 0, 0, 23940, 0, -3481, 0, 0, -392, 9590, 0, 0, 0, 0, 0, 0, 0, 6496, 0, 0, 3584, -3874, 0, 0, -8496, 0, 0, -10822, 0, 0, 0, 0, -3776, -33134, 0, 0, 0, 0, 0, 0, 0, -9086, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23408, 0, -14112, 0, 0, 7288, 0, 0, 0, 0, 0, 0, 0, 0, 10087, 0, 0, -12224, 11606, 0, 3983, 0, 0, 0, 0, 0, 0, 0, 0, 15448, 0, 0, 16520, 16384, 0, 0, 0, 0, -6035, 0, 0, 0, -25970, 0, 0, 0, 0, 0, 17150, 0, 0, 0, 0, 0, 18302, 0, 0, 0, 0, 0, 0, 0, 20657, 0, 0, 0, 4548, 0, 0, 0, 0, 0, 6962, 0, 0, 0, 0, -27216, 0, 0, 0, -15232, 0, 0, 7322, 0, 0, 0, 0, 0, 0, 0, -19561, -13360, 0, 0, 0, 0, -10577, 0, 0, -11464, 0, 0, 0, 0, 0, 0, -24034, 0, 0, 0, 0, 23488, 0, 0, 0, 7552, 0, 0, -41702, 0, 0, 0, 0, -5096, 0, 0, 0, 0, 0, 0, 18172, 0, 8024, 0, 0, 0, 26550, 0, 9317, 0, 0, 0, 0, 0, -3731, 0, 0, 0, 19592, 0, 5231, 0, 0, 0, -26050, 0, -28721, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11351, -56448, 0, 0, 0, 0, 44107, 0, 0, 0, 0, 0, -17129, 0, 0, 0, 0, 0, 13720, 0, 0, -7288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28672, 29246, 0, -60703, 0, 0, 0, -12880, 0, 55224, 0, 0, 0, 0, 0, 0, 29696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20768, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3276, 0, 16339, 0, 0, 0, 0, 0, 0, 42592, 0, 0, -39442, 0, 28336, 0, 0, 43864, 33040, 0, 0, 0, 0, 0, 19022, 0, 41659, 0, 0, 0, 0, 0, -15379, 13136, 0, 0, 0, 0, 26656, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12334, 0, -127386, 0, 0, 0, -48668, 0, -24367, 36112, 0, 0, 4270, 0, 0, 0, 0, 10384, 0, 0, -6959, 0, 0, 0, -50464, 0, 0, 0, 0, 0, 53842, 0, 0, 62720, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30071, 0, 0, 0, 0, 0, 0, 0, 0, -2560, -19138, 0, 64393, -96656, 0, 0, 0, 0, 0, 0, 0, 76464, 0, 0, -31388, 0, 0, 0, 102896, 0, 1681, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50638, 0, -20653, 0, 0, -26432, 0, 0, 82145, 0, 0, 0, -60970, 0, 0, 0, 0, 0, 99788, 0, 0, 0, 0, 0, -119440, 0, 0, 0, 0, 5992, 0, 0, -63602, 0, 0, 0, 37814, 0, 0, 0, 0, 0, 0, 0, 0, 129536, 0, 0, 0, 0, 0, 0, 0, 0, -63490, 0, 0, 0, 0, 0, 0, 0, -40964, 0, 0, 0, 0, 0, 98784, -70304, 0, 0, 0, 0, 0, 0, 0, -71960, -5306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -944, 0, 0, -191520, 0, 0, 0, 0, 0, 0, 0, 27848, 29858, 0, -88979, 0, 0, 0, 0, 0, -50519, 0, 0, 3136, 0, 0, 34117, -76720, 0, 0, 156464, 0, 21620, 0, 0, 0, -39592, 0, 3186, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11023, 0, 0, -51968, 39722, 0, 0, 0, 0, 0, 0, 0, -105256, 0, 0, -28672, 0, 0, 91933, 30992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45430, 67968, 0, 0, -171136, 0, 19537, 0, 0, 0, 0, 0, 144479, 86576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -58421, 0, 0, 30208, 0, 0, 0, 265072, 0, 0, 0, 0, 0, 0, 0, 0, -56182, 0, -19019, 0, 0, 0, 147766, 0, 0, 0, 0, 0, -50562, 0, -99911, 0, 0, 0, 77198, 0, 0, 0, 0, 72688, -27706, 0, 91337, 0, 0, 0, 0, 0, 10739, 0, 0, 0, 0, 0, -7959, 0, 0, 0, 0, 0, 0, 0, 0, 0, -101182, 0, -109541, 0, 0, 0, 104954, 0, -121835, 0, 0, 0, -165758, 0, 0, -187264, 0, 0, 0, 0, 0, 0, 0, 112896, -85904, 0, 0, 0, 0, 0, 41738, 0, 0, 0, 0, -58304, 0, 0, 0, 0, 0, 0, 0, 0, 103741, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167796, 0, 103381, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 141482, 0, 0, -80696, 0, 0, -1652, 0, 0, 0, 0, 0, 0, 0, 0, 97792, 119164, 0, -60773, -92848, 0, 0, 0, 0, -102424, 0, 0, -31864, 113680, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 62776, 0, 0, 0, 0, 0, 0, 0, 32767, 0, 0, 0, -123718, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 59, 2, -1, 2, -59], [1, 1, 3, 2, -1, 2, 0], [1, 1, 177, 4, 1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "177.4.d.b", "char_is_minimal": true, "conrey_index": 176, "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-2, 0, -1, -1], [-8, 0, 0, 0], [0, 4, -3, -4], [0, 0, 0, 0], [-16, -2, -1, -4], [0, 0, 0, 0], [3, 1, -1, 6], [0, 0, 0, 0], [0, 0, 0, 0], [16, 0, 8, 8], [0, 0, 0, 0], [0, 0, 0, 0], [-46, -15, 1, 22], [64, 0, 0, 0], [0, 8, 8, -8], [0, 0, 0, 0], [-52, 10, 5, 20], [0, -32, 24, 32], [98, 3, 1, 22], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-231, -14, -7, -28], [0, 0, 0, 0], [-112, 11, 11, -11], [128, 16, 8, 32], [0, -44, 9, 44], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -120, 11, 120], [-24, -8, 8, -48], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 88, -87, -88], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [30, 101, 46, -30], [0, 0, 0, 0], [0, 0, 0, 0], [-128, 0, -64, -64], [309, 58, 29, 116], [0, 0, 0, 0], [104, -72, 16, 16], [0, 0, 0, 0], [0, 100, -9, -100], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-226, -15, 127, 22], [0, 0, 0, 0], [0, -59, -59, 59], [368, 120, -8, -176], [0, 0, 0, 0], [0, 0, 0, 0], [-510, 29, -44, -138], [-512, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -64, -64, 64], [0, 0, 0, 0], [0, 0, 0, 0], [0, -154, -154, 154], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [924, 21, 126, 273], [416, -80, -40, -160], [0, 0, 0, 0], [0, 0, 0, 0], [344, -98, -49, -196], [0, 256, -192, -256], [367, -99, 134, 134], [0, 0, 0, 0], [0, 0, 0, 0], [-784, -24, -8, -176], [-320, -112, -56, -224], [0, 0, 0, 0], [170, 237, -35, -194], [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, 72, 341, -72], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1848, 112, 56, 224]]}