# Stored data for newform 775.3.d.d, downloaded from the LMFDB on 05 June 2024. {"Nk2": 6975, "analytic_conductor": 21.11722048792301, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 31, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": -1, "char_values": [775, 2, [652, 251], [2, 1]], "cm_discs": [-31], "conrey_index": 526, "dim": 3, "field_disc": 837, "field_disc_factorization": [[3, 3], [31, 1]], "field_poly": [-1, -6, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 0, "hecke_cutters": [[2, [-15, -12, 0, 1]], [3, [0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511005090874119, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 2, -1, 2, -31]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": true, "is_twist_minimal": false, "label": "775.3.d.d", "level": 775, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 31], "level_radical": 155, "minimal_twist": "31.3.b.b", "nf_label": "3.3.837.1", "prim_orbit_index": 2, "qexp_display": "q-\\beta _{2}q^{2}+(4+\\beta _{1}-2\\beta _{2})q^{4}+(-5\\beta _{1}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "2.2.1.d2", "self_twist_discs": [-31], "self_twist_type": 1, "space_label": "775.3.d", "trace_display": [0, 0, 0, 0], "trace_hash": 2048810949165539550, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.774", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "72.748", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2121.365", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.839", "prec": 17}, "traces": [0, 3, 0, 0, 12, 0, 0, 0, 45, 27, 0, 0, 0, 0, -9, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -75, 0, 0, -93, 180, 0, 0, 0, 108, 0, -135, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 147, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 483, 0, 0, -30, 0, 0, 0, 0, 405, 0, 0, 0, -381, 0, 0, 0, 0, 243, 345, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -495, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -135, 0, 0, 0, 0, 0, -615, 0, 0, 363, 0, 0, -372, 0, -81, 0, 720, 0, 0, 414, 0, 690, 0, 0, 0, 0, 0, 0, 0, 0, -15, 0, 432, 0, 0, 0, 0, -594, 0, 0, -540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 891, 0, 0, 0, 0, 507, 0, 0, 0, 450, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360, 0, 0, 0, 0, 0, -1161, 0, -561, 0, 0, 0, 0, 0, -375, 0, 0, 0, -1089, 0, 0, 0, 0, 0, 0, 0, -1041, 0, 0, 0, -1215, 0, 0, 0, 0, 0, -1125, 0, 519, -990, 0, 0, 0, 0, 0, 0, 0, 0, -909, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1395, 0, 0, 0, -675, 0, 0, 0, 1932, 0, 0, 0, 0, 0, 0, 0, 0, 0, -729, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -837, 0, 0, 0, 1650, -621, 0, 0, -1350, 1620, 867, 0, 0, 0, -270, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2025, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1791, 0, 0, 0, 0, 0, 0, 0, 0, 0, 972, 0, -369, 0, 1380, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1215, 1290, 0, 0, 0, 0, 0, 606, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1083, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1350, 0, 0, -1074, 0, 0, 2265, 0, 0, 0, -2241, 0, -2235, 0, 0, 0, 225, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 0, 0, 0, 0, 0, 0, 0, -1635, -990, 0, 0, 0, 0, 0, 0, 0, 0, 2025, 810, 0, 0, 0, 0, -2475, 0, 0, 2214, 0, 0, 279, 0, -1941, 0, 0, 0, 0, 1323, 0, 0, 0, 0, 0, 0, -540, 0, 0, 0, 1845, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 471, 0, 0, 0, 0, 0, -2460, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1452, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1488, 2970, 0, 0, 0, 0, 0, 0, -324, 0, 0, 0, 0, 0, 0, 0, 4365, 0, 2991, 0, 0, 0, 0, 0, 0, -2826, 0, 0, 1656, 0, 0, 0, 0, 1587, 0, 0, 405, 0, 0, 0, -450, 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, 1185, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 1119, 0, 4347, 2490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2376, 0, 0, 0, 0, 0, 0, -270, 0, 0, 0, -3270, -5715, 0, 0, 0, 0, 0, 1359, 0, 0, 2250, 0, 0, 0, 0, -2895, 0, 0, 0, 0, 0, 3765, 0, 0, 0, 0, 0, -3729, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3645, 0, 0, 0, 645, -2430, 0, 0, 5175, 0, -270, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2028, 0, 0, 726, 0, 0, 0, 0, -3429, 0, -441, 0, 0, 0, 0, 0, 1800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3870, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3225, 0, 0, -1626, 225, 0, 0, 0, 0, 0, 0, 2187, 0, 0, 0, 0, 0, 0, 0, 0, 3105, 0, 0, 0, 0, 0, 0, 0, 2151, 0, 0, 3006, 0, 0, 1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1230, 4491, 0, 0, 0, 0, 0, 0, 0, -3795, 0, 0, 0, -4644, 0, 0, -4626, 0, 0, 0, 0, -5073, 0, 0, 0, 0, 0, 0, -4554, 0, 0, 2439, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1500, 0, 0, -4434, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4356, 0, 4119, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2505, -4266, 0, 2523, -495, 0, 2739, 0, 0, 0, 0, 0, 0, 0, 0, -3630, 0, 0, -4164, 810, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2325, 0, 0, 0, -4860, 0, 0, 0, 0, 0, -5175, 0, 0, 0, -4455, 0, 0, 0, 759, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1449, 0, 0, 0, 0, 0, 0, 0, 2076, 0, 0, 0, -3960, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3786, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5214, -1035, 0, -1929, 0, 0, 330, 90, 0, 0, 0, 0, 0, -9225, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5505, 0, 0, 2883, 0, 0, 0, 0, 0, 0, 5445, 0, 0, -3474, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5580, 0, -5289, 0, 0, 0, 0, 0, 0], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0], [1, 0, 0], [0, 0, -1], [0, 0, 0], [4, 1, -2], [0, 0, 0], [0, 0, 0], [0, -5, 1], [15, 0, -4], [9, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-3, 9, 2], [0, 0, 0], [16, 0, -15], [0, 0, 0], [0, 0, -9], [0, -11, 7], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-25, 0, 3], [0, 0, 0], [0, 0, 0], [-31, 0, 0], [60, 15, -30], [0, 0, 0], [0, 0, 0], [0, 0, 0], [36, 9, -18], [0, 0, 0], [-45, 15, 14], [0, 0, 0], [0, 0, 0], [0, 21, -17], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [30, 0, 0], [0, 0, 0], [49, -19, 23], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-12, -39, 23], [0, 0, 0], [0, 0, 0], [0, 21, 23], [0, 0, 0], [0, 0, 0], [0, 0, 31], [0, -45, 9], [161, 0, -60], [0, 0, 0], [0, 0, 0], [-10, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -51, 7], [135, 0, -36], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-127, 0, 45], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [81, 0, 0], [115, -25, -34], [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, -30], [0, 0, 0], [0, 0, 0], [0, -5, 49], [-165, 15, -3], [0, 0, 0], [0, 0, 0]]}