# Stored data for newform 28.3.b.a, downloaded from the LMFDB on 24 April 2024.
{"label": "28.3.b.a", "space_label": "28.3.b", "level": 28, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 68769808412, "dim": 2, "is_polredabs": true, "nf_label": "2.0.24.1", "trace_hash": 412235027117734662, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta q^{3}-\\beta q^{5}+(5-\\beta )q^{7}-15q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "b", "char_is_real": true, "Nk2": 252, "analytic_conductor": 0.7629447402088313, "hecke_ring_index": 2, "level_radical": 14, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [28, 2, [15, 17], [2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 7], "conrey_indexes": [13], "field_disc": -24, "field_disc_factorization": [[-1, 1], [2, 3], [3, 1]], "field_poly": [6, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "1.928", "prec": 17}, {"__RealLiteral__": 0, "data": "0.058", "prec": 17}, {"__RealLiteral__": 0, "data": "14.994", "prec": 20}, {"__RealLiteral__": 0, "data": "1.062", "prec": 17}, {"__RealLiteral__": 0, "data": "144.886", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 10], "traces": [0, 2, 0, 0, 0, 0, 0, 10, 0, -30, 0, -12, 0, 0, 0, 48, 0, 0, 0, 0, 0, 48, 0, -60, 0, 2, 0, 0, 0, -12, 0, 0, 0, 0, 0, -48, 0, 20, 0, -48, 0, 0, 0, 20, 0, 0, 0, 0, 0, 2, 0, 192, 0, 180, 0, 0, 0, -240, 0, 0, 0, 0, 0, -150, 0, 48, 0, -140, 0, 0, 0, 84, 0, 0, 0, 0, 0, -60, 0, 148, 0, 18, 0, 0, 0, -192, 0, 0, 0, 0, 0, 48, 0, 0, 0, 240, 0, 0, 0, 180, 0, 0, 0, 0, 0, 240, 0, -300, 0, -172, 0, 0, 0, 180, 0, 0, 0, 0, 0, -192, 0, -170, 0, -480, 0, 0, 0, 100, 0, 0, 0, 0, 0, 240, 0, -288, 0, 420, 0, 0, 0, 192, 0, 0, 0, 0, 0, 480, 0, -396, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, -300, 0, 340, 0, -288, 0, 0, 0, 290, 0, 0, 0, 0, 0, 10, 0, 240, 0, 84, 0, 0, 0, -240, 0, 0, 0, 0, 0, -288, 0, -492, 0, -460, 0, 0, 0, -300, 0, 0, 0, 0, 0, -60, 0, 480, 0, 900, 0, 0, 0, -652, 0, 0, 0, 0, 0, 0, 0, 1056, 0, 192, 0, 0, 0, -30, 0, 0, 0, 0, 0, -288, 0, 420, 0, -192, 0, 0, 0, 228, 0, 0, 0, 0, 0, -480, 0, -240, 0, -624, 0, 0, 0, 360, 0, 0, 0, 0, 0, 100, 0, 180, 0, 660, 0, 0, 0, -1440, 0, 0, 0, 0, 0, -240, 0, -12, 0, 340, 0, 0, 0, 228, 0, 0, 0, 0, 0, 480, 0, -190, 0, -768, 0, 0, 0, -240, 0, 0, 0, 0, 0, 100, 0, -720, 0, 240, 0, 0, 0, 1632, 0, 0, 0, 0, 0, 720, 0, 180, 0, 72, 0, 0, 0, 960, 0, 0, 0, 0, 0, -192, 0, -76, 0, -300, 0, 0, 0, -460, 0, 0, 0, 0, 0, -470, 0, -1440, 0, -300, 0, 0, 0, 288, 0, 0, 0, 0, 0, 960, 0, -636, 0, -478, 0, 0, 0, -1056, 0, 0, 0, 0, 0, 900, 0, -620, 0, 1248, 0, 0, 0, 884, 0, 0, 0, 0, 0, 288, 0, -300, 0, -1452, 0, 0, 0, 720, 0, 0, 0, 0, 0, -1200, 0, 948, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, -240, 0, 624, 0, 1200, 0, 0, 0, 628, 0, 0, 0, 0, 0, 240, 0, 288, 0, -732, 0, 0, 0, -288, 0, 0, 0, 0, 0, -30, 0, 180, 0, 1440, 0, 0, 0, -1212, 0, 0, 0, 0, 0, 240, 0, -460, 0, -1152, 0, 0, 0, -620, 0, 0, 0, 0, 0, -700, 0, 1296, 0, -120, 0, 0, 0, -2700, 0, 0, 0, 0, 0, -1440, 0, 768, 0, 260, 0, 0, 0, 468, 0, 0, 0, 0, 0, 420, 0, 788, 0, 1632, 0, 0, 0, 720, 0, 0, 0, 0, 0, -1056, 0, 1440, 0, -1632, 0, 0, 0, 1872, 0, 0, 0, 0, 0, 48, 0, 0, 0, 742, 0, 0, 0, -480, 0, 0, 0, 0, 0, -12, 0, -812, 0, 240, 0, 0, 0, -1580, 0, 0, 0, 0, 0, 740, 0, 480, 0, -300, 0, 0, 0, -1152, 0, 0, 0, 0, 0, 90, 0, 1524, 0, 1684, 0, 0, 0, -60, 0, 0, 0, 0, 0, 624, 0, -1080, 0, -720, 0, 0, 0, 0, 0, 0, 0, 0, 0, -960, 0, -3360, 0, -1452, 0, 0, 0, 2100, 0, 0, 0, 0, 0, -288, 0, 192, 0, -2060, 0, 0, 0, 180, 0, 0, 0, 0, 0, 1440, 0, -1198, 0, 1440, 0, 0, 0, 2068, 0, 0, 0, 0, 0, 480, 0, -1260, 0, 564, 0, 0, 0, 480, 0, 0, 0, 0, 0, 0, 0, 2580, 0, -720, 0, 0, 0, 948, 0, 0, 0, 0, 0, 1200, 0, 360, 0, 1152, 0, 0, 0, -700, 0, 0, 0, 0, 0, 768, 0, -3888, 0, -1260, 0, 0, 0, -720, 0, 0, 0, 0, 0, 900, 0, -1200, 0, 1920, 0, 0, 0, 468, 0, 0, 0, 0, 0, 720, 0, -652, 0, -2220, 0, 0, 0, -288, 0, 0, 0, 0, 0, -1632, 0, -960, 0, -12, 0, 0, 0, 2322, 0, 0, 0, 0, 0, 48, 0, 840, 0, 148, 0, 0, 0, -1020, 0, 0, 0, 0, 0, -1500, 0, 1508, 0, -1680, 0, 0, 0, 1460, 0, 0, 0, 0, 0, -860, 0, 2880, 0, 240, 0, 0, 0, -2304, 0, 0, 0, 0, 0, 480, 0, -2400, 0, -504, 0, 0, 0, -1296, 0, 0, 0, 0, 0, 900, 0, -240, 0, 4320, 0, 0, 0, -768, 0, 0, 0, 0, 0, 1440, 0, 4560, 0, -972, 0, 0, 0, 960, 0, 0, 0, 0, 0, -720, 0, 468, 0, 2260, 0, 0, 0, 180, 0, 0, 0, 0, 0, -1920, 0, -1632, 0, 0, 0, 0, 0, -1610, 0, 0, 0, 0, 0, -850, 0, 3312, 0, -600, 0, 0, 0, -3600, 0, 0, 0, 0, 0, -2400, 0, 660, 0, -1872, 0, 0, 0, -888, 0, 0, 0, 0, 0, -1248, 0, 820, 0, -1488, 0, 0, 0, 1460, 0, 0, 0, 0, 0, 500, 0, -108, 0, 960, 0, 0, 0, 1440, 0, 0, 0, 0, 0, 480, 0, -240, 0, 500, 0, 0, 0, -156, 0, 0, 0, 0, 0, -720, 0, 2708, 0, -1008, 0, 0, 0, 20, 0, 0, 0, 0, 0, 2400, 0, -2400, 0, 1152, 0, 0, 0, -2208, 0, 0, 0, 0, 0, -1440, 0, -780, 0, 1056, 0, 0, 0, -540, 0, 0, 0, 0, 0, 2100, 0, 1922, 0, 4500, 0, 0, 0, -2300, 0, 0, 0, 0, 0, -1200, 0, -48, 0, -60, 0, 0, 0, 2580, 0, 0, 0, 0, 0, 960, 0, -600, 0, -3436, 0, 0, 0, 3360, 0, 0, 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, 7, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "28.3.b.a", "char_is_minimal": true, "conrey_index": 13, "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], [0, 1], [0, 0], [0, -1], [0, 0], [5, -1], [0, 0], [-15, 0], [0, 0], [-6, 0], [0, 0], [0, 1], [0, 0], [24, 0], [0, 0], [0, -4], [0, 0], [0, 5], [0, 0], [24, 5], [0, 0], [-30, 0], [0, 0], [1, 0], [0, 0], [0, -6], [0, 0], [-6, 0], [0, 0], [0, 0], [0, 0], [0, -6], [0, 0], [-24, -5], [0, 0], [10, 0], [0, 0], [-24, 0], [0, 0], [0, 10], [0, 0], [10, 0], [0, 0], [0, 15], [0, 0], [0, -4], [0, 0], [1, -10], [0, 0], [96, 0], [0, 0], [90, 0], [0, 0], [0, 6], [0, 0], [-120, 0], [0, 0], [0, -5], [0, 0], [0, 5], [0, 0], [-75, 15], [0, 0], [24, 0], [0, 0], [-70, 0], [0, 0], [0, -30], [0, 0], [42, 0], [0, 0], [0, -22], [0, 0], [0, 1], [0, 0], [-30, 6], [0, 0], [74, 0], [0, 0], [9, 0], [0, 0], [0, 13], [0, 0], [-96, 0], [0, 0], [0, -6], [0, 0], [0, 30], [0, 0], [24, 5], [0, 0], [0, 0], [0, 0], [120, 0], [0, 0], [0, 16], [0, 0], [90, 0], [0, 0]]}