# Stored data for newform 189.2.p.c, downloaded from the LMFDB on 19 April 2024. {"label": "189.2.p.c", "space_label": "189.2.p", "level": 189, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9008230080446653, "dim": 4, "is_polredabs": true, "nf_label": "4.0.3600.3", "trace_hash": 1463610132268960956, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [25, 0, -5, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+3\\beta _{2}q^{4}+(-3+2\\beta _{2})q^{7}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "p", "char_is_real": false, "Nk2": 756, "analytic_conductor": 1.5091725982021993, "hecke_ring_index": 1, "level_radical": 21, "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": "0.592", "prec": 17}, "analytic_rank_proved": true, "char_values": [189, 6, [29, 136], [3, 5]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [3, 7], "conrey_indexes": [26, 80], "field_disc": 3600, "field_disc_factorization": [[2, 4], [3, 2], [5, 2]], "field_poly": [25, 0, -5, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "3.937", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "90.632", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2857.404", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, -8], "traces": [0, 4, 0, 0, 6, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -12, 0, 0, 40, 0, 0, 10, 0, 0, -30, 0, 0, -6, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, -28, 0, 0, -20, 0, 0, 4, 0, 0, -18, 0, 0, 0, 0, 0, -20, 0, 0, 30, 0, 0, 52, 0, 0, 2, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -22, 0, 0, 60, 0, 0, 0, 0, 0, 20, 0, 0, -12, 0, 0, -60, 0, 0, 0, 0, 0, -30, 0, 0, -18, 0, 0, 40, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, -18, 0, 0, -4, 0, 0, 0, 0, 0, 36, 0, 0, 60, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, -60, 0, 0, 26, 0, 0, -80, 0, 0, 48, 0, 0, 0, 0, 0, 26, 0, 0, -60, 0, 0, 40, 0, 0, -42, 0, 0, -50, 0, 0, -120, 0, 0, 0, 0, 0, 20, 0, 0, -120, 0, 0, 0, 0, 0, 14, 0, 0, 78, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, -76, 0, 0, -20, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 90, 0, 0, -40, 0, 0, 0, 0, 0, 120, 0, 0, 54, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, -80, 0, 0, 18, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 6, 0, 0, 40, 0, 0, -10, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, -86, 0, 0, 72, 0, 0, 0, 0, 0, -80, 0, 0, 56, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, -132, 0, 0, 40, 0, 0, 100, 0, 0, -30, 0, 0, 0, 0, 0, 8, 0, 0, 60, 0, 0, -40, 0, 0, 0, 0, 0, 40, 0, 0, 120, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -80, 0, 0, -14, 0, 0, 18, 0, 0, -36, 0, 0, 0, 0, 0, -4, 0, 0, -60, 0, 0, 68, 0, 0, -80, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 40, 0, 0, -102, 0, 0, 20, 0, 0, -6, 0, 0, -20, 0, 0, -78, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, -136, 0, 0, 20, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 12, 0, 0, 120, 0, 0, 0, 0, 0, -104, 0, 0, 120, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 32, 0, 0, 40, 0, 0, -10, 0, 0, -60, 0, 0, 0, 0, 0, 40, 0, 0, -30, 0, 0, 108, 0, 0, 80, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 62, 0, 0, 180, 0, 0, 0, 0, 0, -6, 0, 0, -24, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 40, 0, 0, -6, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, -180, 0, 0, 44, 0, 0, 100, 0, 0, -22, 0, 0, 90, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 80, 0, 0, 32, 0, 0, -180, 0, 0, -138, 0, 0, 0, 0, 0, 40, 0, 0, 60, 0, 0, 24, 0, 0, 10, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, -78, 0, 0, 108, 0, 0, 0, 0, 0, -46, 0, 0, -100, 0, 0, 18, 0, 0, 0, 0, 0, -50, 0, 0, 144, 0, 0, 116, 0, 0, -20, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 120, 0, 0, 156, 0, 0, 0, 0, 0, 60, 0, 0, -96, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 8, 0, 0, 60, 0, 0, 12, 0, 0, -60, 0, 0, 0, 0, 0, -14, 0, 0, -114, 0, 0, -80, 0, 0, -120, 0, 0, -30, 0, 0, 60, 0, 0, 0, 0, 0, -22, 0, 0, -120, 0, 0, 0, 0, 0, -20, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, -120, 0, 0, -46, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, -60, 0, 0, -100, 0, 0, 0, 0, 0, -10, 0, 0, -180, 0, 0, 0, 0, 0, -42, 0, 0, -30, 0, 0, -80, 0, 0, -80, 0, 0, -22, 0, 0, 66, 0, 0, 0, 0, 0, -30, 0, 0, 234, 0, 0, 240, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 84, 0, 0, 0, 0, 0, 86, 0, 0, -120, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 36, 0, 0, -114, 0, 0, 18, 0, 0, 300, 0, 0, 0, 0, 0, 20, 0, 0, 18, 0, 0, 280, 0, 0, 0, 0, 0, 54, 0, 0, -6, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 32, 0, 0, 160, 0, 0, 8, 0, 0, -252, 0, 0, 0, 0, 0, 40, 0, 0, -120, 0, 0, 80, 0, 0, -10, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 26, 0, 0, -60, 0, 0, -100, 0, 0, 60, 0, 0, -60, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, -280, 0, 0, 24, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 162, 0, 0, -100, 0, 0, 0, 0, 0, 60, 0, 0, 30, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 72, 0, 0, 98, 0, 0, 40, 0, 0, -162, 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, 3, 2, -1, 2, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 21, 7, 1, 6, 0]], "char_orbit_index": 16, "prim_orbit_index": 7, "minimal_twist": "189.2.p.c", "char_is_minimal": true, "conrey_index": 26, "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, 1, 0, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 2, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, -2], [0, 0, 0, 0], [-1, 0, 2, 0], [0, -3, 0, 2], [0, 0, 0, 0], [1, 0, -1, 0], [0, -2, 0, -2], [0, 0, 0, 0], [-2, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, 5, 0], [0, -1, 0, 2], [0, 0, 0, 0], [-6, 0, -3, 0], [0, 0, 0, 2], [0, 0, 0, 0], [-2, 0, 1, 0], [0, 3, 0, -3], [0, 0, 0, 0], [10, 0, -20, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5, 0, 5, 0], [0, -2, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, -2], [0, 0, 0, 0], [-7, 0, 0, 0], [0, 6, 0, 0], [0, 0, 0, 0], [0, 0, -10, 0], [0, -2, 0, 4], [0, 0, 0, 0], [5, 0, -8, 0], [0, 0, 0, 5], [0, 0, 0, 0], [-6, 0, 3, 0], [0, 2, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -1], [0, 0, 0, 0], [-10, 0, 10, 0], [0, 2, 0, 2], [0, 0, 0, 0], [5, 0, 5, 0], [0, -2, 0, 1], [0, 0, 0, 0], [13, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 6, 0, -12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [8, 0, -4, 0], [0, -5, 0, 5], [0, 0, 0, 0], [6, 0, -12, 0], [0, -2, 0, 6], [0, 0, 0, 0], [-11, 0, 11, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10, 0, 10, 0], [0, -4, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, -7, 0, 0], [0, 0, 0, 0], [0, 0, 10, 0], [0, -4, 0, 8], [0, 0, 0, 0], [-1, 0, -4, 0], [0, 0, 0, -6], [0, 0, 0, 0], [-20, 0, 10, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, -2, 0], [0, 5, 0, -8], [0, 0, 0, 0], [-15, 0, 15, 0]]}