# Stored data for newform 441.2.g.c, downloaded from the LMFDB on 25 April 2024. {"label": "441.2.g.c", "space_label": "441.2.g", "level": 441, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007611605156281, "dim": 6, "is_polredabs": true, "nf_label": "6.0.19683.1", "trace_hash": 710694199609477606, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [9, 0, 9, 6, 9, 3, 1]], [5, [3, 0, -3, 1]]], "qexp_display": "q+(-1+\\zeta_{18}+\\zeta_{18}^{5})q^{2}+(-\\zeta_{18}^{2}+\\cdots)q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "g", "char_is_real": false, "Nk2": 1764, "analytic_conductor": 3.521402729138465, "hecke_ring_index": 3, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 18, "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": "0.005", "prec": 17}, "analytic_rank_proved": true, "char_values": [441, 3, [344, 199], [1, 2]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [67, 79], "field_disc": -19683, "field_disc_factorization": [[-1, 1], [3, 9]], "field_poly": [1, 0, 0, -1, 0, 0, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.035", "prec": 17}, {"__RealLiteral__": 0, "data": "1.623", "prec": 17}, {"__RealLiteral__": 0, "data": "138.026", "prec": 24}, {"__RealLiteral__": 0, "data": "140.726", "prec": 24}, {"__RealLiteral__": 0, "data": "5470.434", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [-3, 0, 6, 0], "traces": [0, 6, -3, 0, -3, 6, -9, 0, 12, 0, 0, 12, -9, 3, 0, -9, -3, -6, 9, 3, 6, 0, -9, 24, 18, -12, 3, 27, 0, -9, -9, 3, 0, 9, -9, 0, -27, 3, 12, -18, -18, 0, 0, 3, -15, -18, 0, -3, 0, 0, 6, -9, -42, -6, 0, 0, 0, -9, -18, 3, 9, -6, -60, 0, 24, -15, -18, 12, 12, -9, 0, 18, 45, 21, -60, -9, -15, 0, 54, 21, 15, 0, 9, 18, 0, -9, 12, 36, 54, -12, 27, 0, -3, -27, 18, 12, 0, 3, 0, 18, 15, -42, 9, 12, 60, 0, -18, -3, -27, -15, 9, -27, 0, -36, 18, 18, 36, 54, 54, 0, -18, -30, 12, 18, 30, -24, 0, -24, -3, 9, -36, -30, -36, 0, -42, 27, 0, 30, -36, -15, 0, 45, -9, 24, -27, -36, 48, 0, 30, -12, 18, -6, -12, 18, 0, 3, -90, 3, 30, -9, 9, 0, -27, -6, -18, -18, 18, 9, 0, -36, -9, -27, -6, -39, -54, 0, -24, 0, 18, 21, 9, -42, 0, 27, 90, 3, -9, -9, -30, 0, -18, -3, -27, -15, 30, -54, 0, 90, 0, -6, -78, -27, 36, 0, 27, 0, -24, 9, 57, -3, 0, 3, 66, -27, -18, 3, 54, 0, -24, 45, 18, -12, -9, -15, 0, -27, -36, -42, 0, 30, 18, 0, 45, -21, 72, 0, -42, 27, 0, -9, 27, -60, -3, 0, -42, 0, 0, -30, -21, 9, -18, -36, 0, 54, -51, -18, 51, 96, -9, 0, 48, 54, 27, -6, 72, 9, 0, -63, 12, 21, 0, -24, 3, 0, -36, -42, -18, 12, -60, 81, 0, -54, -9, -15, 18, -9, 45, 0, -54, 33, 72, -72, -114, -9, 0, 18, -21, 54, 27, 48, 36, 0, 21, -18, 48, -15, -27, 12, 0, 27, -54, 48, 45, 3, -96, 0, -42, 24, -45, 9, 60, -36, 0, -12, -81, -42, 30, -27, -9, 0, 0, -42, -18, 81, -63, 21, 0, -15, 144, 18, -18, 6, 45, 0, 15, -36, -90, -15, 9, -24, 0, 0, -9, 48, 36, 72, -39, 0, 18, 6, 0, 36, -6, 45, 0, 12, 27, 30, -21, -27, -54, 0, -18, 30, -18, 63, -36, 126, 0, -6, 3, 117, 18, -66, 18, 0, 66, -27, -60, -42, 36, -9, 0, -63, -45, 30, -90, 57, -24, 0, 33, 24, -9, -102, 39, -27, 0, 6, 18, 12, 9, 63, -33, 0, 27, 27, 0, -45, 54, 36, 0, 39, 21, -72, -45, 3, -27, 0, -3, 0, 18, -15, 0, 102, 0, 54, 30, 21, 27, -33, -36, 0, 18, 6, -18, 18, -6, -63, 0, 0, 9, 0, 108, -81, 9, 0, 0, 57, -87, 0, 27, -18, 0, 12, -144, -90, -36, 69, -135, 0, 27, 45, -9, 6, -27, 3, 0, -9, -63, -150, 27, -102, 12, 0, -30, 48, 81, 21, -3, 27, 0, 27, -9, 54, 60, -27, -6, 0, -27, 12, -51, -90, 81, -72, 0, -36, -18, 36, -105, -48, 54, 0, -150, 27, -18, -6, 18, -9, 0, -90, 27, 39, -135, -33, 78, 0, 36, -66, -27, 42, 18, -90, 0, 18, 126, 9, -12, -9, -27, 0, 54, -33, 66, 27, 18, -24, 0, -24, -78, -27, 36, 54, 9, 0, 39, -90, 210, 3, -9, 42, 0, -9, 54, 30, 9, -18, 192, 0, -126, 51, -18, 39, -174, 72, 0, -84, -54, 48, -48, 0, -9, 0, 126, -27, 42, 99, 27, -54, 0, 24, 0, -27, -6, -57, 0, 0, 69, -27, 18, -42, -63, 66, 0, 27, 84, -84, 63, 102, -27, 0, 0, 57, 45, 3, 21, 27, 0, -72, -18, -132, -6, 108, -126, 0, 9, -30, -69, -18, 93, -66, 0, 12, 6, 36, 81, -132, 108, 0, -126, -81, -45, 84, 45, 57, 0, 18, 0, 21, 27, -9, -60, 0, -6, -48, 27, 72, 0, -54, 0, 9, 36, -15, -15, 99, 36, 0, -9, -36, 234, 54, -54, -3, 0, -42, 39, -54, -72, -3, -54, 0, 36, 9, -126, -96, -27, -54, 0, 108, -6, 42, -27, 12, 204, 0, 36, 30, -27, 9, 120, 45, 0, 36, 27, 24, 12, 72, 0, 0, 9, -6, -54, -54, -117, -69, 0, -18, -42, -90, 90, 33, -45, 0, 45, 27, -6, -18, 45, 39, 0, 81, 9, 6, -18, 66, -60, 0, 36, 15, 0, 93, -6, -54, 0, 18, 108, 72, -24, -81, 54, 0, 36, 66, -12, -54, -171, 120, 0, 84, 3, 9, 9, 60, 36, 0, 24, 54, 72, 6, 72, -60, 0, -36, -42, 3, -9, 21, -111, 0, 36, -18, 63, -18, -9, -81, 0, -42, 45, 57, -18, -126, 27, 0, 135, 6, -60, 9, 66, -72, 0, 18, 0, 9, -99, 51, 9, 0, -30, -63, -72, -24, -81, -24, 0, -27, -126, -15, -72, -12, -60, 0, 0, 15, -45, -96, 42, -45, 0, 18, -126, -15, 18, -54, -42, 0, -135, 63, -48, 27, 90, -27, 0, -66, -60, 63, -42, -36, -27, 0, -51, -27, 9, -69, 27, -33, 0, -9, -54, -24, 126, -186, -6, 0, -117, 6, 0, -27, -69, 45, 0, 33, 27, -84, 6, -54, 90, 0, -189, 12, -123, 45, 27, 198, 0, 30, 42, 36, -36, 24, 108, 0, -126, 27, 39, -42, 18, 18, 0, -81, 27, -18, 108, -9, 18, 0, -126, -42, 9, 102, 12, -9, 0, -27, 45, 27, 84, 27, -123, 0, -81, -24, 36, -72, 54, -99, 0, 21, 12, 27, 54, -75, 90, 0, 60, -27, -108, 0, -18, 12, 0, -63, -18, 93, -144, -27, 84, 0, 18, 24, -99, -3, -78, 72, 0, 108, -81, 27, 162, 54, 72, 0, -36, -72, -30, 36, 3, -6, 0, 66, 66, 27, -144, 78, -162, 0, 75, -9, 21, -51, -9, -54, 0, 54, 126, 192, 27, 144, -18, 0, 69, 39, 27, -105, 81, 45, 0, 3, 63, 12, -24, 27, 90], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 63, 7, 1, 3, 0]], "char_orbit_index": 7, "prim_orbit_index": 7, "minimal_twist": "63.2.f.a", "char_is_minimal": false, "conrey_index": 67, "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, 0, 0], [1, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, 1], [0, 0, -1, 0, -1, 0], [0, -1, -1, 2, 2, -2], [1, 0, 0, 0, 1, 0], [-2, 1, 2, -2, -1, 2], [0, 0, 0, 0, 0, 0], [2, 0, 0, 1, -2, 0], [0, 0, 1, 0, -1, -1], [0, 0, -2, 2, 0, -1], [2, 0, 0, 0, -1, 0], [0, -3, -2, 3, 3, -2], [1, -1, -4, 4, 0, -2], [0, 0, 0, 0, 0, 0], [-2, 1, -2, 1, 0, 0], [-1, 1, 3, -3, 0, 3], [-2, 2, -1, 1, 0, 0], [0, 3, 3, -3, 0, 3], [0, 1, -1, 2, 2, -2], [0, 2, 1, -1, -1, 1], [0, 0, 0, 0, 0, 0], [-3, 3, 2, -2, 0, 4], [4, 0, 0, 3, 1, 0], [5, -4, 1, -4, -5, 1], [-2, 0, 0, -1, 1, 0], [0, 1, 6, -7, -7, 7], [6, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -3, 4, -5, -5, 5], [0, -3, 1, 0, -1, -1], [0, 1, -3, -3, -3, 3], [0, 0, 0, 3, 3, -3], [2, -1, -1, -1, -3, 0], [0, -3, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0], [-3, -3, -2, 3, 5, -4], [0, 1, -3, -3, -3, 3], [2, 0, 0, 1, -2, 0], [0, -6, 1, 0, -2, -3], [-3, 0, 0, 4, 2, 0], [0, 0, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, -1], [0, -5, -4, 7, 7, -7], [-3, 0, 3, 0, 0, 0], [0, 0, 1, -1, 0, 5], [-1, 1, 3, -3, 0, -2], [-3, 6, 1, -3, 0, 4], [0, 0, 0, 0, 0, 0], [2, -2, -3, 3, 0, -5], [-1, -1, 3, -1, -1, 2], [-7, 0, 0, 5, 10, 0], [-2, 2, 2, -2, 0, 3], [-3, 6, 0, -3, -3, 6], [0, 0, 0, 1, 2, 0], [0, 0, 0, 0, 0, 0], [0, -3, -2, 3, 1, 0], [-3, 0, 0, -3, 6, 0], [0, 1, 0, 5, 5, -5], [1, 1, 1, -2, -3, 3], [-2, 2, 0, 0, 0, -3], [-10, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 3, 0], [-5, 5, -5, 5, 0, 1], [-6, 6, 5, -6, -2, 7], [0, 4, -3, 0, 0, 0], [2, 0, 0, -1, -3, 0], [1, -5, -2, -5, -6, 3], [0, 0, 0, 0, 0, 0], [3, 0, 0, -3, 3, 0], [6, 3, -3, 0, -3, -6], [7, -7, 1, -1, 0, -4], [-10, 0, 0, 1, 1, 0], [-3, 3, 0, 3, 4, -1], [-5, 5, 3, -3, 0, 3], [0, 0, 0, 0, 0, 0], [5, 8, 7, -13, -8, 7], [7, -7, 3, -3, 0, 0], [5, -5, 2, -2, 0, -1], [0, 0, -6, 0, -3, -3], [0, 3, 0, 0, 0, 0], [0, 6, 1, 4, 4, -4], [0, 0, 0, 0, 0, 0], [-3, 3, -4, 4, 0, -2], [2, 0, 0, 1, 1, 0], [3, 6, 5, -9, -2, 1], [9, 0, 0, -1, -8, 0], [0, -4, -7, 3, 3, -3], [6, -3, 0, 0, 3, -3], [0, 0, 0, 0, 0, 0], [0, -1, -2, 8, 8, -8], [-9, 9, 3, 0, -4, -2], [0, 6, -1, 2, 2, -2], [0, 4, -1, 1, 1, -1], [3, -6, -3, 3, 3, 0], [0, 1, -8, 7, 7, -7], [0, 0, 0, 0, 0, 0], [3, 0, 0, 0, -3, -3], [0, 5, 4, -8, -8, 8]]}