# Stored data for newform 728.2.t.a, downloaded from the LMFDB on 15 January 2025. {"Nk2": 2912, "analytic_conductor": 5.813109267149212, "analytic_rank": 1, "analytic_rank_proved": true, "char_conductor": 91, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 20, "char_orbit_label": "t", "char_order": 3, "char_parity": 1, "char_values": [728, 3, [183, 365, 521, 561], [3, 3, 1, 2]], "cm_discs": [], "conrey_index": 9, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[3, [1, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 1305703613144, "hecke_ring_generator_nbound": 13, "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, 91, 7, 1, 3, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "728.2.t.a", "level": 728, "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": [2, 7, 13], "level_radical": 182, "minimal_twist": "728.2.q.a", "nf_label": "2.0.3.1", "prim_orbit_index": 7, "qexp_display": "q-q^{3}+(-3+3\\zeta_{6})q^{5}+(-1+3\\zeta_{6})q^{7}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "728.2.t", "trace_display": [0, -2, -3, 1], "trace_hash": 1939764193577566389, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.901", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10.781", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "95.526", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.004", "prec": 17}, "traces": [0, 2, 0, -2, 0, -3, 0, 1, 0, -4, 0, -2, 0, -2, 0, 3, 0, 2, 0, -6, 0, -1, 0, 0, 0, -4, 0, 10, 0, 9, 0, -1, 0, 2, 0, -15, 0, -10, 0, 2, 0, -3, 0, -3, 0, 6, 0, -11, 0, -13, 0, -2, 0, -3, 0, 3, 0, 6, 0, -12, 0, -10, 0, -2, 0, 21, 0, -18, 0, 0, 0, 1, 0, -11, 0, 4, 0, -1, 0, 9, 0, 2, 0, -16, 0, 6, 0, -9, 0, 10, 0, 17, 0, 1, 0, 9, 0, 13, 0, 4, 0, 22, 0, -7, 0, 15, 0, 16, 0, -15, 0, 10, 0, 1, 0, 0, 0, 4, 0, 10, 0, -20, 0, 3, 0, -6, 0, 7, 0, 3, 0, 17, 0, -3, 0, -15, 0, 6, 0, -3, 0, 11, 0, 2, 0, 27, 0, 13, 0, -18, 0, -1, 0, -4, 0, 6, 0, 5, 0, 3, 0, 0, 0, 42, 0, -3, 0, -9, 0, -22, 0, 12, 0, -26, 0, 16, 0, 12, 0, -42, 0, -12, 0, 10, 0, 60, 0, -2, 0, 5, 0, -6, 0, -34, 0, -21, 0, -23, 0, 4, 0, 18, 0, 45, 0, -9, 0, 0, 0, 6, 0, -5, 0, -1, 0, 18, 0, 4, 0, 11, 0, -14, 0, -21, 0, 8, 0, -12, 0, 13, 0, 1, 0, -3, 0, -33, 0, -9, 0, 24, 0, 10, 0, -32, 0, 6, 0, 6, 0, 16, 0, -3, 0, 0, 0, -6, 0, -6, 0, 40, 0, -18, 0, -18, 0, 18, 0, -10, 0, -10, 0, -24, 0, -17, 0, 4, 0, -22, 0, 2, 0, 60, 0, 54, 0, -9, 0, -15, 0, 13, 0, -13, 0, -19, 0, -36, 0, -10, 0, 0, 0, 12, 0, -22, 0, 15, 0, -40, 0, 7, 0, -5, 0, -11, 0, 30, 0, 1, 0, -9, 0, -16, 0, -6, 0, -20, 0, 15, 0, -55, 0, -46, 0, 20, 0, 27, 0, -4, 0, -1, 0, 1, 0, -20, 0, 0, 0, -16, 0, 25, 0, -10, 0, 30, 0, -6, 0, -10, 0, 29, 0, -20, 0, 20, 0, 66, 0, -58, 0, 6, 0, 12, 0, -34, 0, 6, 0, -63, 0, 11, 0, -7, 0, 34, 0, 15, 0, 6, 0, 9, 0, 0, 0, -17, 0, 27, 0, 30, 0, 3, 0, 10, 0, -5, 0, -3, 0, 10, 0, -22, 0, -6, 0, -60, 0, 24, 0, 3, 0, -29, 0, -28, 0, 22, 0, -16, 0, -5, 0, -2, 0, 38, 0, 29, 0, -27, 0, 0, 0, -8, 0, 26, 0, 33, 0, -60, 0, 18, 0, 1, 0, 3, 0, 1, 0, -3, 0, 2, 0, 10, 0, -35, 0, 64, 0, -6, 0, -27, 0, -9, 0, -5, 0, 3, 0, 12, 0, 6, 0, -50, 0, -50, 0, 0, 0, -78, 0, -16, 0, -42, 0, 35, 0, -18, 0, -6, 0, -4, 0, -43, 0, 9, 0, -11, 0, -33, 0, 22, 0, 34, 0, 44, 0, -30, 0, -21, 0, 11, 0, 26, 0, 17, 0, -28, 0, -16, 0, -4, 0, 23, 0, 24, 0, 21, 0, -96, 0, 42, 0, 13, 0, 37, 0, 12, 0, 90, 0, 8, 0, 20, 0, -27, 0, 45, 0, -60, 0, 54, 0, -15, 0, 2, 0, -4, 0, -6, 0, 1, 0, 6, 0, 15, 0, 6, 0, 0, 0, -23, 0, 34, 0, -8, 0, 3, 0, -42, 0, -45, 0, 3, 0, 23, 0, 21, 0, -24, 0, -4, 0, -5, 0, 5, 0, 36, 0, 30, 0, -30, 0, -45, 0, 77, 0, 94, 0, 9, 0, 33, 0, 7, 0, 0, 0, -40, 0, 29, 0, -6, 0, -40, 0, -43, 0, 5, 0, 21, 0, 31, 0, -2, 0, 18, 0, 41, 0, -18, 0, 6, 0, 12, 0, -4, 0, 30, 0, 51, 0, 22, 0, 1, 0, 46, 0, 14, 0, 45, 0, 0, 0, 21, 0, 10, 0, -23, 0, -20, 0, 49, 0, -52, 0, 12, 0, -44, 0, 18, 0, -13, 0, -15, 0, -12, 0, 2, 0, 18, 0, 6, 0, 3, 0, -92, 0, 30, 0, 33, 0, 11, 0, 54, 0, -18, 0, 0, 0, -21, 0, -24, 0, -6, 0, -35, 0, -10, 0, -72, 0, -32, 0, 26, 0, -12, 0, 1, 0, -6, 0, 18, 0, 38, 0, -6, 0, -33, 0, 27, 0, 32, 0, -64, 0, 36, 0, 3, 0, 6, 0, 5, 0, 0, 0, -50, 0, 60, 0, -12, 0, 84, 0, 21, 0, 6, 0, 14, 0, -4, 0, -40, 0, 9, 0, -1, 0, 45, 0, -30, 0, -4, 0, 18, 0, -4, 0, 10, 0, -18, 0, 45, 0, 22, 0, -20, 0, 11, 0, 0, 0, 10, 0, -10, 0, 40, 0, 24, 0, -63, 0, 9, 0, -34, 0, -2, 0, 40, 0, -4, 0, 24, 0, 70, 0, 22, 0, -4, 0, -27, 0, -5, 0, 17, 0, -52, 0, -60, 0, -3, 0, -10, 0, -54, 0, 0, 0, -44, 0, -18, 0, -7, 0, 21, 0, 15, 0, -31, 0, 39, 0, -13, 0, -9, 0, 18, 0, -26, 0, -3, 0, -10, 0, 19, 0, 25, 0, -56, 0, 36, 0, -48, 0, 35, 0, -2, 0, 33, 0, 63, 0, 0, 0, -18, 0, -12, 0, -12, 0, 18, 0, -26, 0, -44, 0, -32, 0, 16, 0, -15, 0, 85, 0, 106, 0, 40, 0, 5, 0, -40, 0, 14, 0, -58, 0, 39, 0, 5, 0, -6, 0, -68, 0, 11, 0, -39, 0, 0, 0, -75, 0, 12, 0, -55, 0, -1, 0, -39, 0, 9, 0, 9, 0, 30, 0, 30, 0, -32, 0, 51, 0, -80, 0, 6, 0, -6, 0, 12, 0, 20, 0, -10, 0, -10, 0, 30, 0, -61, 0, -69, 0, 55, 0, 0, 0, 110, 0, 46, 0, 12, 0, -26, 0, -50, 0], "weight": 2, "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], [1, 0], [0, 0], [-1, 0], [0, 0], [-3, 3], [0, 0], [-1, 3], [0, 0], [-2, 0], [0, 0], [-1, 0], [0, 0], [1, -4], [0, 0], [3, -3], [0, 0], [2, -2], [0, 0], [-3, 0], [0, 0], [1, -3], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [5, 0], [0, 0], [9, -9], [0, 0], [0, -1], [0, 0], [1, 0], [0, 0], [-6, -3], [0, 0], [0, -10], [0, 0], [-1, 4], [0, 0], [-3, 3], [0, 0], [0, -3], [0, 0], [6, -6], [0, 0], [-11, 11], [0, 0], [-8, 3], [0, 0], [-2, 2], [0, 0], [0, -3], [0, 0], [3, -3], [0, 0], [3, 0], [0, 0], [-12, 12], [0, 0], [-5, 0], [0, 0], [2, -6], [0, 0], [9, 3], [0, 0], [-9, 0], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [0, -11], [0, 0], [0, 4], [0, 0], [1, -3], [0, 0], [9, -9], [0, 0], [1, 0], [0, 0], [-8, 0], [0, 0], [0, 6], [0, 0], [-9, 9], [0, 0], [0, 10], [0, 0], [11, -5], [0, 0], [0, 1], [0, 0], [9, -9], [0, 0], [0, 13], [0, 0], [2, 0], [0, 0]]}