# Stored data for newform 1050.2.i.p, downloaded from the LMFDB on 18 September 2025. {"Nk2": 4200, "analytic_conductor": 8.38429221223444, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 3, "char_parity": 1, "char_values": [1050, 3, [701, 127, 451], [3, 3, 2]], "cm_discs": [], "conrey_index": 151, "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": [[11, [25, -5, 1]], [13, [-5, 1]]], "hecke_orbit": 16, "hecke_orbit_code": 67554544199926810, "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, 7, 3, 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": false, "label": "1050.2.i.p", "level": 1050, "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, 3, 5, 7], "level_radical": 210, "minimal_twist": "210.2.i.b", "nf_label": "2.0.3.1", "prim_orbit_index": 3, "qexp_display": "q+\\zeta_{6}q^{2}+(-1+\\zeta_{6})q^{3}+(-1+\\zeta_{6})q^{4}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1050.2.i", "trace_display": [1, -1, 0, 4], "trace_hash": 2281497277329873736, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.936", "prec": 17}, {"__RealLiteral__": 0, "data": "0.061", "prec": 17}, {"__RealLiteral__": 0, "data": "11.009", "prec": 20}, {"__RealLiteral__": 0, "data": "0.614", "prec": 17}, {"__RealLiteral__": 0, "data": "97.512", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.014", "prec": 17}, "traces": [0, 2, 1, -1, -1, 0, -2, 4, -2, -1, 0, 5, -1, 10, -1, 0, -1, -4, 1, 7, 0, -5, 10, 1, 1, 0, 5, 2, -5, 0, 0, 2, 1, 5, -8, 0, 2, 1, -7, -5, 0, 10, -4, -24, 5, 0, -1, -11, 2, 2, 0, -4, -5, -9, 1, 0, -4, -14, 0, -4, 0, -4, 4, 1, 2, 0, -5, -12, -4, -2, 0, 4, 1, 10, -1, 0, -14, 25, -10, 12, 0, -1, 5, 24, 1, 0, -12, 0, -5, -14, 0, 20, -2, 2, 11, 0, 1, 16, -11, -10, 0, 0, 4, 8, -10, 0, -18, -2, -1, 2, 0, -2, 1, 28, -7, 0, 0, -5, -8, -20, 0, -14, 4, -5, 2, 0, 5, -18, 1, 12, 0, 9, -10, -7, -24, 0, 4, -2, -1, -8, 0, 22, 2, 25, -1, 0, 20, -13, -2, -12, 0, -14, -7, 8, 20, 0, -5, 11, -12, -9, 0, -1, -2, -24, -5, 0, 12, -22, 5, 24, 0, 7, 12, -13, 0, 0, -10, -4, 14, 23, 0, 40, -5, 8, -1, 0, -2, 20, 22, 4, 0, -14, -1, 10, 8, 0, -13, 6, -5, 4, 0, -12, 0, 0, 8, 0, -8, 1, -5, 70, 0, 34, -9, -2, 2, 0, -2, 10, 4, 10, 0, -20, -1, 24, 5, 0, 14, -12, 7, -10, 0, -5, 0, -14, 5, 0, -4, -24, -16, -44, 0, -15, 14, -1, 8, 0, -10, 35, -2, -12, 0, 2, 4, 10, -9, 0, -1, -16, 24, -1, 0, 0, -9, 0, -5, 0, -35, 28, -12, 24, 0, 0, 8, -25, -4, 0, 1, 14, -4, -4, 0, 14, 11, -10, -2, 0, 50, 20, -2, 1, 0, -8, 10, -18, -2, 0, -1, 5, 12, 5, 0, -48, -28, 0, 7, 0, 4, -16, -5, -16, 0, -8, 5, 16, 22, 0, -24, -22, 9, 0, 0, 4, -5, -56, -1, 0, 24, 2, -10, 11, 0, -31, -12, 1, -11, 0, 4, 32, 12, -14, 0, -10, 14, -20, 24, 0, 13, -18, 0, -8, 0, 10, -5, 24, 4, 0, 28, 4, 46, 20, 0, -30, 20, 28, -25, 0, 4, 7, 1, -5, 0, -45, -4, -22, -20, 0, 11, 0, -1, 2, 0, 9, 14, 21, -2, 0, 20, 12, -8, -18, 0, -8, -2, -18, 3, 0, 5, -14, 8, -28, 0, 21, 12, 10, 0, 0, 0, 10, 4, -10, 0, -2, -16, -20, 2, 0, 5, 4, 35, 30, 0, 20, 17, -11, 9, 0, -4, 4, 4, 25, 0, -12, -1, -48, 8, 0, 2, -7, -10, 40, 0, 11, -40, -28, 1, 0, 12, 24, 4, -58, 0, 25, -14, -14, -24, 0, 14, -14, 10, -4, 0, -8, -25, 38, 0, 0, 14, -20, 10, -60, 0, 11, 4, -60, -12, 0, 4, 18, -22, -18, 0, 5, -30, -4, 28, 0, 1, 0, 4, 48, 0, -72, -5, 0, -35, 0, -4, 8, -24, -40, 0, 11, 1, 40, -1, 0, 5, -12, 9, 10, 0, 50, -2, 7, 16, 0, 12, -110, -5, 26, 0, 33, 0, -22, -18, 0, 0, 8, 5, 22, 0, 8, -28, 50, 14, 0, 12, 23, 48, 65, 0, -2, 0, -20, 4, 0, -20, -56, -2, -4, 0, 0, 2, -12, 28, 0, 4, 37, -2, -120, 0, -40, 7, -18, -11, 0, -20, -5, -4, -39, 0, -40, 25, 28, -5, 0, -1, 26, -1, 10, 0, 48, -16, 45, -10, 0, -9, 60, 11, 28, 0, -3, 1, 36, 10, 0, 24, 4, -5, 10, 0, -20, 12, 24, -14, 0, 0, -27, 14, 0, 0, -55, -4, -43, -8, 0, -25, 16, -8, -25, 0, 1, -16, 14, 10, 0, -16, -35, 11, -8, 0, 12, -12, -17, 22, 0, 18, 10, 0, -2, 0, -21, 2, -68, -4, 0, -28, -23, 1, 20, 0, -2, 48, -19, -2, 0, -5, -20, 55, -40, 0, 40, 31, -20, -24, 0, 2, 0, 11, -12, 0, -40, -1, 8, 16, 0, -12, 33, -28, 32, 0, -12, 10, -4, 7, 0, -37, 20, 12, -45, 0, -28, 26, -20, -36, 0, 0, -20, -4, 28, 0, 60, 5, -7, 5, 0, 48, 0, 8, -28, 0, 12, 14, 4, 20, 0, 23, 22, -20, 6, 0, -8, -60, -15, -20, 0, 14, 6, -20, 2, 0, 48, -4, 9, 14, 0, 2, 60, 5, 15, 0, -70, -36, -30, -2, 0, 22, -12, -40, 2, 0, 50, -11, -1, 0, 0, -5, 68, 1, -5, 0, 37, 18, 10, 28, 0, -21, -20, -1, -10, 0, 32, 10, -5, -12, 0, -16, -4, -36, 35, 0, 10, -4, 0, 11, 0, -9, 2, -3, 0, 0, 56, 10, -20, 14, 0, 4, 108, 7, 88, 0, -14, -21, -50, 24, 0, 20, 24, 0, -25, 0, 42, 0, 0, 5, 0, -4, -84, -20, 5, 0, -10, 2, 40, -8, 0, -16, 12, 1, 52, 0, 14, 10, -52, 8, 0, -35, 2, 15, 24, 0, -58, 10, -7, -17, 0, -22, 14, 18, -10, 0, -1, -2, 22, 20, 0, 2, 2, -25, 4, 0, -25, -24, 45, 1, 0, -24, -2, -2, 120, 0, -60, -2, -8, -14, 0, -20, -37, -40, 9, 0, 6, 13, 100, -20, 0, 28, -44, 2, -36, 0, 5, -12, 77, 12, 0, -1, -10, -29, 0, 0, -36, 50, 60, -28, 0, 14, -18, -12, 0, 0, 60, 7, 60, 14, 0, 20, -9, -8, -28, 0, 8, -4, 20, -20, 0, 19, 8, 0, -19, 0, -77, 28, -8, 20, 0, 5, 0, -48, -32, 0, 6, -11, 5, 8, 0, -120, -42, 12, 50, 0, 44, 20, -24, 9, 0, 22, 0, -36, -10, 0, 27, -5, -2, -15, 0, 1, -8, 14, 28, 0, -15, 2, -16, 0, 0, -4, -30, 24, -140, 0, -4, -36, -25, 5, 0, 0, 44, -70, -12, 0, 38, -2, 62, -2, 0, -12, -22, 40, 1, 0, 125, 22, -16, -1, 0, 20, -126, -5, -74, 0, -16, -5, 63, -24, 0, 18, -14, -10, -4, 0, -68, 40, 20, -1, 0, -7, 60, 32, -17, 0, -14, -12, 44, -55, 0, -4, 32, 13, 40, 0, -18, 66, 12, 0, 0, 22, 4, -9, -4, 0, 10, 0, -5, -8, 0, 10, -70, 44, 24, 0, -30, 4, 38, 7, 0, 25, 40, -14, 54, 0, 16, 24, 0, -23, 0, 24, -40, 10, 120, 0, 11, 2, -30, 0, 0, -40, -17, -4, -14, 0, -10, 5, 22, -28, 0, 2, 38, -8, 55, 0, 7, 0, -47, 1, 0, -60, 10, 14, 4, 0, 0, 8, 9, 74, 0, 2, -5, -60, 44, 0, -56, -20, -16, -7, 0, -36, -11, -22, 7, 0, 0, -10, 80, -4, 0, -2, -1, 39, -48, 0, 24, -80, 9, -25, 0, 14, 4, -25, -42, 0, -14, 1, 26, 52, 0, -2, -70, -10, 28, 0, -24, -12, -52, -8, 0, -45, -18, -20, -44, 0, 17, 9, 4, 30, 0, 13, -20, 14, 9, 0, 14, -6, 48, 2, 0, -36, 48, 5, 0, 0, 28, 12, -12, -4, 0, -10, 35, 20, -10, 0, 43, -10, -42, 60, 0, 12, -8, 14, 10, 0, 13, 0, 10, 27, 0, 7, -36, 0, -18, 0, -5, 55, -36, -8, 0, -86, -10, 8, -48, 0, 60, -20, 4, 8, 0, 8, 26, -50, 4, 0, 40, -1, 70, -8, 0, 70, 0, 5, -21, 0, 4, -32, 115, -70, 0, -11, -15, -4, -80, 0, 80, 6, -10, 12, 0, -34, 80, 44, -11, 0, 10, 9, -168, -55, 0, 0, -47, 2, -48, 0, 16, -42, 48, -2, 0, -34, -50, 1, -34, 0, -3, 28, -12, -46, 0, 2, 4, -20, 24, 0, -60, -10, -32, 24, 0, 19, 18, -4, -20, 0, -7, 5, 0, -10, 0, 44, -80, -20, -24, 0, -55, 80, 2, 62, 0, 20, 17, -12, 56, 0, -30, 1, -24, 0, 0, 22, 14, -24, 40, 0, -12, -20, -96, -5, 0, 4, 29, -16, 14, 0, 50, -24, 25, -33, 0, -14, -8, -8, 28, 0, -11, 12, 0, 20, 0, -8, -37, -7, 36, 0, 28, -17, -74, 10, 0, -12, -4, -90, 12, 0, 52, 28, 4, 13, 0, 5, 140, -18, -19, 0, -10, 0, 20, -40, 0, 4, -45, 14, -12, 0, 40, 30, 4, -5, 0, -14, 12, 10, 39, 0, -48, 24, -22, 0, 0, 4, 10, 28, -60, 0, 0, 24, 1, -14, 0, 2, -16, 16, 20, 0, -9, -23, 26, 44, 0, -40, -18, -6, -36, 0, 90, -40, -10, -30, 0, 15, 55, -40, 5, 0, -60, -14, -41, 3, 0, 5, -44, 1, 7, 0, 0, 96, 140, -8, 0, -9, -24, 7, 140, 0, 60, 1, 36, -60, 0, 10, 68, 30, 0, 0, -15, -35, -148, 9, 0, -15, -16, 2, 62, 0, -10, 44, 35, 12, 0, -20, 80, 10, -94, 0, -84, -50, 11, -22, 0, -2, 10, 0, -20, 0, -44, -4, 112, 34, 0, -1, 5, -10, 26, 0, -12, -37, -12, 9, 0, 8, -20, 14, -20, 0, -43, -42, -10, -40, 0, 1, 0, -5, -14, 0, -24, 16, -48, -10, 0, -10, -100, -24, 34, 0, 55, -8, -52, 1, 0, -18, -13, -35, 14, 0, 48, 20, 33, 4, 0, 0, 62, 13, 44, 0, -51, 9, -70, 4, 0, -6, 84, 0, -4, 0, -16, -14, 6, 5, 0, 20, 22, 28, -60, 0, -12, -4, -4, 54, 0, 35, 4, 44, -25, 0, -69, -28, 10, -42, 0, 50, 45, 12, 142, 0, -46, 10, 30, -24, 0, 0, -55, -50, 27, 0, -2, 21, 4, 0, 0, 0, 30, -5, -20, 0, 14, -8, 2, 84, 0, -10, 66, 25, -120, 0, 28, 10, 18, 4, 0, 80, -4, 8, -32, 0, -90, 4, 0, 6, 0, -1, 44, 104, -48, 0, 70, -14, 25, 5, 0, -8, 4, 4, -46, 0, 37, -70, -88, 4, 0, -15, 60, 12, 20, 0, -32, -29, 20, -10, 0, -14, -75, -34, -18, 0, 98, -11, 4, 70, 0, 9, 16, 10, -3, 0, 1, -2, 45, 2, 0, 11, 78, 16, -120, 0, 0, -2, -40, 4, 0, -50, 0, -4, -14, 0, 18, -20, -4, -12, 0, -45, -55, 2, -35, 0, 26, 24, -51, -1, 0, -10, -20, 60, 11, 0, 8, -120, -60, -4, 0, 8, 22, -7, -90, 0, -64, -10, 30, 37, 0, -80, 4, 18, 72, 0, -30, 3, -120, 2, 0, 50, -14, 20, 0, 0, 20, 56, -3, 44, 0, 1, 60, 9, -72, 0, -10, -5, 47, -24, 0, 154, 4, -12, 28, 0, -8, -5, -240, -5, 0, 29, 10, 0, 16, 0, -1, 36, 10, 25, 0, 48, -40, -14, -12, 0, 23, 28, -11, -36, 0, 12, -12, 0, 16, 0, 54, 30, -9, -7, 0, 120, 0, 28, 8, 0, 4, 10, 110, -45, 0, -4, -55, 28, -43, 0, 0, 16, 56, 4, 0, 10, -130, 5, 202, 0, -8, -19, 8, 16, 0, 0, -25, 19, 60, 0, -16, -91, -2, 14, 0, 8, -46, 40, 56, 0, 84, -5, 56, 0, 0, 12, -82, -16, -28, 0, -35, 12, 120, -22, 0, -5, 4, 4, -102, 0, -16, -60, -6, 42, 0, 24, 0, 100, -17, 0, 56, 22, -130, 16, 0, -12, 58, -9, 12, 0, -65, 44, 20, 0, 0, -18, 4, -8, 0, 0, -56, -27, -21, -10, 0, -4, -55, 15, 34, 0, -114, 5, -90, -4, 0, -14, -60, 56, 70, 0, -23, 15, 0, 1, 0, 4, -40, 0, 80, 0, 22, -8, -8, -60, 0, -24, -56, -70, 38, 0, -18, -2, -70, 36, 0, -50, 28, 10, -115, 0, 10, 0, 84, -11, 0, -35, 20, 12, 59, 0, -50, 76, 40, 2, 0, 31, 124, -10, 40, 0, 100, 12, -28, -44, 0, 80, 25, -1, 34, 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, 1], [-1, 1], [-1, 1], [0, 0], [-1, 0], [1, 2], [-1, 0], [0, -1], [0, 0], [5, -5], [0, -1], [5, 0], [-2, 3], [0, 0], [0, -1], [-4, 4], [1, -1], [0, 7], [0, 0], [-3, 1], [5, 0], [0, 1], [1, -1], [0, 0], [0, 5], [1, 0], [-3, 1], [0, 0], [0, 0], [2, -2], [1, -1], [0, 5], [-4, 0], [0, 0], [1, 0], [0, 1], [-7, 7], [-5, 5], [0, 0], [5, 0], [-1, -2], [-12, 0], [0, 5], [0, 0], [-1, 1], [0, -11], [1, 0], [-3, 8], [0, 0], [0, -4], [-5, 5], [-9, 9], [0, 1], [0, 0], [-1, -2], [-7, 0], [0, 0], [-4, 4], [0, 0], [0, -4], [2, 0], [2, -3], [1, 0], [0, 0], [-5, 5], [-12, 12], [0, -4], [-1, 0], [0, 0], [2, 0], [0, 1], [10, -10], [-1, 1], [0, 0], [-7, 0], [15, -5], [-5, 0], [0, 12], [0, 0], [-1, 1], [0, 5], [12, 0], [2, -3], [0, 0], [0, -12], [0, 0], [-5, 5], [0, -14], [0, 0], [5, 10], [-1, 0], [0, 2], [11, -11], [0, 0], [0, 1], [8, 0], [-8, 5], [-5, 0], [0, 0]]}