# Stored data for newform 841.2.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "841.2.a.d", "space_label": "841.2.a", "level": 841, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666761, "dim": 2, "is_polredabs": true, "nf_label": "2.2.8.1", "trace_hash": 715450528518444315, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-1, -2, 1]]], "qexp_display": "q+(1+\\beta )q^{2}+(-1-\\beta )q^{3}+(1+2\\beta )q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3364, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 6.71541880998968, "hecke_ring_index": 1, "level_radical": 29, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 8, "field_poly_is_real_cyclotomic": true, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.020", "prec": 17}, "analytic_rank_proved": true, "char_values": [841, 1, [2], [1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [29], "conrey_indexes": [1], "field_disc": 8, "field_disc_factorization": [[2, 3]], "field_poly": [-2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.950", "prec": 17}, {"__RealLiteral__": 0, "data": "0.312", "prec": 17}, {"__RealLiteral__": 0, "data": "9.154", "prec": 17}, {"__RealLiteral__": 0, "data": "3.529", "prec": 17}, {"__RealLiteral__": 0, "data": "60.016", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[29, 1]], "trace_display": [2, -2, -2, 0], "traces": [0, 2, 2, -2, 2, -2, -6, 0, 6, 0, -2, -2, -10, -2, -8, 2, 6, 4, 8, -12, -2, 8, 2, -4, -10, -8, -10, -2, -16, 0, 6, -6, -6, -2, -4, 0, 16, 8, -12, 10, -6, -8, 16, -10, 6, 0, 12, -2, -6, 2, -8, 4, -18, 2, 2, 2, -8, 12, 0, 4, 10, 4, -26, -16, -14, 2, -2, 0, -12, -12, 8, -12, 8, -8, 8, 8, -12, -8, 22, 2, -6, -2, 16, 4, 24, -4, -6, 0, -2, 8, -8, 16, 28, 26, 10, 12, 2, 8, 2, 8, -8, 16, 4, -4, -14, -8, 26, -24, 6, 14, -2, -8, 0, 4, 36, 4, 0, -16, -12, 16, 10, -16, 12, -16, -46, 18, -16, 20, -10, 6, 10, -20, -2, 0, 16, 2, 4, -24, -20, 28, 16, -10, -20, -6, 0, 0, -8, -2, 8, -10, 24, 0, -36, -16, 0, 6, 34, 0, 6, -26, 6, -32, -26, -22, 40, 2, 20, -12, 32, -8, 4, 0, -2, 36, 0, 0, -6, 12, 32, 4, -16, -6, 24, -12, 4, -8, 58, -12, 22, -8, 12, -28, 22, 16, -16, -10, 2, 4, 0, 16, -24, -16, 0, 0, 4, 8, -12, 32, -6, 12, -16, 2, 50, 20, -32, 10, -2, 40, 30, 8, -6, 12, -24, -12, -8, 0, 36, 12, 60, 24, -12, 0, 0, 14, -24, 2, -28, -6, 0, -28, 6, -14, -24, 32, 20, -2, -24, 12, -38, -20, 18, -26, -16, 20, 4, -4, -26, -42, 22, 0, 18, 0, -52, -14, -6, -2, 48, -32, 32, -12, -2, -2, 12, -24, -24, 8, -28, -12, 28, -40, 8, 30, -18, 12, -28, -12, -2, -48, 8, -10, 0, 16, -8, -4, -6, -4, 24, 6, -18, -28, 40, -8, -40, 0, -36, -4, 0, 14, 8, 12, 26, -28, 42, 14, -24, 16, 10, 12, -54, 0, 14, 32, -16, -24, -50, 8, -2, -30, 0, -24, 2, 2, 36, 0, -4, 0, 24, -4, 8, -36, 12, -14, -48, 0, -26, 12, 20, -12, 0, 18, 32, -6, 10, 20, 20, 12, 56, 0, -20, -22, -8, 34, 26, 24, 32, 8, -28, -36, -12, 48, -8, -48, 90, -30, 4, -18, 6, 0, 0, -20, 12, -4, -60, -24, 54, 8, 8, 8, -40, -40, -22, -40, 6, 52, 4, -2, -8, 50, -8, -48, -24, -26, -32, 46, -16, 2, 0, -8, 12, 4, -16, 24, -20, 32, 16, -4, -2, -28, -12, -36, -24, -12, 54, 24, 30, -16, 52, -16, -40, 2, 6, 28, -6, -16, 64, 0, 46, 24, 24, -12, 2, 0, 4, 60, -40, -8, -4, 18, 16, 36, -32, 32, 68, 40, -28, -16, 60, 36, 0, -12, -28, -28, 8, -52, 0, -26, 46, 6, -32, -32, -10, 24, -4, 14, -14, 48, -16, 48, -44, 6, -2, -8, -46, 16, -32, -8, 48, -40, 20, 2, -2, 34, -32, 0, 60, -8, -18, 16, -44, 4, 18, 4, -46, -26, -48, -16, -4, -8, -12, -38, -4, 0, -54, 12, -34, 4, 38, 14, -32, -20, 14, -30, 0, 32, -84, -32, -2, 28, -6, 26, -26, -32, 96, -40, -72, 24, 16, 20, -84, -2, -6, 32, -46, -26, -20, -14, -64, 32, -24, 16, -8, 0, -44, -8, -44, 8, 28, -12, -64, 2, 0, -4, 78, 10, -26, -4, 28, 48, -44, 68, -36, -16, 2, 60, -16, 16, -16, 20, -42, -8, 0, -32, 24, 22, -24, 16, -20, 4, -10, 36, 12, -4, 24, -22, -2, -16, -26, 8, -28, 34, 40, 40, 32, 32, -80, 16, -16, -10, 36, 0, -12, -22, 16, -18, -14, 16, -16, -24, 28, -70, 46, 20, 4, -48, 30, 22, 22, 12, -48, 16, 16, -68, 10, -54, 84, -20, -82, -2, 0, -16, 10, 4, 88, 48, 0, -6, 24, 68, -30, -20, 40, -64, 18, 32, -74, 20, -24, 0, -16, -26, 2, 44, 6, -4, 28, 0, 32, 0, 4, 4, -16, 4, -16, 2, -60, 8, 24, 44, -76, 48, -4, 28, -6, 8, -96, 24, 48, 0, -30, -50, 20, 96, 4, 16, 12, -28, 0, -64, -22, -46, 64, -18, -2, -48, 6, 10, 68, 32, 28, 30, 20, 8, 48, -68, -16, 6, -44, 44, -2, -12, 0, 16, 34, 46, 58, 0, 64, 20, 56, -42, 8, -28, -44, -8, -36, 2, 28, 16, 16, 6, -8, -60, -56, -36, 110, 10, -62, 32, 20, 16, -54, -28, -6, 46, 0, 0, 8, -68, 28, 4, 36, 12, -28, -32, -92, 16, 0, 28, 74, 36, 0, 34, 0, 56, -32, 24, 0, 32, 8, 48, -34, 4, 8, 0, 6, 0, 124, -12, 4, 2, -6, -64, 16, -20, 34, 26, -32, 4, -96, -28, 24, 48, -42, 8, -48, 32, 90, 84, 32, -16, 26, 16, 0, 46, 8, 22, 12, 60, 52, 16, -40, 14, 72, 52, -20, 8, 16, -46, 0, 20, -20, 44, 30, 4, -84, 12, -36, -14, -12, 30, -32, 0, -100, -78, 106, 8, 16, 16, 6, -28, 16, -16, 84, 12, -32, 0, -80, -18, 10, -14, 2, 16, 44, -28, 10, -36, -80, 42, 88, 2, 0, -32, 58, -48, -72, 0, 40, -46, 4, 20, 6, -28, 8, -8, -4, -12, 44, -54, -40, 32, -32, -22, 4, 12, 46, -4, 88, 28, 84, 0, -64, -44, -8, -32, 44, 6, 80, 12, -68, -32, -24, 62, 36, 12, -12, 12, -24, 64, 4, -12, -4, 14, -28, 28, 16, -32, -52, -16, 0, 60, -58, -12, 78, -4, 106, 12, -56, 12, -32, -22, -22, -34, 48, 112, 12, 8, -10, -42, -22, 8, 48, -84, 32, -26, 56, 28, -60, 0, -22, 0, -22, 56, -40, -16, -78, -16, 64, 62, -56, -24, 16, 20, 64, 0, -16, -40, 12, 78, 26, 16, -2, 32, 46, -10, -56, -4, 0, 16, 108, 36, 0, -20, -2, -6, 64, -16, -68, 0, 52, -8, 54], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "29.2.a.a", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [1, 1], [-1, -1], [1, 2], [-1, 0], [-3, -2], [0, -2], [3, 1], [0, 2], [-1, -1], [-1, 1], [-5, -3], [-1, -2], [-4, -2], [1, 1], [3, 0], [2, -2], [4, 2], [-6, 0], [-1, -2], [4, 2], [1, 0], [-2, 4], [-5, -4], [-4, 0], [-5, -3], [-1, 1], [-8, -2], [0, 0], [3, 2], [-3, -5], [-3, 1], [-1, 0], [-2, 0], [0, 2], [8, 2], [4, 0], [-6, -6], [5, 3], [-3, -1], [-4, 6], [8, 6], [-5, 1], [3, -1], [0, -2], [6, 2], [-1, 3], [-3, -3], [1, 0], [-4, -4], [2, 0], [-9, -4], [1, 6], [1, 0], [1, -1], [-4, -6], [6, 6], [0, 0], [2, -4], [5, 3], [2, 2], [-13, -8], [-8, 0], [-7, -2], [1, 2], [-1, -1], [0, 4], [-6, 2], [-6, -2], [4, 2], [-6, -2], [4, 6], [-4, 0], [4, 4], [4, 4], [-6, -12], [-4, 2], [11, 8], [1, 1], [-3, 0], [-1, -6], [8, 2], [2, 4], [12, 10], [-2, 2], [-3, -4], [0, 0], [-1, 2], [4, 6], [-4, -2], [8, 2], [14, 0], [13, 8], [5, 2], [6, 0], [1, 2], [4, -6], [1, 1], [4, -2], [-4, -8]]}