# Stored data for newform 936.2.a.g, downloaded from the LMFDB on 14 January 2025. {"Nk2": 3744, "analytic_conductor": 7.473997629191844, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, 1], [13, 1]], "atkin_lehner_string": "-++", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [936, 1, [703, 469, 209, 145], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 0, "hecke_cutters": [[5, [-2, 1]], [7, [-2, 1]], [11, [-4, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27021597797778344, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "936.2.a.g", "level": 936, "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, 13], "level_radical": 78, "minimal_twist": "936.2.a.c", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+2q^{5}+2q^{7}+4q^{11}-q^{13}-2q^{19}+\\cdots", "related_objects": ["EllipticCurve/Q/936/g"], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "936.2.a", "trace_display": [0, 0, 2, 2], "trace_hash": 753679036312000101, "trace_moments": [{"__RealLiteral__": 0, "data": "0.014", "prec": 17}, {"__RealLiteral__": 0, "data": "1.028", "prec": 17}, {"__RealLiteral__": 0, "data": "0.070", "prec": 17}, {"__RealLiteral__": 0, "data": "2.114", "prec": 17}, {"__RealLiteral__": 0, "data": "0.220", "prec": 17}, {"__RealLiteral__": 0, "data": "5.406", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.021", "prec": 17}, "traces": [0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, -10, 0, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, -3, 0, 0, 0, 12, 0, 8, 0, 0, 0, 12, 0, -6, 0, 0, 0, -2, 0, -6, 0, 0, 0, -8, 0, -2, 0, 0, 0, 8, 0, 12, 0, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, -2, 0, 0, 0, -4, 0, -10, 0, 0, 0, -8, 0, 4, 0, 0, 0, -4, 0, 10, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 5, 0, 0, 0, -12, 0, 16, 0, 0, 0, -12, 0, -4, 0, 0, 0, -6, 0, -12, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, -2, 0, 0, 0, 4, 0, -14, 0, 0, 0, 8, 0, -14, 0, 0, 0, 8, 0, 1, 0, 0, 0, -24, 0, -2, 0, 0, 0, 12, 0, -2, 0, 0, 0, -20, 0, 0, 0, 0, 0, -20, 0, -14, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, -8, 0, 0, 0, 16, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, -28, 0, 18, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -6, 0, 2, 0, 0, 0, -16, 0, 16, 0, 0, 0, -28, 0, -20, 0, 0, 0, -16, 0, 24, 0, 0, 0, -8, 0, 26, 0, 0, 0, -4, 0, -6, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, -17, 0, 0, 0, 30, 0, 24, 0, 0, 0, -4, 0, 16, 0, 0, 0, -12, 0, -26, 0, 0, 0, 20, 0, -6, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -30, 0, 0, 0, -12, 0, 30, 0, 0, 0, 8, 0, -20, 0, 0, 0, -24, 0, 6, 0, 0, 0, -22, 0, -16, 0, 0, 0, 24, 0, -15, 0, 0, 0, -4, 0, 0, 0, 0, 0, 24, 0, -10, 0, 0, 0, 0, 0, -18, 0, 0, 0, 24, 0, 16, 0, 0, 0, 36, 0, 0, 0, 0, 0, 24, 0, 22, 0, 0, 0, 30, 0, -2, 0, 0, 0, -40, 0, 38, 0, 0, 0, 24, 0, -8, 0, 0, 0, -12, 0, -22, 0, 0, 0, 0, 0, -12, 0, 0, 0, 40, 0, -2, 0, 0, 0, -8, 0, -20, 0, 0, 0, -12, 0, 28, 0, 0, 0, 30, 0, 8, 0, 0, 0, -4, 0, -2, 0, 0, 0, -30, 0, -6, 0, 0, 0, 40, 0, -12, 0, 0, 0, 32, 0, 2, 0, 0, 0, 24, 0, 10, 0, 0, 0, -20, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -30, 0, 0, 0, -16, 0, -16, 0, 0, 0, 26, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, -12, 0, -4, 0, 0, 0, 0, 0, -7, 0, 0, 0, -2, 0, -8, 0, 0, 0, -12, 0, 18, 0, 0, 0, 20, 0, 36, 0, 0, 0, 0, 0, 24, 0, 0, 0, -2, 0, -8, 0, 0, 0, 12, 0, -8, 0, 0, 0, 4, 0, -20, 0, 0, 0, -4, 0, -14, 0, 0, 0, -8, 0, 48, 0, 0, 0, -12, 0, -4, 0, 0, 0, 14, 0, 0, 0, 0, 0, 40, 0, 42, 0, 0, 0, 10, 0, 32, 0, 0, 0, 0, 0, -18, 0, 0, 0, -22, 0, -26, 0, 0, 0, 28, 0, -19, 0, 0, 0, 0, 0, 30, 0, 0, 0, 32, 0, 3, 0, 0, 0, 8, 0, -14, 0, 0, 0, -24, 0, 48, 0, 0, 0, -24, 0, -24, 0, 0, 0, 16, 0, -34, 0, 0, 0, -8, 0, 0, 0, 0, 0, -24, 0, -42, 0, 0, 0, -12, 0, -20, 0, 0, 0, 36, 0, -12, 0, 0, 0, -12, 0, 34, 0, 0, 0, -24, 0, 0, 0, 0, 0, 20, 0, 20, 0, 0, 0, -16, 0, 10, 0, 0, 0, 8, 0, -8, 0, 0, 0, -36, 0, 8, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 10, 0, 0, 0, -24, 0, -2, 0, 0, 0, -16, 0, -20, 0, 0, 0, -8, 0, -28, 0, 0, 0, -4, 0, -34, 0, 0, 0, 42, 0, 20, 0, 0, 0, -12, 0, -14, 0, 0, 0, -18, 0, -2, 0, 0, 0, -4, 0, -32, 0, 0, 0, -28, 0, -18, 0, 0, 0, -8, 0, 6, 0, 0, 0, -28, 0, 0, 0, 0, 0, -8, 0, 16, 0, 0, 0, 12, 0, 38, 0, 0, 0, -28, 0, -16, 0, 0, 0, -2, 0, 4, 0, 0, 0, -52, 0, 30, 0, 0, 0, 0, 0, 16, 0, 0, 0, -24, 0, -29, 0, 0, 0, 2, 0, 10, 0, 0, 0, -40, 0, 22, 0, 0, 0, -36, 0, 8, 0, 0, 0, 32, 0, -48, 0, 0, 0, 48, 0, 6, 0, 0, 0, -24, 0, 38, 0, 0, 0, 12, 0, -12, 0, 0, 0, -36, 0, 32, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 52, 0, 0, 0, -4, 0, -16, 0, 0, 0, -24, 0, 60, 0, 0, 0, 8, 0, 10, 0, 0, 0, 10, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, -10, 0, 8, 0, 0, 0, 12, 0, 2, 0, 0, 0, -60, 0, -40, 0, 0, 0, -12, 0, -27, 0, 0, 0, -28, 0, -22, 0, 0, 0, 48, 0, -24, 0, 0, 0, 6, 0, 56, 0, 0, 0, 8, 0, 4, 0, 0, 0, 32, 0, -8, 0, 0, 0, 0, 0, -58, 0, 0, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, -10, 0, 0, 0, 2, 0, 8, 0, 0, 0, 0, 0, -3, 0, 0, 0, 12, 0, 8, 0, 0, 0, 12, 0, -6, 0, 0, 0, -2, 0, -6, 0, 0, 0, -8, 0, -2, 0, 0, 0, 8, 0, 12, 0, 0, 0, -4, 0, 0, 0, 0, 0, 14, 0, -2, 0, 0, 0, -4, 0, -10, 0, 0, 0, -8, 0, 4, 0, 0, 0, -4, 0, 10, 0, 0, 0, -4, 0, 8, 0, 0, 0, 0, 0, 5, 0, 0, 0, -12, 0, 16, 0, 0, 0, -12, 0, -4, 0, 0, 0, -6, 0, -12, 0, 0, 0, -4, 0, 0, 0, 0, 0, -10, 0, -2, 0, 0, 0, 4, 0, -14, 0, 0, 0, 8, 0, -14, 0, 0, 0, 8, 0, 1, 0, 0, 0, -24, 0, -2, 0, 0, 0, 12, 0, -2, 0, 0, 0, -20, 0, 0, 0, 0, 0, -20, 0, -14, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -8, 0, -8, 0, 0, 0, 16, 0, 4, 0, 0, 0, 0, 0, 10, 0, 0, 0, -28, 0, 18, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, -10, 0, 0, 0, -6, 0, 2, 0, 0, 0, -16, 0, 16, 0, 0, 0, -28, 0, -20, 0, 0, 0, -16, 0, 24, 0, 0, 0, -8, 0, 26, 0, 0, 0, -4, 0, -6, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, -17, 0, 0, 0, 30, 0, 24, 0, 0, 0, -4, 0, 16, 0, 0, 0, -12, 0, -26, 0, 0, 0, 20, 0, -6, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -30, 0, 0, 0, -12, 0, 30, 0, 0, 0, 8, 0, -20, 0, 0, 0, -24, 0, 6, 0, 0, 0, -22, 0, -16, 0, 0, 0, 24, 0, -15, 0, 0, 0, -4, 0, 0, 0, 0, 0, 24, 0, -10, 0, 0, 0, 0, 0, -18, 0, 0, 0, 24, 0, 16, 0, 0, 0, 36, 0, 0, 0, 0, 0, 24, 0, 22, 0, 0, 0, 30, 0, -2, 0, 0, 0, -40, 0, 38, 0, 0, 0, 24, 0, -8, 0, 0, 0, -12, 0, -22, 0, 0, 0, 0, 0, -12, 0, 0, 0, 40, 0, -2, 0, 0, 0, -8, 0, -20, 0, 0, 0, -12, 0, 28, 0, 0, 0, 30, 0, 8, 0, 0, 0, -4, 0, -2, 0, 0, 0, -30, 0, -6, 0, 0, 0, 40, 0, -12, 0, 0, 0, 32, 0, 2, 0, 0, 0, 24, 0, 10, 0, 0, 0, -20, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -30, 0, 0, 0, -16, 0, -16, 0, 0, 0, 26, 0, -4, 0, 0, 0, 8, 0, 0, 0, 0, 0, -12, 0, -4, 0, 0, 0, 0, 0, -7, 0, 0, 0, -2, 0, -8, 0, 0, 0, -12, 0, 18, 0, 0, 0, 20, 0, 36, 0, 0, 0, 0, 0, 24, 0, 0, 0, -2, 0, -8, 0, 0, 0, 12, 0, -8, 0, 0, 0, 4, 0, -20, 0, 0, 0, -4, 0, -14, 0, 0, 0, -8, 0, 48, 0, 0, 0, -12, 0, -4, 0, 0, 0, 14, 0, 0, 0, 0, 0, 40, 0, 42, 0, 0, 0, 10, 0, 32, 0, 0, 0, 0, 0, -18, 0, 0, 0, -22, 0, -26, 0, 0, 0, 28, 0, -19, 0, 0, 0, 0, 0, 30, 0, 0, 0, 32, 0, 3, 0, 0, 0, 8, 0, -14, 0, 0, 0, -24, 0, 48, 0, 0, 0, -24, 0, -24, 0, 0, 0, 16, 0, -34, 0, 0, 0, -8, 0, 0, 0, 0, 0, -24, 0, -42, 0, 0, 0, -12, 0, -20, 0, 0, 0, 36, 0, -12, 0, 0, 0, -12, 0, 34, 0, 0, 0, -24, 0, 0, 0, 0, 0, 20, 0, 20, 0, 0, 0, -16, 0, 10, 0, 0, 0, 8, 0, -8, 0, 0, 0, -36, 0, 8, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 10, 0, 0, 0, -24, 0, -2, 0, 0, 0, -16, 0, -20, 0, 0, 0, -8, 0, -28, 0, 0, 0, -4, 0, -34, 0, 0, 0, 42, 0, 20, 0, 0, 0, -12, 0, -14, 0, 0, 0, -18, 0, -2, 0, 0, 0, -4, 0, -32, 0, 0, 0, -28, 0, -18, 0, 0, 0, -8, 0, 6, 0, 0, 0, -28, 0, 0, 0, 0, 0, -8, 0, 16, 0, 0, 0, 12, 0, 38, 0, 0, 0, -28, 0, -16, 0, 0, 0, -2, 0, 4, 0, 0, 0, -52, 0, 30, 0, 0, 0, 0, 0, 16, 0, 0, 0, -24, 0, -29, 0, 0, 0, 2, 0, 10, 0, 0, 0, -40, 0, 22, 0, 0, 0, -36, 0, 8, 0, 0, 0, 32, 0, -48, 0, 0, 0, 48, 0, 6, 0, 0, 0, -24, 0, 38, 0, 0, 0, 12, 0, -12, 0, 0, 0, -36, 0, 32, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 52, 0, 0, 0, -4, 0, -16, 0, 0, 0, -24, 0, 60, 0, 0, 0, 8, 0, 10, 0, 0, 0, 10, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, -10, 0, 8, 0, 0, 0, 12, 0, 2, 0, 0, 0, -60, 0, -40, 0, 0, 0, -12, 0, -27, 0, 0, 0, -28, 0, -22, 0, 0, 0, 48, 0, -24, 0, 0, 0, 6, 0, 56, 0, 0, 0, 8, 0, 4, 0, 0, 0, 32, 0, -8, 0, 0, 0, 0, 0, -58, 0, 0, 0]}