# Stored data for newform 1274.2.d.c, downloaded from the LMFDB on 09 June 2024.
{"Nk2": 5096, "analytic_conductor": 10.172941217511122, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": 1, "char_values": [1274, 2, [885, 197], [2, 1]], "cm_discs": [], "conrey_index": 883, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[3, [-1, 1]], [5, [9, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007405446726906, "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, 13, 2, 1, 2, 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": "1274.2.d.c", "level": 1274, "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": "26.2.b.a", "nf_label": "2.0.4.1", "prim_orbit_index": 2, "qexp_display": "q+iq^{2}+q^{3}-q^{4}+3iq^{5}+iq^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1274.2.d", "trace_display": [0, 2, 0, 0], "trace_hash": 985166628404643205, "trace_moments": [{"__RealLiteral__": 0, "data": "0.032", "prec": 17}, {"__RealLiteral__": 0, "data": "1.910", "prec": 17}, {"__RealLiteral__": 0, "data": "0.358", "prec": 17}, {"__RealLiteral__": 0, "data": "14.667", "prec": 20}, {"__RealLiteral__": 0, "data": "4.500", "prec": 17}, {"__RealLiteral__": 0, "data": "141.636", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.513", "prec": 17}, "traces": [0, 2, 0, 2, -2, 0, 0, 0, 0, -4, -6, 0, -2, -4, 0, 0, 2, -6, 0, 0, 0, 0, 0, -12, 0, -8, 6, -10, 0, 0, -6, 0, 0, 0, 0, 0, 4, 0, -12, -4, 6, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, -6, 4, -12, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -2, 18, 0, 0, 6, -12, 0, 0, 0, 0, -6, -8, 0, 0, 6, 20, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 12, 0, 6, -36, 0, 0, 0, 0, 8, -24, 0, -28, -6, 0, 0, -24, 10, 0, 0, 0, 0, -12, -12, 0, 0, 8, -12, 0, 6, 22, 0, 0, 0, 0, 0, -4, 0, -2, 12, 6, 0, 0, 24, 0, 0, 0, 0, -10, 0, 0, -30, 0, -4, 0, 12, 0, 0, 0, 0, 0, 12, 12, 0, 0, 4, 44, 0, -12, -6, 0, 0, 0, 0, 0, 12, 0, 0, -10, 18, 0, 2, 12, 0, 0, 0, 0, -12, 30, 0, -4, 0, 16, 0, -18, 0, 0, 0, 0, 0, 24, -2, 0, -24, 18, 0, 0, 0, 40, 0, 0, 0, 0, 6, 0, 0, 24, -4, 0, 0, -46, 12, 0, 0, 0, 0, 0, -18, 0, 0, 12, -6, 0, 0, 16, 0, 0, 0, 0, 36, 0, 0, -42, -12, 18, 0, 20, 0, 0, 0, 0, 0, 32, -16, 0, 0, 36, 0, 0, -6, -24, 0, 0, 0, 0, 2, -6, 0, 0, -18, 0, 0, 48, 0, 0, 0, 0, 0, 0, 30, 0, -6, 0, -36, 0, 12, 16, 0, 0, 0, 0, 6, -8, 0, -36, 0, 0, 0, -16, 0, 0, 0, 0, 0, -36, 6, 0, 12, 24, 8, 0, 30, -24, 0, 0, 0, 0, 0, -28, 0, 36, -6, -38, 0, 0, -20, 0, 0, 0, 0, -24, 0, 0, -2, 16, -12, 0, 0, 0, 0, 0, 0, 0, -24, 72, 0, 26, -24, -12, 0, 0, 24, 0, 0, 0, 0, 66, 0, 0, 0, 20, 0, 0, -12, -90, 0, 0, 0, 0, -12, -34, 0, 22, 0, 36, 0, -16, -12, 0, 0, 0, 0, 8, 0, 0, -6, 0, 0, 0, 36, -4, 0, 0, 0, 0, -12, 4, 0, -60, 12, 36, 0, 6, -6, 0, 0, 0, 0, 0, -8, 0, 24, 0, 24, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 36, 6, -10, 0, -30, 0, 0, 0, 0, 0, 24, -30, 0, 24, 0, 6, 0, -10, 22, 0, 0, 0, 0, 12, 20, 0, 0, -18, -42, 0, -36, -18, 0, 0, 0, 0, 0, 12, 0, -24, 0, 12, 0, 18, 30, 0, 0, 0, 0, 0, 0, 0, 24, -8, 0, 0, 44, 12, 0, 0, 0, 0, 24, -18, 0, -6, 18, -60, 0, -22, -72, 0, 0, 0, 0, 0, 54, 0, 0, 24, 0, 0, 0, 12, 0, 0, 0, 0, 12, 0, 0, 0, -10, 4, 0, 18, 0, 0, 0, 0, 0, 2, 0, 0, 12, -12, -54, 0, 32, -6, 0, 0, 0, 0, 26, 36, 0, 0, 0, -12, 0, -24, 30, 0, 0, 0, 0, 30, -4, 0, -54, 0, -74, 0, -32, 0, 0, 0, 0, 0, -18, 10, 0, 0, 4, 0, 0, 60, -78, 0, 0, 0, 0, 30, 90, 0, -46, 0, 24, 0, 48, 4, 0, 0, 0, 0, 0, -24, 0, -12, -36, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, -36, -60, 0, -74, 0, 0, 0, 0, 0, 44, -12, 0, -48, -18, -12, 0, 36, 0, 0, 0, 0, 0, 0, 60, 0, 0, -4, -58, 0, 0, -44, 0, 0, 0, 0, -46, -36, 0, 12, 0, 0, 0, 6, -36, 0, 0, 0, 0, 36, 84, 0, 0, -24, 0, 0, -72, -18, 0, 0, 0, 0, 0, 0, 0, -60, 12, -12, 0, 12, 0, 0, 0, 0, 0, 0, -2, 0, 40, 10, -36, 0, 0, -18, 0, 0, 0, 0, -108, 0, 0, -2, 24, 36, 0, -12, 0, 0, 0, 0, 0, -42, -42, 0, 84, -30, -36, 0, 18, 12, 0, 0, 0, 0, -40, 12, 0, 0, 0, -30, 0, -48, 0, 0, 0, 0, 0, 4, 0, 0, -56, 0, 26, 0, 6, -16, 0, 0, 0, 0, 0, 0, 0, 18, 36, 0, 0, 0, 36, 0, 0, 0, 0, -6, 64, 0, -24, 0, 90, 0, -4, 12, 0, 0, 0, 0, 0, -24, 0, -18, 36, 2, 0, 0, -6, 0, 0, 0, 0, 24, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 48, -60, 0, 0, -32, 36, 0, -40, -36, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 30, -6, 0, 0, 0, 0, -36, -6, 0, -12, 0, 0, 0, -36, 28, 0, 0, 0, 0, -24, 40, 0, 16, 4, 0, 0, -72, 0, 0, 0, 0, 0, -58, 30, 0, 46, -72, -12, 0, -12, -8, 0, 0, 0, 0, 0, 72, 0, -36, 0, -80, 0, 0, 30, 0, 0, 0, 0, -16, 0, 0, 0, -72, 18, 0, 72, 0, 0, 0, 0, 0, 0, 66, 0, -22, -12, -36, 0, 24, 6, 0, 0, 0, 0, 36, 12, 0, 0, 24, -48, 0, -16, 36, 0, 0, 0, 0, 30, -34, 0, 48, 0, 24, 0, 0, -36, 0, 0, 0, 0, -40, -36, 0, -30, 90, 0, 0, 48, 56, 0, 0, 0, 0, 42, 36, 0, 0, 12, 4, 0, -38, -18, 0, 0, 0, 0, 0, 0, 0, -20, -36, 48, 0, 0, 18, 0, 0, 0, 0, 78, 0, 0, 62, 12, 48, 0, -36, 0, 0, 0, 0, 0, -54, -32, 0, 24, 16, 16, 0, -12, 0, 0, 0, 0, 0, 0, -18, 0, 0, -36, 12, 0, 4, 0, 0, 0, 0, 0, -16, 72, 0, 6, 0, -24, 0, 24, 72, 0, 0, 0, 0, 72, 26, 0, 72, -24, 0, 0, 24, -12, 0, 0, 0, 0, 0, -2, 0, 60, -40, 6, 0, 84, 24, 0, 0, 0, 0, 0, -48, 0, 80, 18, 66, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, -48, -4, 0, 0, 0, 0, 0, 0, 0, 0, 24, 32, 0, -90, 0, 0, 0, -20, 72, 0, 0, 0, 0, 8, 0, 0, 0, -36, -30, 0, 30, -34, 0, 0, 0, 0, 6, -44, 0, -24, 0, 8, 0, 36, 36, 0, 0, 0, 0, -16, 0, 0, -12, -54, 0, 0, -16, -60, 0, 0, 0, 0, 54, -54, 0, 76, -6, 8, 0, -72, 0, 0, 0, 0, 0, 0, -6, 0, 36, 0, 8, 0, 0, -72, 0, 0, 0, 0, 36, 0, 0, 8, 0, 54, 0, 0, 0, 0, 0, 0, 0, -58, -84, 0, 16, 36, -12, 0, 0, 10, 0, 0, 0, 0, 0, -60, 0, 0, -24, 94, 0, 36, 36, 0, 0, 0, 0, -12, 36, 0, -6, 0, -6, 0, 72, -54, 0, 0, 0, 0, -12, -108, 0, -54, -24, 0, 0, 0, -8, 0, 0, 0, 0, -180, -48, 0, -30, 0, -66, 0, 24, -52, 0, 0, 0, 0, 0, 72, 0, 0, -12, -108, 0, 0, -12, 0, 0, 0, 0, -124, 0, 0, 24, 72, 28, 0, 48, 0, 0, 0, 0, 0, -36, 36, 0, 0, 6, 110, 0, 20, 38, 0, 0, 0, 0, -30, 18, 0, 0, 72, 30, 0, 20, 0, 0, 0, 0, 0, 12, 0, 0, 144, 0, 24, 0, 84, 60, 0, 0, 0, 0, -72, 24, 0, 72, 0, 0, 0, 6, 46, 0, 0, 0, 0, 2, -4, 0, 22, -16, -24, 0, -52, 12, 0, 0, 0, 0, 0, -18, 0, 0, 48, -24, 0, 0, 20, 0, 0, 0, 0, 60, 0, 0, 48, -18, -64, 0, -42, 0, 0, 0, 0, 0, -36, 24, 0, -18, 56, -72, 0, 0, -60, 0, 0, 0, 0, -26, -180, 0, 0, 24, 0, 0, 90, 12, 0, 0, 0, 0, 126, -24, 0, 0, 0, -12, 0, -24, 56, 0, 0, 0, 0, 18, 0, 0, -6, -36, 0, 0, 64, 0, 0, 0, 0, 0, 72, -66, 0, 30, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, -96, -20, 180, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 12, 54, 12, 0, 90, 0, 0, 0, 0, 0, 0, 54, 0, -20, 0, 60, 0, -78, -18, 0, 0, 0, 0, 60, 12, 0, 0, 18, 34, 0, -60, 124, 0, 0, 0, 0, -22, 28, 0, -72, 0, 0, 0, -40, -36, 0, 0, 0, 0, -54, -18, 0, 16, 24, 0, 0, 12, 54, 0, 0, 0, 0, 72, 0, 0, -6, 24, 2, 0, 0, 78, 0, 0, 0, 0, 0, -8, 0, -24, -108, 0, 0, 0, -120, 0, 0, 0, 0, 6, 0, 0, 0, 0, 12, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, -36, 20, -60, 0, 4, -64, 0, 0, 0, 0, -36, -14, 0, 0, 24, 108, 0, 0, 48, 0, 0, 0, 0, -8, 12, 0, 42, 0, -4, 0, 0, 0, 0, 0, 0, 0, 60, -24, 0, 60, -12, 0, 0, -54, -36, 0, 0, 0, 0, 32, -132, 0, -6, -44, -24, 0, 6, 72, 0, 0, 0, 0, 0, -12, 0, -108, 48, 26, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, -18, 0, 8, 0, 24, 0, 0, 0, 0, 0, -24, 70, 0, -60, 0, 132, 0, 108, -24, 0, 0, 0, 0, -76, 0, 0, 0, 18, 30, 0, 0, 8, 0, 0, 0, 0, 12, -54, 0, 84, 0, 0, 0, -74, -90, 0, 0, 0, 0, -80, -28, 0, 0, 8, 0, 0, -36, -180, 0, 0, 0, 0, -36, 0, 0, 128, -6, 36, 0, 66, 10, 0, 0, 0, 0, 0, 0, 0, 30, 4, 48, 0, 0, 82, 0, 0, 0, 0, 60, 0, 0, -78, 30, -72, 0, 32, 0, 0, 0, 0, 0, 70, -24, 0, 36, -12, 30, 0, -78, 90, 0, 0, 0, 0, -24, -46, 0, 0, 0, 72, 0, -48, -6, 0, 0, 0, 0, 48, 78, 0, 10, 0, -36, 0, -22, -72, 0, 0, 0, 0, 0, 18, 0, -44, -48, 0, 0, -126, 48, 0, 0, 0, 0, 84, -12, 0, -6, -90, -20, 0, -18, 100, 0, 0, 0, 0, 0, 36, 0, 0, 18, 0, 0, 0, 42, 0, 0, 0, 0, -116, 0, 0, 36, 108, 0, 0, 18, 0, 0, 0, 0, 0, -90, -80, 0, 0, -36, -144, 0, -60, 0, 0, 0, 0, 0, -74, 0, 0, 0, 20, -12, 0, 12, 126, 0, 0, 0, 0, 24, -120, 0, 72, 0, 44, 0, 12, -12, 0, 0, 0, 0, 0, -48, 0, -18, -18, 0, 0, -30, 0, 0, 0, 0, 0, 36, -144, 0, 0, 60, -96, 0, -84, 24, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, -12, 0, 0, 0, 0, -24, 0, 0, -156, 8, -22, 0, -58, 0, 0, 0, 0, 0, 0, -90, 0, -44, 0, 0, 0, -12, -60, 0, 0, 0, 0, -96, 36, 0, 0, -24, 92, 0, -96, -36, 0, 0, 0, 0, -66, -24, 0, -72, 0, 18, 0, 0, -54, 0, 0, 0, 0, 6, 36, 0, -36, -18, 0, 0, 0, 60, 0, 0, 0, 0, 88, -6, 0, 22, -36, 36, 0, 72, 84, 0, 0, 0, 0, 0, 0, 0, -120, -24, 56, 0, 0, 24, 0, 0, 0, 0, -72, 0, 0, 36, -90, -54, 0, -18, 0, 0, 0, 0, 0, 0, 72, 0, -80, -24, 0, 0, -30, 0, 0, 0, 0, 0, 108, -60, 0, 0, -24, -120, 0, -12, 62, 0, 0, 0, 0, 30, 40, 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, 0], [-1, 0], [0, 3], [0, 1], [0, 0], [0, -1], [-2, 0], [-3, 0], [0, 0], [-1, 0], [-2, -3], [0, 0], [0, 3], [1, 0], [-3, 0], [0, -2], [0, 6], [0, -3], [0, 0], [0, 0], [-6, 0], [0, -1], [-4, 0], [3, -2], [-5, 0], [0, 0], [0, 0], [-3, 0], [0, 0], [0, 1], [0, 0], [0, -3], [0, 0], [2, 0], [0, 3], [-6, 0], [-2, -3], [3, 0], [0, 0], [0, 0], [-1, 0], [0, 0], [0, -6], [0, -6], [0, -3], [1, 0], [0, 0], [0, -4], [-3, 0], [2, 3], [-6, 0], [0, -5], [0, 0], [0, 0], [0, 6], [0, 0], [0, 6], [0, -3], [8, 0], [0, 0], [0, 0], [-1, 0], [9, -6], [0, 0], [0, -12], [3, 0], [-6, 0], [0, 0], [0, 15], [0, 2], [0, -6], [-3, 0], [-4, 0], [0, -6], [0, 0], [3, -2], [10, 0], [0, 3], [1, 0], [0, 0], [0, -6], [0, 0], [0, -9], [0, -1], [0, 0], [0, 0], [0, 6], [6, 0], [0, 0], [6, 0], [0, 0], [3, 0], [-18, 0], [0, 1], [0, 12], [0, 0], [0, 0], [4, 0]]}