# Stored data for newform 74.2.e.b, downloaded from the LMFDB on 24 April 2024. {"label": "74.2.e.b", "space_label": "74.2.e", "level": 74, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538831946, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 1446538950909923141, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [3, -3, 1]]], "qexp_display": "q+\\zeta_{12}q^{2}+(-\\zeta_{12}-\\zeta_{12}^{2}-\\zeta_{12}^{3})q^{3}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 37, "char_orbit_label": "e", "char_is_real": false, "Nk2": 296, "analytic_conductor": 0.5908929749574748, "hecke_ring_index": 1, "level_radical": 74, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.185", "prec": 17}, "analytic_rank_proved": true, "char_values": [74, 6, [39], [5]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 37], "conrey_indexes": [11, 27], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.832", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "50.609", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "982.755", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [0, -2, 6, 4], "traces": [0, 4, 0, -2, 2, 6, 0, 4, 0, -2, 0, -12, 2, -12, 0, -6, -2, 6, -12, -6, 6, 4, -6, 0, 6, -4, 0, 16, -4, 0, -6, 0, 0, 12, 12, 12, -4, -2, 12, 12, 0, -6, 12, 0, -6, 0, 6, 12, 4, 6, 0, 0, -12, -12, 0, -18, 0, -12, 0, -12, 0, 6, -6, -8, -4, -12, 0, 10, 0, -24, 0, 0, -12, 16, -24, 8, -6, -12, 12, 6, 0, -2, 0, -6, 8, 12, 12, -30, 0, 18, -12, -24, 6, 12, 6, -6, 6, 0, 0, 18, -8, 36, 18, 0, 0, 0, 12, 0, 8, 30, -12, 34, -8, -12, 0, -6, 30, 0, 12, 0, 6, 4, 0, -30, 6, 0, -24, 26, 0, -12, 0, -18, -12, -12, 0, 24, -12, 36, -24, 10, 0, -12, 0, 36, -2, -30, 0, -12, 2, -36, 12, 2, 6, -78, 0, -6, 0, -2, -60, 0, 0, 12, 0, 24, 6, 36, 30, -48, 12, -2, 36, 0, -24, -18, -60, -16, 6, 0, -24, 0, -6, -2, 0, -6, 12, -6, 0, -54, 6, 16, 18, 0, 2, 0, 12, 24, 12, -6, 42, 0, 0, 28, 12, 60, 42, -18, -24, 42, 0, 0, 12, 32, -24, -12, 0, 24, 0, 12, -12, -8, -18, -24, 6, 44, 0, -4, 0, -6, 0, -34, 0, -24, 0, 60, 24, 18, 0, 84, -24, -60, 6, 12, 36, 34, 6, 0, -42, 12, -12, -48, 0, 0, -4, 0, -18, -42, -2, -18, 24, 4, -24, 30, 30, -36, -24, 0, 12, 0, -10, 24, 0, -26, -6, 0, -36, 12, -24, 18, 54, -30, 0, -54, 0, -48, 0, -24, 24, 12, 0, 44, 0, -42, 8, -18, -18, -24, -12, -48, -24, 12, 4, -48, 0, -30, 0, 6, -48, -88, 12, 60, 0, 0, -12, 42, 0, -12, 6, 6, 24, 0, -6, 36, 24, 60, 2, 0, 12, 0, 24, 12, 24, 0, -12, 4, 0, 30, 4, 2, 0, 0, 6, 0, 6, 80, 24, -24, 12, 0, -30, -2, 0, -48, 6, -6, 0, 0, 0, 84, -12, 72, -24, -14, 0, -38, 0, 24, -6, -4, 6, 108, -36, -48, 12, -14, -42, 42, 0, 60, 0, 28, -12, -16, -6, -12, 0, -36, 12, 48, 6, -90, 36, 42, 0, 0, -12, 6, 36, -92, 0, 0, -4, 0, 48, 12, 18, -6, 0, 42, 36, 78, -24, 18, 12, 0, 18, 0, 0, -128, -24, 36, 12, 0, -36, -18, 12, -12, -12, 12, 0, -72, 0, -30, -8, -20, -24, -30, 0, -12, 0, -84, -6, 6, -72, -72, -4, 36, 18, 42, -4, -12, 0, 42, 0, -16, 12, -48, 0, -90, 0, 24, 6, -12, -48, 0, 30, 12, 0, 0, 12, -20, 12, 4, -12, 0, 24, 0, -12, 12, 0, 12, 12, 12, 48, -48, 2, -6, 6, 0, 0, 0, 0, 84, -60, 30, -36, 0, 6, 0, -12, -18, -42, 48, 0, -18, 0, 54, -24, 4, 52, 6, 0, 16, 0, -24, 24, -12, -12, -48, -24, 12, 0, -24, 60, 102, 0, 8, 0, -30, -24, 44, 12, -60, 0, 36, -6, 0, -18, 48, -36, -18, 24, 0, 54, 34, -24, 60, -24, 0, 18, 0, 12, 30, -12, 12, 24, 72, 20, 102, 6, -48, -12, 0, -24, 0, 12, -24, 24, 4, 12, 0, 0, -2, 36, 0, 48, 12, 2, -24, 0, -54, 30, -24, -36, 24, 0, -12, 0, 42, -6, 24, 36, 36, 4, 36, -24, 12, -18, 36, 0, -78, 0, 46, 48, -92, -2, 6, 0, -114, -6, -60, 0, -36, -78, 26, 0, 0, 12, -60, 24, 80, 6, 0, -36, 0, -12, 22, 24, 36, -4, -144, -48, -90, -30, 20, -36, 0, 0, 0, -30, 48, 0, -30, 36, 0, 12, -12, -18, -24, -12, 0, 0, 24, 0, -90, 18, -36, 12, -8, 0, 12, 0, 6, 0, 84, 30, -24, 24, -60, -48, -40, 18, -18, 0, -32, 0, -16, -4, 108, -12, 12, 0, -12, 12, 12, -30, 54, 0, -70, -24, 0, -36, -2, -36, 72, -6, 0, -30, 0, -36, -30, -8, 24, 0, -30, 12, -36, -36, 36, 24, 0, -12, 0, 24, 24, 72, 36, -12, 0, 60, -78, -6, 24, -36, -84, 2, 60, 0, 96, 0, -92, 0, 48, 0, -16, 0, -18, 6, -48, 60, 68, 0, 48, 24, 42, 0, -54, 0, 54, 0, 0, 84, 160, -6, 60, 0, 6, -16, 18, 72, 108, 18, -30, -60, 0, 18, -78, 0, 48, -2, 0, -12, 0, 18, -54, -36, 12, 24, -8, 0, -54, 12, 12, 54, 0, 6, 0, 12, -40, -12, -48, -90, 0, 42, -12, 0, 0, -36, 72, 0, 54, 0, 126, 0, -48, 56, 12, 0, 24, 0, 96, 12, -20, 60, -56, 72, 48, 42, -60, -24, 24, 0, -12, 0, -58, -48, -48, -24, -48, 0, 36, 30, -54, 12, 18, -84, -48, 0, 0, -48, 54, 24, -184, 0, 0, 16, 0, -42, 4, -12, 12, -48, 30, -24, 6, 0, 30, -36, 0, -48, 0, -24, -120, -36, 12, 0, 0, 72, 116, 12, 72, -90, -60, 12, 78, 0, -84, 8, 28, 24, 18, 0, -78, 0, -66, -12, -24, 12, -108, -18, 104, -72, -6, 22, 0, 0, 12, 0, 48, 96, -60, 4, 36, 0, -24, 0, -6, -12, -54, -6, -42, 0, 0, 12, -12, -48, -12, 34, 0, 48, 0, 18, 44, -72, 0, -48, 8, -120, -132, 0, 30, 0, 0, 30, 0, -12, -108, 48, -34, -36, 0, 18, -18, 6, -90, 12, 48, -12, 108, 0, -48, -12, 60, -48, -12, 0, -18, 0, 180, 12, 36, 6, 76, 72, -144, 12, -18, -24, 0, 0, -12, 0, 66, 68, 40, -6, -24, 0, -12, 36, 18, 18, 42, 18, -66, -42, 0, 180, 24, 24, -24, 42, 0, -6, 0, 24, 36, -24, -36, -60, -8, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 37, 5, 1, 6, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "74.2.e.b", "char_is_minimal": true, "conrey_index": 11, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, -1, -1, -1], [0, 0, 1, 0], [2, 0, -1, 0], [1, 0, -2, -1], [0, 0, 2, 0], [0, 0, 0, 1], [-1, -2, 1, 4], [0, 2, 0, -1], [-3, -2, 0, 1], [1, 1, -1, -2], [-4, 0, 2, 0], [0, 0, 0, 2], [-1, -3, -1, 0], [-1, 0, 1, 0], [1, 6, 1, 0], [-4, -1, 2, 1], [-2, 3, 1, -3], [1, 0, 1, 0], [2, 2, -2, -4], [-1, -3, -1, 0], [1, 0, -2, -3], [2, 1, -1, -1], [-2, 0, 2, 0], [0, -4, 0, 2], [4, 0, 0, 0], [-2, 0, 2, 0], [5, 0, -10, 0], [0, -1, -3, -1], [1, 0, -2, 3], [0, -1, 0, 1], [0, 4, 6, 4], [0, 1, 6, 1], [2, 0, 2, 0], [-1, -4, 0, 2], [0, -6, -1, 6], [3, -2, 0, 1], [2, 6, 2, 0], [0, 1, 0, 1], [0, -4, -3, -4], [4, 2, -2, -2], [-4, 0, 8, -6], [0, -1, -3, -1], [-1, 0, 2, 6], [3, 1, -3, -2], [3, 2, 0, -1], [1, 2, 0, -1], [3, 0, -3, 0], [0, -2, 0, 2], [7, 0, -14, -9], [-2, 0, -2, 0], [-6, 2, 6, -4], [0, 4, 0, 0], [-6, -3, 3, 3], [0, -2, 0, 2], [-2, 0, -2, 0], [0, 5, 0, -10], [-2, 6, -2, 0], [1, 0, -2, -3], [2, 0, -1, 0], [-3, 1, 3, -2], [-2, -8, 0, 4], [-1, 0, 0, 0], [-6, 0, 6, 0], [-4, 0, 8, 6], [0, 3, 5, 3], [-1, 0, 2, 6], [-8, -6, 4, 6], [0, 2, 0, 2], [0, -2, 0, -2], [-2, -1, -2, 0], [4, 0, 0, 0], [-6, 0, 0, -1], [2, 4, 0, -2], [-1, 3, -1, 0], [0, -2, -6, -2], [0, 2, 6, 2], [2, -15, -1, 15], [-1, 0, 2, 0], [0, 2, -1, 2], [4, 0, -8, -3], [-3, 5, 3, -10], [2, 4, 0, -2], [3, 12, 0, -6], [6, -4, -6, 8], [-10, -15, 5, 15], [1, 0, -2, -3], [3, -12, 3, 0], [-6, -1, 6, 2], [-4, 0, -4, 0], [2, 3, -1, -3], [4, 0, -2, 0], [1, 3, 1, 0], [-3, 3, 3, -6], [1, 1, 1, 0], [1, 0, -2, -6], [0, 3, 0, -3], [9, 7, -9, -14], [-2, 0, 0, 0]]}