# Stored data for newform 232.2.a.d, downloaded from the LMFDB on 19 April 2024.
{"label": "232.2.a.d", "space_label": "232.2.a", "level": 232, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510798915666152, "dim": 3, "is_polredabs": true, "nf_label": "3.3.568.1", "trace_hash": 561043936281873109, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [8, -5, -2, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{3}+(1-\\beta _{2})q^{5}+(2+\\beta _{2})q^{9}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 928, "fricke_eigenval": -1, "atkin_lehner_string": "+-", "analytic_conductor": 1.8525293268937049, "hecke_ring_index": 1, "level_radical": 58, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "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": "0.007", "prec": 17}, "analytic_rank_proved": true, "char_values": [232, 1, [175, 117, 89], [1, 1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [2, 29], "conrey_indexes": [1], "field_disc": 568, "field_disc_factorization": [[2, 3], [71, 1]], "field_poly": [-2, -6, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "2.831", "prec": 17}, {"__RealLiteral__": 0, "data": "0.057", "prec": 17}, {"__RealLiteral__": 0, "data": "20.117", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "209.291", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[2, 1], [29, -1]], "trace_display": [0, 2, 4, 0], "traces": [0, 3, 0, 2, 0, 4, 0, 0, 0, 5, 0, 2, 0, 4, 0, -2, 0, 6, 0, -4, 0, 0, 0, -4, 0, 7, 0, 2, 0, 3, 0, -14, 0, -2, 0, 0, 0, -2, 0, -18, 0, 10, 0, -6, 0, -10, 0, -2, 0, -21, 0, 4, 0, 0, 0, -26, 0, -12, 0, 8, 0, 2, 0, 0, 0, -2, 0, 20, 0, -28, 0, 12, 0, 2, 0, 16, 0, 0, 0, -30, 0, -17, 0, 32, 0, 8, 0, 2, 0, 10, 0, 0, 0, -22, 0, 28, 0, -14, 0, 32, 0, 6, 0, -4, 0, 0, 0, 12, 0, -4, 0, 8, 0, -2, 0, 4, 0, 14, 0, 0, 0, 29, 0, 48, 0, 30, 0, -8, 0, -26, 0, 28, 0, 0, 0, -26, 0, 2, 0, 0, 0, 46, 0, 38, 0, 4, 0, -14, 0, -12, 0, -24, 0, 10, 0, -14, 0, 22, 0, -30, 0, 0, 0, -18, 0, -62, 0, 12, 0, 15, 0, -40, 0, 2, 0, 0, 0, -20, 0, -24, 0, 16, 0, 52, 0, -36, 0, 4, 0, 0, 0, -8, 0, -6, 0, -38, 0, -22, 0, -48, 0, 64, 0, 0, 0, 28, 0, -16, 0, -60, 0, 22, 0, -36, 0, 30, 0, 0, 0, -40, 0, 8, 0, -4, 0, -29, 0, -8, 0, 6, 0, 0, 0, 40, 0, -50, 0, 2, 0, 28, 0, 36, 0, 8, 0, -28, 0, -20, 0, -4, 0, -30, 0, 4, 0, -4, 0, 48, 0, 0, 0, 5, 0, 18, 0, 26, 0, -16, 0, 18, 0, -42, 0, 0, 0, -88, 0, 10, 0, -28, 0, -56, 0, 40, 0, 60, 0, 0, 0, -39, 0, 0, 0, -22, 0, 20, 0, 62, 0, 36, 0, 0, 0, 64, 0, -16, 0, 10, 0, -28, 0, -48, 0, 16, 0, 0, 0, 26, 0, 2, 0, 40, 0, -8, 0, -54, 0, 62, 0, 0, 0, 30, 0, 30, 0, 8, 0, 46, 0, -20, 0, -6, 0, 0, 0, -4, 0, -16, 0, 40, 0, 38, 0, -26, 0, 92, 0, 0, 0, 2, 0, 15, 0, 56, 0, -12, 0, -48, 0, 2, 0, 0, 0, 40, 0, 98, 0, 4, 0, -4, 0, 36, 0, 56, 0, 0, 0, -48, 0, -66, 0, -8, 0, 28, 0, -78, 0, -48, 0, 0, 0, 8, 0, 2, 0, -32, 0, 56, 0, -42, 0, -8, 0, 0, 0, 52, 0, -76, 0, -16, 0, 10, 0, 44, 0, 14, 0, 0, 0, -22, 0, -28, 0, -14, 0, -2, 0, 24, 0, -20, 0, -35, 0, -12, 0, -68, 0, 54, 0, -18, 0, -64, 0, 16, 0, 0, 0, -34, 0, 4, 0, -6, 0, 44, 0, 6, 0, -30, 0, 0, 0, 24, 0, -58, 0, 72, 0, -26, 0, -34, 0, 12, 0, 0, 0, -52, 0, 8, 0, 58, 0, -26, 0, 6, 0, 0, 0, 0, 0, -56, 0, -36, 0, -26, 0, -44, 0, -112, 0, 16, 0, 0, 0, -60, 0, 4, 0, 46, 0, 20, 0, 4, 0, 20, 0, 0, 0, -28, 0, -13, 0, 4, 0, -84, 0, 64, 0, 28, 0, -14, 0, 30, 0, -54, 0, -74, 0, -4, 0, 22, 0, -4, 0, 0, 0, -56, 0, 18, 0, -2, 0, -4, 0, 62, 0, 64, 0, 0, 0, 6, 0, 20, 0, -28, 0, -32, 0, -42, 0, 56, 0, 0, 0, -22, 0, 28, 0, -24, 0, 28, 0, 4, 0, 36, 0, 0, 0, 0, 0, -54, 0, 58, 0, 52, 0, 70, 0, 46, 0, 0, 0, -50, 0, -60, 0, 64, 0, 50, 0, 22, 0, 4, 0, 0, 0, 51, 0, -116, 0, -4, 0, -28, 0, 34, 0, 4, 0, -28, 0, -56, 0, -10, 0, 100, 0, 58, 0, 28, 0, 12, 0, 0, 0, 38, 0, 4, 0, 18, 0, 10, 0, 50, 0, -36, 0, 0, 0, -4, 0, 60, 0, -12, 0, -44, 0, -88, 0, 42, 0, 0, 0, 84, 0, -36, 0, 36, 0, 64, 0, 34, 0, 12, 0, 0, 0, 28, 0, 20, 0, 38, 0, 4, 0, -64, 0, -46, 0, 0, 0, 12, 0, -12, 0, 44, 0, 98, 0, 44, 0, -20, 0, 0, 0, -38, 0, 7, 0, -48, 0, -13, 0, -12, 0, 38, 0, 14, 0, 0, 0, -6, 0, -4, 0, -48, 0, 6, 0, 44, 0, 0, 0, -16, 0, -26, 0, 16, 0, -46, 0, -76, 0, -10, 0, 0, 0, -20, 0, 52, 0, 6, 0, 78, 0, 38, 0, -44, 0, 0, 0, 16, 0, -100, 0, 2, 0, -4, 0, -8, 0, 50, 0, 0, 0, -80, 0, 22, 0, 50, 0, -4, 0, 98, 0, 72, 0, 0, 0, -108, 0, 58, 0, 44, 0, -34, 0, 10, 0, 84, 0, 0, 0, -36, 0, 48, 0, -104, 0, 14, 0, -110, 0, -76, 0, -42, 0, 92, 0, -6, 0, 70, 0, 3, 0, -58, 0, 50, 0, 0, 0, 20, 0, -16, 0, -86, 0, 32, 0, 32, 0, 38, 0, 0, 0, -60, 0, -64, 0, -26, 0, 34, 0, -56, 0, 10, 0, 0, 0, -120, 0, 4, 0, -34, 0, -4, 0, -12, 0, -54, 0, 0, 0, -18, 0, -92, 0, -108, 0, -52, 0, -14, 0, 0, 0, 0, 0, 90, 0, 4, 0, 62, 0, 6, 0, 28, 0, 12, 0, 0, 0, -28, 0, -98, 0, 28, 0, -86, 0, -16, 0, -18, 0, 28, 0, -92, 0, -52, 0, -74, 0, 6, 0, -20, 0, -96, 0, 0, 0, 82, 0, 100, 0, -52, 0, 16, 0, -92, 0, -2, 0, 0, 0, -15, 0, -28, 0, -60, 0, 22, 0, -24, 0, -60, 0, 0, 0, -8, 0, 24, 0, 192, 0, 62, 0, 62, 0, -96, 0, 0, 0, 52, 0, 12, 0, -62, 0, -16, 0, 54, 0, 56, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "232.2.a.d", "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, 0], [1, 0, 0], [0, 0, 0], [1, -1, 0], [0, 0, 0], [1, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [2, 0, 1], [0, 0, 0], [1, 1, 2], [0, 0, 0], [1, 2, 1], [0, 0, 0], [-1, -1, -2], [0, 0, 0], [2, 0, 0], [0, 0, 0], [-2, 0, -2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 2, 0], [0, 0, 0], [2, -2, -3], [0, 0, 0], [1, 1, 2], [0, 0, 0], [1, 0, 0], [0, 0, 0], [-5, 1, 0], [0, 0, 0], [1, -2, 3], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 2], [0, 0, 0], [-5, -3, 0], [0, 0, 0], [4, -4, -2], [0, 0, 0], [-3, 1, -2], [0, 0, 0], [-4, 2, 0], [0, 0, 0], [1, -3, 2], [0, 0, 0], [-7, 0, 0], [0, 0, 0], [2, -2, 0], [0, 0, 0], [-1, 2, -1], [0, 0, 0], [-9, 5, 4], [0, 0, 0], [-6, 2, -4], [0, 0, 0], [2, 2, 0], [0, 0, 0], [2, -4, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-1, 4, 3], [0, 0, 0], [8, -4, 0], [0, 0, 0], [-10, 0, -2], [0, 0, 0], [2, 2, -4], [0, 0, 0], [0, 4, 2], [0, 0, 0], [4, 0, -4], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-9, -1, 2], [0, 0, 0], [-5, -2, 0], [0, 0, 0], [10, 2, 0], [0, 0, 0], [2, 0, -2], [0, 0, 0], [1, -1, 0], [0, 0, 0], [4, 4, 6], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-9, 4, -1], [0, 0, 0], [10, -4, -2], [0, 0, 0], [-4, 0, 2], [0, 0, 0], [12, -2, 2], [0, 0, 0]]}