# Stored data for newform 378.2.a.d, downloaded from the LMFDB on 26 March 2023.
{"level_primes": [2, 3, 7], "is_polredabs": true, "sato_tate_group": "1.2.3.c1", "rm_discs": [], "conrey_indexes": [1], "cm_discs": [], "trace_hash": 1867142822492264639, "level_radical": 42, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": ["EllipticCurve/Q/378/d"], "prim_orbit_index": 1, "is_cm": false, "hecke_orbit": 4, "analytic_conductor": 3.0183451964043986, "inner_twist_count": 1, "field_disc_factorization": [], "is_rm": false, "char_order": 1, "level_is_square": false, "weight_parity": 1, "label": "378.2.a.d", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": true, "minimal_twist": "378.2.a.d", "field_poly_is_cyclotomic": false, "dim": 1, "trace_zratio": {"__RealLiteral__": 0, "data": "0.012", "prec": 17}, "traces": [0, 1, -1, 0, 1, 0, 0, 1, -1, 0, 0, 0, 0, 5, -1, 0, 1, -3, 0, 2, 0, 0, 0, 9, 0, -5, -5, 0, 1, 3, 0, 5, -1, 0, 3, 0, 0, 2, -2, 0, 0, 6, 0, -1, 0, 0, -9, 6, 0, 1, 5, 0, 5, -3, 0, 0, -1, 0, -3, 3, 0, -10, -5, 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-24, 0, 0, -35, 0, 14, 9, 0, 2, 0, 0, -30, -45, 0, -10, 22, 0, -3, -30, 0, 2, 12, 0, 24, 0, 0, 56, 13, 0, 0, 30, 0, 54, 3, 0, 0, 6, 0, 10, 10, 0, 3, 36, 0, 0, -12, 0, 36, -18, 0, -6, -10, 0, -10, 0, 0, -4, 11, 0, 0, 57, 0, 14, -38, 0, -10, -42, 0, 0, 0, 0, 12, 0, 0, 0, 9, 0, 10, -9, 0, 2, -5, 0, 9, 0, 0, -19, 4, 0, 0], "hecke_ring_index_factorization": [], "nf_label": "1.1.1.1", "field_poly": [0, 1], "atkin_lehner_string": "++-", "has_non_self_twist": 0, "atkin_lehner_eigenvals": [[2, 1], [3, 1], [7, -1]], "char_values": [378, 1, [29, 325], [1, 1]], "Nk2": 1512, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "a", "weight": 2, "trace_display": [-1, 0, 0, 1], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": true, "qexp_display": "q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\\cdots", "self_twist_discs": [], "char_is_real": true, "field_disc": 1, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[5, [0, 1]], [17, [3, 1]]], "space_label": "378.2.a", "level": 378, "is_self_dual": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_degree": 1, "char_conductor": 1, "char_orbit_index": 1, "hecke_ring_generator_nbound": 1, "hecke_orbit_code": 13510798915666298, "fricke_eigenval": -1, "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "0.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.058", "prec": 17}, {"__RealLiteral__": 0, "data": "1.944", "prec": 17}, {"__RealLiteral__": 0, "data": "0.247", "prec": 17}, {"__RealLiteral__": 0, "data": "4.777", "prec": 17}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "artin_degree": null, "qexp": [[0], [1], [-1], [0], [1], [0], [0], [1], [-1], [0], [0], [0], [0], 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