# Stored data for newform 539.2.e.j, downloaded from the LMFDB on 31 March 2023.
{"level_primes": [7, 11], "is_polredabs": true, "sato_tate_group": "1.2.3.c3", "rm_discs": [], "conrey_indexes": [67, 177], "cm_discs": [], "trace_hash": 188100110170437681, "level_radical": 77, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 3, "is_cm": false, "hecke_orbit": 10, "analytic_conductor": 4.303936668947013, "inner_twist_count": 2, "field_disc_factorization": [[3, 2], [5, 2]], "is_rm": false, "char_order": 3, "level_is_square": false, "weight_parity": 1, "label": "539.2.e.j", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "77.2.a.d", "field_poly_is_cyclotomic": false, "dim": 4, "trace_zratio": {"__RealLiteral__": 0, "data": "0.029", "prec": 17}, "traces": [0, 4, 0, 2, -6, -4, 20, 0, 0, -6, 0, 2, 6, -4, 0, -8, 2, -2, 20, 4, 24, 0, 0, 4, -10, 2, 10, -40, 0, 16, -20, -10, 0, -2, 20, 0, 36, 8, 20, 8, 0, 36, 0, 32, 6, -12, -20, 10, 4, 0, 0, -8, 6, -8, -20, -8, 0, -32, 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1], "has_non_self_twist": 1, "char_values": [539, 3, [199, 442], [2, 3]], "Nk2": 2156, "field_poly_root_of_unity": 0, "analytic_rank": 0, "char_orbit_label": "e", "weight": 2, "trace_display": [0, 2, -4, 0], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 4, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q-\\beta _{2}q^{2}+(-\\beta _{1}+\\beta _{2}+\\beta _{3})q^{3}+3\\beta _{1}q^{4}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": 225, "level_is_prime_power": false, "relative_dim": 2, "hecke_cutters": [[2, [25, 0, 5, 0, 1]], [3, [16, 8, 8, -2, 1]]], "space_label": "539.2.e", "level": 539, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_degree": 2, "char_conductor": 7, "char_orbit_index": 5, "hecke_ring_generator_nbound": 3, "hecke_orbit_code": 40532671557796379, "trace_moments": [{"__RealLiteral__": 0, "data": "0.053", "prec": 17}, {"__RealLiteral__": 0, "data": "3.782", "prec": 17}, {"__RealLiteral__": 0, "data": "1.125", "prec": 17}, {"__RealLiteral__": 0, "data": "55.337", "prec": 20}, {"__RealLiteral__": 0, "data": "30.865", "prec": 20}, {"__RealLiteral__": 0, "data": "1373.826", "prec": 27}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, -1, 0], [0, -1, 1, 1], [0, 3, 0, 0], [-2, -2, 0, 0], [5, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, -1], [-3, -3, 2, 0], [0, 0, 2, 2], [0, -1, 0, 0], [3, 3, -3, 0], [-1, 0, 0, 1], [0, 0, 0, 0], [-2, 0, 0, -2], [1, 1, 0, 0], [0, 1, 1, 1], [0, -10, 3, 3], [2, 2, 2, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [2, 2, -2, 0], [0, 5, -1, -1], [0, -1, 0, 0], 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[0, 0, 0, 0], [-6, 0, 0, -6], [10, 10, -6, 0], [0, 5, -5, -5], [0, -4, -4, -4], [15, 15, -3, 0], [-4, 0, 0, 6], [0, 0, 0, 0], [-3, 0, 0, -2], [3, 3, 0, 0]]}