# Stored data for newform 39.2.e.a, downloaded from the LMFDB on 25 April 2024.
{"label": "39.2.e.a", "space_label": "39.2.e", "level": 39, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461415, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 989859820770642191, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 1, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}+(1-\\zeta_{6})q^{3}+\\zeta_{6}q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "e", "char_is_real": false, "Nk2": 156, "analytic_conductor": 0.3114165678829935, "hecke_ring_index": 1, "level_radical": 39, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [39, 3, [14, 28], [3, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [3, 13], "conrey_indexes": [16, 22], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.479", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "107.127", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 1, -2, -2], "traces": [0, 2, -1, 1, 1, -2, 1, -2, -6, -1, 1, 2, 2, -7, 4, -1, 1, 7, 2, 6, -1, -4, 2, 6, -3, -8, 5, -2, 2, 1, -1, 8, -5, -2, -14, 2, 1, -1, -12, -5, 6, -9, 2, -6, 4, 1, 6, 12, -1, 3, 4, 14, -2, -18, 1, -2, 6, 12, 1, 0, -2, -1, -4, -2, 14, 7, 4, 2, -7, 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-3, 24, -36, 8, 0, 32, -6, -17, -14, 62, -49, 42, 12, 16, 12, -8, -16, -12, -12, 28, 19, -19, 16, -23, 12, 14, -9, -18, 56, 6, -6, 42, -2, -6, -18, -62, -14, 68, -6, 18, 30, 20, 5, -6, 38, 32, 8, -8, -2, -10, 12, 2, -36, -18, 22, -17, -14, 18, 2, -37, 3, 32, 35, 0, 4, 0, -3, 80, -14, 2, -32, 36, 3, -2, -12, 12, 68, 4, -4, -63, -36, 12, -45, 14, -2, -12, -14, 6, 14, -80, 6, -28, 13, 2, -22, 16, 14, -24, 18, 14, 38, 12, -8, 4, 26, -6, -10, 27, -4, 36, 10, 18, -6, -28, -6, -98, 4, 6, -6, -76, -3, 54, 0, -2, 12, 48, -8, -77, 48, -25, -42, -6, -18, -4, 30, -4, -24, 6, -7, -30, 2, -12, 7, -9, -12, 4, -21, 42, 4, -36, -1, -24, 36, 20, -2, -33, -4, -28, -6, 2, -6, 8, -27, 6, -7, -24, 30, -72, -2, 2, -20, 8, -12, 14, -28, 35, -24, 1, -54], "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, 13, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "39.2.e.a", "char_is_minimal": true, "conrey_index": 16, "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], [1, 0], [-1, 1], [1, -1], [0, 1], [-1, 0], [0, 1], [0, -2], [-3, 0], [0, -1], [1, -1], [2, -2], [1, 0], [-3, -1], [2, 0], [-1, 1], [1, -1], [0, 7], [1, 0], [0, 6], [0, -1], [-2, 0], [0, 2], [6, -6], [-3, 3], [-4, 0], [4, -3], [-1, 0], [2, -2], [1, -1], [0, -1], [4, 0], [0, -5], [0, -2], [-7, 0], [0, 2], [1, -1], [-1, 1], [-6, 0], [-4, 3], [3, 0], [-9, 9], [2, -2], [0, -6], [2, 0], [0, 1], [0, 6], [6, 0], [0, -1], [3, -3], [4, -4], [7, 0], [1, -4], [-9, 0], [1, -1], [-2, 2], [0, 6], [6, 0], [0, 1], [0, 0], [-1, 0], [0, -1], [-4, 4], [-2, 2], [7, 0], [3, 1], [2, 0], [2, -2], [-7, 7], [0, -6], [-2, 0], [0, -6], [0, 3], [11, 0], [0, -1], [-4, 4], [-6, 6], [-4, 0], [1, -4], [-4, 0], [-1, 1], [-1, 1], [0, -9], [-14, 0], [0, -2], [0, -7], [6, 0], [0, -1], [-6, 6], [14, -14], [-1, 0], [-2, 8], [6, 0], [4, -4], [-6, 6], [0, -6], [-5, 0], [0, 2], [0, 3], [-2, 0], [0, -4]]}