# Stored data for newform 392.2.e.e, downloaded from the LMFDB on 01 May 2024.
{"label": "392.2.e.e", "space_label": "392.2.e", "level": 392, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014673420943752, "dim": 12, "is_polredabs": true, "nf_label": "12.0.144054149089536.2", "trace_hash": 38401658292192229, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [3, 0, 15, 0, 9, 0, 1]], [5, [-21, 0, 51, 0, -15, 0, 1]]], "qexp_display": "q-\\beta _{5}q^{2}-\\beta _{10}q^{3}+\\beta _{1}q^{4}-\\beta _{9}q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 56, "char_orbit_label": "e", "char_is_real": true, "Nk2": 1568, "analytic_conductor": 3.130135759234191, "hecke_ring_index": 256, "level_radical": 14, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.764", "prec": 17}, "analytic_rank_proved": true, "char_values": [392, 2, [295, 197, 297], [1, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 7], "conrey_indexes": [195], "field_disc": 144054149089536, "field_disc_factorization": [[2, 8], [3, 14], [7, 6]], "field_poly": [4, -12, 96, -340, 624, -654, 431, -189, 48, 1, 0, -3, 1], "hecke_ring_index_factorization": [[2, 8]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.099", "prec": 17}, {"__RealLiteral__": 0, "data": "9.114", "prec": 17}, {"__RealLiteral__": 0, "data": "14.054", "prec": 20}, {"__RealLiteral__": 0, "data": "881.629", "prec": 24}, {"__RealLiteral__": 0, "data": "2242.337", "prec": 27}, {"__RealLiteral__": 0, "data": "117844.298", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -12, 0, 36, 0, 0, 0, -48, -12, 0, 0, 0, 0, 0, -36, -36, 0, 12, 0, 0, 0, -72, 24, 0, -60, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 60, 0, 0, -12, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, -24, 24, 0, 0, 0, 0, 0, -96, 36, 0, 0, 0, 0, 0, 24, -24, 0, 24, 0, 0, 0, -84, -72, 0, 120, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 60, 0, 0, 36, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 60, 72, 0, 12, 0, 0, 0, -60, -36, 0, 0, 0, 0, 0, -12, 72, 0, 0, 0, 0, 0, -24, 12, 0, -132, 0, 0, 0, 0, -84, 0, 24, 0, 0, 0, 84, 0, 0, -12, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, -48, 0, 48, 0, 0, 0, -36, 60, 0, 0, 0, 0, 0, 48, -36, 0, 96, 0, 0, 0, 0, 84, 0, 132, 0, 0, 0, 0, -24, 0, 36, 0, 0, 0, 60, 0, 0, -24, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -12, 12, 0, -60, 0, 0, 0, -12, -96, 0, 0, 0, 0, 0, -24, -48, 0, 0, 0, 0, 0, -48, 72, 0, -216, 0, 0, 0, 0, 84, 0, -36, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, -132, 72, 0, 12, 0, 0, 0, 36, 12, 0, 0, 0, 0, 0, -24, 120, 0, -48, 0, 0, 0, 0, -156, 0, 276, 0, 0, 0, 0, -72, 0, -36, 0, 0, 0, -24, 0, 0, 48, 0, 0, 0, 0, 36, 0, 48, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 24, -84, 0, -72, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 60, -36, 0, 24, 0, 0, 0, 48, -108, 0, -144, 0, 0, 0, 0, 12, 0, -12, 0, 0, 0, -156, 0, 0, 24, 0, 0, 0, 0, -120, 0, -84, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 72, 24, 0, 12, 0, 0, 0, 12, 84, 0, 0, 0, 0, 0, -24, -96, 0, -192, 0, 0, 0, 36, 180, 0, 132, 0, 0, 0, 0, 120, 0, 84, 0, 0, 0, -156, 0, 0, 0, 0, 0, 0, 0, 108, 0, 72, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 120, -72, 0, 84, 0, 0, 0, 48, -84, 0, 0, 0, 0, 0, -132, 96, 0, 48, 0, 0, 0, 240, 84, 0, -324, 0, 0, 0, 0, -24, 0, 72, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 12, 0, 60, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, -24, -120, 0, -24, 0, 0, 0, 216, 132, 0, 0, 0, 0, 0, -12, 36, 0, -24, 0, 0, 0, 168, -204, 0, 204, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, -84, 0, 0, -48, 0, 0, 0, 0, -144, 0, 192, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 24, 84, 0, 48, 0, 0, 0, 180, -48, 0, 0, 0, 0, 0, 72, -180, 0, -60, 0, 0, 0, 24, -108, 0, -84, 0, 0, 0, 0, 252, 0, -120, 0, 0, 0, -12, 0, 0, 36, 0, 0, 0, 0, 108, 0, 12, 0, 0, 0, -132, 0, 0, 0, 0, 0, 0, -144, -24, 0, -228, 0, 0, 0, 132, 24, 0, 0, 0, 0, 0, 120, 84, 0, 24, 0, 0, 0, 84, 300, 0, 252, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -36, 0, 0, -96, 0, 0, 0, 0, 60, 0, -72, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, -48, -156, 0, 24, 0, 0, 0, 132, -132, 0, 0, 0, 0, 0, 108, 84, 0, -108, 0, 0, 0, 24, 60, 0, -228, 0, 0, 0, 0, -252, 0, 72, 0, 0, 0, -144, 0, 0, 120, 0, 0, 0, 0, -204, 0, 84, 0, 0, 0, -204, 0, 0, 0, 0, 0, 0, -36, 96, 0, 0, 0, 0, 0, -12, 24, 0, 0, 0, 0, 0, -132, -12, 0, 24, 0, 0, 0, 24, -216, 0, 108, 0, 0, 0, 0, 144, 0, 12, 0, 0, 0, -204, 0, 0, 36, 0, 0, 0, 0, 48, 0, -168, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 192, 48, 0, -96, 0, 0, 0, -48, 24, 0, 0, 0, 0, 0, 156, 204, 0, -24, 0, 0, 0, 96, -132, 0, -12, 0, 0, 0, 0, -36, 0, 132, 0, 0, 0, -120, 0, 0, 12, 0, 0, 0, 0, 60, 0, 252, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 96, -120, 0, 24, 0, 0, 0, 12, -132, 0, 0, 0, 0, 0, -264, -84, 0, 48, 0, 0, 0, -24, 408, 0, 84, 0, 0, 0, 0, -144, 0, -144, 0, 0, 0, 12, 0, 0, -72, 0, 0, 0, 0, -240, 0, -192, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 204, 0, -204, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, -168, 108, 0, -72, 0, 0, 0, 168, 24, 0, -216, 0, 0, 0, 0, 72, 0, 204, 0, 0, 0, 12, 0, 0, -204, 0, 0, 0, 0, 36, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276, -24, 0, 108, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 56, 5, 1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "56.2.m.a", "char_is_minimal": true, "conrey_index": 195, "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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0, 1, -1, 0, 1, 0, 0], [1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0], [0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], [0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0], [-1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0], [0, 0, 0, -2, 0, 0, -1, 0, 0, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 0, 2, 0, 0, 1, 0, 0, 1], [0, 0, 0, -2, -1, 0, -1, 1, 0, 1, 2, 0], [0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, -1, 1, 0, 1, 2, 0], [0, 0, 0, 0, -1, 0, 1, -2, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0], [2, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0], [0, 0, 0, 2, 2, 0, 2, -1, 0, -1, -1, 0], [0, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0], [0, 0, 0, 1, 0, 0, 1, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], [0, -2, 2, 0, 0, 0, 0, 0, 2, 0, 0, -1], [0, 0, 0, 1, -1, 0, 1, 0, 0, -1, -1, 0], [0, -1, -2, 0, 0, 3, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 1, 1, 0, 1, -2, 0], [0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1], [0, 0, 0, -4, -1, 0, -1, 2, 0, -2, 2, 0], [3, -1, -2, 0, 0, -1, 0, 0, -2, 0, 0, -1], [0, 0, 0, -2, 0, 0, 0, 1, 0, -3, 1, 0], [0, 0, 0, -2, 0, 0, -2, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0], [0, 0, 0, -2, 0, 0, -2, 4, 0, 0, 4, 0], [0, 0, 4, 0, 0, -4, 0, 0, 0, 0, 0, 1], [0, 0, 0, -1, -1, 0, -1, -2, 0, 1, -1, 0], [0, 0, 0, 2, 1, 0, 1, -1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0], [-3, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, -2, 0, 2, -4, 0, 0, -1, 0], [1, -1, 4, 0, 0, -2, 0, 0, 0, 0, 0, -1], [0, 0, 0, 4, 3, 0, 3, -2, 0, 1, -2, 0], [0, 0, 0, 1, 1, 0, 3, -4, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2], [2, -1, 2, 0, 0, 1, 0, 0, -1, 0, 0, 0], [0, 0, 0, 1, -1, 0, 0, -2, 0, 0, -2, 0], [-5, 1, -3, 0, 0, -2, 0, 0, 1, 0, 0, 0], [0, 0, 0, 2, 2, 0, 1, -2, 0, 1, 1, 0], [0, 0, 0, -4, 0, 0, 0, 2, 0, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2], [0, -2, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, -2, 1, 0, 0, 2, 0], [-2, 2, -4, 0, 0, 1, 0, 0, 2, 0, 0, -2], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0], [0, 0, 0, 2, 1, 0, 0, -3, 0, 2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -3], [0, 0, 0, 2, 2, 0, -2, -2, 0, 0, -2, 0], [-1, 1, 2, 0, 0, 3, 0, 0, 1, 0, 0, 0], [0, 0, 0, -2, 1, 0, 1, 5, 0, -1, 4, 0], [0, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -4, 0, 0, 2, 0, 0, -2, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 4, 1, 0, 1, -2, 0, 0, -2, 0], [-1, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 2, 1, 0, 1, 1, 0, 3, -4, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, -1, 4, 0, 0, -2, 0, 0, 2, 0, 0, -1], [0, 2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 3], [0, 0, 0, 3, 1, 0, 3, -2, 0, 3, -3, 0], [0, 3, -5, 0, 0, 2, 0, 0, -3, 0, 0, -1], [0, 0, 0, 4, 2, 0, 0, 2, 0, 0, -2, 0], [0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -6, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -2, 0, 0, -1, 0, 0, 1, 0, 0, 0], [2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2]]}