# Stored data for newform 1078.2.e.o, downloaded from the LMFDB on 20 April 2024.
{"label": "1078.2.e.o", "space_label": "1078.2.e", "level": 1078, "weight": 2, "hecke_orbit": 15, "hecke_orbit_code": 63050669694649398, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 2109482058383143234, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [64, 0, 8, 0, 1]], [5, [0, 1]], [13, [-18, 0, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+2\\beta _{1}q^{3}+(-1-\\beta _{2})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 4312, "analytic_conductor": 8.607873337894025, "hecke_ring_index": 1, "level_radical": 154, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [1078, 3, [199, 981], [2, 3]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 4, "level_primes": [2, 7, 11], "conrey_indexes": [67, 177], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.778", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "93.871", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3588.057", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 0, 0, 0], "traces": [0, 4, -2, 0, -2, 0, 0, 0, 4, -10, 0, 2, 0, 0, 0, 0, -2, 0, -10, 0, 0, 0, -4, -12, 0, 10, 0, 0, 0, -16, 0, 0, -2, 0, 0, 0, 20, -4, 0, -24, 0, 0, 0, 40, 2, 0, -12, 0, 0, 0, -20, 16, 0, -4, 0, 0, 0, -48, 8, 0, 0, 0, 0, 0, 4, 0, 0, -16, 0, 0, 0, 64, -10, 0, -4, 0, 0, 0, 48, 16, 0, -2, 0, 0, 0, 0, -20, 0, 2, 0, 0, 0, 24, 40, 0, 0, 0, 0, 0, -20, 10, 0, 16, 0, 0, 0, 8, 28, 0, 28, 0, 0, 0, 64, 24, 0, 8, 0, 0, 0, 0, -2, 0, -16, 0, 0, 0, -80, -2, 0, 0, 0, 0, 0, 32, 0, 0, 12, 0, 0, 0, -144, -32, 0, -10, 0, 0, 0, 8, -16, 0, 16, 0, 0, 0, 0, -24, 0, 16, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 20, 0, 0, -20, 0, 0, 0, -4, -64, 0, 24, 0, 0, 0, -112, -12, 0, 40, 0, 0, 0, 0, -20, 0, -12, 0, 0, 0, -8, 10, 0, 10, 0, 0, 0, -32, 0, 0, -60, 0, 0, 0, 104, -4, 0, 28, 0, 0, 0, -56, 48, 0, 24, 0, 0, 0, -100, -32, 0, 24, 0, 0, 0, -16, -52, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 32, 36, 0, 72, 0, 0, 0, -24, 40, 0, -2, 0, 0, 0, 0, 40, 0, -8, 0, 0, 0, 80, -16, 0, 0, 0, 0, 0, -24, -10, 0, 16, 0, 0, 0, 88, 72, 0, -32, 0, 0, 0, 20, 18, 0, 40, 0, 0, 0, 0, -4, 0, -16, 0, 0, 0, -32, 8, 0, 0, 0, 0, 0, -16, 0, 0, -24, 0, 0, 0, -32, -36, 0, -8, 0, 0, 0, 48, -2, 0, 8, 0, 0, 0, 0, -16, 0, -20, 0, 0, 0, -88, -10, 0, 0, 0, 0, 0, 40, 0, 0, -52, 0, 0, 0, 96, 2, 0, -64, 0, 0, 0, -48, -24, 0, 2, 0, 0, 0, 0, 56, 0, -12, 0, 0, 0, -80, 20, 0, 0, 0, 0, 0, 96, 0, 0, -20, 0, 0, 0, 24, -100, 0, 60, 0, 0, 0, 80, 4, 0, 10, 0, 0, 0, -20, 60, 0, 60, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 120, 0, 0, -104, 0, 0, 0, -8, -52, 0, -4, 0, 0, 0, -56, 24, 0, -16, 0, 0, 0, 0, 28, 0, 48, 0, 0, 0, -48, -24, 0, 0, 0, 0, 0, 64, 50, 0, -32, 0, 0, 0, -48, 44, 0, 32, 0, 0, 0, -64, 8, 0, -52, 0, 0, 0, 0, -48, 0, 20, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 4, 0, 0, -76, 0, 0, 0, 48, -16, 0, 36, 0, 0, 0, -144, -72, 0, 80, 0, 0, 0, 0, 12, 0, 40, 0, 0, 0, 4, 48, 0, 0, 0, 0, 0, 80, 0, 0, 40, 0, 0, 0, 16, -40, 0, -26, 0, 0, 0, 48, -40, 0, -16, 0, 0, 0, 0, 60, 0, -64, 0, 0, 0, -112, 12, 0, -10, 0, 0, 0, -32, 0, 0, 12, 0, 0, 0, 32, -44, 0, 72, 0, 0, 0, 64, -84, 0, -40, 0, 0, 0, -120, -10, 0, 18, 0, 0, 0, -80, 4, 0, 0, 0, 0, 0, 120, 0, 0, -4, 0, 0, 0, 32, -56, 0, 0, 0, 0, 0, 160, 16, 0, 8, 0, 0, 0, 0, 108, 0, 32, 0, 0, 0, 112, 8, 0, 0, 0, 0, 0, 48, -50, 0, -24, 0, 0, 0, -120, 16, 0, -36, 0, 0, 0, 16, -160, 0, -88, 0, 0, 0, 0, -24, 0, -2, 0, 0, 0, -16, 60, 0, 0, 0, 0, 0, 120, 0, 0, -16, 0, 0, 0, 40, 48, 0, -120, 0, 0, 0, -184, 44, 0, -10, 0, 0, 0, 0, 40, 0, -64, 0, 0, 0, -256, -20, 0, 0, 0, 0, 0, 104, 0, 0, 16, 0, 0, 0, -40, -48, 0, 2, 0, 0, 0, 128, 76, 0, 80, 0, 0, 0, 0, 24, 0, -24, 0, 0, 0, -4, 48, 0, -40, 0, 0, 0, -172, 0, 0, 56, 0, 0, 0, 24, 16, 0, 24, 0, 0, 0, -32, 40, 0, 20, 0, 0, 0, 0, 4, 0, 32, 0, 0, 0, 184, -48, 0, 0, 0, 0, 0, 40, 0, 0, -96, 0, 0, 0, 80, -12, 0, -100, 0, 0, 0, -120, 24, 0, 32, 0, 0, 0, 0, -40, 0, 4, 0, 0, 0, -20, 84, 0, 0, 0, 0, 0, 144, 10, 0, 60, 0, 0, 0, -120, -64, 0, 12, 0, 0, 0, 96, 4, 0, 16, 0, 0, 0, 0, 16, 0, 4, 0, 0, 0, 112, -60, 0, 0, 0, 0, 0, 208, 0, 0, 80, 0, 0, 0, -52, 4, 0, -52, 0, 0, 0, 8, -40, 0, -24, 0, 0, 0, 0, 28, 0, 24, 0, 0, 0, 32, -12, 0, 0, 0, 0, 0, 32, 0, 0, 28, 0, 0, 0, -96, 4, 0, 120, 0, 0, 0, -48, 24, 0, -24, 0, 0, 0, 0, 2, 0, -108, 0, 0, 0, 288, -32, 0, 50, 0, 0, 0, 64, 0, 0, -32, 0, 0, 0, 120, 24, 0, 44, 0, 0, 0, -64, 32, 0, -120, 0, 0, 0, -40, 32, 0, 8, 0, 0, 0, 104, 8, 0, 0, 0, 0, 0, -336, 0, 0, -48, 0, 0, 0, -40, -8, 0, 72, 0, 0, 0, -184, -20, 0, 0, 0, 0, 0, 0, -38, 0, 140, 0, 0, 0, -208, -2, 0, 0, 0, 0, 0, 152, 120, 0, 64, 0, 0, 0, -280, -24, 0, -16, 0, 0, 0, -72, -120, 0, 32, 0, 0, 0, 0, 72, 0, -72, 0, 0, 0, -160, 64, 0, 0, 0, 0, 0, -200, 0, 0, 12, 0, 0, 0, -80, -160, 0, 52, 0, 0, 0, 80, -2, 0, 48, 0, 0, 0, 0, -72, 0, 68, 0, 0, 0, 112, -40, 0, 0, 0, 0, 0, -80, 0, 0, 152, 0, 0, 0, -80, -8, 0, -40, 0, 0, 0, 52, -88, 0, 44, 0, 0, 0, 0, -24, 0, -40, 0, 0, 0, 32, 16, 0, 100, 0, 0, 0, -216, 0, 0, 60, 0, 0, 0, 128, 0, 0, -10, 0, 0, 0, 56, 56, 0, 12, 0, 0, 0, 20, 120, 0, -16, 0, 0, 0, 64, 16, 0, 0, 0, 0, 0, -24, 0, 0, -4, 0, 0, 0, -192, -16, 0, -44, 0, 0, 0, -144, -20, 0, 96, 0, 0, 0, 0, -32, 0, -84, 0, 0, 0, 80, 200, 0, 0, 0, 0, 0, -176, 60, 0, -10, 0, 0, 0, -36, -60, 0, -84, 0, 0, 0, -184, 40, 0, 4, 0, 0, 0, 0, 96, 0, 96, 0, 0, 0, 56, -60, 0, 0, 0, 0, 0, 8, 0, 0, -24, 0, 0, 0, 288, -16, 0, -56, 0, 0, 0, 0, -28, 0, 28, 0, 0, 0, 0, -80, 0, 16, 0, 0, 0, -16, 12, 0, 0, 0, 0, 0, 48, 0, 0, 108, 0, 0, 0, -64, -160, 0, 112, 0, 0, 0, -120, -56, 0, 8, 0, 0, 0, 0, -48, 0, 32, 0, 0, 0, -160, -24, 0, -50, 0, 0, 0, 48, 0, 0, -80, 0, 0, 0, -120, 60, 0, 16, 0, 0, 0, 72, 144, 0, 40, 0, 0, 0, 160, -8, 0, -160, 0, 0, 0, 176, 24, 0, 0, 0, 0, 0, 136, 0, 0, -24, 0, 0, 0, 4, -76, 0, -168, 0, 0, 0, 160, 8, 0, 60, 0, 0, 0, 0, 144, 0, 12, 0, 0, 0, 288, -60, 0, 0, 0, 0, 0, 32, 20, 0, -128, 0, 0, 0, -4, -20, 0, 48, 0, 0, 0, 240, 12, 0, -80, 0, 0, 0, 0, 92, 0, 44, 0, 0, 0, 20, 16, 0, 0, 0, 0, 0, -160, 0, 0, 40, 0, 0, 0, 128, 48, 0, 66, 0, 0, 0, -136, 128, 0, -20, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 144, -52, 0, 0, 0, 0, 0, -32, 0, 0, -40, 0, 0, 0, 288, 20, 0, -48, 0, 0, 0, -4, 104, 0, -72, 0, 0, 0, 0, -64, 0, 76, 0, 0, 0, -160, -32, 0, -120, 0, 0, 0, -280, 0, 0, 24, 0, 0, 0, 48, 160, 0, -48, 0, 0, 0, 96, 2, 0, 48, 0, 0, 0, 80, 76, 0, 52, 0, 0, 0, 360, 86, 0, 0, 0, 0, 0, -112, 0, 0, 40, 0, 0, 0, 64, -12, 0, 16, 0, 0, 0, -48, -64, 0, -60, 0, 0, 0, 0, 16, 0, 40, 0, 0, 0, -40, -144, 0, 0, 0, 0, 0, -80, 0, 0, 4, 0, 0, 0, -64, -12, 0, -112, 0, 0, 0, -80, -92, 0, -48, 0, 0, 0, 0, -50, 0, -72, 0, 0, 0, 192, -20, 0, 0, 0, 0, 0, 192, 0, 0, 16, 0, 0, 0, 192, -40, 0, -12, 0, 0, 0, 200, 12, 0, -72, 0, 0, 0, 0, 60, 0, 24, 0, 0, 0, -64, 8, 0, 0, 0, 0, 0, 48, 0, 0, -40, 0, 0, 0, -8, -108, 0, -152, 0, 0, 0, -160, 10, 0, 84, 0, 0, 0, 0, -40, 0, -128, 0, 0, 0, -216, -72, 0, 10, 0, 0, 0, -120, 0, 0, -64, 0, 0, 0, -240, 60, 0, -64, 0, 0, 0, -24, 4, 0, 76, 0, 0, 0, 0, -48, 0, 4, 0, 0, 0, -32, -192, 0, 0, 0, 0, 0, -32, 0, 0, 16, 0, 0, 0, -8, 112, 0, -40, 0, 0, 0, 192, -56, 0, -60, 0, 0, 0, 0, -16, 0, 88, 0, 0, 0, -304, -104, 0, 0, 0, 0, 0, -160, 80, 0, -240, 0, 0, 0, -132, 26, 0, 4, 0, 0, 0, 104, -232, 0, 60, 0, 0, 0, 0, -4, 0, -40, 0, 0, 0, 48, -60, 0, 0, 0, 0, 0, -24, 0, 0, 28, 0, 0, 0, -48, -8, 0, -100, 0, 0, 0, 112, -16, 0, -12, 0, 0, 0, 0, 56, 0, 48, 0, 0, 0, 120, -16, 0, 0, 0, 0, 0, -56, 0, 0, 120, 0, 0, 0, 16, 48, 0, 4, 0, 0, 0, -240, -160, 0, -32, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 48, 20, 0, 160, 0, 0, 0, 96, 0, 0, 2, 0, 0, 0, 216, 72, 0, 60, 0, 0, 0, 16, -144, 0, -32, 0, 0, 0, -100, -28, 0, -64, 0, 0, 0, 312, -32, 0, 0, 0, 0, 0, 64, 0, 0, 96, 0, 0, 0, -192, -60, 0, 24, 0, 0, 0, -88, 160, 0, 96, 0, 0, 0, 0, 32, 0, 32, 0, 0, 0, 240, -60, 0, 0, 0, 0, 0, 228, 20, 0, 32, 0, 0, 0, -16, 80, 0, 10, 0, 0, 0, 24, -52, 0, 8, 0, 0, 0, 0, 132, 0, -120, 0, 0, 0, -144, 168, 0, 0, 0, 0, 0, 96, 0, 0, 32, 0, 0, 0, 280, 20, 0, -8, 0, 0, 0, -144, -260, 0, -84, 0, 0, 0, 0, 92, 0, -20, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 24, 0, 0, -38, 0, 0, 0, -280, 72, 0, 192, 0, 0, 0, 96, 104, 0, -2, 0, 0, 0, 0, -184, 0, 64, 0, 0, 0, -128, -76, 0, 120, 0, 0, 0, -128, 0, 0, -12, 0, 0, 0, 16, 140, 0, -24, 0, 0, 0, 32, -24, 0, 96, 0, 0, 0, 160, 36, 0, -120, 0, 0, 0, -64, 96, 0, 0, 0, 0, 0, -240, 0, 0, 72, 0, 0, 0, 144, 36, 0, 136, 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, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 7, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "1078.2.a.v", "char_is_minimal": false, "conrey_index": 67, "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], [1, 0, 0, 0], [0, 0, 1, 0], [0, 2, 0, 0], [-1, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 5, 0], [0, 0, 0, 0], [1, 0, 1, 0], [0, -2, 0, -2], [0, 0, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, -2, 0, 0], [-5, 0, -5, 0], [0, 3, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 6, 0], [0, 2, 0, 0], [5, 0, 5, 0], [0, -3, 0, -3], [0, 0, 0, 4], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 0], [0, -5, 0, 0], [-1, 0, -1, 0], [0, 2, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [5, 0, 0, 0], [0, 0, 2, 0], [0, -3, 0, 0], [-12, 0, -12, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [10, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [-6, 0, -6, 0], [0, 9, 0, 9], [0, 0, 0, 2], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 0, -8, 0], [0, 3, 0, 0], [-2, 0, -2, 0], [0, -4, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [-12, 0, 0, 0], [0, 0, -4, 0], [0, 8, 0, 0], [0, 0, 0, 0], [0, 7, 0, 7], [0, 0, 0, -5], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 0], [-8, 0, -8, 0], [0, 2, 0, 2], [0, 0, 0, 12], [0, 0, 0, 0], [16, 0, 0, 0], [0, 0, 5, 0], [0, -6, 0, 0], [-2, 0, -2, 0], [0, 10, 0, 10], [0, 0, 0, -3], [0, 0, 0, 0], [12, 0, 0, 0], [0, 0, -8, 0], [0, 0, 0, 0], [-1, 0, -1, 0], [0, -2, 0, -2], [0, 0, 0, -9], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 10, 0], [0, -8, 0, 0], [1, 0, 1, 0], [0, -5, 0, -5], [0, 0, 0, 0], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, -20, 0], [0, -9, 0, 0], [0, 0, 0, 0], [0, -2, 0, -2], [0, 0, 0, -5], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 0, -5, 0]]}