# Stored data for newform 336.2.bq.a, downloaded from the LMFDB on 25 April 2024. {"label": "336.2.bq.a", "space_label": "336.2.bq", "level": 336, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 2886251577680, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 290675495340942789, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [2401, -2744, 1568, -1008, 527, -144, 32, -8, 1]]], "qexp_display": "q+(\\zeta_{24}-\\zeta_{24}^{7})q^{2}+\\zeta_{24}^{5}q^{3}+(2-2\\zeta_{24}^{4}+\\cdots)q^{4}+\\cdots", "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 112, "char_orbit_label": "bq", "char_is_real": false, "Nk2": 1344, "analytic_conductor": 2.6829735079150208, "hecke_ring_index": 1, "level_radical": 42, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "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": "0.264", "prec": 17}, "analytic_rank_proved": true, "char_values": [336, 12, [127, 85, 113, 241], [12, 3, 12, 4]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [37, 109, 205, 277], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "7.535", "prec": 17}, {"__RealLiteral__": 0, "data": "4.405", "prec": 17}, {"__RealLiteral__": 0, "data": "300.687", "prec": 24}, {"__RealLiteral__": 0, "data": "621.727", "prec": 24}, {"__RealLiteral__": 0, "data": "21424.425", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c12", "trace_display": [0, 0, 8, 0], "traces": [0, 8, 0, 0, 8, 8, 8, 0, 0, 0, -4, 4, 0, -8, 0, -8, -16, 16, 0, 8, 32, -12, 8, 0, 8, 0, 8, 0, 0, 32, 0, 4, 0, 4, 0, -16, 0, -8, 0, 0, 8, 0, -4, 48, -8, 8, -24, 8, 0, -20, -64, 8, -8, -16, -4, 0, 48, 0, -12, -20, -8, -4, 0, -8, -64, -24, 0, -32, -32, -24, -44, 0, 0, 0, 0, -16, 32, -8, -16, -28, 32, 4, -8, -8, 0, 80, 8, 0, 8, 0, -8, -28, 0, -4, 0, -32, -16, -24, 0, -8, 0, -16, 16, 0, 32, 0, 24, -20, 0, 24, 24, 0, 0, -48, 16, -20, 32, -4, -40, 0, 0, 0, 16, 4, -8, 16, 0, 56, 0, -8, 0, 36, 16, 16, -16, 0, 0, 0, 16, 24, -40, 24, 56, -16, 0, 76, 0, 0, -32, 8, 16, 0, 0, 0, 28, 8, 0, -48, 0, 12, 32, 32, 0, 12, 0, -12, -44, 0, 8, 0, 48, -8, 48, -48, 64, 80, -32, -20, 88, 64, -16, -24, -16, 0, 48, 0, 4, -24, 32, 12, 0, -32, 0, 28, 0, 40, -80, 48, 4, 0, -64, 0, 16, 52, 32, 20, 32, -16, 16, 32, -32, -56, 32, -28, -36, 0, -16, 0, -80, 0, 0, -32, 0, 40, 96, 32, 0, -12, 0, -52, -64, 0, -48, 0, 8, -4, 40, -24, 112, 32, 16, -36, 16, 0, -16, 16, 16, 0, 0, 0, -60, -72, -8, 8, 0, -48, -64, 64, 0, 16, -96, 16, 28, 0, 0, 0, -48, 88, 64, -40, 16, -52, -128, 16, -32, -32, -24, -16, -56, 0, 16, 0, 8, -72, 0, -8, 0, 32, 0, -28, 0, 32, 0, -48, -20, 0, 0, 0, 48, -8, -64, -48, 16, 8, 32, 0, 16, -40, 16, 32, -12, 0, -16, 0, -32, 4, -112, -16, 0, 44, -64, -72, 0, 64, -8, 48, 48, 0, -32, 0, -40, 0, -8, -8, 0, -240, 48, -104, -32, 28, 80, 0, 0, 0, 32, 0, 0, -24, 0, -16, 0, 16, -16, -32, 0, 20, 0, 16, -32, 0, -8, 0, 72, 16, -40, 64, -8, 28, 0, 8, 32, -52, -16, -28, 32, 0, 0, 0, -8, 8, 64, 12, 0, 88, -64, -92, 0, -24, -24, -56, -24, 0, 0, 0, 16, 44, -8, 48, 32, -48, 0, 96, -64, 4, 32, 16, 24, 0, -32, 0, 24, -8, 0, 40, 0, 28, 32, 56, 0, 48, 0, 56, -8, 0, 24, 0, 48, -8, -80, -12, -80, 16, 0, 0, 16, -80, -48, 32, 16, 0, 96, 0, 96, 4, 0, -44, 0, 96, 0, -48, 0, 12, -48, 4, 120, 0, 64, 0, -24, -8, 40, 64, -16, 128, -64, 12, 16, 40, -16, 56, 80, 0, -40, 0, -28, -64, 0, 32, 0, 72, 0, 16, 0, -36, 0, -56, 4, 0, -32, 0, 40, 88, -8, 88, -32, -20, -32, -144, -16, 28, 16, 0, -28, 0, 0, 0, 8, 16, 56, -24, 0, -16, 0, 0, 0, 80, 16, -8, 48, 0, 0, 0, -12, 44, 144, 32, -96, 0, 16, 44, 16, 40, 16, 32, 0, 0, -16, 0, 120, -40, 0, -16, 0, -72, 0, 272, 0, -48, 0, 4, -48, 0, 64, 0, -128, 8, 24, -48, -8, -128, -16, 64, -16, -20, 24, -76, -16, 0, 224, 0, -32, -68, 32, -64, 0, 64, 0, -116, 0, 0, 304, 128, -24, 0, 0, 0, 28, 40, -48, 16, -120, -16, -32, -72, -16, -184, 32, 8, -8, 0, -32, 0, 16, -64, 0, 56, 0, -92, 0, -84, 0, 16, 0, 4, 64, 0, 40, 0, -48, 76, 8, 12, -176, 0, 0, 12, -16, -8, 96, -64, 52, 0, 0, 0, -68, 44, 48, 68, 0, 24, 32, 32, 0, 192, -112, -80, -32, 0, 0, 0, 128, -8, 48, 24, 48, -172, 0, 32, -72, -160, 24, 16, -32, 0, -176, 0, 0, -28, 0, 44, 0, 16, 32, 24, 0, -16, 0, -16, -48, 0, 192, 0, -4, -4, 16, -144, 72, -48, -96, 8, -40, 36, -192, -16, 128, 0, 64, 0, -8, 16, -64, -144, 0, 32, -32, 40, 0, -40, -80, -28, -88, 0, -176, 0, -32, -88, -128, 20, -32, -24, -64, -96, 0, 40, -24, -112, -32, 0, -64, 0, -16, 112, 0, 0, 0, 116, 192, 56, 0, 36, 0, -32, -84, 0, -8, 0, -40, -4, -96, 40, 32, -92, 32, 28, 88, -184, 24, 8, 32, 0, 0, 0, 56, 96, -128, -40, 0, 80, 0, 136, 0, 24, -56, -40, -8, 0, 0, 0, -128, -16, 40, -4, 32, -24, -80, -352, 72, -140, 48, -24, -40, 0, 16, 0, -64, -8, 0, 112, 0, -32, 128, 0, 0, -16, 0, 116, 0, 0, 16, 0, 4, 0, 40, -72, -16, -96, 32, 96, -64, 8, 80, 0, -40, 0, -64, 0, -140, -200, 32, 40, 0, -64, 64, -160, 0, 48, 32, 4, 112, 0, -80, 0, -48, 8, -56, -40, 48, -64, 128, -8, -192, 32, 56, -16, 40, 0, 72, 0, -16, -72, 0, -20, 0, 72, -16, 192, 0, 128, 0, -32, 76, 0, -80, 0, -96, 188, 0, -80, 88, -28, 0, 336, 0, -152, 64, 60, -44, 0, 0, 0, 352, -4, 40, -16, 0, 544, 0, -16, 0, 4, 32, 40, -32, 0, 0, 0, -44, -12, 24, 32, 104, -208, 0, 36, 128, -28, -208, 72, -32, 0, -64, 0, 0, -64, 0, -64, 0, 48, -48, -72, 0, 40, 0, -44, 16, 0, -16, 0, -184, -16, 8, 24, -96, -8, 160, 8, 128, -72, -24, 16, -64, 0, 160, 0, 12, 32, 32, 28, 0, 88, 64, 112, 0, -20, 72, 112, 32, 0, -32, 0, 140, 4, 0, 156, 176, 64, -16, 88, 24, 88, -128, 48, -28, 0, 16, 0, -224, -12, 0, 72, 0, 60, 0, -64, 0, 240, 0, 56, 56, 0, -240], "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, 16, 5, 1, 4, 0], [1, 1, 112, 23, 1, 12, 0]], "char_orbit_index": 43, "prim_orbit_index": 23, "minimal_twist": "336.2.bq.a", "char_is_minimal": true, "conrey_index": 37, "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], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 1, 0, 0], [2, 0, 0, 0, -2, 0, 0, 0], [0, 0, -2, 0, 2, 0, 2, 1], [1, 0, 0, 0, 0, 0, 1, 0], [0, -2, 1, 1, 0, 1, 0, 1], [0, 2, 0, -2, 0, -2, 0, 0], [0, 0, -1, 0, 0, 0, 1, 0], [-1, 0, 1, 0, 1, 4, 0, 0], [1, 0, 1, 1, -1, 0, 0, -1], [0, 2, 0, 0, 0, 0, 0, 0], [-1, -2, 0, 0, 0, 2, 1, 0], [-2, 1, 0, 1, 4, -1, 0, 0], [-1, -2, 0, -2, 0, 2, 0, 0], [0, 0, 0, 0, -4, 0, 0, 0], [4, 0, 0, 2, -4, -2, 0, -2], [0, 0, 0, -1, 0, 1, 0, 1], [0, 0, 2, 0, 2, 0, -2, 0], [4, 0, 0, 2, 0, 0, 4, 0], [-2, 0, -1, 0, 1, 0, -1, 1], [1, 2, 0, 0, 0, -2, -1, 0], [0, -3, 4, 0, 0, 0, -4, 3], [2, 0, 2, 0, -2, 0, 0, 0], [0, 0, -4, -4, 0, -4, 0, 4], [0, 0, -2, 0, 2, 0, 2, 2], [0, 0, 0, -1, 0, 0, 0, 0], [0, -2, 2, 4, 0, 4, -2, -2], [4, 3, 0, 0, 0, -3, -4, 0], [0, -1, -4, 0, 0, 0, 4, 1], [1, 0, 0, -1, -1, 1, 0, 1], [0, 0, 0, -4, 0, -4, 0, 4], [0, 1, 0, 0, 1, 0, 0, 1], [0, 4, 0, -4, 0, -4, -4, 0], [-1, -5, -2, 0, -2, -3, 3, 0], [0, 0, 0, 0, 0, 0, 2, 0], [0, 0, 2, 0, -2, 0, -2, 0], [0, 0, 0, 4, 0, 0, 0, -4], [0, 0, -2, -1, 0, -1, 0, 1], [0, 8, 2, 0, 2, 0, -2, 0], [0, 1, 0, -1, 0, -1, -2, 0], [-1, -4, 1, 0, 1, 2, 0, 0], [6, 0, 0, 2, 0, 0, 6, 0], [0, 0, 2, 0, -2, 0, -2, -2], [2, 0, -2, 0, -2, -1, 0, 0], [-6, 0, 0, 4, 6, -4, 0, -4], [0, -3, 0, 0, 2, 0, 0, -3], [0, 4, 0, 0, 0, -4, 0, 0], [0, -2, 0, -4, -5, 4, 0, 2], [-8, -4, 0, -4, 0, 4, 0, 0], [0, 4, 2, 0, 2, 0, -2, 0], [-2, 0, 2, 0, 2, 4, 0, 0], [-4, 0, -4, 3, 4, 0, 0, -3], [0, 0, -1, 0, -1, 0, 1, 0], [0, -3, 0, 3, 0, 3, 5, 0], [4, 0, 0, 2, 4, -2, 0, -2], [0, -2, 0, 2, 0, 2, 0, 0], [0, 0, 3, 0, -3, 0, -3, -8], [-5, 0, -5, -5, 5, 0, 0, 5], [-2, 0, 0, -4, 2, 4, 0, 4], [0, 4, -1, 0, -1, 0, 1, 0], [0, 1, 0, -1, 0, -1, 2, 0], [-1, -1, 0, 1, 0, -1, 0, -2], [-8, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, -6, 0, 0, -5], [0, 0, 2, 1, 0, 1, 0, -1], [-8, 0, 8, 0, 8, -2, 0, 0], [0, -4, 0, 0, -8, 0, 0, -4], [-3, 0, 0, 4, 0, 0, -3, 0], [-8, 0, -5, -4, 5, 0, -3, 6], [0, -7, 0, 7, 0, 7, -6, 0], [0, 2, 0, 0, 0, 0, 0, 2], [0, 0, -4, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -4, 0, 0], [0, 0, 4, 0, -4, 0, -4, -4], [4, 0, 0, 0, 0, 0, -4, 0], [-2, -1, 2, 0, 2, 4, 0, 0], [-2, -2, 0, -2, 0, 2, 0, 0], [0, 3, 0, 0, -7, 0, 0, 3], [8, 0, 8, 4, -8, 0, 0, -4], [1, 0, 0, 0, -1, 0, 0, 0], [0, -2, 0, 0, -2, 0, 0, -2], [-1, 11, 0, 0, 0, -11, 1, 0], [-2, 0, -4, 2, 4, 0, 2, 0], [10, 0, 0, 12, 0, 0, 10, 0], [0, 12, 2, 0, 2, 0, -2, 0], [0, 0, 3, 4, 0, 4, 0, -4], [2, 0, -2, 0, -2, -4, 0, 0], [0, 11, 0, 0, 0, 0, 0, -11], [-1, 0, 0, -4, 0, 0, -1, 0], [-3, 0, 1, -4, -1, 0, -4, 0], [0, -6, 0, 6, 0, 6, -8, 0], [0, 1, -1, 0, -1, 0, 1, 0], [0, 0, -6, 2, 0, 2, 0, -2], [-8, 0, 0, -2, 8, 2, 0, 2], [0, 0, 4, 0, -4, 0, -4, 0], [-3, -8, 0, -8, 0, 8, 0, 0], [0, 0, -4, -5, 0, -5, 8, 5], [-1, -1, 0, 0, 0, 1, 1, 0], [0, -8, -8, 0, 0, 0, 8, 8]]}