# Stored data for newform 2352.2.q.bd, downloaded from the LMFDB on 18 April 2024. {"label": "2352.2.q.bd", "space_label": "2352.2.q", "level": 2352, "weight": 2, "hecke_orbit": 30, "hecke_orbit_code": 130605488738928944, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 2182910248687254769, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [4, 8, 14, 4, 1]], [11, [4, 2, 1]], [13, [14, -8, 1]], [17, [196, -56, 30, 4, 1]]], "qexp_display": "q+(1+\\beta _{2})q^{3}+(-\\beta _{1}+2\\beta _{2}-\\beta _{3})q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "q", "char_is_real": false, "Nk2": 9408, "analytic_conductor": 18.780814555405147, "hecke_ring_index": 1, "level_radical": 42, "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": "0.039", "prec": 17}, "analytic_rank_proved": true, "char_values": [2352, 3, [1471, 1765, 785, 2257], [3, 3, 3, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [961, 1537], "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": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "3.927", "prec": 17}, {"__RealLiteral__": 0, "data": "0.448", "prec": 17}, {"__RealLiteral__": 0, "data": "56.964", "prec": 20}, {"__RealLiteral__": 0, "data": "8.508", "prec": 17}, {"__RealLiteral__": 0, "data": "1391.370", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 2, -4, 0], "traces": [0, 4, 0, 2, 0, -4, 0, 0, 0, -2, 0, -4, 0, 16, 0, -8, 0, -4, 0, 0, 0, 0, 0, -4, 0, -2, 0, -4, 0, -16, 0, -8, 0, 4, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, -4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 16, 0, 0, 0, -8, 0, -16, 0, 0, 0, -12, 0, 0, 0, -8, 0, 8, 0, -8, 0, 2, 0, 0, 0, 16, 0, -2, 0, 16, 0, -8, 0, -8, 0, 20, 0, 0, 0, 8, 0, -8, 0, 16, 0, 8, 0, -20, 0, -8, 0, 0, 0, -12, 0, 0, 0, 16, 0, 24, 0, -24, 0, -8, 0, 0, 0, 14, 0, 4, 0, 0, 0, -16, 0, 0, 0, -8, 0, 0, 0, 4, 0, 0, 0, 48, 0, 0, 0, -16, 0, 24, 0, 0, 0, -12, 0, 24, 0, 8, 0, 16, 0, -32, 0, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 20, 0, 0, 0, -28, 0, 0, 0, 8, 0, -28, 0, -16, 0, -32, 0, 16, 0, -8, 0, 0, 0, -36, 0, 12, 0, -24, 0, 8, 0, 32, 0, 0, 0, 0, 0, -20, 0, -4, 0, 0, 0, 16, 0, 4, 0, 16, 0, 0, 0, 8, 0, -28, 0, -32, 0, 4, 0, 8, 0, -8, 0, 0, 0, -16, 0, -8, 0, 32, 0, 40, 0, 24, 0, 2, 0, 0, 0, 8, 0, 8, 0, 16, 0, 16, 0, -4, 0, -4, 0, 0, 0, 8, 0, -12, 0, -16, 0, 40, 0, 4, 0, 8, 0, 0, 0, -4, 0, -4, 0, 16, 0, -32, 0, 0, 0, 8, 0, 0, 0, -10, 0, 8, 0, 72, 0, 16, 0, 4, 0, 0, 0, 0, 0, 20, 0, -44, 0, -64, 0, -16, 0, -16, 0, 16, 0, 0, 0, -20, 0, 16, 0, -24, 0, -48, 0, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 32, 0, -96, 0, 12, 0, -16, 0, 0, 0, 24, 0, 44, 0, 0, 0, -16, 0, 4, 0, 24, 0, 0, 0, -12, 0, 22, 0, 28, 0, 88, 0, 16, 0, -4, 0, 0, 0, 44, 0, 0, 0, -48, 0, -80, 0, -8, 0, -48, 0, 0, 0, 0, 0, 8, 0, -80, 0, -16, 0, 48, 0, -32, 0, 0, 0, -16, 0, -40, 0, 8, 0, -32, 0, 40, 0, 0, 0, 0, 0, 16, 0, 24, 0, -144, 0, -24, 0, 0, 0, 44, 0, 0, 0, 16, 0, -20, 0, -64, 0, 48, 0, -32, 0, 48, 0, 0, 0, 36, 0, 52, 0, -24, 0, 24, 0, -8, 0, -24, 0, 0, 0, 36, 0, 4, 0, -72, 0, 16, 0, 8, 0, 40, 0, 0, 0, 32, 0, 0, 0, 64, 0, -8, 0, 32, 0, 32, 0, 0, 0, -12, 0, 8, 0, 0, 0, -88, 0, -8, 0, -8, 0, 0, 0, -16, 0, 0, 0, 0, 0, 40, 0, 10, 0, 20, 0, 0, 0, 0, 0, 8, 0, 0, 0, -56, 0, 68, 0, -40, 0, 0, 0, -40, 0, -26, 0, 16, 0, 8, 0, -8, 0, 28, 0, 0, 0, -12, 0, -8, 0, -32, 0, 80, 0, -16, 0, 16, 0, 0, 0, -16, 0, -52, 0, 32, 0, -16, 0, -8, 0, 8, 0, 0, 0, 16, 0, 56, 0, -72, 0, 136, 0, 48, 0, -12, 0, 0, 0, 8, 0, -12, 0, 80, 0, -32, 0, 4, 0, 28, 0, 0, 0, -32, 0, -4, 0, -32, 0, 0, 0, 28, 0, -48, 0, 0, 0, 8, 0, -32, 0, -40, 0, -64, 0, 24, 0, 4, 0, 0, 0, -6, 0, 0, 0, -32, 0, -48, 0, 8, 0, 0, 0, 0, 0, -4, 0, 16, 0, -32, 0, 32, 0, 48, 0, -16, 0, 0, 0, -56, 0, -48, 0, 16, 0, 8, 0, 16, 0, 28, 0, 0, 0, 48, 0, -16, 0, 64, 0, 48, 0, 2, 0, -60, 0, 0, 0, -8, 0, -28, 0, 80, 0, -16, 0, 16, 0, -24, 0, 0, 0, -64, 0, 28, 0, -32, 0, -80, 0, 0, 0, 8, 0, 0, 0, 16, 0, 16, 0, -32, 0, 48, 0, 20, 0, 16, 0, 0, 0, -24, 0, 40, 0, -16, 0, 4, 0, -48, 0, -40, 0, 0, 0, 0, 0, 32, 0, 16, 0, 136, 0, -56, 0, -8, 0, 0, 0, 16, 0, 8, 0, -96, 0, 128, 0, 8, 0, -28, 0, 0, 0, 4, 0, -40, 0, 0, 0, -8, 0, -12, 0, 24, 0, 0, 0, -24, 0, -8, 0, 16, 0, 104, 0, 72, 0, 12, 0, 0, 0, -52, 0, -8, 0, 40, 0, -48, 0, 20, 0, -16, 0, 0, 0, -4, 0, 28, 0, 48, 0, 16, 0, -32, 0, 32, 0, 0, 0, 44, 0, -16, 0, -8, 0, -168, 0, -24, 0, 4, 0, 0, 0, -56, 0, 8, 0, -192, 0, -20, 0, -16, 0, 12, 0, 0, 0, 0, 0, 16, 0, 0, 0, 16, 0, -28, 0, 64, 0, 0, 0, 12, 0, -76, 0, -20, 0, -64, 0, 16, 0, -8, 0, 0, 0, 0, 0, 36, 0, 104, 0, 64, 0, 8, 0, 0, 0, 0, 0, -4, 0, -16, 0, 144, 0, 0, 0, 16, 0, 8, 0, 0, 0, 12, 0, -32, 0, 40, 0, 72, 0, -16, 0, 44, 0, 0, 0, 40, 0, -32, 0, 96, 0, -16, 0, -8, 0, 36, 0, 0, 0, 16, 0, 8, 0, 128, 0, 32, 0, -28, 0, -56, 0, 0, 0, 84, 0, -4, 0, -40, 0, 8, 0, -72, 0, -16, 0, 0, 0, 14, 0, -12, 0, 16, 0, -112, 0, -24, 0, -56, 0, 0, 0, -8, 0, 48, 0, -80, 0, 0, 0, -16, 0, -8, 0, 0, 0, 64, 0, 8, 0, -16, 0, -160, 0, -16, 0, -8, 0, 0, 0, -40, 0, 16, 0, 0, 0, 56, 0, -48, 0, -52, 0, 0, 0, -12, 0, 4, 0, -64, 0, -32, 0, -52, 0, 48, 0, 0, 0, 28, 0, -24, 0, 48, 0, -8, 0, -64, 0, -44, 0, 0, 0, -16, 0, 0, 0, 24, 0, 144, 0, -8, 0, 32, 0, 0, 0, -4, 0, 104, 0, -48, 0, 48, 0, -16, 0, -16, 0, 0, 0, -32, 0, 64, 0, -24, 0, 128, 0, -32, 0, -22, 0, 0, 0, -16, 0, 14, 0, 112, 0, -208, 0, 44, 0, 36, 0, 0, 0, -16, 0, 28, 0, 0, 0, -8, 0, 20, 0, -40, 0, 0, 0, 80, 0, 12, 0, 88, 0, -32, 0, 8, 0, 0, 0, 0, 0, -8, 0, -24, 0, 32, 0, -144, 0, -40, 0, 48, 0, 0, 0, 8, 0, -4, 0, -64, 0, -96, 0, -48, 0, 8, 0, 0, 0, 68, 0, -24, 0, 0, 0, 8, 0, 8, 0, -8, 0, 0, 0, 40, 0, -40, 0, 64, 0, 48, 0, -8, 0, 44, 0, 0, 0, -48, 0, 36, 0, -80, 0, -64, 0, -36, 0, -56, 0, 0, 0, 0, 0, 72, 0, -32, 0, -120, 0, -104, 0, 40, 0, 0, 0, 8, 0, 4, 0, 24, 0, -16, 0, -16, 0, 32, 0, 0, 0, -40, 0, -12, 0, 192, 0, 0, 0, -16, 0, 24, 0, 0, 0, 68, 0, -24, 0, 32, 0, 64, 0, 24, 0, -24, 0, 0, 0, -40, 0, -72, 0, 176, 0, 72, 0, -12, 0, -48, 0, 0, 0, 0, 0, 8, 0, 64, 0, 88, 0, 4, 0, 16, 0, 0, 0, -4, 0, -68, 0, 32, 0, -40, 0, 0, 0, 20, 0, 0, 0, 0, 0, -32, 0, -104, 0, 16, 0, 24, 0, -88, 0, 0, 0, 32, 0, -100, 0, -16, 0, 96, 0, 48, 0, -48, 0, 0, 0, 4, 0, 56, 0, 72, 0, -144, 0, -32, 0, -52, 0, 0, 0, -56, 0, -12, 0, 32, 0, -88, 0, 12, 0, 64, 0, 0, 0, 8, 0, -24, 0, -32, 0, -48, 0, -12, 0, 16, 0, 0, 0, -4, 0, 42, 0, 72, 0, 112, 0, 0, 0, -4, 0, 0, 0, -64, 0, -36, 0, -48, 0, 112, 0, 8, 0, -64, 0, 0, 0, -8, 0, 16, 0, -80, 0, 80, 0, -80, 0, 8, 0, 0, 0, -4, 0, -112, 0, 64, 0, 48, 0, -16, 0, 0, 0, 0, 0, -96, 0, 32, 0, -16, 0, 112, 0, -4, 0, -124, 0, 0, 0, -32, 0, 36, 0, 32, 0, 64, 0, 28, 0, 88, 0, 0, 0, 4, 0, 48, 0, -24, 0, -32, 0, 64, 0, -8, 0, 0, 0, -68, 0, 0, 0, 160, 0, -144, 0, -44, 0, 24, 0, 0, 0, 8, 0, 68, 0, 0, 0, -16, 0, 16, 0, 8, 0, 0, 0, -28, 0, -56, 0, -32, 0, -24, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, -8, 0, 20, 0, 16, 0, 0, 0, -10, 0, 92, 0, 128, 0, 40, 0, -48, 0, -40, 0, 0, 0, 104, 0, -16, 0, 0, 0, 128, 0, 0, 0, -8, 0, 0, 0, -44, 0, 0, 0, -24, 0, -16, 0, -28, 0, 0, 0, 0, 0, -68, 0, 4, 0, 80, 0, -80, 0, 40, 0, 56, 0, 0, 0, 64, 0, -24, 0, -80, 0, -136, 0, -40, 0, 26, 0, 0, 0, 0, 0, 8, 0, -96, 0, -24, 0, 4, 0, -108, 0, 0, 0, 8, 0, -20, 0, -80, 0, 56, 0, -68, 0, 32, 0, 0, 0, 52, 0, -40, 0, -24, 0, -32, 0, -32, 0, 8, 0, 0, 0, 120, 0, -16, 0, 40, 0, 48, 0, 40, 0, 16, 0, 0, 0, 16, 0, -28, 0, -96, 0, 32, 0, -16, 0, -48, 0, 0, 0, 48, 0, 64, 0, -32, 0, -88, 0, 88, 0, 52, 0, 0, 0, -64, 0, 16, 0, 256, 0, -76, 0, -8, 0, 112, 0, 0, 0, 8, 0, 24, 0, 32, 0, 16, 0, -4, 0, 56, 0, 0, 0, 0, 0, -16, 0, 32, 0, 216, 0, 16, 0, -56, 0, 0, 0, -100, 0, -36, 0, 200, 0, 112, 0, 68, 0, -64, 0, 0, 0, -48, 0, -56, 0, -240, 0, -24, 0, 0, 0, 80, 0, 0, 0, 28, 0, 8, 0, 16, 0, 176, 0, 8, 0, 12, 0, 0, 0, 64, 0, 40, 0, -96, 0, -88, 0, -16, 0, 88, 0, 0, 0, -4, 0, 124, 0, -176, 0, 56, 0, 40, 0, -56, 0, 0, 0, 84, 0, -36, 0, -64, 0, 0, 0, -8, 0, 4, 0, 0, 0, -4, 0, -16, 0, -88, 0, 160, 0, 0, 0, 56, 0, 0, 0, -28, 0, 96, 0, 144, 0, -96, 0, 32, 0, -120, 0, 0, 0, -48, 0, 40, 0, 16, 0, 0, 0, 0, 0, 32, 0, 0, 0, 8, 0, -20, 0, -256, 0, -44, 0, -32, 0, -48, 0, 0, 0, -24, 0, -20, 0, 96, 0, 8, 0, 56, 0, -72, 0, 0, 0, -68, 0, 12, 0, -12, 0, -152, 0, 8, 0, 0, 0, 0, 0, 64, 0, -16, 0, -104, 0, 80, 0, -24, 0, 48, 0, 0, 0, -8, 0, -44, 0, 112, 0, 0, 0, -72, 0, 112, 0, 0, 0, 48, 0, -80, 0, -8, 0, -80, 0, -120, 0, -16, 0, 0, 0, -24, 0, -16, 0, -176, 0, 184, 0, 16, 0, -16, 0, 0, 0, -48, 0, 32, 0, -112, 0, -32, 0, 76, 0, -32, 0, 0, 0, 72, 0, 48, 0, -112, 0, 32, 0, 96, 0, 48, 0, 0, 0, -56, 0, 8, 0, -56, 0, -160, 0, 4, 0, 56, 0, 0, 0, -16, 0, -12, 0, 16, 0, 56, 0, 16, 0, -128, 0, 0, 0, 24, 0, -72, 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]], "char_orbit_index": 17, "prim_orbit_index": 3, "minimal_twist": "147.2.a.d", "char_is_minimal": false, "conrey_index": 961, "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, 0, 0], [1, 0, 1, 0], [0, 0, 0, 0], [0, -1, 2, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-2, 0, -2, 0], [0, 0, 0, 0], [4, 0, 0, -1], [0, 0, 0, 0], [-2, 0, 0, -1], [0, 0, 0, 0], [-2, -3, -2, 0], [0, 0, 0, 0], [0, -2, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 2, -4], [0, 0, 0, 0], [-1, 4, -1, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 0, -2], [0, 0, 0, 0], [-4, -2, -4, 0], [0, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 0], [4, 1, 4, 0], [0, 0, 0, 0], [2, 0, 0, 3], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [-2, 1, -2, 0], [0, 0, 0, 0], [0, -2, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, -2, -3], [0, 0, 0, 0], [2, 0, 2, 0], [0, 0, 0, 0], [4, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [-4, -2, -4, 0], [0, 0, 0, 0], [0, -3, 8, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 6, -2], [0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [-2, 0, 0, -4], [0, 0, 0, 0], [2, 0, 0, -8], [0, 0, 0, 0], [-4, 7, -4, 0], [0, 0, 0, 0], [0, 4, -1, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, -8, 4], [0, 0, 0, 0], [-1, 0, -1, 0], [0, 0, 0, 0], [4, 0, 0, -8], [0, 0, 0, 0], [-2, 0, 0, -4], [0, 0, 0, 0], [-4, 2, -4, 0], [0, 0, 0, 0], [0, 3, -10, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, -4, -2], [0, 0, 0, 0], [-4, 4, -4, 0], [0, 0, 0, 0], [4, 0, 0, -1], [0, 0, 0, 0], [2, 0, 0, 0], [0, 0, 0, 0]]}