# Stored data for newform 1764.2.b.b, downloaded from the LMFDB on 23 April 2024. {"label": "1764.2.b.b", "space_label": "1764.2.b", "level": 1764, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503668380403428, "dim": 4, "is_polredabs": true, "nf_label": "4.0.441.1", "trace_hash": 2216787582780080263, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [3, 0, 1]], [11, [7, 0, 1]], [19, [0, 1]], [29, [5, 1]], [53, [7, 1]]], "qexp_display": "q+\\beta _{2}q^{2}+(-2-\\beta _{2})q^{4}+\\beta _{3}q^{5}+(2+\\cdots)q^{8}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 28, "char_orbit_label": "b", "char_is_real": true, "Nk2": 7056, "analytic_conductor": 14.08561091655386, "hecke_ring_index": 4, "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": "0.763", "prec": 17}, "analytic_rank_proved": true, "char_values": [1764, 2, [883, 785, 1081], [1, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [1567], "field_disc": 441, "field_disc_factorization": [[3, 2], [7, 2]], "field_poly": [4, -2, -1, -1, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.051", "prec": 17}, {"__RealLiteral__": 0, "data": "3.818", "prec": 17}, {"__RealLiteral__": 0, "data": "1.515", "prec": 17}, {"__RealLiteral__": 0, "data": "125.402", "prec": 24}, {"__RealLiteral__": 0, "data": "54.220", "prec": 20}, {"__RealLiteral__": 0, "data": "5057.576", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, 0, 0, 0], "traces": [0, 4, -2, 0, -6, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 14, 0, 0, 8, 0, 0, 0, -20, 0, 0, -22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 28, 0, 0, 0, -4, 0, 0, -28, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 18, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 56, 0, -14, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 56, 0, 0, 30, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 26, 0, 12, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -24, 0, -56, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, -56, 0, 0, 20, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 42, 0, 98, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -50, 80, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, -42, 0, -62, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -16, 0, 0, 0, -64, 0, 0, -28, 0, 0, 0, 0, -124, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 70, 0, 0, -72, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, -42, -28, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, -2, 0, -72, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 28, 0, 0, -76, 0, 0, 0, 48, 0, 0, 84, 0, 0, 0, 0, 136, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, -6, 0, 0, -40, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 4, -32, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 28, 0, -70, 0, 0, 0, -98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 72, 0, 0, 0, 56, 0, 0, -84, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, -10, 0, -40, 0, 0, 0, -84, 0, 0, -112, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -24, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 28, 0, 42, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, -56, 0, 0, -20, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, -24, 0, 28, 0, 0, 0, 8, 0, 0, 28, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -28, 32, 0, 0, 0, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -126, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 36, 0, 0, 56, 0, 0, 0, 8, 0, 0, -42, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, -42, 0, 14, 0, 0, 0, -70, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 172, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 42, 0, -6, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 28, 0, 0, -96, 0, 0, 0, -92, 0, 0, -70, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, -28, 0, 56, 0, 0, 0, 38, 0, 0, -40, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 28, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 20, 0, 0, -56, 0, 0, 0, -48, 0, 0, 84, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, -44, 0, 16, 0, 0, 0, 84, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 196, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 4, 0, -28, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, 140, 0, 0, 96, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, -144, 0, -98, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 140, 24, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 110, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 56, 0, 0, 96, 0, 0, 0, 112, 0, 0, 28, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 40, 0, 30, 0, 0, 0, 14, 0, 0, 128, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 24, 0, 84, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, -168, 0, 0, 196, 0, 0, 0, 288, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, -168, 0, 0, 0, 10, 0, 0, -100, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, -168, 0, 40, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -14, 0, 0, -96, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 84, 0, -16, 0, 0, 0, -84, 0, 0, -72, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 186, 144, 0, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -196, 0, 0, 126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 56, 0, 0, -168, 0, 0, 0, 36, 0, 0, -70, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 108, 0, -168, 0, 0, 0, -28, 0, 0, -140, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -42, -192, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, -42, 0, 126, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, -76, 0, 0, -72, 0, 0, 0, -224, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 84, 0, -86, 0, 0, 0, -126, 0, 0, -96, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, -56, -56, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, -42, 0, 126, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 14, 0, 0, -148, 0, 0, 0, -104, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, -84, 0, 0, 0, 48, 0, 0, 84, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 98, -56, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, -28, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, 20, 0, 0, 168, 0, 0, 0, -168, 0, 0, -72, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 252, 0, 0, -280, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, -204, 196, 0, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, -84, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -252, 0, 0, 140, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 28, 0, 0, 156, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 336, 0, 36, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, -56, 0, 0, 112, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 60, 0, -98, 0, 0, 0, 252, 0, 0, 240, 0, 0, 0, 0, -182, 0, 0, 0, 0, 0, -42, -140, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 116, 8, 0, 12, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 154, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 308, 0, 0, 294, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, -140, 0, -140, 0, 0, 0, -48, 0, 0, 236, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, -28, 0, 240, 0, 0, 0, 98, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, 168, 0, 0, -84, 0, 0, 0, 0, -312, 0, 0, 0, 0, 0, 0, 28, 0, -12, 0, 0, 0, -196, 0, 0, -168, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 162, -252, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -276, 0, 0, -84, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 0, 0, 0, 168, 0, 0, -156, 0, 0, 0, -28, 0, 0, 84, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 168, 0, -196, 0, 0, 0, -48, 0, 0, -56, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 28, -304, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 210, 0, 8, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, -266, 0, 0, 96, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, -28, 52, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 28, 4, 1, 2, 0], [1, 1, 7, 2, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 4, "minimal_twist": "252.2.bf.a", "char_is_minimal": true, "conrey_index": 1567, "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, 0, 0, 0], [-2, 0, -1, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, -1, 0], [0, 0, 0, 0], [0, 1, 0, 0], [-1, 0, -2, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 3, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, -2], [0, 0, 0, 0], [4, 0, 1, 0], [-2, 0, -4, 0], [0, 0, 0, 0], [2, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, 1], [-6, 0, -1, 0], [0, 0, 0, 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, -1, 0, 2], [0, 0, 0, -2], [0, 0, 0, 0], [-4, 0, -8, 0], [-2, 0, 3, 0], [0, 0, 0, 0], [8, 0, 2, 0], [0, -4, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [0, -2, 0, -4], [-7, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -5, 0], [0, -6, 0, -3], [0, 0, 0, 0], [0, 0, 0, 6], [0, -1, 0, -4], [0, 0, 0, 0], [2, 0, -5, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 8], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, -4, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 0, -6, 0], [0, 3, 0, 2], [0, 0, 0, 0], [0, -2, 0, 0], [0, 2, 0, 1], [0, 0, 0, 0], [12, 0, 0, 0], [16, 0, 4, 0], [0, 0, 0, 0], [-6, 0, -5, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 0, 6, 0], [0, 0, 0, 0], [0, 2, 0, 8], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 5], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 0, -2, 0]]}