# Stored data for newform 735.2.b.d, downloaded from the LMFDB on 24 April 2024. {"label": "735.2.b.d", "space_label": "735.2.b", "level": 735, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13510867635143391, "dim": 8, "is_polredabs": true, "nf_label": "8.0.856615824.2", "trace_hash": 936919093493200328, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4, 0, 32, 0, 36, 0, 11, 0, 1]], [17, [12, -42, 42, -12, 1]]], "qexp_display": "q-\\beta _{1}q^{2}-\\beta _{3}q^{3}+(-1+\\beta _{2})q^{4}-q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 21, "char_orbit_label": "b", "char_is_real": true, "Nk2": 2940, "analytic_conductor": 5.869004548564108, "hecke_ring_index": 8, "level_radical": 105, "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": "0.518", "prec": 17}, "analytic_rank_proved": true, "char_values": [735, 2, [491, 442, 346], [1, 2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [146], "field_disc": 856615824, "field_disc_factorization": [[2, 4], [3, 6], [271, 2]], "field_poly": [4, 0, 32, 0, 36, 0, 11, 0, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.002", "prec": 17}, {"__RealLiteral__": 0, "data": "2.261", "prec": 17}, {"__RealLiteral__": 0, "data": "266.561", "prec": 24}, {"__RealLiteral__": 0, "data": "346.238", "prec": 24}, {"__RealLiteral__": 0, "data": "15391.027", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 1, -8, 0], "traces": [0, 8, 0, 1, -6, -8, 5, 0, 0, 1, 0, 0, -9, 0, 0, -1, -2, 24, -7, 0, 6, 0, -40, 0, -23, 8, 12, 4, 0, 0, -5, 0, 0, 2, 0, 0, 9, -14, 24, -12, 0, -30, 0, 16, 0, -1, 14, 12, -25, 0, 0, -6, 0, 0, -10, 0, 0, 6, 26, 24, 9, 0, 24, 0, 38, 0, -38, -8, 0, -13, 0, 0, 1, 0, 0, 1, 0, 0, -6, 58, 2, 13, 0, 30, 0, -24, 0, -61, 4, 6, 7, 0, 0, -36, 0, 0, -39, 0, 0, -34, -6, 6, 6, 0, -24, 0, -16, 0, -60, 40, 40, -16, 0, 0, 12, 0, 0, 30, 0, 0, 23, -24, 30, -21, 0, -8, 0, -26, 0, -7, -12, -12, -42, 0, 0, -4, 0, 0, -53, 0, 0, 0, -52, 36, -7, 0, 72, 0, 48, 0, 5, -44, 12, 42, 0, 0, 30, 0, 0, 32, 0, 0, 83, -8, 78, -2, 0, 30, 0, 62, 0, 36, 6, -12, -5, 0, 0, 12, 0, 0, -9, 0, 0, -51, -26, 14, -54, 0, -48, 0, -24, 0, -5, -26, 48, 12, 0, 0, -2, 0, 0, 23, 0, 0, -66, 30, 30, 71, 0, 72, 0, 16, 0, -4, 2, -16, 10, 0, 0, 12, 0, 0, -32, 0, 0, 1, 32, 0, 36, 0, -14, 0, -122, 0, -54, -12, 60, 32, 0, 0, 25, 0, 0, 31, 0, 0, -57, -30, -72, 21, 0, -48, 0, 32, 0, 6, -42, -120, 1, 0, 0, 23, 0, 0, -34, 0, 0, 117, -30, -102, 10, 0, 12, 0, 56, 0, 81, -26, 36, -30, 0, 0, 48, 0, 0, -6, 0, 0, -3, -16, -26, 54, 0, -84, 0, -24, 0, 32, 50, -84, -9, 0, 0, 15, 0, 0, 18, 0, 0, -45, -24, -72, 30, 0, 12, 0, 36, 0, 64, 44, -38, 101, 0, 0, -75, 0, 0, 23, 0, 0, 38, -62, 18, -106, 0, 8, 0, -38, 0, 44, 0, -60, -36, 0, 0, 13, 0, 0, 57, 0, 0, -6, 84, 0, -72, 0, -126, 0, 20, 0, -1, 86, 114, -69, 0, 0, -51, 0, 0, 45, 0, 0, 102, 58, -84, -1, 0, -84, 0, 22, 0, -16, -124, 6, 53, 0, 0, 41, 0, 0, 6, 0, 0, -84, 20, -58, -30, 0, 156, 0, -2, 0, 7, -6, 54, -13, 0, 0, -30, 0, 0, -16, 0, 0, -191, -30, -36, -24, 0, -96, 0, -20, 0, 60, 64, 24, -8, 0, 0, -36, 0, 0, -16, 0, 0, 61, 30, -72, 114, 0, -4, 0, -12, 0, 120, -6, -36, -43, 0, 0, -7, 0, 0, 74, 0, 0, 36, 82, -36, 24, 0, 48, 0, -20, 0, 36, 92, -42, -6, 0, 0, -54, 0, 0, -68, 0, 0, 80, -148, 96, 39, 0, -108, 0, 30, 0, 77, -74, -102, 80, 0, 0, -15, 0, 0, 34, 0, 0, -39, 22, 6, 39, 0, 30, 0, -6, 0, 49, 0, -102, -6, 0, 0, -6, 0, 0, -57, 0, 0, -84, 24, -132, -59, 0, 192, 0, 2, 0, 34, -78, 16, 0, 0, 0, 9, 0, 0, 50, 0, 0, 60, 40, -60, -81, 0, -40, 0, -74, 0, 93, -40, 12, 71, 0, 0, 16, 0, 0, -102, 0, 0, 36, -40, -18, -72, 0, 0, 0, -8, 0, -12, -2, -12, 74, 0, 0, 37, 0, 0, 98, 0, 0, 102, 128, 24, -30, 0, 168, 0, 42, 0, -22, 32, -96, -92, 0, 0, -36, 0, 0, -23, 0, 0, 35, 60, 24, -69, 0, 0, 0, -30, 0, 6, 100, 78, 21, 0, 0, 81, 0, 0, 50, 0, 0, -30, 8, -36, 36, 0, -132, 0, 100, 0, -16, 140, 26, -96, 0, 0, -52, 0, 0, 73, 0, 0, 7, 24, -54, 19, 0, 12, 0, -216, 0, -53, 12, 42, 6, 0, 0, 42, 0, 0, -36, 0, 0, -92, -82, -18, -42, 0, 72, 0, -2, 0, 4, -42, 0, 100, 0, 0, -36, 0, 0, 12, 0, 0, 66, 14, -48, 53, 0, 0, 0, 182, 0, 23, -24, 66, -22, 0, 0, 36, 0, 0, 0, 0, 0, -24, -158, 52, 50, 0, -72, 0, -36, 0, 122, -112, 24, 7, 0, 0, 24, 0, 0, 39, 0, 0, 40, -72, 96, 111, 0, -186, 0, 54, 0, 75, -62, -48, 12, 0, 0, -30, 0, 0, -9, 0, 0, -5, 10, 0, -18, 0, 44, 0, -128, 0, -122, -12, 84, 16, 0, 0, -42, 0, 0, 15, 0, 0, -72, -84, -24, 25, 0, 108, 0, 140, 0, -30, -112, -96, -22, 0, 0, -108, 0, 0, 89, 0, 0, 26, -144, -96, -32, 0, -144, 0, 96, 0, -21, 110, 192, -27, 0, 0, 63, 0, 0, -83, 0, 0, -36, 136, 8, -114, 0, -174, 0, -78, 0, -56, 226, -90, 2, 0, 0, -63, 0, 0, 62, 0, 0, 42, -30, -12, 150, 0, 180, 0, -126, 0, -88, -72, -62, 48, 0, 0, 48, 0, 0, -96, 0, 0, -36, 202, 60, 48, 0, -6, 0, 20, 0, -42, 12, -72, -89, 0, 0, 5, 0, 0, -66, 0, 0, 30, 4, -12, -144, 0, -162, 0, 58, 0, -12, 110, 102, -64, 0, 0, 122, 0, 0, -131, 0, 0, 30, 230, -108, 9, 0, 240, 0, 88, 0, -134, 76, 132, 141, 0, 0, -36, 0, 0, 51, 0, 0, 0, 46, 26, 69, 0, 48, 0, -14, 0, -123, -234, 18, 54, 0, 0, 84, 0, 0, 30, 0, 0, -42, 48, 156, -78, 0, -24, 0, -44, 0, -108, 6, 24, -190, 0, 0, 64, 0, 0, -98, 0, 0, 5, -82, 60, -43, 0, 26, 0, 28, 0, -12, -48, -108, 105, 0, 0, -12, 0, 0, 136, 0, 0, -37, -4, 222, 135, 0, 24, 0, 24, 0, 2, -98, -36, 38, 0, 0, -21, 0, 0, -172, 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, 21, 3, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 3, "minimal_twist": "105.2.s.c", "char_is_minimal": true, "conrey_index": 146, "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, 0], [0, 0, 0, -1, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, -1, 0, 0], [0, 0, 0, 0, -1, 1, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 1], [-1, -1, 0, 1, -1, 0, -1, 0], [0, 0, 0, -1, 1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, -1, 0, 0], [3, 0, 0, 0, 0, 0, 1, 0], [-1, -1, 0, -2, 3, -1, 1, -1], [0, 1, 0, 0, 1, 0, 0, -1], [1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 0, 1, 1, 0, -1, 0, 0], [0, -1, 0, -2, 4, -2, 0, -2], [-3, 0, 0, 0, -1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, 1, 0, -1, -1, 0], [1, 0, -2, 0, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -3, 0, -3, 0, -1], [-1, 1, 1, 0, -1, 1, 0, 0], [0, 0, 0, -1, 1, -1, 0, 2], [0, 2, 0, -1, -2, -1, 0, 0], [1, -3, -2, -1, 2, -3, 1, -1], [0, -3, 0, -1, 2, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, 2, 1, -3, -1, 1], [-2, 0, 2, 1, 0, -1, -3, 0], [3, 0, 0, 0, 0, 0, -1, 0], [-2, 0, 1, 0, 0, 2, 0, 1], [0, 0, 0, 1, 0, 1, 0, 0], [-4, 0, 1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 1, 0], [0, 4, 0, 0, -2, 0, 0, 2], [0, 0, 0, 0, 1, -1, -1, -1], [3, 0, -1, 4, 0, -4, -4, 0], [2, 0, -2, 0, 0, 0, 2, 0], [-3, 0, 0, 0, 1, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0], [-1, 0, -1, -3, 0, 1, 0, -1], [0, -1, 0, 1, -2, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, -4], [-2, -3, 1, -1, 2, 3, 1, -1], [0, 2, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, 0, 0, 2, -1, 0], [5, 0, -5, 2, 0, -2, 0, 0], [2, 0, 3, -1, 0, 1, -1, 0], [1, 1, 0, -1, 1, 0, 1, 0], [0, -1, 0, -4, 4, -4, 0, -3], [5, 0, -4, 4, 0, -4, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, 0, -4, 1, 0, -1, 2, 0], [0, 0, 0, 1, -1, 1, 0, 1], [-4, -1, 0, 5, 0, -1, -2, -1], [-1, 0, -1, -1, 0, 1, 1, 0], [0, 0, 2, 2, 0, -2, 0, 0], [-3, -3, 3, -2, 3, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, -2, 0, 0, 1], [1, 0, -2, 3, -1, 0, 1, -1], [0, 5, 0, 2, -3, 2, 0, 0], [0, 6, 0, 2, -8, 2, 0, 3], [0, 0, 0, -1, 0, 0, 0, 0], [0, -1, 0, 1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, -2, 2, -2, 0, 0], [6, 0, 3, -2, 0, 2, 0, 0], [0, 0, 0, -1, 0, 1, 0, 0], [2, 4, -2, 1, 1, 2, 1, 1], [0, 5, 0, -2, 2, -2, 0, -1], [3, 0, 2, -1, 0, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, -1, 0], [0, -2, 0, -1, 2, -1, 0, -1], [-8, 1, 0, 1, -3, 4, 2, 4], [2, 0, -4, 2, 0, -2, 2, 0], [0, 0, -1, -4, 0, 4, -1, 0], [1, 1, 0, 2, -3, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 5, -8, 5, 0, 0], [-5, -3, 1, -3, 0, -1, 3, -2], [0, -4, 0, 0, 4, 0, 0, -2], [0, -1, 0, 0, -1, 0, 0, 1], [-5, 4, 0, 2, -5, 3, 1, 3], [0, 5, 0, 5, -4, 5, 0, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -2, -2, -2, 6, 0, 2, -1], [-1, 0, 1, 0, 0, 0, 0, 0]]}