# Stored data for newform 55.2.e.b, downloaded from the LMFDB on 18 April 2024.
{"label": "55.2.e.b", "space_label": "55.2.e", "level": 55, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538831927, "dim": 4, "is_polredabs": true, "nf_label": "4.0.1936.1", "trace_hash": 2301911465009835400, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [0, 1]]], "qexp_display": "q+(-1+\\beta _{1}-\\beta _{3})q^{3}+2\\beta _{2}q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 55, "char_orbit_label": "e", "char_is_real": false, "Nk2": 220, "analytic_conductor": 0.4391772111170421, "hecke_ring_index": 1, "level_radical": 55, "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": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.687", "prec": 17}, "analytic_rank_proved": true, "char_values": [55, 4, [12, 46], [1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [5, 11], "conrey_indexes": [32, 43], "field_disc": 1936, "field_disc_factorization": [[2, 4], [11, 2]], "field_poly": [9, 0, -5, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.731", "prec": 17}, {"__RealLiteral__": 0, "data": "0.277", "prec": 17}, {"__RealLiteral__": 0, "data": "105.065", "prec": 24}, {"__RealLiteral__": 0, "data": "30.856", "prec": 20}, {"__RealLiteral__": 0, "data": "4523.892", "prec": 27}], "related_objects": [], "self_twist_discs": [-11], "cm_discs": [-11], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.1.d4", "trace_display": [0, -2, 0, 0], "traces": [0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -8, -16, 0, 0, 0, 12, 0, 0, 18, 0, 2, 0, 22, 0, 0, 0, 0, 0, -22, 0, 0, 24, -14, 0, 0, 0, 0, 0, 0, 0, -18, 0, -24, 8, 0, 0, 0, 0, -12, 0, 22, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, -12, 0, 0, 0, 32, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 66, 0, 0, 0, -34, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -44, 0, 0, -52, 0, -42, 0, -38, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44, 0, 0, 44, 0, 6, 0, 0, 0, 68, 0, 0, 0, 0, 0, -14, 28, 0, 0, 0, 0, 0, 0, -66, 0, 46, 0, 0, 0, 0, 0, -32, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 44, 0, 0, 0, 0, 12, 0, 0, 48, 0, 0, 0, 16, 0, 0, 0, -56, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, -24, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -66, 0, 0, 0, 0, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 32, 0, 0, 4, 0, 42, 0, 0, 0, 0, 0, 108, 0, -22, 0, 0, 64, 36, 0, 0, 0, 0, 0, 0, 0, 62, 0, -18, -52, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 22, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 38, 0, 0, 0, -54, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 72, 0, 0, 0, 0, 0, -132, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, -72, 0, 0, 0, 0, -76, 0, -22, 0, 0, 0, -74, -72, 0, 0, 0, 132, 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 88, -4, 0, 0, -8, 0, 0, 0, 0, -66, 0, 66, 0, 0, 0, 148, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -116, 0, 0, 0, 0, 0, 0, 0, 0, -88, 58, 0, 0, 0, 0, 0, 0, 0, 84, 0, -42, 0, 54, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, -62, 0, -66, 0, 6, 0, 0, 0, -112, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, -18, 0, 86, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, -78, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, -44, 0, 0, 0, 0, 0, 42, 0, 0, 44, 0, 0, 66, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, -154, 0, 42, -96, -94, 0, 0, 0, 0, 0, 88, 0, 0, 0, 96, 28, 0, 0, 0, 56, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 176, 0, 0, 0, -98, 0, 0, -92, 0, 0, 28, 0, 0, 0, 0, -152, 0, 0, 0, 0, 0, 0, -82, 0, 0, 0, -54, 0, 0, 0, 0, -64, -102, 0, 0, 0, 0, 0, 0, -88, -52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 104, 0, 0, 0, 0, 0, 0, 48, 0, -68, 0, -198, 0, 0, 0, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 154, 0, 0, -44, 0, 0, 0, 0, 66, 0, 0, 168, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 106, 0, 0, 0, 0, 0, 0, 0, -98, 0, 66, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 96, -54, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, -212, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 114, 0, 6, 0, 0, 0, 108, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 98, 0, 22, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 0, -116, 0, 0, 0, -78, 0, 0, 48, 0, 0, -192, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, -34, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, -88, 228, 0, -112, 0, 44, 0, 0, 0, 0, 0, -132, -4, 0, 0, -126, 0, 0, 0, 0, 12, 0, 0, 0, 0, -66, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 108, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, -114, 0, 0, 0, 208, 0, 0, 0, 154, 0, 0, 0, 0, 112, 272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, -102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, -11], [1, 1, 5, 3, -1, 4, 0], [1, 1, 55, 5, 1, 4, 0]], "char_orbit_index": 5, "prim_orbit_index": 5, "minimal_twist": "55.2.e.b", "char_is_minimal": true, "conrey_index": 32, "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, 1, 0, -1], [0, 0, 2, 0], [0, -1, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, -3, 2], [0, 0, 0, 0], [0, -2, 1, 0], [0, 2, -2, 2], [0, 0, 0, 0], [0, 0, 0, 0], [-3, -1, 4, -2], [-4, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [4, 1, -5, -1], [0, 0, 0, 0], [2, 0, 0, 3], [0, 0, 0, 0], [5, -1, 6, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 6, -3, 0], [0, 0, 0, 0], [-6, 1, 5, -1], [0, 0, 0, 0], [0, 0, 0, 0], [6, -4, 2, 0], [-5, -3, -2, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 0, 0, -4], [-3, 3, -7, 3], [0, 0, 0, 0], [-5, 2, -7, 2], [4, -4, 0, 4], [0, 0, 7, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-1, -4, 5, 4], [0, 0, 0, 0], [7, 0, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 2], [-8, 4, -6, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [5, -3, 8, -3], [0, 0, 0, 0], [-4, 0, -1, -8], [0, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [7, -1, 9, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 4, 4, 0], [-2, 6, -3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 9, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10, 2, 8, 2], [18, -3, -15, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-10, -3, -7, -3], [0, 0, 0, 0], [3, 0, -11, 6], [0, -6, 4, 0]]}