# Stored data for newform 552.2.j.a, downloaded from the LMFDB on 19 April 2024. {"label": "552.2.j.a", "space_label": "552.2.j", "level": 552, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 618508845608, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 2130328210773545285, "analytic_rank": 1, "is_twist_minimal": true, "hecke_cutters": [[5, [4, 1]]], "qexp_display": "q+\\beta q^{2}+(-1+\\beta )q^{3}-2q^{4}-4q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 24, "char_orbit_label": "j", "char_is_real": true, "Nk2": 2208, "analytic_conductor": 4.407742191574677, "hecke_ring_index": 1, "level_radical": 138, "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": "0.520", "prec": 17}, "analytic_rank_proved": true, "char_values": [552, 2, [415, 277, 185, 97], [1, 1, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 23], "conrey_indexes": [323], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.052", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.522", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "164.473", "prec": 24}], "related_objects": ["ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-529.1-b", "EllipticCurve/2.2.24.1/529.1/b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -2, -8, 0], "traces": [0, 2, 0, -2, -4, -8, -4, 0, 0, -2, 0, 0, 4, 0, -8, 8, 8, 0, 8, -4, 16, -8, -16, 2, 8, 22, 16, 10, 0, 0, 16, 0, 0, -16, -8, 0, 4, 0, 0, 16, 0, 0, 8, -12, 0, 8, 0, 0, -8, -2, 0, -8, 0, -24, -4, 0, 16, 4, 0, 0, -16, 0, 16, 16, -16, 0, 16, 4, 0, -2, 32, -16, -16, -12, -8, -22, 8, -32, -16, 0, -32, -14, 16, 0, 16, 0, 0, 0, 32, 0, -32, 32, -4, 16, 0, 16, -16, -4, 0, 32, -44, 16, 8, 0, -32, 32, 0, 0, -20, 0, 64, -8, 0, 0, 8, -8, 0, -32, 8, -16, -32, -42, 8, 16, 0, -48, 8, 0, 0, 12, -64, 0, 32, 0, 0, -40, 16, 0, -4, 20, 0, 0, 0, 64, -8, 0, 0, 2, 0, -24, -44, 0, 0, 16, 0, 0, -32, 0, -8, 24, 0, 0, -16, -12, 0, 64, 16, -48, -16, -38, 32, 4, 24, 32, 0, 0, 0, 8, 24, 0, -16, 0, 0, 8, 0, 0, -16, -32, 0, -8, 0, -48, 16, 36, 0, -64, 4, 32, 16, 0, 0, -4, 0, 0, 16, 0, -8, -2, 0, 0, -32, -20, 48, 16, 32, 48, 8, 32, 24, 12, 0, 32, 8, 0, -32, -22, 8, 0, -8, 0, 0, 32, 0, 0, -16, 0, 0, -8, 0, -48, 32, -28, 0, -2, 0, 8, -16, 0, -32, 16, 0, 0, -32, 0, -48, 32, 32, 0, 24, -16, 0, 0, 8, 48, -32, 96, 16, 24, -8, -32, 16, 0, 0, -32, -8, 0, 4, 0, 0, -32, -64, 0, 0, 44, 32, -16, 0, 32, 32, 18, 0, 4, 24, -8, 4, 0, 16, -16, 0, 0, 44, 0, 32, -16, -16, 0, 8, -20, 64, -8, -64, 32, 32, -52, -56, -64, 0, 32, 48, 0, 64, 32, -8, 0, 28, 0, 0, 24, -32, 0, -64, 4, 0, 16, 0, -16, -32, -36, 0, 8, 0, 64, -16, 0, 0, 8, 0, 0, 0, 0, -88, 16, -64, 0, -8, 64, 0, 16, -40, -32, 64, -30, -24, 42, -64, 48, -8, 0, 8, -32, 32, 0, -32, 0, 0, 48, 0, 0, -40, 36, -32, -48, 0, 0, 32, 128, 0, 12, 8, -72, 64, 0, 0, 8, 0, 0, -64, 0, 24, 16, 88, 0, -8, -64, -32, 56, 0, -32, -16, -60, -64, -8, 0, 16, 8, 0, 64, -20, 32, 0, -64, 0, 0, 0, 0, 0, 32, 16, 0, -64, 0, -48, 40, 28, 0, 0, 0, -4, 24, 0, -128, 2, 0, 0, 16, 0, -32, 24, 0, 0, 88, 64, 0, 32, 32, -128, -16, -76, 24, -8, 16, -64, 64, 0, 0, -64, -48, 0, 64, 0, 0, -56, -16, 0, 8, -44, 32, 24, 0, 32, 64, 32, 0, -8, 84, 16, 44, 0, -16, 12, 0, 0, -32, 0, -32, -128, 0, 0, -16, 12, 96, 48, 0, 0, -16, -64, -16, 38, 0, 0, -32, 0, 0, -20, 80, 0, -24, 0, 0, -32, 128, 0, 0, -60, 0, -88, 0, 32, -64, 2, 0, -16, 0, -64, -24, 0, 0, -40, 0, 0, 80, 0, -16, -24, -32, 0, -64, -44, 0, -16, -176, 0, 8, -16, -16, 32, -40, -24, -16, 0, 0, 32, 56, 0, 0, 0, 0, -32, 0, 0, -32, 60, -128, 48, 0, 22, 16, -36, 0, -36, 0, 32, 8, 0, 0, 128, 0, 0, -4, 0, -32, -32, 0, 0, -80, 64, 48, 24, 16, 48, 88, 4, 48, -4, 0, 168, -32, 0, 0, 0, -32, 0, -32, 0, 0, -64, 0, 0, 8, -52, 0, 10, 0, 48, 64, 82, 0, 32, 0, -16, -32, 0, 16, 20, 0, 0, -48, 0, 0, 16, 0, 0, -32, -52, 0, -48, 16, -64, 32, 32, 176, -32, 24, -48, -24, 0, 0, 12, 0, 0, -128, 0, 0, -32, -32, 0, 8, 0, 96, -32, 0, 32, 32, 44, 0, 110, 76, -24, -8, 0, -64, 32, 0, 0, -8, 0, -48, 24, -48, 0, 16, 20, -64, 32, 40, -80, 0, 32, 0, -48, 0, 72, 80, 0, 0, 0, -80, 0, -16, 0, 0, 16, -48, 0, 32, -256, 0, 48, 0, 32, 32, -16, 0, 28, 0, 0, 84, 0, 0, 46, 0, 0, -16, 0, -40, -8, 0, 0, -16, -4, 0, -32, 96, -48, 32, 96, -24, -32, 64, 64, 96, 0, 0, 0, 0, 0, 16, 0, 0, -16, 0, 0, 48, 48, 96, -64, 0, -32, -32, -60, 0, 80, -72, 40, -48, 0, 0, 16, 0, 0, 128, 0, -8, 0, -8, 0, -8, -20, -64, -48, 32, 16, -32, -32, 64, -96, 0, 56, -16, 0, 0, -48, 104, 0, 8, 0, 0, 32, 0, 0, 64, -100, 0, -16, 0, 48, -32, 24, 0, -32, 0, 48, 8, 0, 16, -176, 0, 0, 4, 0, -64, -16, 0, 0, -40, 192, 0, 16, 16, 80, 64, -58, 104, 56, 40, 152, 0, 0, -96, -44, -88, 0, -32, 0, 0, -16, -64, 0, -128, 44, -96, -32, 0, 96, -16, -128, 0, -18, -64, -32, 0, 0, -48, 4, 0, 0, -24, 0, 64, 8, 0, 0, -8, 52, -64, -32, -24, 0, -16, -96, -96, -64, 0, 0, 48, 0, 64, 16, 0, 0, 44, 0, 0, 48, -16, 0, -32, 84, 0, -16, 0, -48, 16, 64, 0, -32, 0, 16, -40, 0, 0, 20, 0, 0, -64, 0, -96, 16, 0, 0, 64, 4, 0, -32, 16, 128, 32, 76, -16, 52, 0, -56, 56, 0, 0, 32, 96, 0, 16, 0, 0, -32, 0, 0, -96, 192, 96, 0, 0, -16, -64, -2, 0, -64, 56, -144, 8, 0, 0, 16, 0, 0, 4, 0, 0, 176, 0, 0, 24, 96, -16, -48, -104, 0, 32, -128, 0, 0, 0, -12, -64, 0, 64, -4, 64, 0, -32, 0, 0, -8, 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, 24, 6, 1, 2, 0]], "char_orbit_index": 10, "prim_orbit_index": 6, "minimal_twist": "552.2.j.a", "char_is_minimal": true, "conrey_index": 323, "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], [1, 0], [0, 1], [-1, 1], [-2, 0], [-4, 0], [-2, -1], [0, 2], [0, -2], [-1, -2], [0, -4], [0, 4], [2, -2], [0, -4], [-4, 0], [4, -4], [4, 0], [0, 2], [4, -1], [-2, 0], [8, 0], [-4, -2], [-8, 0], [1, 0], [4, 2], [11, 0], [8, 0], [5, 1], [0, -4], [0, 0], [8, 4], [0, -4], [0, 4], [-8, -4], [-4, 0], [0, -8], [2, 4], [0, 2], [0, -2], [8, 4], [0, 8], [0, -4], [4, -4], [-6, 0], [0, -8], [4, 8], [0, 1], [0, 0], [-4, 4], [-1, 0], [0, 11], [-4, -2], [0, 8], [-12, 0], [-2, 5], [0, -16], [8, 0], [2, -2], [0, 0], [0, -2], [-8, 8], [0, -2], [8, 0], [8, -2], [-8, 0], [0, 16], [8, -8], [2, 0], [0, -4], [-1, 1], [16, 0], [-8, 0], [-8, 2], [-6, 0], [-4, 0], [-11, 11], [4, 0], [-16, 0], [-8, 8], [0, 2], [-16, 0], [-7, 4], [8, 0], [0, -4], [8, 4], [0, -8], [0, -6], [0, 0], [16, 0], [0, -6], [-16, 4], [16, 0], [-2, 0], [8, 4], [0, 0], [8, 0], [-8, -4], [-2, 0], [0, -1], [16, -4], [-22, 0]]}