# Stored data for newform 152.2.c.a, downloaded from the LMFDB on 25 April 2024.
{"label": "152.2.c.a", "space_label": "152.2.c", "level": 152, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 137472508056, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 2216567448721081944, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [0, 1]]], "qexp_display": "q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "c", "char_is_real": true, "Nk2": 608, "analytic_conductor": 1.2137261107234618, "hecke_ring_index": 1, "level_radical": 38, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [152, 2, [39, 77, 97], [2, 1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [77], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.917", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.863", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "145.904", "prec": 24}], "related_objects": ["EllipticCurve/2.2.8.1/361.1/b", "ModularForm/GL2/TotallyReal/2.2.8.1/holomorphic/2.2.8.1-361.1-b"], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, 0, 0, 4], "traces": [0, 2, -2, 0, 0, 0, 0, 4, 4, 6, 0, 0, 0, 0, -4, 0, -8, 4, -6, 0, 0, 0, -8, -4, 0, 10, 4, 0, 0, 0, 0, -16, 8, 0, -4, 0, 0, 0, -2, 0, 0, -12, 0, 0, 16, 0, 4, -4, 0, -6, -10, 0, -8, 0, 0, 0, 8, 0, 4, 0, 0, 0, 16, 12, 0, 0, 0, 0, 0, 0, 0, -24, 12, -20, 20, 0, 4, 0, 0, 8, 0, 18, 12, 0, 0, 0, 8, 0, -16, 12, 0, 0, 0, 0, 4, 0, 0, -20, 6, 0, 0, 0, 0, 16, 8, 0, -4, 0, 0, 0, 0, 0, -16, -12, 0, 0, -8, 0, -24, 8, 0, -10, -16, 0, 0, 0, -12, 24, -16, 0, 0, 0, 0, 0, 8, 0, 8, -12, 0, 0, 0, 0, 24, 16, -24, 0, 20, 0, -40, 0, 0, 24, -4, 12, -16, 0, 0, 0, -8, 0, 0, -8, -18, 0, 0, 0, 8, -24, 0, 18, 0, 0, -16, 0, 0, 20, 0, 0, -12, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -36, 0, 28, 20, 0, 0, 0, -24, 44, 20, 0, 24, 0, 0, 0, -16, -12, 0, -8, 0, 0, 8, 0, 24, 0, 0, -32, -36, 0, 0, 0, 0, 8, 16, 30, 12, 0, 0, 0, 0, 0, 8, 36, 12, 0, 48, 0, -8, -12, 0, -4, 10, 0, 32, 0, 0, 4, -32, 0, 0, 0, 0, 0, -24, 0, 32, -44, 0, 0, 0, 0, 24, 12, 0, 0, -4, 0, -16, 0, 0, -60, -16, 0, 12, 0, 0, 0, 40, -48, 0, 12, 0, 0, 0, 0, -16, -24, 24, -26, 0, 0, 0, 0, 0, 0, 40, 0, 8, 0, 0, 0, -24, 0, 0, 0, -12, 0, 32, 0, 0, -36, 0, -12, -40, 0, 0, 0, 0, 16, 0, 0, 8, 0, 0, 0, 8, 0, -24, -8, 0, 0, -16, 0, 24, 0, 0, 52, -18, 0, 0, 0, -6, -40, 16, 0, -44, 0, 0, 0, -20, 0, 32, 60, 0, 0, 0, 0, -32, -36, 0, -2, 36, 0, -16, 0, 0, -4, 16, -36, 0, 0, 0, 0, -16, 0, -8, -8, 0, 0, 0, 0, 36, 32, 0, 0, -28, 0, 0, 0, 0, -8, -12, 0, 48, 0, 48, 0, -44, 0, -40, 12, 0, 0, -48, 0, 8, 80, 0, -12, 0, 0, 0, 0, 12, 0, -16, 0, 8, 0, 0, 0, -16, -12, -8, 20, 0, 0, -48, 0, 0, 16, 0, -4, 32, 0, 72, 0, 0, 40, 0, -18, 8, 0, 0, 0, -8, 0, 0, 76, -30, 0, 0, 0, 24, 0, 0, 52, -40, 0, 0, 0, 0, 68, 0, 0, -36, 0, -24, 0, 0, 0, -48, 32, 0, 0, 0, 0, 12, 84, 0, -40, 4, 0, 0, 0, 0, 24, -32, 0, 0, 0, 0, 0, -4, 0, 64, -48, 0, 0, 0, 0, -56, -44, 24, 0, 16, 0, 0, 0, 0, -40, -32, 0, 44, 0, 0, 0, 40, 0, 0, 4, 12, 0, -48, 0, -12, -32, 0, -38, 0, 0, 8, 0, 0, 0, 16, 0, 12, 0, 0, 0, 60, 0, 16, 0, 0, 0, 0, 0, -40, 4, 0, 16, -56, 0, -80, 0, 48, -16, 0, 0, -12, 0, 0, 0, 24, 36, -48, -60, 0, 0, 0, 0, 24, -20, 0, -84, 26, 0, 0, 0, 0, -16, -40, 0, 52, 0, 0, 0, 0, 0, 0, 12, 0, 0, -16, 0, -8, 80, 0, -20, 16, 0, 0, 0, 0, 16, 8, 0, 0, 0, 0, 0, -24, 0, -32, -52, 0, 0, 0, 0, 36, 24, 0, 50, 12, 0, 80, 0, 0, -52, 16, 0, -36, 0, 0, 0, -16, -72, 0, 28, 0, 0, 0, 0, -4, 44, 36, -96, 20, 0, -16, 0, 0, 0, 48, -60, 8, 0, 0, 0, -56, 0, 16, 0, 60, 0, 0, 0, 0, -64, 0, -68, -52, 0, 0, 0, 0, -40, 0, 0, 64, 0, 12, 0, 40, 0, 0, 8, 0, 0, 88, 0, 24, 0, 0, -24, -8, 0, 0, 0, 0, 20, -64, 0, -60, 0, 0, 0, 0, 24, 24, 32, 0, 0, 64, 0, 36, -4, 0, 32, 2, 0, -72, 0, 0, -52, 16, 54, 0, 0, 0, 0, 4, 0, -16, 32, 36, 0, 0, 0, -8, 88, 0, 0, 36, 0, 32, 0, 0, -8, 16, 0, 8, 0, 0, 0, 32, 0, 0, 84, 0, 0, 0, 0, -32, 48, 0, 28, 0, 0, 0, 0, 24, -80, -40, 0, -16, 0, 0, 0, 8, 0, 24, 0, 0, 0, -96, 0, 0, -24, -48, 32, -40, 0, 0, 0, 0, -8, 40, 36, -12, 0, 0, 0, -32, 0, 48, -36, 0, 0, -16, 0, -80, 0, 0, 8, 12, 0, 0, 0, 0, 60, 32, 0, -48, 0, 0, 0, 0, 0, 32, -12, 0, 0, 0, 0, 56, 0, 0, 50, -20, 0, 32, 0, 12, -20, 0, 0, -20, 0, 0, 0, -32, 0, 48, -28, 0, 0, 0, 0, -16, -8, 0, 0, 4, 0, 0, 0, 0, -16, -72, -60, 4, 0, 0, 0, -40, 0, 0, 60, 18, 0, -16, 0, -56, -24, 0, 48, 0, 0, 0, 0, 0, 0, -32, 0, -76, 0, 0, 0, 48, 0, -24, 0, 0, 0, -48, 0, 0, 72, 0, 32, -52, 0, 80, 0, 0, -68, 0, 0, -72, 0, 0, 0, -68, 48, -16, -36, 0, 0, 0, 0, -24, 0, 24, 52, 16, 0, 0, 0, 0, 24, 0, 0, -32, 0, 0, 0, -10, 0, 16, 52, -12, 0, 0, 0, -84, -24, 0, 66, 40, 0, 0, 0, 0, -4, -20, 0, 0, 0, 0, 0, -24, 0, 0, 44, 0, 0, 0, 0, 24, -16, 0, 0, 8, 0, 0, 0, 0, -112, -64, 0, 48, 0, 0, 0, -8, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "152.2.c.a", "char_is_minimal": true, "conrey_index": 77, "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], [-1, 1], [0, 0], [0, -2], [0, 0], [0, 0], [2, 0], [2, 2], [3, 0], [0, 0], [0, 4], [0, 0], [0, -2], [-2, 2], [0, 0], [-4, 0], [2, 0], [-3, 3], [0, 1], [0, 0], [0, 0], [-4, -4], [-2, 0], [0, 0], [5, 0], [2, 2], [0, 0], [0, -4], [0, -2], [0, 0], [-8, 0], [4, -4], [0, 0], [-2, 2], [0, 0], [0, -6], [0, -10], [-1, -1], [0, 0], [0, 0], [-6, 0], [0, 0], [0, -4], [8, 0], [0, 0], [2, -2], [-2, 0], [0, 0], [-3, 0], [-5, 5], [0, 0], [-4, 0], [0, 2], [0, 0], [0, 0], [4, 4], [0, 0], [2, 2], [0, 12], [0, 0], [0, 8], [8, -8], [6, 0], [0, 8], [0, 0], [0, 0], [0, -4], [0, -4], [0, 0], [0, 0], [-12, 0], [6, 6], [-10, 0], [10, 10], [0, 0], [2, 0], [0, 8], [0, 0], [4, 0], [0, 0], [9, 0], [6, -6], [0, -4], [0, 0], [0, 0], [4, 4], [0, 0], [-8, 8], [6, 0], [0, 0], [0, -4], [0, 4], [0, 0], [2, -2], [0, 0], [0, 0], [-10, 0], [3, -3], [0, 12], [0, -10]]}