# Stored data for newform 322.2.c.a, downloaded from the LMFDB on 23 April 2024. {"label": "322.2.c.a", "space_label": "322.2.c", "level": 322, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 137472508226, "dim": 4, "is_polredabs": true, "nf_label": "4.0.12544.1", "trace_hash": 2098959674571357959, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [2, 0, 1]], [5, [0, 1]]], "qexp_display": "q-q^{2}+\\beta _{1}q^{3}+q^{4}-\\beta _{1}q^{6}-\\beta _{3}q^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 161, "char_orbit_label": "c", "char_is_real": true, "Nk2": 1288, "analytic_conductor": 2.571182945085228, "hecke_ring_index": 2, "level_radical": 322, "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": [322, 2, [185, 281], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [2, 7, 23], "conrey_indexes": [321], "field_disc": 12544, "field_disc_factorization": [[2, 8], [7, 2]], "field_poly": [9, 0, 8, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.715", "prec": 17}, {"__RealLiteral__": 0, "data": "0.409", "prec": 17}, {"__RealLiteral__": 0, "data": "112.220", "prec": 24}, {"__RealLiteral__": 0, "data": "65.149", "prec": 20}, {"__RealLiteral__": 0, "data": "4299.495", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c2", "trace_display": [-4, 0, 0, 0], "traces": [0, 4, -4, 0, 4, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, -12, 0, -20, 0, 0, 0, 24, 0, 0, -4, 0, 0, 0, 4, 0, 0, -24, 0, 0, 0, 0, 0, 0, 12, 0, 0, 28, 20, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 24, -4, 0, 0, 0, 0, 0, 24, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -48, 0, 0, 0, 0, -28, 0, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, -12, 0, 32, 0, 0, 0, 32, -4, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, -16, -24, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 20, -16, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, 56, 0, -48, 0, 0, 0, 0, 12, 0, 48, 0, 0, 0, 0, 0, 0, -64, 0, 0, 28, 24, 0, 0, 20, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 56, -24, -72, 0, 0, 0, 0, 0, -24, 0, 0, 12, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 56, -32, 0, 4, 0, 0, 0, 0, 24, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 16, 0, 24, 0, 0, 0, -4, -68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 56, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, -20, 0, 16, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, -96, 0, 0, -56, 0, 0, 0, 48, 0, 0, 36, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, -28, -40, -24, 0, 0, 0, 0, 0, -20, 0, 0, -144, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 12, 0, 0, 24, 0, 0, 0, 0, 64, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 28, 0, 96, 0, 0, 0, 0, 0, 48, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -56, 104, 24, 0, 72, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 24, 0, 0, 0, 0, -56, -12, 0, 0, -64, 0, 0, 0, -144, 32, 0, 0, 0, 0, 0, 0, 128, 0, -112, 0, 0, 0, 0, -56, 0, 32, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 56, 0, 0, -24, 0, 0, 0, 0, 0, 0, -20, 0, 0, 56, 96, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 60, 4, 0, 68, 0, 0, -168, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 8, 0, -56, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, -24, 100, 0, 112, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -16, 72, 0, 0, 0, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 80, 0, 0, -20, 0, 0, 56, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 56, -36, 0, 0, -120, 0, 0, 0, -116, 0, 0, 0, 0, 0, 0, 12, -168, 0, -64, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, -16, -64, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 28, 0, 40, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 144, 104, 0, -96, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 24, 0, -64, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -24, 0, 0, -192, 0, 0, 0, 28, 0, 0, -64, 0, 0, 0, 0, 0, 0, 168, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, -136, 0, 0, 0, 0, -28, -64, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, -48, 0, -20, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 56, 0, -104, 0, -24, 0, 0, 0, -72, -160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, -96, 0, 144, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, -164, 0, 0, 0, 0, 56, -88, 12, 0, 0, 0, 0, 0, 64, 120, 0, 0, 0, 0, 0, 0, 144, 0, -32, 0, 0, 0, 0, -168, 0, 128, 0, 0, 0, 0, 0, 0, -128, 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, 7, 2, -1, 2, 0], [1, 1, 23, 2, -1, 2, 0], [1, 1, 161, 3, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "322.2.c.a", "char_is_minimal": true, "conrey_index": 321, "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], [-1, 0, 0, 0], [0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, -1], [-1, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 3, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, -1, 0], [-3, 0, -1, 0], [0, -1, 0, 0], [-5, 0, 0, 0], [0, -3, 0, 0], [0, 4, 0, 0], [0, 0, 0, -1], [6, 0, 0, 0], [0, 0, 0, 0], [0, 6, 0, 0], [-1, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 2], [-6, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 1, 0], [0, 0, -3, 0], [0, 0, 1, 0], [0, 0, 0, 0], [3, 0, 1, 0], [0, 2, 0, 0], [0, 1, 0, 0], [7, 0, 0, 0], [5, 0, 0, 0], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 1, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, -2, 0], [-6, 0, 0, 0], [0, -7, 0, 0], [0, 0, 0, 0], [0, 0, 0, 4], [0, -6, 0, 0], [0, 0, 0, -1], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 3, 0], [0, 0, 0, 0], [0, -3, 0, 2], [0, 0, 0, 0], [6, 0, 0, 0], [-1, 0, 0, 0], [0, -6, 0, 0], [0, 0, -3, 0], [0, -5, 0, 0], [0, 0, 0, -2], [0, -7, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 6], [0, 0, -1, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, 6, 0, 0], [0, 0, -1, 0], [0, 0, 0, 6], [0, 0, 0, 0], [0, 0, -3, 0], [-3, 0, -1, 0], [-12, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, -2], [-7, 0, 0, 0], [0, 0, 1, 0], [-5, 0, 0, 0]]}