# Stored data for newform 315.2.j.c, downloaded from the LMFDB on 20 April 2024. {"label": "315.2.j.c", "space_label": "315.2.j", "level": 315, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007817763586363, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 909697623394413941, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [4, -4, 6, 2, 1]]], "qexp_display": "q+(\\zeta_{12}-\\zeta_{12}^{2}+\\zeta_{12}^{3})q^{2}+(-2+2\\zeta_{12}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "j", "char_is_real": false, "Nk2": 1260, "analytic_conductor": 2.5152876636703323, "hecke_ring_index": 1, "level_radical": 105, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [315, 3, [281, 127, 136], [3, 3, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [46, 226], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.010", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "59.365", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1401.476", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 0, 2, 0], "traces": [0, 4, -2, 0, -4, 2, 0, 0, 24, 0, 2, -2, 0, 16, -18, 0, -16, 10, 0, -2, -8, 0, -8, -6, 0, -2, -2, 0, 24, -4, 0, -6, -16, 0, -8, 0, 0, -4, -14, 0, 12, -4, 0, -8, 8, 0, -12, 4, 0, -22, 4, 0, -4, 4, 0, -4, 12, 0, -16, 10, 0, -8, -12, 0, 64, 8, 0, 12, 8, 0, -12, -4, 0, -8, 14, 0, 56, -12, 0, -6, 16, 0, -4, -12, 0, 20, -14, 0, 0, 6, 0, -6, 48, 0, 4, 2, 0, 32, -4, 0, -4, -18, 0, 8, 72, 0, -80, -6, 0, -22, -4, 0, -72, -8, 0, 6, -32, 0, 16, 12, 0, 14, -8, 0, 12, -4, 0, 40, -48, 0, 2, 24, 0, -36, -84, 0, 48, -6, 0, -4, -12, 0, 20, -14, 0, -2, 76, 0, -56, -16, 0, 4, -36, 0, 0, -12, 0, 8, 30, 0, -32, -18, 0, -16, -8, 0, 48, 36, 0, 24, -4, 0, -28, 36, 0, 0, -16, 0, 48, -20, 0, -28, -54, 0, -48, 4, 0, 16, -16, 0, -28, -4, 0, 8, -40, 0, 52, 36, 0, -44, -12, 0, 24, 18, 0, -2, 26, 0, -40, -20, 0, 56, 80, 0, 12, -4, 0, -24, 44, 0, -8, 46, 0, -40, 96, 0, 28, 14, 0, 6, -24, 0, 48, 0, 0, -4, -16, 0, -24, -56, 0, -20, 26, 0, 32, 4, 0, 4, -12, 0, 2, 36, 0, 0, -2, 0, -32, 6, 0, 54, -8, 0, 36, -4, 0, 8, 36, 0, 84, -32, 0, -20, -112, 0, -24, -2, 0, 12, -22, 0, 36, 0, 0, 24, 40, 0, -32, 6, 0, -22, 16, 0, -76, -48, 0, 20, 12, 0, 32, -18, 0, 18, -56, 0, -64, 8, 0, -80, 0, 0, -6, -6, 0, 8, 56, 0, -120, 2, 0, 20, 32, 0, 48, 4, 0, -8, -64, 0, 0, 0, 0, -30, 96, 0, -48, 24, 0, -32, 36, 0, -8, -18, 0, 0, 24, 0, 24, -56, 0, 88, 6, 0, 32, 18, 0, -2, -192, 0, 40, -6, 0, 12, 74, 0, 72, -16, 0, -12, -72, 0, 28, -72, 0, -8, -20, 0, 24, -52, 0, -44, 28, 0, -28, -12, 0, 6, 20, 0, -80, 42, 0, -48, -132, 0, 12, 6, 0, 52, 88, 0, 32, -12, 0, -36, -24, 0, -36, 44, 0, -34, 4, 0, -104, 36, 0, -6, -16, 0, 4, 128, 0, 28, -4, 0, 96, 10, 0, 0, -48, 0, 14, 0, 0, 40, 6, 0, -44, -18, 0, -8, 0, 0, 16, 12, 0, -6, 56, 0, 48, 88, 0, 8, 56, 0, 32, -18, 0, 16, 6, 0, 24, 36, 0, 96, -56, 0, 60, -28, 0, -60, 8, 0, 24, 22, 0, 4, 144, 0, 4, -24, 0, -34, 64, 0, -104, 16, 0, 32, -48, 0, -26, 56, 0, -28, -38, 0, 0, -18, 0, 34, 4, 0, -72, -16, 0, -36, 12, 0, -4, 16, 0, 60, 64, 0, -24, -8, 0, -8, -12, 0, 36, -4, 0, 52, -144, 0, -64, 42, 0, 22, -40, 0, 36, -28, 0, 6, 132, 0, 40, 26, 0, 30, 4, 0, 32, -44, 0, -8, 24, 0, 4, -34, 0, 108, -84, 0, -44, -12, 0, -68, -48, 0, 48, -36, 0, -4, -132, 0, -96, 6, 0, -58, 32, 0, 0, 12, 0, -40, 38, 0, -64, -42, 0, -32, -108, 0, 48, -156, 0, -36, 8, 0, 40, -10, 0, -6, -128, 0, -24, -28, 0, -28, -18, 0, 56, -14, 0, 4, 224, 0, -16, 16, 0, 40, 82, 0, -48, 48, 0, 74, -12, 0, -72, 126, 0, -2, 38, 0, -56, -76, 0, 112, 36, 0, -100, 20, 0, -88, 8, 0, 48, 18, 0, -72, 48, 0, 52, 10, 0, 28, 4, 0, 256, -58, 0, -24, -8, 0, -24, 16, 0, -14, -6, 0, -240, -24, 0, -12, -96, 0, -42, 16, 0, -144, -74, 0, 72, -42, 0, 24, 96, 0, 12, -18, 0, -12, 114, 0, -40, -20, 0, 10, -96, 0, 64, -2, 0, -16, -44, 0, -36, -28, 0, 32, 16, 0, 48, -12, 0, 16, -20, 0, 120, 12, 0, -28, -40, 0, 0, -48, 0, 54, 24, 0, 148, 2, 0, -88, 12, 0, 38, -38, 0, 20, 60, 0, 192, -18, 0, -14, -28, 0, -48, -68, 0, 16, -86, 0, 80, 54, 0, -50, 32, 0, -52, 8, 0, -56, -38, 0, 36, 90, 0, 0, 112, 0, -72, 58, 0, 140, 0, 0, -20, 42, 0, -6, 288, 0, 24, -10, 0, -16, 36, 0, -32, 16, 0, -20, 24, 0, 60, -24, 0, -32, 70, 0, -88, 92, 0, 40, -16, 0, -48, 22, 0, -12, -60, 0, -96, -4, 0, 0, 48, 0, 8, 16, 0, -32, -28, 0, -16, -6, 0, -16, 84, 0, -12, 112, 0, 30, -48, 0, 160, -130, 0, 18, 8, 0, -76, 44, 0, -4, 10, 0, -8, 12, 0, 36, -352, 0, 4, 6, 0, -24, 48, 0, 0, 34, 0, -8, -56, 0, -120, 8, 0, -36, -38, 0, -36, 84, 0, 18, -132, 0, 120, 0, 0, 36, 4, 0, -8, 16, 0, 152, -16, 0, 24, -54, 0, -18, 96, 0, 112, 4, 0, -40, -144, 0, -92, 42, 0, 16, 8, 0, -144, -14, 0, -36, -32, 0, -36, 52, 0, -36, 46, 0, -24, 36, 0, 34, 48, 0, 72, 20, 0, 8, -54, 0, -128, -46, 0, -4, -240, 0, 20, -16, 0, 120, -66, 0, -8, -22, 0, 0, -16, 0, 16, 6, 0, -2, -14, 0, -48, -8, 0, 4, 8, 0, -96, -36, 0, 20, 50, 0, -64, 16, 0, 8, 108, 0, 40, -48, 0, 24, 44, 0, -64, -2, 0, 72, 44, 0, -112, 30, 0, 18, -136, 0, 152, -6, 0, -34, 48, 0, 72, -88, 0, 60, 22, 0, -24], "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, 7, 3, 1, 3, 0]], "char_orbit_index": 10, "prim_orbit_index": 3, "minimal_twist": "105.2.i.d", "char_is_minimal": true, "conrey_index": 46, "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, 1, -1, 1], [0, 0, 0, 0], [-2, 2, 2, -4], [0, 0, 1, 0], [0, 0, 0, 0], [0, -1, 0, 3], [6, -4, 0, 2], [0, 0, 0, 0], [1, -1, -1, 2], [-1, -1, 1, 2], [0, 0, 0, 0], [4, 2, 0, -1], [-5, 3, 1, -2], [0, 0, 0, 0], [0, 4, -8, 4], [5, 1, -5, -2], [0, 0, 0, 0], [0, 2, -1, 2], [-2, 4, 0, -2], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 1, -3, 1], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 3, -1, 3], [0, 0, 0, 0], [2, -4, 8, -2], [-1, -6, 0, 3], [0, 0, 0, 0], [-3, -2, 3, 4], [-8, 8, 8, -16], [0, 0, 0, 0], [-2, 8, 0, -4], [0, -3, 0, 2], [0, 0, 0, 0], [0, -3, -2, -3], [-7, 3, 7, -6], [0, 0, 0, 0], [0, -2, 6, -2], [-1, -2, 0, 1], [0, 0, 0, 0], [-2, -6, 0, 3], [0, 0, 4, 0], [0, 0, 0, 0], [-6, 4, 6, -8], [0, 0, 2, 0], [0, 0, 0, 0], [-3, 0, -5, 0], [1, -2, 0, 1], [0, 0, 0, 0], [-2, 6, 2, -12], [2, -6, -2, 12], [0, 0, 0, 0], [-1, -2, 0, 1], [8, -6, -10, 18], [0, 0, 0, 0], [0, 2, -8, 2], [5, 3, -5, -6], [0, 0, 0, 0], [0, 0, -4, 0], [-3, -2, 0, 1], [0, 0, 0, 0], [16, -16, 0, 8], [0, 1, 4, 1], [0, 0, 0, 0], [6, -5, -6, 10], [0, -8, 4, -8], [0, 0, 0, 0], [-1, 2, -4, 1], [-1, 6, 0, -3], [0, 0, 0, 0], [-4, 5, 4, -10], [7, -1, -7, 2], [0, 0, 0, 0], [14, -12, 0, 6], [-1, -2, -4, -1], [0, 0, 0, 0], [0, -6, -3, -6], [8, -4, -8, 8], [0, 0, 0, 0], [0, 0, -2, 0], [-3, 14, 0, -7], [0, 0, 0, 0], [5, 2, 0, -1], [0, 1, -7, 1], [0, 0, 0, 0], [0, -4, 0, 8], [0, -7, 3, -7], [0, 0, 0, 0], [-4, -4, 5, 12], [12, -16, 0, 8], [0, 0, 0, 0], [2, -2, -2, 4], [1, -2, -1, 4], [0, 0, 0, 0], [8, -8, 0, 4], [-5, 2, 8, -13], [0, 0, 0, 0], [0, 2, -2, 2]]}