# Stored data for newform 315.2.j.g, downloaded from the LMFDB on 25 April 2024.
{"label": "315.2.j.g", "space_label": "315.2.j", "level": 315, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27022216273068347, "dim": 6, "is_polredabs": true, "nf_label": "6.0.4406832.1", "trace_hash": 316376246566721208, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [36, -24, 28, -4, 8, -2, 1]]], "qexp_display": "q+(\\beta _{1}-\\beta _{2}+\\beta _{4})q^{2}+(-2+\\beta _{1}+\\beta _{3}+\\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": 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": "0.004", "prec": 17}, "analytic_rank_proved": true, "char_values": [315, 3, [281, 127, 136], [3, 3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [46, 226], "field_disc": -4406832, "field_disc_factorization": [[-1, 1], [2, 4], [3, 3], [101, 2]], "field_poly": [1, 5, 24, 7, 6, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.016", "prec": 17}, {"__RealLiteral__": 0, "data": "5.698", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "128.379", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5436.104", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 0, 3, 1], "traces": [0, 6, 2, 0, -6, 3, 0, 1, -12, 0, -2, 10, 0, 14, -2, 0, -4, -2, 0, 1, -12, 0, 4, 10, 0, -3, 0, 0, -8, -8, 0, 1, 24, 0, -24, -1, 0, -11, -28, 0, -6, -4, 0, -6, 30, 0, 16, -2, 0, -3, -4, 0, -24, 4, 0, 20, 42, 0, 14, 4, 0, 22, -60, 0, 40, 7, 0, 15, -10, 0, 14, -32, 0, -9, 6, 0, -60, 26, 0, 7, 4, 0, 6, -28, 0, -4, 18, 0, -40, -30, 0, -3, 36, 0, 32, -1, 0, -8, 68, 0, -6, -4, 0, -21, -68, 0, 48, 32, 0, 5, 2, 0, 56, -16, 0, -10, -14, 0, 44, 14, 0, -15, -30, 0, 10, -6, 0, -42, 8, 0, 0, 2, 0, -29, 72, 0, 16, -8, 0, -34, 20, 0, -58, 38, 0, -4, -100, 0, -8, 14, 0, 16, -58, 0, -88, 2, 0, -26, 32, 0, 48, 50, 0, 28, -38, 0, -8, 48, 0, -16, -12, 0, 20, -22, 0, -2, -48, 0, 46, 16, 0, -26, -30, 0, 56, 11, 0, 2, -8, 0, -56, 4, 0, -7, 22, 0, 6, -48, 0, 12, 6, 0, 108, -40, 0, -2, 6, 0, -20, 8, 0, -32, 20, 0, -20, -3, 0, 70, 104, 0, -30, 0, 0, 40, 24, 0, 28, -16, 0, 25, 32, 0, -72, 14, 0, 2, 82, 0, 18, -116, 0, 26, -24, 0, -80, 6, 0, 3, -18, 0, -2, 28, 0, 36, -52, 0, -8, 12, 0, -47, -48, 0, -72, 26, 0, 8, -50, 0, 32, 26, 0, 12, 72, 0, 24, 10, 0, 27, 28, 0, 54, -52, 0, 15, 46, 0, -8, -50, 0, 39, -14, 0, -68, -20, 0, 8, -30, 0, -28, 8, 0, -7, 100, 0, 112, -22, 0, 58, -114, 0, -30, 28, 0, -11, 56, 0, -12, -6, 0, -8, 20, 0, 92, -56, 0, -7, -28, 0, -160, -46, 0, -17, 2, 0, -28, 30, 0, -26, -30, 0, 10, -42, 0, -74, 68, 0, -40, 60, 0, 4, 16, 0, -100, 24, 0, -16, 124, 0, -40, -8, 0, -26, 16, 0, -28, -18, 0, -33, -108, 0, 12, -28, 0, 3, -50, 0, -12, -8, 0, 106, -30, 0, 52, 56, 0, -2, 116, 0, 32, -36, 0, 32, -90, 0, 32, -7, 0, 49, 60, 0, 8, -16, 0, 41, -14, 0, -80, -24, 0, 57, -6, 0, 176, 38, 0, -14, 76, 0, 138, 144, 0, -66, -90, 0, -32, -2, 0, 16, -76, 0, -18, 2, 0, -62, -60, 0, 50, 80, 0, 28, -80, 0, -76, 18, 0, 30, 32, 0, -60, 80, 0, 28, -28, 0, -152, -27, 0, -39, 2, 0, 18, 12, 0, 90, -72, 0, -24, -56, 0, -40, 64, 0, -156, -44, 0, -2, 58, 0, -20, 6, 0, -1, 36, 0, 148, -4, 0, -49, -36, 0, 52, -76, 0, -14, -110, 0, 88, 56, 0, 9, 6, 0, -50, 40, 0, -8, -122, 0, 76, -52, 0, 32, 144, 0, 28, 21, 0, 64, -54, 0, -34, 44, 0, -17, 64, 0, 120, -30, 0, -63, 24, 0, 200, 60, 0, -32, -34, 0, -104, 28, 0, 17, -26, 0, 28, 10, 0, -32, -82, 0, -2, 54, 0, -23, 20, 0, -26, -78, 0, -82, -20, 0, -24, -8, 0, -8, -44, 0, 120, 58, 0, -47, 110, 0, -132, -20, 0, 15, -20, 0, -28, -32, 0, -4, 118, 0, -76, -24, 0, -106, 22, 0, 40, -60, 0, 16, 24, 0, 106, -18, 0, -30, 24, 0, 92, 15, 0, -69, 128, 0, -60, 34, 0, 44, 0, 0, -20, -24, 0, -25, -10, 0, 108, -12, 0, -3, -110, 0, 24, 12, 0, -56, 2, 0, -40, -21, 0, 23, 172, 0, -8, -26, 0, -178, -138, 0, -32, 4, 0, -68, 0, 0, -72, -50, 0, -2, -96, 0, 52, -168, 0, 3, 42, 0, -48, 26, 0, -74, 2, 0, 36, 108, 0, 154, -8, 0, -8, -10, 0, -2, 32, 0, -114, 60, 0, -16, -62, 0, -8, 0, 0, 47, -24, 0, 104, -17, 0, -6, 52, 0, 28, 92, 0, -25, 48, 0, 248, -122, 0, 34, 58, 0, 64, 36, 0, 76, 40, 0, -106, 82, 0, 107, -112, 0, 50, 4, 0, 94, 110, 0, -50, -18, 0, -27, -200, 0, 8, -26, 0, 41, -4, 0, -36, -144, 0, -14, -44, 0, -88, 40, 0, 73, -48, 0, 72, 32, 0, -116, 26, 0, 58, 8, 0, -54, 96, 0, 8, 64, 0, 74, -32, 0, -4, -6, 0, 1, 112, 0, -124, 56, 0, -20, -2, 0, -208, -52, 0, -36, 122, 0, 64, -80, 0, 32, -10, 0, -52, -64, 0, 64, 24, 0, -16, 36, 0, -14, -168, 0, 20, -58, 0, -24, 44, 0, 24, -28, 0, 25, -4, 0, -76, 70, 0, 26, 134, 0, -224, -28, 0, 61, 8, 0, 56, 52, 0, 24, -122, 0, 88, 72, 0, -86, 52, 0, 64, -8, 0, 127, -144, 0, 12, 90, 0, 86, 72, 0, -12, 48, 0, 52, 40, 0, 56, -38, 0, 22, -16, 0, 28, 104, 0, 11, -90, 0, 72, -1, 0, -34, 30, 0, -24, -236, 0, 78, -34, 0, -12, 32, 0, 65, 92, 0, 0, 54, 0, 32, -8, 0, -28, -24, 0, 24, 140, 0, -144, -13, 0, -19, -94, 0, 42, -36, 0, -22, 156, 0, -180, 142, 0, -65, -56, 0, -134, -8, 0, 22, 20, 0, 12, -78, 0, 166, -224, 0, 64, -2, 0, -98, -60, 0, -4, 36, 0, -98, -384, 0, 128, 92, 0, -27, -28, 0, -4, 104, 0, -4, 156, 0, -200, -106, 0, -46, -30, 0, -36, -14, 0, -42, 118, 0, -22, 30, 0, -105, -152, 0, 52, -22, 0, -152, -42, 0, 20, -40, 0, -24, -12, 0, -184, -2, 0, -15, -24, 0, 100, 24, 0, 33, -58, 0, 12], "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": "315.2.j.f", "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, 0, 0], [1, 0, 0, 0, 0, 0], [0, 1, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0], [-2, 1, 0, 1, 2, -1], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, -1], [-2, 0, 2, 2, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, 1, 0], [3, 0, 0, -1, -3, 1], [0, 0, 0, 0, 0, 0], [2, 0, 0, -1, 0, 0], [1, 0, 2, 1, -3, 1], [0, 0, 0, 0, 0, 0], [0, -4, 4, 0, -2, 2], [-1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 3, -3, 0, 1, -1], [-2, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, -5, -1, 0, 0], [0, -3, 3, 0, 3, 2], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0], [0, 4, -4, 0, 1, -1], [0, 0, 0, 0, 0, 0], [2, -4, 1, -1, -6, 2], [-1, 0, -2, -1, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 2, 0, -2, 1, 2], [8, -2, 0, -2, -8, 2], [0, 0, 0, 0, 0, 0], [-4, 0, 1, 1, 0, 0], [0, -1, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, -4, -2], [-9, 3, 0, 4, 9, -4], [0, 0, 0, 0, 0, 0], [0, -2, 2, 0, -2, 2], [-1, 0, -2, -3, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, -1, 2, 0, 0], [0, 4, -4, 0, 10, -4], [0, 0, 0, 0, 0, 0], [4, -1, 0, -5, -4, 5], [0, -2, 2, 0, -2, -2], [0, 0, 0, 0, 0, 0], [1, -3, 0, -1, -3, -1], [-1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-8, 3, 0, 3, 8, -3], [2, -2, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0], [3, 0, 0, -1, 0, 0], [12, -2, -4, -2, -8, 0], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 4, -3], [1, -4, 0, -5, -1, 5], [0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 8, 1], [-9, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0], [8, 0, -4, 0, 0, 0], [0, 0, 0, 0, 2, -1], [0, 0, 0, 0, 0, 0], [6, -2, 0, 1, -6, -1], [0, -4, 4, 0, -4, 2], [0, 0, 0, 0, 0, 0], [3, -2, 2, -1, -2, 2], [-7, 0, 4, -1, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 5, 0, 2, 4, -2], [3, 0, 0, 3, -3, -3], [0, 0, 0, 0, 0, 0], [-12, 0, 11, 5, 0, 0], [1, 4, 1, 0, 4, -2], [0, 0, 0, 0, 0, 0], [0, -3, 3, 0, 1, -1], [2, -4, 0, -2, -2, 2], [0, 0, 0, 0, 0, 0], [0, 5, -5, 0, 2, -5], [-5, 0, -1, -2, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0], [0, -4, 4, 0, 5, 1], [0, 0, 0, 0, 0, 0], [-14, 8, 0, 6, 14, -6], [0, -2, 2, 0, -11, -1], [0, 0, 0, 0, 0, 0], [-4, -1, 4, 1, 5, -1], [8, 0, -8, -2, 0, 0], [0, 0, 0, 0, 0, 0], [10, 2, 0, 0, -10, 0], [-1, 3, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0], [0, 0, -1, 3, 0, 0], [13, 2, -3, -2, -4, -2], [0, 0, 0, 0, 0, 0], [0, -1, 1, 0, -2, 1]]}