# Stored data for newform 370.2.g.c, downloaded from the LMFDB on 18 April 2024. {"label": "370.2.g.c", "space_label": "370.2.g", "level": 370, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9007611605156210, "dim": 4, "is_polredabs": true, "nf_label": "4.0.256.1", "trace_hash": 1702450284762560747, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [16, 0, 0, 0, 1]]], "qexp_display": "q+\\zeta_{8}^{2}q^{2}+2\\zeta_{8}q^{3}-q^{4}+(2\\zeta_{8}-\\zeta_{8}^{3})q^{5}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 185, "char_orbit_label": "g", "char_is_real": false, "Nk2": 1480, "analytic_conductor": 2.9544648747873743, "hecke_ring_index": 1, "level_radical": 370, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 8, "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": "0.250", "prec": 17}, "analytic_rank_proved": true, "char_values": [370, 4, [297, 261], [3, 3]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 5, 37], "conrey_indexes": [43, 327], "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "3.905", "prec": 17}, {"__RealLiteral__": 0, "data": "0.058", "prec": 17}, {"__RealLiteral__": 0, "data": "57.963", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1424.435", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 8], "traces": [0, 4, 0, 0, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, 8, 4, 4, -4, -12, 0, 0, 4, 0, 0, 16, -8, 0, -8, -24, -16, -8, 0, 16, 0, 4, 0, 0, 12, 24, 0, 0, -8, 0, 0, 0, -16, -16, 0, 0, -12, -16, 0, 0, 0, 8, 8, 0, -24, -16, -8, 40, 8, -8, -4, 12, 16, -12, -4, 8, -8, -24, 4, 24, 0, 0, 12, 16, 24, 16, 0, 44, 28, 8, 0, -24, -28, -8, -4, 24, 0, -4, 0, 0, 16, -16, 0, -28, -8, 4, -16, 0, 16, -8, 8, -16, 0, -8, 0, 16, 24, -48, 8, -4, 32, 4, 24, -8, 16, 0, 16, 8, -40, 0, 8, 0, -8, 16, 0, 0, 36, -4, -16, 0, -12, 32, 0, 28, 8, -36, -4, 0, 0, -40, 0, -8, -24, -32, 0, 0, 0, 0, -12, 0, 16, -12, -24, 32, -16, 24, 0, -28, 0, -36, 0, 16, 8, -16, 8, -36, 8, 12, 0, -24, 0, 8, 0, 0, 24, -24, 0, 8, -4, 0, 16, -52, 24, 0, 16, 16, 32, -8, 0, 0, 0, -32, 0, -8, 0, 24, 12, 48, -16, -100, 16, 0, 0, -16, 0, -44, -48, -36, 0, 32, 8, 0, 0, 0, -16, 0, -8, 0, 8, 64, -8, -12, 0, 4, 0, 0, 12, 72, 24, -28, 0, -24, 16, 0, 0, 48, 8, 20, 0, 0, -40, -16, 0, -24, -8, -32, 0, -32, 8, 0, -16, 8, 4, 64, 0, -24, -12, -24, 4, -16, -16, 24, 64, 16, 12, 0, 16, 16, 4, 80, -28, 12, -8, 0, 0, 8, 8, 16, 48, 112, 24, 24, 0, 56, -4, -32, -4, 0, -24, 24, -32, 16, 0, -32, 16, -56, 0, -56, -48, -40, -12, -4, -4, 32, -16, 88, 24, -16, -24, 0, -32, -8, -16, 48, 0, 32, 0, 0, -28, 20, -44, -24, 0, 0, -28, 0, 8, 16, -8, 0, 0, 48, 0, 0, 0, -16, 24, -32, 12, 24, 28, -64, 24, 0, 8, 0, -56, -48, 4, 52, -32, 48, -24, 0, -24, 0, 0, 0, 0, -32, 4, 0, 8, -24, 0, 28, -16, 12, 0, -32, -28, -16, -16, -36, 0, 0, 16, 0, -8, 0, 0, 72, -48, -28, 28, 16, -16, 0, 8, 0, 8, 32, -4, 0, 24, 88, 16, 0, 0, -20, 0, 0, 0, 40, -16, 0, 0, 0, 8, 0, 0, -32, -8, 16, -44, 0, 16, -56, 0, 16, 0, 16, -32, 0, 8, 8, 0, 0, 0, -36, 44, -144, -16, 32, 0, 40, -24, -8, -56, -44, 48, 16, 64, 24, -8, -12, -16, -28, 4, 0, 0, 80, -32, -60, 0, -32, -4, 56, 0, 0, -24, 16, 28, -36, 8, -24, 48, 0, -16, 28, -64, -12, 0, 0, -48, 0, -16, 60, 20, 0, -8, 0, 0, 40, 40, -32, -48, -8, 0, -16, -24, 24, -8, -32, 0, -24, 0, 16, 32, 0, 8, -20, 0, 96, -16, 56, -16, 0, 0, -64, 0, 132, 0, -64, 4, 0, -36, 0, 24, 0, 4, -24, 16, 16, 16, 20, 12, 16, 0, 56, 0, -40, 12, -96, -8, 72, -32, -32, 0, 32, 0, -28, 0, 0, -28, -40, 16, 160, -8, 0, 48, 0, 36, 0, 8, -56, 4, 0, 16, 0, 0, -24, 0, 88, 0, -52, 72, 108, 40, 40, 56, -48, 0, 64, 0, -48, 8, 16, 0, -24, 24, 36, 24, 0, 32, 0, -32, 0, 0, -48, 32, -28, 0, -112, 0, 0, 0, -100, -56, -12, 0, -48, -40, 0, 12, -64, 8, -40, 0, -40, 32, 112, -16, -60, -88, 28, 12, -16, 16, 104, 24, 28, -48, -128, -32, 56, -4, -16, 16, 0, 48, -8, -24, 80, -32, 0, 0, -12, 80, -132, 28, -112, -20, 0, 0, 16, -32, 64, 36, -56, 56, 8, 0, -24, 88, -24, -16, -16, 16, 56, -8, 44, 0, -92, 16, -24, 24, 32, -8, -76, 0, 0, 36, -88, 16, -56, -8, -48, -32, 0, -12, 8, 24, -8, 0, -36, -32, 0, 24, 16, 24, 24, 0, 0, 40, 0, -8, 40, 48, 96, 0, 32, 0, -52, 0, 40, -16, -16, -24, 20, 56, 12, 24, 0, -8, 0, 0, 28, -60, -48, -8, -168, 32, 0, 4, 0, 0, 0, 0, 8, 24, -32, -16, -36, 0, 36, 52, -80, 0, 40, -24, 12, 32, 8, 0, 0, -88, 0, -16, 0, 36, 0, -16, 88, 72, 56, -32, 0, 16, 0, 8, 8, -72, 80, 0, -88, 36, 16, 0, 32, 0, -8, 0, -80, -16, -84, 32, 0, -32, 0, 0, -12, -16, 48, 8, 0, -64, -16, 0, -92, 0, 0, -24, 0, 88, 32, -12, 24, 0, 24, -48, 0, -20, 112, 16, 92, 0, -32, 100, -40, -56, -48, -16, 84, 0, -4, 0, -104, -16, -48, 0, 112, 48, 4, 16, 0, -16, -112, 0, 0, -16, 24, 44, -48, -40, -40, 48, 0, 56, 0, 36, 144, 16, 0, 0, 0, -12, 20, -32, -120, -156, 32, -8, -4, -8, -84, 0, 56, 0, 80, 0, 68, -36, -32, 0, 80, 48, -96, 16, 0, 32, -8, 0, -8, 40, -88, 8, 0, 0, 124, 0, 32, 44, 8, -8, 0, 8, 0, -64, 0, 24, -96, 8, 112, 12, 108, 12, -24, 0, -56, 0, 48, 0, -56, -4, -16, 40, 104, 0, 24, 0, -80, 0, 0, -32, -48, -12, -112, 56, 0, -72, 0, -16, 0, -24, 60, 48, 88, 28, 0, 0, 0, 0, 24, 0, 64, 24, 112, 24, 112, -16, 96, 0, 44, 0, -48, 84, 40, 0, 104, 0, 40, -48, 0, 0, 0, -8, 0, -84, 8, -20, -24, 0, -80, 0, 0, 0, -68, 0, -64, 0, 168, 40, 0, 32, -40, 16, -16, 0, 80, 0, 0, -16, 128, 24, -112, -8, 96, 8, -16, 32, -112, 32, 48, -24, -16, 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, 185, 6, 1, 4, 0]], "char_orbit_index": 7, "prim_orbit_index": 6, "minimal_twist": "370.2.g.c", "char_is_minimal": true, "conrey_index": 43, "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, 0, 1, 0], [0, 2, 0, 0], [-1, 0, 0, 0], [0, 2, 0, -1], [0, 0, 0, 2], [2, 1, 2, 0], [0, 0, -1, 0], [0, 0, 1, 0], [0, 1, 0, 2], [0, -2, -1, -2], [0, -2, 0, 0], [0, -3, 2, -3], [-2, 0, 2, 1], [2, 0, 4, 0], [1, 0, 0, 0], [1, -2, 0, 2], [-1, 0, 0, 0], [-3, -4, -3, 0], [0, -2, 0, 1], [0, 4, 2, 4], [1, 2, 0, -2], [0, -1, 4, -1], [0, 0, 0, -2], [4, 0, 3, 0], [-2, 3, 0, -3], [0, 0, 0, -4], [-2, -1, -2, 0], [-6, 0, 6, 1], [-4, 0, 2, 0], [-2, -3, -2, 0], [0, 0, 1, 0], [4, 0, -4, -2], [0, -2, 1, -2], [1, 6, 2, 2], [0, 0, -1, 0], [0, -1, 0, 6], [3, 0, -3, -4], [6, 0, -6, 4], [0, -1, 0, -2], [0, 0, -7, 0], [-2, -4, 0, 4], [0, 0, 7, 0], [0, 2, 1, 2], [0, 1, 0, 2], [-4, 1, 0, -1], [-4, -6, -4, 0], [0, 2, 0, 0], [0, 4, 2, 4], [-3, 0, 4, 0], [-4, 2, -4, 0], [0, 3, -2, 3], [0, 0, 0, -3], [0, 4, 0, 0], [2, -1, -6, -2], [2, 0, -2, -1], [0, -6, -8, -6], [-6, -1, -6, 0], [-4, 4, -4, 0], [-2, 0, -4, 0], [10, -1, 10, 0], [2, 0, -2, -3], [-2, 0, 2, 1], [-1, 0, 0, 0], [3, 2, -9, 4], [4, 2, 4, 0], [-3, 0, 3, -6], [-1, 2, 0, -2], [2, 0, -2, 8], [-2, -2, 1, 6], [-6, 4, 0, -4], [1, 0, 0, 0], [6, 0, 6, 0], [0, -6, 0, -1], [0, 8, 0, 6], [3, 4, 3, 0], [4, 0, -4, -9], [6, -4, 6, 0], [4, 8, 4, 0], [0, 2, 0, -1], [11, 0, 0, 0], [7, 0, 0, 0], [2, 0, -2, 4], [0, -4, -2, -4], [-6, 2, -2, -1], [-7, 0, 0, 0], [-2, -12, 0, 12], [-1, -2, 0, 2], [6, 0, -6, -2], [0, -2, 0, 1], [-1, 0, 1, -10], [0, 1, -4, 1], [0, -4, -6, -4], [4, 0, -4, -6], [-4, -9, -8, -3], [0, 0, 0, 2], [-7, 0, 0, 0], [-2, -4, 0, 4], [1, 2, 0, -2], [-4, 0, -3, 0]]}