# Stored data for newform 370.2.n.c, downloaded from the LMFDB on 09 May 2026. {"Nk2": 1480, "analytic_conductor": 2.9544648747873743, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 185, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 14, "char_orbit_label": "n", "char_order": 6, "char_parity": 1, "char_values": [370, 6, [297, 261], [3, 4]], "cm_discs": [], "conrey_index": 269, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[3, [0, 1]], [7, [4, -12, 14, -6, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008092641493362, "hecke_ring_generator_nbound": 2, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 185, 14, 1, 6, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "370.2.n.c", "level": 370, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": true, "level_primes": [2, 5, 37], "level_radical": 370, "minimal_twist": "370.2.n.a", "nf_label": "4.0.144.1", "prim_orbit_index": 14, "qexp_display": "q+\\zeta_{12}q^{2}+\\zeta_{12}^{2}q^{4}+(2-\\zeta_{12}-2\\zeta_{12}^{2}+\\cdots)q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "370.2.n", "trace_display": [0, 0, 4, 6], "trace_hash": 1173402184799311864, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.687", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "49.520", "prec": 20}, {"__RealLiteral__": 0, "data": "8.344", "prec": 17}, {"__RealLiteral__": 0, "data": "1077.249", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.187", "prec": 17}, "traces": [0, 4, 0, 0, 2, 4, 0, 6, 0, -6, -2, 12, 0, 12, -4, 0, -2, -6, 0, 6, 8, 0, 6, 0, 0, -6, 8, 0, 6, 0, 0, -4, 0, 0, 0, 4, -12, 0, 0, 0, 2, 2, 0, 0, 6, 12, 4, 0, 0, -6, -16, 0, 12, -36, 0, 6, -2, 0, -6, -12, 0, -12, -30, 0, -4, -8, 0, -6, 0, 0, -10, -6, 0, 0, -20, 0, -6, 12, 0, 14, 4, -18, 0, 12, 0, -12, 14, 0, 0, -6, 12, 8, 12, 0, -10, 24, 0, 0, -12, -18, 6, 8, 0, 0, 4, 0, -4, -18, 0, -16, 6, 0, 0, -24, 0, -28, 0, 0, 12, -12, 0, 4, 0, 0, -2, -8, 6, -24, 0, 0, -4, 8, 0, 12, 28, 0, 0, 0, 0, 8, 14, 0, 0, 48, -6, 6, -4, 0, 0, 16, 0, 28, -6, 18, 0, 26, 0, 0, 0, 0, 4, -8, 0, -42, -2, 0, 12, 48, 0, 6, 0, -36, -6, 24, 0, -10, -6, 0, 12, 32, -12, 8, 0, 0, 8, 20, 0, -18, 6, 0, 18, -8, 0, 0, 4, 0, -12, -24, -18, -28, -8, 0, 6, 6, 0, 8, 18, 36, 0, 24, 0, -4, 0, 0, 4, -2, 0, 24, -18, 0, 24, -24, 0, 0, 2, 36, 20, 30, 0, -20, -20, 0, 0, 0, -12, -2, -24, 0, 6, 2, 0, 28, 36, 0, 12, 24, 0, 48, 0, 0, -22, 68, -18, 0, 8, 0, -2, -18, 0, -2, 20, 0, 24, 24, 0, -68, 0, 0, -6, 16, 0, -14, 6, 0, 0, -42, 0, -36, -24, 6, -8, 6, 0, -18, 6, 0, 48, -18, 0, -28, -12, 0, -48, -48, 0, 12, -22, 0, 54, -32, 0, 20, 0, 0, -12, -48, 0, 0, 12, 0, -58, -6, 0, 18, -34, 30, -14, -60, 0, -12, -4, 0, 0, 0, 18, -52, -6, 0, -24, -16, 0, 20, 0, 0, -16, -28, 0, 18, 48, 0, -12, -72, -18, 0, 28, 0, 14, 0, 0, 36, -18, 0, -6, -6, 0, -24, -12, 0, -24, 56, 6, 14, 0, 0, 16, 100, 0, -48, 12, -12, 4, -64, 0, 0, -6, 0, -20, -12, 0, 42, 18, 0, 60, -78, 0, 0, 16, -18, -18, -20, 0, -12, -12, 0, -26, 56, -36, 0, -18, 0, 12, -8, 0, -72, 4, -72, -12, -18, 0, 34, 50, 0, 18, 0, 12, 12, -4, 0, 0, 46, 0, 24, -66, 18, 4, 0, 0, -42, -18, 0, -22, -22, 0, 0, -56, 0, -32, 48, 0, -40, 18, -18, -12, 0, 0, 0, -16, 0, -6, 36, 24, 30, 0, 0, 52, -16, 0, -18, 0, 0, -8, -12, 0, 90, 0, 0, -24, 0, -36, -20, 14, 0, 12, 0, 0, -6, -6, 108, 54, -12, 0, 4, 0, 0, 2, 32, 0, 0, -6, 0, 12, -84, 0, 0, 24, 54, 2, 24, 0, 30, -4, 0, 18, 66, 12, 2, 24, 0, 0, 36, 0, 44, 0, 0, -36, -54, 0, 0, -18, 0, 16, 20, 18, 36, 16, 0, 64, 6, 0, 28, -16, -36, 0, 60, 0, -4, 14, 0, -48, -30, 0, 104, 6, 0, 0, 50, 0, 0, 6, 72, -48, -6, 0, 72, -36, 0, 16, 24, 90, -16, 10, 0, 0, 0, 0, -68, -44, -54, 42, -20, 0, 4, 48, 0, 22, -20, 6, 0, 0, 0, 0, 0, 0, -120, -8, 84, 60, 24, 0, -36, 24, 0, 0, 0, 0, -18, 8, 0, 0, 38, 0, -26, 0, 0, -28, -32, 0, 102, -6, 0, 0, 8, 18, -60, 38, 0, 0, 72, 0, -4, -8, 0, 6, 0, 0, 14, 16, 0, 0, 0, 6, 16, 30, 0, -6, -56, 0, 0, -18, 36, 2, 2, 0, 0, 8, 0, 6, 18, 0, -24, -60, 0, 0, 60, 0, -40, -4, -144, 0, -36, 0, 80, -36, 0, -12, 24, -6, 0, 48, 0, 34, -30, 0, -72, 16, 0, 12, 0, 0, 22, -6, 0, -96, 30, -18, -12, 8, 0, -6, -160, 0, 34, 0, 0, 0, 8, 0, 0, -54, 0, 16, 20, 0, -42, -12, 0, 24, 6, 0, -32, -90, -84, 12, 0, 0, -48, 16, 0, -12, 4, -24, 0, -36, 0, -8, 24, 0, -84, 0, 108, 56, 6, 0, 12, 80, 0, 4, 24, -72, -96, 22, 0, 24, -30, 0, -38, -4, -36, 0, -20, 0, 100, 6, 0, -24, 112, 0, 12, -54, 0, 12, -2, 0, 0, -4, 0, -28, 0, 0, 56, -12, 0, -30, 48, 42, 126, 8, 0, 0, -30, 0, -60, -12, 0, -6, 34, 0, 0, 0, 0, -46, -88, -18, -60, -14, 0, -14, -12, 0, -6, 8, -18, -60, 0, 0, -32, -128, 0, 0, -12, -18, 60, 6, 0, -60, -78, 0, 24, 72, 24, 28, -56, 0, 60, 36, 0, 24, -96, 0, -76, 48, 0, -12, 18, 0, 16, -24, 0, -18, -84, 0, -104, 78, 0, -2, -60, -30, -30, 36, 0, 24, 44, 0, -48, 18, -18, 2, 0, 0, -76, -28, 0, 0, -84, 0, 34, 8, 0, 24, 12, 0, 16, -18, -54, 48, -34, 0, 0, 0, 0, 18, -42, 0, 36, -12, 0, -8, 0, 0, -64, 12, -54, -24, -12, 0, 56, 4, 0, 0, 60, 18, 36, 0, 0, -20, 32, 0, 6, 30, -12, -16, 48, 0, 72, -56, 0, 20, 0, 0, 40, -4, 0, 96, -120, 0, -8, 20, 54, 6, 66, 0, -60, 6, 0, 36, -30, -24, -30, 48, 0, 20, 20, 0, 60, -12, 0, 36, -72, 0, 104, -6, 0, 0, 24, 24, -68, 4, 0, -12, -6, 0, 180, -36, 0, -28, 44, 0, 96, 0, 0, 10, -16, 0, 0, -60, 0, 24, -48, 0, -6, 0, -48, 30, 126, 0, -22, 6, 0, 0, -32, 36, 84, 30, 0, -36, -10, 0, 36, 0, 0, -44], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [2, -1, -2, 0], [0, 0, 0, 0], [2, -1, -1, 1], [0, 0, 0, 1], [-3, 0, 3, 0], [0, 2, -1, -2], [3, 2, 0, -1], [0, 0, 0, 0], [4, 2, -2, -2], [-1, 2, 0, -1], [0, 0, 0, 0], [-1, 0, 1, 0], [-1, 0, -1, 0], [0, -3, 0, 3], [0, 1, 3, 1], [2, 0, 0, -1], [0, 0, 0, 0], [1, 3, 1, 0], [2, 0, -4, -2], [0, 0, 0, 0], [0, -4, -3, 4], [2, 4, 0, -2], [0, 0, 0, 0], [1, -1, 1, 0], [0, -2, 0, 1], [0, 0, 0, 0], [-1, -10, 0, 5], [0, -1, 0, 1], [0, 0, 0, 0], [0, -1, 0, -1], [3, -2, -4, 3], [-3, 0, 0, 0], [0, -3, 0, 7], [-1, 0, 2, 3], [0, 0, 0, 0], [1, 2, -1, 0], [0, 4, 1, 4], [0, 0, 0, 0], [-1, 0, 2, -7], [0, 1, 3, 1], [0, 3, 6, -3], [2, 2, -2, -4], [1, 0, -2, 5], [0, 0, 0, 0], [-3, -2, 3, 4], [-4, 0, 0, -3], [0, 0, 0, 0], [2, 2, 2, 0], [-6, -2, -6, 0], [0, 0, 0, 0], [5, -1, -7, -4], [0, 1, -1, 1], [0, 0, 0, 0], [-1, 0, -1, 0], [-6, 2, 6, -4], [0, 0, 0, 0], [0, 1, -6, 1], [-5, -1, -5, 0], [-3, 0, 6, -3], [-1, 0, 0, 0], [2, -4, -8, -2], [0, 0, 0, 0], [-2, 7, 1, -7], [1, 0, -2, 0], [0, 0, 0, 0], [-3, 3, 1, -4], [0, -7, -3, -7], [0, -3, 0, 0], [-8, 0, 16, 2], [-7, 0, 4, 0], [0, 0, 0, 0], [-3, -1, 3, 2], [4, 0, -2, 0], [0, 0, 0, 0], [0, -5, 7, -5], [0, 1, 2, -1], [0, 0, -9, 0], [-4, 0, 8, 1], [2, 6, 2, 0], [0, 0, 0, 0], [-4, 1, 2, 1], [7, -1, -7, 2], [0, 0, 0, 0], [-1, 0, 2, 3], [-3, 2, 3, -4], [3, 0, 0, 6], [4, 0, -4, 0], [4, 2, -2, -2], [0, 0, 0, 0], [-5, 1, 5, -2], [7, 4, -2, -5], [0, 0, 0, 0], [-3, 0, 6, -2], [-4, -3, 2, 3], [-9, -3, 9, 6], [3, -4, -3, 0]]}