# Stored data for newform 392.2.i.h, downloaded from the LMFDB on 19 April 2024. {"label": "392.2.i.h", "space_label": "392.2.i", "level": 392, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31525747180962184, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.2", "trace_hash": 502077787898660387, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4, 0, 2, 0, 1]], [5, [64, 0, 8, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+(-2\\beta _{1}-2\\beta _{3})q^{5}-\\beta _{2}q^{9}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "i", "char_is_real": false, "Nk2": 1568, "analytic_conductor": 3.130135759234191, "hecke_ring_index": 1, "level_radical": 14, "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": "0.512", "prec": 17}, "analytic_rank_proved": true, "char_values": [392, 3, [295, 197, 297], [3, 3, 1]], "hecke_ring_generator_nbound": 9, "inner_twist_count": 4, "level_primes": [2, 7], "conrey_indexes": [177, 361], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, 2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "3.872", "prec": 17}, {"__RealLiteral__": 0, "data": "0.234", "prec": 17}, {"__RealLiteral__": 0, "data": "92.601", "prec": 20}, {"__RealLiteral__": 0, "data": "8.319", "prec": 17}, {"__RealLiteral__": 0, "data": "3486.236", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, -12, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, -6, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -4, 0, 16, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 32, 0, -8, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 8, 0, 10, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 24, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -8, 0, 20, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, -50, 0, 4, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 32, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 12, 0, -16, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -4, 0, -48, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, -4, 0, -40, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 8, 0, -32, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 28, 0, 16, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -16, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -48, 0, -4, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, -12, 0, 8, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, -36, 0, -28, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 30, 0, -36, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 48, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 44, 0, 72, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 28, 0, 4, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, -32, 0, -20, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 16, 0, 2, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, -52, 0, 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 20, 0, 60, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 36, 0, 32, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -8, 0, 60, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 96, 0, -72, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, -72, 0, 24, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 48, 0, 16, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, -48, 0, -120, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -72, 0, -72, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 56, 0, 8, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -48, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 14, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, -20, 0, -48, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, -16, 0, -36, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 44, 0, 20, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 24, 0, -32, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -32, 0, -84, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 62, 0, 72, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, -24, 0, 12, 0, 0, 0, 160, 0, 0, 0, 0, 0, 0, 0, 52, 0, -120, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 48, 0, -32, 0, 0, 0, -176, 0, 0, 0, 0, 0, 0, 0, -28, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 4, 0, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, -68, 0, -8, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 4, 0, 36, 0, 0, 0, 116, 0, 0, 0, 0, 0, 0, 0, -48, 0, 12, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 24, 0, -4, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 8, 0, 16, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, -12, 0, 144, 0, 0, 0, 192, 0, 0, 0, 0, 0, 0, 0, -96, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, -80, 0, 64, 0, 0, 0, -64, 0, 0, 0, 0, 0, 0, 0, 36, 0, 112, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 16, 0, 32, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 60, 0, -16, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 76, 0, -8, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, 60, 0, -24, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -96, 0, 40, 0, 0, 0, -192, 0, 0, 0, 0, 0, 0, 0, 64, 0, 4, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 32, 0, -48, 0, 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 84, 0, -112, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 46, 0, 8, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 48, 0, -24, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -80, 0, 64, 0, 0, 0, 288, 0, 0, 0, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0], [1, 1, 7, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0]], "char_orbit_index": 9, "prim_orbit_index": 3, "minimal_twist": "392.2.a.g", "char_is_minimal": false, "conrey_index": 177, "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, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, -2, 0, -2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [-6, 0, -6, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [4, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 3, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [-3, 0, -3, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, -6, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [8, 0, 8, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [10, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 2, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [2, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 12], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 6, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -16, 0], [0, 0, 0, 0], [-4, 0, -4, 0], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 0, 0], [-12, 0, 0, 0], [0, 0, 0, 0], [0, -7, 0, 0], [0, 0, 0, 0], [0, -3, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 0], [5, 0, 5, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [4, 0, 0, 0], [0, 0, 0, 0], [0, -6, 0, 0], [0, 0, 0, 0], [0, 3, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [12, 0, 12, 0], [0, 0, 0, 0], [0, 0, 0, 9], [0, 0, 0, 0], [-6, 0, 0, 0], [0, 0, 0, 0]]}