# Stored data for newform 370.2.e.e, downloaded from the LMFDB on 25 April 2024.
{"label": "370.2.e.e", "space_label": "370.2.e", "level": 370, "weight": 2, "hecke_orbit": 5, "hecke_orbit_code": 18014673420943730, "dim": 4, "is_polredabs": true, "nf_label": "4.0.14400.7", "trace_hash": 601812266852507117, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, -1, 1]], [7, [36, -24, 22, 4, 1]]], "qexp_display": "q-\\beta _{2}q^{2}+(1+\\beta _{2})q^{3}+(-1-\\beta _{2})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 37, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1480, "analytic_conductor": 2.9544648747873743, "hecke_ring_index": 1, "level_radical": 370, "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": "0.015", "prec": 17}, "analytic_rank_proved": true, "char_values": [370, 3, [297, 261], [3, 2]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 5, 37], "conrey_indexes": [121, 211], "field_disc": 14400, "field_disc_factorization": [[2, 6], [3, 2], [5, 2]], "field_poly": [100, 0, 10, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.800", "prec": 17}, {"__RealLiteral__": 0, "data": "0.792", "prec": 17}, {"__RealLiteral__": 0, "data": "56.411", "prec": 20}, {"__RealLiteral__": 0, "data": "30.729", "prec": 20}, {"__RealLiteral__": 0, "data": "1437.277", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 2, -2, -4], "traces": [0, 4, 2, 2, -2, -2, 4, -4, -4, 4, -4, 8, 2, 2, -8, 2, -2, 4, -4, -4, -2, 4, 4, 0, -2, -2, 4, 20, -4, 8, -2, 4, 2, 4, -4, -4, -8, -18, -8, -2, 2, 2, -4, 4, -4, -8, 0, 8, -4, -14, 2, 8, 2, -22, 10, -4, 4, 4, 4, -4, -4, 4, 2, -16, 4, 2, 8, 4, -8, 0, 4, 0, -4, -24, 0, -4, -4, 12, 2, 4, 4, -2, 4, 8, -8, -8, 2, 4, -8, 8, -4, 24, 0, 2, 4, -4, -2, -24, 14, 8, 4, 64, 4, -16, -2, -8, 22, 14, -10, -20, -8, -18, 8, 0, -4, 0, -4, 8, 4, 24, -2, 12, 8, -2, -2, 4, -8, -24, 2, 2, -2, 36, 4, -48, 8, -10, -4, 8, 0, 12, 8, 4, 0, -16, 4, -4, -12, -28, 18, 48, -2, -26, 4, -8, 24, -2, 4, 14, 8, -44, 2, -20, -4, 14, 2, 4, -8, 4, -4, 4, -4, -16, -2, 8, 8, 8, -4, -8, -8, -48, 4, -28, -24, -4, 0, 18, 4, 28, -4, -20, 4, 28, 2, -40, -12, 4, 28, -34, -8, -36, 2, -4, 32, -48, -4, 2, -8, 0, -4, 32, -4, -8, 44, 0, 28, -2, -20, -24, 20, -12, -4, -32, -18, 16, 4, 4, 0, 18, -8, 28, 0, -12, -8, 16, 4, -4, 8, -4, 12, 4, 2, -4, 6, 32, 4, 28, 2, 44, -4, 16, 2, 24, 8, -40, 24, -4, -2, -16, 4, 16, -4, 8, -36, -4, -4, 44, 48, 16, 4, 96, -20, -34, 4, 48, 4, -4, 0, -2, -12, 4, 4, -22, 8, 2, 0, -8, -32, -36, 8, 6, -8, -12, 12, 18, -14, 8, 18, 40, 24, 20, 2, -44, -52, 32, 8, 4, -16, -4, 12, -8, -4, -10, 2, 20, -14, 8, 4, -6, -22, -64, -2, -14, -40, 64, -2, -4, -14, -40, -2, -28, -4, -48, -16, 0, 8, 4, 4, 4, -4, 0, 4, -32, -8, 160, -4, 0, -8, -56, 4, -4, 4, 10, 4, 0, -4, 0, -16, 12, -24, -20, 8, -50, -56, 6, -48, 12, 4, -12, 0, 8, 18, 128, 2, -2, -28, 2, -8, 44, -40, -44, 8, -48, 14, -4, 4, 12, -20, 4, 12, -32, 2, -20, 14, 72, 34, 4, -16, 4, -18, -96, -2, -32, 4, 22, -32, -2, -96, -16, -8, 14, -2, 4, 8, -24, 0, -16, -2, 24, 64, 4, 4, -8, -4, 8, 22, 4, 0, 48, 14, 16, -4, 10, -10, -64, -48, 4, 40, -40, -24, -22, 4, 28, -16, 124, 0, -16, 8, 24, -4, -38, 8, 44, 0, 26, 36, -48, -4, 24, 56, 20, 0, 28, 12, 0, -4, 2, 8, -116, -4, 48, -8, 28, 4, -72, 4, 8, -12, 44, -4, -58, 4, 2, -8, 20, -6, 12, -32, 8, -4, 28, 14, 88, 4, -32, -44, -16, -2, -40, 8, 48, -2, -4, 12, -12, 16, -32, -20, 8, 48, -4, -8, -36, -4, -20, 16, 8, 2, -24, 56, 16, -2, -22, -8, 10, -72, 4, -8, -16, -8, -52, 22, 8, 96, 38, 8, 14, -4, -24, 48, 52, -10, 8, 34, 28, 8, 40, 24, 20, -4, 16, 4, -88, 0, 8, -4, 0, -24, 46, -4, 42, -4, 56, 22, 56, 4, 0, 4, -4, 0, 84, -4, -32, -16, 14, 36, 0, 4, 80, 12, -20, -4, -32, -24, -24, 24, -4, 36, -26, 14, -44, 4, -68, 0, -88, 20, -12, -24, -18, 40, 30, 4, 10, -88, 16, -26, -6, 64, 52, 4, 48, -4, 24, -8, 36, -2, 4, -12, 36, -16, -136, -2, 0, 10, -192, -2, -2, -20, -32, -28, 40, 16, -30, -4, -4, 6, 48, 22, -188, -32, 0, -4, -50, 14, 116, -20, 2, 32, -40, 2, -28, -2, 24, -28, -18, -20, -72, -4, -24, -56, -48, -8, -36, 48, -16, -8, 96, 36, 80, 4, 8, -4, -32, 8, 0, 8, -10, -8, -40, 0, 64, 8, -18, -16, -30, 8, -4, 80, -28, -2, -84, 0, -24, -16, 48, -28, -24, -4, 88, 4, 8, -4, 20, 20, -4, 8, 4, 0, -44, 4, 64, 0, 16, -8, 40, 24, -16, 24, 8, -10, -34, 4, 76, 50, 4, -28, -4, 12, -16, -24, 52, 24, -36, 8, -12, -24, 14, 0, -32, 4, 24, 0, 88, 64, 16, -2, -24, -4, -16, -56, 28, 4, 20, -4, 12, 88, -26, -20, -26, 44, -20, 4, -16, -24, 0, -14, -8, -8, 32, 2, -16, -12, -32, 20, -10, -4, -2, 24, -40, -64, -76, -2, 40, 20, 40, -14, -28, 36, 44, 68, 4, -4, -80, -8, -44, 2, 22, 18, 66, -48, -12, -4, -16, -16, -168, 8, -20, 44, 48, -64, -30, 2, 8, -48, -68, 40, -28, -4, -84, -14, -48, -4, 76, 8, -52, 16, -8, -12, 44, 0, 4, -8, 2, 2, -52, 12, 4, 32, 20, -4, 54, 8, 60, -4, -44, 4, -8, -8, 68, -22, -2, 8, -20, 0, -46, -48, 8, -14, 72, -16, 48, -2, -72, 20, 0, 10, -16, -32, -6, -24, 8, -4, -44, 20, -24, -80, -4, -12, 148, -44, -18, 8, -72, 56, 14, 16, 4, 62, 24, 18, 16, -8, -4, -8, -48, 48, 24, -8, -20, -76, 88, 4, 24, 88, 44, 0, -28, -26, -60, 18, 64, -24, 100, 4, 16, 48, 8, 28, -144, -20, 64, 0, -2, -28, 40, 24, 0, 0, -16, 4, 14, -2, 376, -8, -20, -58, -56, -8, -12, -48, 40, -4, 0, 14, -40, -4, -20, -36, 86, 8, 48, 4, -12, -24, -68, 88, -14, -8, -32, 58, -68, 2, -80, -38, 56, -4, 20, -20, 16, -12, 32, 24, 52, -64, -168, 4, -2, -8, 20, 14, -64, -14, 40, 44, 12, 2, 68, 32, 28, -88, 80, -8, -28, 2, -96, 40, 18, -8, 30, 96, -90, -4], "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, 37, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "370.2.e.e", "char_is_minimal": true, "conrey_index": 121, "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], [1, 0, 1, 0], [-1, 0, -1, 0], [-1, 0, -1, 0], [1, 0, 0, 0], [-2, 1, -2, 0], [-1, 0, 0, 0], [0, 0, -2, 0], [-1, 0, 0, 0], [2, 0, 0, -1], [0, 0, -1, 0], [1, -1, 1, 0], [-2, 0, 0, -1], [0, 0, -1, 0], [0, 0, 1, 0], [0, -1, -2, -1], [-2, 0, -2, 0], [-2, 2, -2, 0], [0, 0, 1, 0], [0, 1, -2, 1], [0, -1, -2, -1], [0, 0, 0, 1], [-1, 0, -1, 0], [0, 0, 1, 0], [1, 0, 0, 1], [5, 0, 0, 0], [0, -1, 2, -1], [2, 0, 0, 2], [-1, 0, -1, 0], [1, 0, 0, 1], [1, 0, 1, 0], [2, 1, 2, 0], [-2, -1, -2, 0], [0, -1, 2, -1], [-2, 0, 0, 0], [-3, 1, 3, 0], [-2, 0, 0, -2], [0, -1, 1, -1], [1, 0, 1, 0], [1, 2, 1, 0], [-2, 1, -2, 0], [1, 0, 0, 2], [-2, -1, -2, 0], [-2, 0, 0, 0], [0, 1, 0, 1], [2, 0, 0, 1], [-1, 0, 0, 0], [0, -4, 7, -4], [1, 0, 1, 0], [2, 0, 0, -1], [0, 1, -1, 1], [0, -1, 11, -1], [0, 0, -5, 0], [-2, -1, -2, 0], [2, -1, 2, 0], [0, 2, -2, 2], [0, 2, -2, 2], [0, 1, 2, 1], [-1, 0, 0, 0], [2, -2, 2, 0], [0, 1, -1, 1], [-4, 0, 0, -2], [1, 0, 0, 0], [0, 1, -1, 1], [2, 0, 0, -1], [2, -2, 2, 0], [-2, 0, 0, 1], [0, -1, 0, 0], [2, -1, 2, 0], [0, 2, 0, 0], [0, 0, 2, 0], [-6, 0, 0, 3], [3, 0, 6, -1], [-1, 0, 0, 0], [0, -2, 2, -2], [6, 0, 6, 0], [1, -1, 1, 0], [2, 0, 2, 0], [1, 0, 0, 0], [-1, 0, -1, 0], [1, 0, 0, -2], [0, 0, -4, 0], [-2, 0, 0, -1], [-2, 0, 0, 1], [0, 2, -1, 2], [2, -2, 2, 0], [-2, 0, 0, 1], [0, 4, -4, 4], [0, 0, 2, 0], [0, 3, -12, 3], [0, 1, 0, 0], [1, -1, 1, 0], [0, 1, -2, 1], [0, -2, 2, -2], [0, 0, 1, 0], [-6, 0, 0, -2], [7, -4, 7, 0], [0, -2, -4, -2], [1, 0, 0, 0]]}