# Stored data for newform 370.2.e.b, downloaded from the LMFDB on 19 April 2024.
{"label": "370.2.e.b", "space_label": "370.2.e", "level": 370, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538832242, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 2251760597673217724, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 1, 1]], [7, [4, 2, 1]]], "qexp_display": "q+(1-\\zeta_{6})q^{2}-\\zeta_{6}q^{3}-\\zeta_{6}q^{4}+\\zeta_{6}q^{5}+\\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": true, "field_poly_root_of_unity": 6, "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": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [370, 3, [297, 261], [3, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 5, 37], "conrey_indexes": [121, 211], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.031", "prec": 17}, {"__RealLiteral__": 0, "data": "0.133", "prec": 17}, {"__RealLiteral__": 0, "data": "12.464", "prec": 20}, {"__RealLiteral__": 0, "data": "0.634", "prec": 17}, {"__RealLiteral__": 0, "data": "117.193", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [1, -1, 1, -2], "traces": [0, 2, 1, -1, -1, 1, -2, -2, -2, 2, 2, 0, -1, -5, -4, 1, -1, 0, -2, -2, 1, -2, 0, 0, 1, -1, -10, -10, -2, 12, -1, -2, 1, 0, 0, 2, -4, 11, -4, -5, -1, 9, 2, -2, 0, 4, 0, -12, 2, 3, 1, 0, -5, 9, -5, 0, 2, -2, 6, 12, -2, 10, 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-24, 12, 22, 9, -5, 0, 0, -24, 37, -20, -4, 3, -24, 0, 40, -1, -36, 18, 24, -5, 12, -16, 17, 2, 0, -6, 20, 14, 4, 0, 2, -8, 106, 38, 15, 0, -18, -12, 43, 0, -12, 15, -84, 1, 32, -6, 0, 28, 12, 0, -12, -4, 0, 30, -12, 2, 0, 0, 2, 0, 14, -7, 4, -3, 0, -10, 102, -2, 0, 56, 20, -26, 24, 0, 40, 0, -29, -18, 60, 0, -10, 32, -8, 6, -21, 1, -12, -18, 42, -27, 0, 20, 34, -8, 52, -6, 36, 17, 0, 12, -10, 0, 21, -8, -40, 2, 6, 0, 36, -36, 3, 0, 0, -15, -24, 1, -60, -55, -12, 10, -4, 0, 16, 22, 0, 4, -12, 32, -64, -34, -5, -20, 6, 11, 0, -3, 28, -36, 42, -9, 30, 0, 12, 20, 0, 0, 94, -1, -44, -24, -13, 12, -53, -64, -55, 2], "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.b", "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], [1, 0], [1, -1], [0, -1], [0, -1], [0, 1], [-1, 0], [0, -2], [-1, 0], [2, -2], [1, 0], [0, 0], [-1, 1], [0, -5], [-2, 0], [1, -1], [-1, 1], [0, 0], [0, -2], [0, -2], [1, -1], [-2, 2], [0, 0], [0, 0], [0, 1], [-1, 1], [-5, 0], [-5, 0], [-2, 2], [6, 0], [0, -1], [-1, 0], [0, 1], [0, 0], [0, 0], [2, -2], [-2, 0], [4, 3], [-2, 0], [-5, 5], [0, -1], [0, 9], [0, 2], [-1, 0], [0, 0], [2, 0], [0, 0], [-6, 0], [1, 0], [3, -3], [0, 1], [0, 0], [-5, 5], [9, -9], [-5, 5], [0, 0], [0, 2], [-2, 2], [6, -6], [12, -12], [-1, 0], [0, 10], [-1, 1], [-4, 0], [1, 0], [5, -5], [0, 0], [0, 4], [0, 0], [0, 0], [0, -2], [0, 12], [-2, 2], [8, 0], [7, -4], [1, 0], [-2, 2], [0, 0], [0, 5], [0, 4], 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