# Stored data for newform 378.2.e.b, downloaded from the LMFDB on 30 March 2023.
{"level_primes": [2, 3, 7], "is_polredabs": true, "sato_tate_group": "1.2.3.c3", "rm_discs": [], "conrey_indexes": [37, 235], "cm_discs": [], "trace_hash": 876307388132561875, "level_radical": 42, "hecke_ring_index_proved": true, "self_twist_type": 0, "related_objects": [], "prim_orbit_index": 8, "is_cm": false, "hecke_orbit": 2, "analytic_conductor": 3.0183451964043986, "inner_twist_count": 2, "field_disc_factorization": [[-1, 1], [3, 1]], "is_rm": false, "char_order": 3, "level_is_square": false, "weight_parity": 1, "label": "378.2.e.b", "field_poly_is_real_cyclotomic": false, "is_self_twist": false, "is_twist_minimal": false, "minimal_twist": "126.2.e.a", "field_poly_is_cyclotomic": true, "dim": 2, "trace_zratio": {"__RealLiteral__": 0, "data": "0.009", "prec": 17}, "traces": [0, 2, 2, 0, 2, 3, 0, -4, 2, 0, 3, -3, 0, 1, -4, 0, 2, 3, 0, 7, 3, 0, -3, -9, 0, -4, 1, 0, -4, 3, 0, 16, 2, 0, 3, -15, 0, 1, 7, 0, 3, 3, 0, 1, -3, 0, -9, 0, 0, 2, -4, 0, 1, 3, 0, -18, -4, 0, 3, 0, 0, 4, 16, 0, 2, 6, 0, -8, 3, 0, -15, -24, 0, -11, 1, 0, 7, -3, 0, -32, 3, 0, 3, -9, 0, -9, 1, 0, -3, 3, 0, 1, -9, 0, 0, 42, 0, 1, 2, 0, -4, 3, 0, 13, 1, 0, 3, 9, 0, 13, -18, 0, -4, -9, 0, 27, 3, 0, 0, -15, 0, 2, 4, 0, 16, 6, 0, -8, 2, 0, 6, 15, 0, 7, -8, 0, 3, -9, 0, 7, -15, 0, -24, 3, 0, -9, -11, 0, 1, -9, 0, 7, 7, 0, -3, 24, 0, -44, -32, 0, 3, 45, 0, 19, 3, 0, -9, -15, 0, 12, -9, 0, 1, 12, 0, -4, -3, 0, 3, -21, 0, 4, 1, 0, -9, 6, 0, -18, 0, 0, 42, 0, 0, 28, 1, 0, 2, -36, 0, 25, -4, 0, 3, -15, 0, 18, 13, 0, 1, 21, 0, -5, 3, 0, 9, -3, 0, -32, 13, 0, -18, 6, 0, 1, -4, 0, -9, -3, 0, 13, 27, 0, 3, 3, 0, 0, 0, 0, -15, -3, 0, 13, 2, 0, 4, 39, 0, -7, 16, 0, 6, -24, 0, 54, -8, 0, 2, -21, 0, 1, 6, 0, 15, 9, 0, -9, 7, 0, -8, 15, 0, -5, 3, 0, -9, -12, 0, 1, 7, 0, -15, -21, 0, -8, -24, 0, 3, 3, 0, 8, -9, 0, -11, -9, 0, 0, 1, 0, -9, -18, 0, -5, 7, 0, 7, 6, 0, -56, -3, 0, 24, 48, 0, -20, -44, 0, -32, -36, 0, -18, 3, 0, 45, 42, 0, 4, 19, 0, 3, 0, 0, 16, -9, 0, -15, -12, 0, 13, 12, 0, -9, -24, 0, 20, 1, 0, 12, -24, 0, -23, -4, 0, -3, 3, 0, -36, 3, 0, -21, 9, 0, -30, 4, 0, 1, 33, 0, -17, -9, 0, 6, -15, 0, 13, -18, 0, 0, 6, 0, -56, 42, 0, 0, 15, 0, 36, 28, 0, 1, 27, 0, 27, 2, 0, -36, -48, 0, 13, 25, 0, -4, 27, 0, 8, 3, 0, -15, 3, 0, -68, 18, 0, 13, 0, 0, 27, 1, 0, 21, 9, 0, -35, -5, 0, 3, -24, 0, -8, 9, 0, -3, 27, 0, 4, -32, 0, 13, -126, 0, 16, -18, 0, 6, -72, 0, 18, 1, 0, -4, -12, 0, 9, -9, 0, -3, -12, 0, -20, 13, 0, 27, -9, 0, -41, 3, 0, 3, -3, 0, 16, 0, 0, 0, -6, 0, 28, -15, 0, -3, -3, 0, -1, 13, 0, 2, -3, 0, 25, 4, 0, 39, 21, 0, -9, -7, 0, 16, 48, 0, 25, 6, 0, -24, 48, 0, 18, 54, 0, -8, -9, 0, 55, 2, 0, -21, -39, 0, 0, 1, 0, 6, 3, 0, 7, 15, 0, 9, 24, 0, -58, -9, 0, 7, -3, 0, 54, -8, 0, 15, 33, 0, -11, -5, 0, 3, -39, 0, -11, -9, 0, -12, 42, 0, 64, 1, 0, 7, -9, 0, 2, -15, 0, -21, -24, 0, -54, -8, 0, -24, 36, 0, 64, 3, 0, 3, 72, 0, 25, 8, 0, -9, 45, 0, -18, -11, 0, -9, 3, 0, 56, 0, 0, 1, 39, 0, -9, -9, 0, -18, 48, 0, 25, -5, 0, 7, -6, 0, 13, 7, 0, 6, 0, 0, -23, -56, 0, -3, -45, 0, -17, 24, 0, 48, 3, 0, 29, -20, 0, -44, 6, 0, 16, -32, 0, -36, -12, 0, -11, -18, 0, 3, -33, 0, -29, 45, 0, 42, -21, 0, 0, 4, 0, 19, 15, 0, -45, 3, 0, 0, 3, 0, -44, 16, 0, -9, -84, 0, 27, -15, 0, -12, -6, 0, -35, 13, 0, 12, 60, 0, -5, -9, 0, -24, -9, 0, -54, 20, 0, 1, 6, 0, 88, 12, 0, -24, 42, 0, 18, -23, 0, -4, 36, 0, -7, -3, 0, 3, 3, 0, 52, -36, 0, 3, -72, 0, -9, -21, 0, 9, -15, 0, -65, -30, 0, 4, -24, 0, 13, 1, 0, 33, -3, 0, 1, -17, 0, -9, 12, 0, -23, 6, 0, -15, 21, 0, 27, 13, 0, -18, 9, 0, 13, 0, 0, 6, 42, 0, -44, -56, 0, 42, -45, 0, -65, 0, 0, 15, 0, 0, -23, 36, 0, 28, 27, 0, -32, 1, 0, 27, -21, 0, 36, 27, 0, 2, -66, 0, -56, -36, 0, -48, -9, 0, 2, 13, 0, 25, -21, 0, 0, -4, 0, 27, 66, 0, 27, 8, 0, 3, -33, 0, 40, -15, 0, 3, 114, 0, 14, -68, 0, 18, 84, 0, -80, 13, 0, 0, -72, 0, -11, 27, 0, 1, 39, 0, -90, 21, 0, 9, 15, 0, 20, -35, 0, -5, -36, 0, -10, 3, 0, -24, -18, 0, 1, -8, 0, 9, 3, 0, 25, -3, 0, 27, -51, 0, 18, 4, 0, -32, 48, 0, -4, 13, 0, -126, -12, 0, -47, 16, 0, -18, 36, 0, 40, 6, 0, -72, -33, 0, 16, 18, 0, 1, 0, 0, 63, -4, 0, -12, 24, 0, -9, 9, 0, -9, 6, 0, 43, -3, 0, -12, 39, 0, 54, -20, 0, 13, -75, 0, -53, 27, 0, -9, -12, 0, 4, -41, 0, 3, -36, 0, -77, 3, 0, -3, -27, 0, 52, 16, 0, 0, 12, 0, -54, 0, 0, -6, -24, 0, -22, 28, 0, -15, -12, 0, 0, -3, 0, -3, -9, 0, 66, -1, 0, 13, 42, 0, -41, 2, 0, -3, 33, 0, 7, 25, 0, 4, 60, 0, 9, 39, 0, 21, -15, 0, -54, -9, 0, -7, 9, 0, 25, 16, 0, 48, -75, 0, 13, 25, 0, 6], "hecke_ring_index_factorization": [], "nf_label": "2.0.3.1", "field_poly": [1, -1, 1], "has_non_self_twist": 1, "char_values": [378, 3, [29, 325], [1, 1]], "Nk2": 1512, "field_poly_root_of_unity": 6, "analytic_rank": 0, "char_orbit_label": "e", "weight": 2, "trace_display": [2, 0, 3, -4], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+q^{2}+q^{4}+(3-3\\zeta_{6})q^{5}+(-1-2\\zeta_{6})q^{7}+\\cdots", "self_twist_discs": [], "char_is_real": false, "field_disc": -3, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[5, [9, -3, 1]]], "space_label": "378.2.e", "level": 378, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 63, 8, 1, 3, 0]], "char_degree": 2, "char_conductor": 63, "char_orbit_index": 5, "hecke_ring_generator_nbound": 7, "hecke_orbit_code": 4503874538832250, "trace_moments": [{"__RealLiteral__": 0, "data": "0.001", "prec": 17}, {"__RealLiteral__": 0, "data": "2.017", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.460", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "115.824", "prec": 24}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0], [1, 0], [1, 0], [0, 0], [1, 0], [3, -3], [0, 0], [-1, -2], [1, 0], [0, 0], [3, -3], [0, -3], [0, 0], [0, 1], [-1, -2], [0, 0], [1, 0], [3, -3], [0, 0], [0, 7], [3, -3], [0, 0], [0, -3], [-9, 9], [0, 0], [0, -4], [0, 1], [0, 0], [-1, -2], [3, -3], [0, 0], [8, 0], [1, 0], [0, 0], [3, -3], [-9, 3], [0, 0], [0, 1], [0, 7], [0, 0], [3, -3], [0, 3], [0, 0], [1, -1], [0, -3], [0, 0], [-9, 9], [0, 0], [0, 0], [-3, 8], [0, -4], [0, 0], [0, 1], [3, -3], [0, 0], [-9, 0], [-1, -2], [0, 0], [3, -3], [0, 0], [0, 0], [2, 0], [8, 0], [0, 0], [1, 0], [3, 0], [0, 0], [-4, 0], [3, -3], [0, 0], [-9, 3], [-12, 0], [0, 0], [-11, 11], [0, 1], [0, 0], [0, 7], [-6, 9], [0, 0], [-16, 0], [3, -3], [0, 0], [0, 3], [-9, 9], [0, 0], [0, -9], [1, -1], [0, 0], [0, -3], [0, 3], [0, 0], [2, -3], [-9, 9], [0, 0], [0, 0], [21, 0], [0, 0], [1, -1], [-3, 8], [0, 0], [0, -4]]}