# Stored data for newform 1400.1.m.c, downloaded from the LMFDB on 18 April 2024.
{"label": "1400.1.m.c", "space_label": "1400.1.m", "level": 1400, "weight": 1, "hecke_orbit": 3, "hecke_orbit_code": 9008023905240440, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 578394944507430476, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [0, 1]], [11, [3, 0, 1]], [23, [-1, 1]], [113, [1, 1]]], "qexp_display": "q+\\zeta_{6}^{2}q^{2}-\\zeta_{6}q^{4}+q^{7}+q^{8}-q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 56, "char_orbit_label": "m", "char_is_real": true, "Nk2": 1400, "analytic_conductor": 0.6986910176862033, "hecke_ring_index": 1, "level_radical": 70, "projective_image": "D6", "projective_image_type": "Dn", "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "projective_field_label": "6.0.109760000.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.755", "prec": 17}, "analytic_rank_proved": true, "char_values": [1400, 2, [351, 701, 1177, 801], [2, 1, 2, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 4, "level_primes": [2, 5, 7], "conrey_indexes": [1301], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.024", "prec": 20}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "-0.328", "prec": 20}, {"__RealLiteral__": 0, "data": "23.285", "prec": 20}, {"__RealLiteral__": 0, "data": "-5.044", "prec": 20}, {"__RealLiteral__": 0, "data": "341.168", "prec": 24}], "related_objects": [], "self_twist_discs": [-7], "cm_discs": [-7], "rm_discs": [], "relative_dim": 2, "trace_display": [-1, 0, 0, 2], "traces": [0, 2, -1, 0, -1, 0, 0, 2, 2, -2, 0, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 3, 2, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, 0, -1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 3, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, -3, 0, 0, 0, 0, -4, 0, 0, 0, 0, 1, 2, -1, 0, 0, 0, 0, 0, -3, 0, 0, -4, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, -3, 0, 0, -2, 0, 0, 3, 0, 0, 0, -1, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, -2, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -6, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, -3, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 3, 0, -1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 2, 0, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -3, 0, 0, 0, 3, -2, 0, 2, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -4, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 0, -4, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 3, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -4, 0, 2, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, -3, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -6, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 6, 0, 2, 0, 0, 3, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 3, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 3, 0, 3, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, -2, 0, -4, 0, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, -3, 0, 0, 0, 3, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 2, 0, 0, 0, 0, -3, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0], "projective_field": [56, 0, 8, 0, -2, 0, 1], "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, -7], [1, 1, 8, 2, 1, 2, 0], [1, 1, 56, 8, -1, 2, 0]], "char_orbit_index": 13, "prim_orbit_index": 8, "minimal_twist": "1400.1.m.c", "char_is_minimal": true, "conrey_index": 1301, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[1, 2]], [], [[-1, 1]], [], [], [[1, 0]], [[1, 0]], [[-1, 0]], [], [[-1, 1], [-1, 2]], [], [], [[1, 2]], [], [[1, 2]], [], [[-1, 2]], [], [], [], [[1, 0], [1, 1]], [[1, 0]], [], [], [], [], [[-1, 1]], [[-1, 1], [-1, 2]], [], [], [[-1, 1]], [], [], [], [[1, 1]], [[-1, 1], [-1, 2]], [], [], [], [], [], [[1, 1], [1, 2]], [[-1, 0], [1, 2]], [], [[1, 2]], [], [], [[1, 0]], [], [], [], [], [], [], [[1, 0]], [], [[1, 0], [1, 1]], [], [], [], [], [[-1, 0]], [[1, 0]], [], [], [[1, 1], [1, 2]], [], [], [], [[1, 0]], [[-1, 0]], [], [[1, 0], [1, 1]], [], [], [[-1, 1], [-1, 2]], [], [[1, 0]], [], [[1, 0]], [], [], [], [], [[-1, 0], [-1, 1]], [], [[-1, 1], [-1, 2]], [], [], [], [[-1, 1]], [], [], [], [], [], [[1, 2]], [[1, 1], [1, 2]], []]}