# Stored data for newform 1408.2.g.d, downloaded from the LMFDB on 01 June 2024.
{"Nk2": 5632, "analytic_conductor": 11.242936604596277, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 88, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 2, "char_parity": 1, "char_values": [1408, 2, [639, 133, 1025], [1, 1, 1]], "cm_discs": [], "conrey_index": 703, "dim": 4, "field_disc": 3136, "field_disc_factorization": [[2, 6], [7, 2]], "field_poly": [2, -8, 9, -2, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [-1, 1]], [7, [-14, 0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511211232527744, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 2, -1, 2, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 88, 7, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "1408.2.g.d", "level": 1408, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 11], "level_radical": 22, "minimal_twist": "1408.2.g.a", "nf_label": "4.0.3136.2", "prim_orbit_index": 7, "qexp_display": "q+q^{3}-\\beta _{3}q^{5}+\\beta _{1}q^{7}-2q^{9}+(-3+\\cdots)q^{11}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1408.2.g", "trace_display": [0, 4, 0, 0], "trace_hash": 285961792888263720, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.551", "prec": 17}, {"__RealLiteral__": 0, "data": "0.776", "prec": 17}, {"__RealLiteral__": 0, "data": "106.146", "prec": 24}, {"__RealLiteral__": 0, "data": "45.915", "prec": 20}, {"__RealLiteral__": 0, "data": "4063.813", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.758", "prec": 17}, "traces": [0, 4, 0, 4, 0, 0, 0, 0, 0, -8, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -20, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 12, 0, -56, 0, 0, 0, 0, 0, -12, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 28, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -36, 0, 84, 0, 0, 0, 0, 0, 84, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -56, 0, 12, 0, 0, 0, 0, 0, -56, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -12, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 132, 0, -28, 0, 0, 0, 0, 0, 4, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, -56, 0, -60, 0, 0, 0, 0, 0, -84, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, -12, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 64, 0, 72, 0, 0, 0, 0, 0, 84, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 84, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 108, 0, 0, 0, 0, 0, -124, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, -180, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -132, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 112, 0, -168, 0, 0, 0, 0, 0, 84, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, -144, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, -224, 0, -56, 0, 0, 0, 0, 0, -24, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, 112, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -116, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, -124, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 280, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 168, 0, 0, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, -72, 0, -180, 0, 0, 0, 0, 0, -108, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 224, 0, 132, 0, 0, 0, 0, 0, -28, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 4, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, -84, 0, 252, 0, 0, 0, 0, 0, -204, 0, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 28, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, 0, 120, 0, 168, 0, 0, 0, 0, 0, 216, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, -156, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 36, 0, -140, 0, 0, 0, 0, 0, -60, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, -84, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, -84, 0, -144, 0, 0, 0, 0, 0, -112, 0, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, -56, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, -220, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 0, 0, -88, 0, 36, 0, 0, 0, 0, 0, -336, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 276, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -112, 0, 0, 0, 0, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 140, 0, 64, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 192, 0, -168, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 156, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48, 0, 264, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108, 0, 0, 0, 0, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, -228, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 96, 0, -48, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 300, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, -116, 0, -48, 0, 0, 0, 0, 0, 108, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -124, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -280, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 308, 0, 0, 0, 0, 0, 0, 0, -84, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, -168, 0, -112, 0, 0, 0, 0, 0, 364, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, -224, 0, 0, 0, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 1, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 0, 0, 0], [-3, 0, 1, 0], [0, 0, 0, 0], [0, 0, 7, 0], [0, 0, 0, 0], [0, 0, 0, 3], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 4], [0, 0, 0, 0], [7, 0, 0, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, -1, 0, 3], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [-9, 0, 0, 0], [0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, -7, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 0, -9, 0], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, -2], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 6, 0], [0, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [3, 0, 0, 0], [0, 0, 0, 0], [-14, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -3], [0, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [6, 0, -2, 0], [0, 0, 0, 0]]}