# Stored data for newform 1638.2.x.a, downloaded from the LMFDB on 25 April 2024. {"label": "1638.2.x.a", "space_label": "1638.2.x", "level": 1638, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 1580581520998, "dim": 8, "is_polredabs": true, "nf_label": "8.0.836829184.2", "trace_hash": 538586829438250559, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [16, -32, 32, 8, 1, -4, 8, 4, 1]]], "qexp_display": "q-\\beta _{3}q^{2}-\\beta _{7}q^{4}+(\\beta _{2}-\\beta _{5})q^{5}+(-1+\\cdots)q^{7}+\\cdots", "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 91, "char_orbit_label": "x", "char_is_real": false, "Nk2": 6552, "analytic_conductor": 13.079495851085728, "hecke_ring_index": 1, "level_radical": 546, "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": "0.259", "prec": 17}, "analytic_rank_proved": true, "char_values": [1638, 4, [911, 703, 379], [4, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [307, 811], "field_disc": 836829184, "field_disc_factorization": [[2, 16], [113, 2]], "field_poly": [4, 0, 84, 0, 61, 0, 14, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.179", "prec": 17}, {"__RealLiteral__": 0, "data": "6.948", "prec": 17}, {"__RealLiteral__": 0, "data": "7.112", "prec": 17}, {"__RealLiteral__": 0, "data": "198.631", "prec": 24}, {"__RealLiteral__": 0, "data": "420.936", "prec": 24}, {"__RealLiteral__": 0, "data": "9156.030", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, -4, -8], "traces": [0, 8, 0, 0, 0, -4, 0, -8, 0, 0, -4, 0, 0, -16, 4, 0, -8, 4, 0, 8, -4, 0, -12, 0, 0, 0, -16, 0, 0, -12, 0, 8, 0, 0, 8, 24, 0, -4, -4, 0, 0, 12, 0, 0, 0, 0, 24, 0, 0, -32, 8, 0, 4, -40, 0, 0, -4, 0, 4, -8, 0, 0, 8, 0, 0, 12, 0, 32, 0, 0, 0, 12, 0, -20, -20, 0, 8, 8, 0, 24, 4, 0, -40, 44, 0, 20, 20, 0, 0, 16, 0, -12, 28, 0, 0, 0, 0, 8, -16, 0, -12, -16, 0, -12, -4, 0, 4, -8, 0, 28, -12, 0, 8, -40, 0, 8, 0, 0, 0, 4, 0, 0, -28, 0, 8, 4, 0, 0, 0, 0, 32, 0, 0, -40, 0, 0, -8, -28, 0, 0, -20, 0, 0, -24, 0, -44, 0, 0, -4, 20, 0, 24, 0, 0, 12, 0, 0, 0, -12, 0, 4, 36, 0, -40, 12, 0, 0, -40, 0, 28, 20, 0, 20, -8, 0, -52, 0, 0, 0, 0, 0, 64, -12, 0, 24, 0, 0, -16, 0, 0, -28, 44, 0, 12, 40, 0, 0, -44, 0, -28, 8, 0, -28, 16, 0, 0, 56, 0, 16, 0, 0, 36, 0, 0, 24, 24, 0, -48, 0, 0, 20, -16, 0, 28, -4, 0, -48, -24, 0, 24, 0, 0, -4, 0, 0, -8, 8, 0, -36, -48, 0, 80, -32, 0, -44, -12, 0, -48, 0, 0, 0, 44, 0, 4, 4, 0, 8, -8, 0, 16, -4, 0, -4, 40, 0, 24, 12, 0, -32, 0, 0, 28, -4, 0, 28, 8, 0, 0, -8, 0, -8, 0, 0, -24, -12, 0, 56, -40, 0, -36, -36, 0, 20, 56, 0, -48, 0, 0, 0, 64, 0, -8, 108, 0, -8, -60, 0, -8, -20, 0, -16, -32, 0, 0, 52, 0, 0, 48, 0, -16, 4, 0, -24, -56, 0, 0, -104, 0, 0, 8, 0, -40, 44, 0, 0, 8, 0, 0, 32, 0, 20, 0, 0, 88, 20, 0, 24, 48, 0, -44, -44, 0, 12, 64, 0, 64, -16, 0, -76, 12, 0, 0, -20, 0, 0, 76, 0, 0, 0, 0, 16, 44, 0, 48, -28, 0, -16, 28, 0, 52, -36, 0, -32, -112, 0, -8, -24, 0, 8, 0, 0, 0, 16, 0, 0, -44, 0, 148, 24, 0, 0, -64, 0, -24, 0, 0, 28, 0, 0, -28, -8, 0, 0, 64, 0, 0, 16, 0, -8, 0, 0, 0, -4, 0, -4, 0, 0, 48, 0, 0, 0, 40, 0, 48, 0, 0, -28, -12, 0, 28, -12, 0, -24, -64, 0, -16, -32, 0, 0, -124, 0, 0, 0, 0, 8, -36, 0, -140, 0, 0, -8, 116, 0, 8, 12, 0, -20, 156, 0, -72, -8, 0, 0, 12, 0, -40, -52, 0, 0, -96, 0, 4, 0, 0, -20, 0, 0, -96, -28, 0, 32, 0, 0, -132, -8, 0, -8, -88, 0, 104, -4, 0, 12, 0, 0, 36, 0, 0, 8, -12, 0, -36, 0, 0, -8, -40, 0, -24, 16, 0, 4, 0, 0, 0, 52, 0, -20, -40, 0, -108, -64, 0, 20, -72, 0, 16, 48, 0, 68, -40, 0, 100, 0, 0, -8, -132, 0, 104, -28, 0, 0, 72, 0, -36, -36, 0, 80, 68, 0, 36, -24, 0, 40, 44, 0, 8, 68, 0, 16, 0, 0, 0, -8, 0, 52, 16, 0, 40, 64, 0, -44, 8, 0, 80, 4, 0, 0, -64, 0, 0, 76, 0, 4, 104, 0, -32, -20, 0, -28, 84, 0, 0, -32, 0, 24, -80, 0, 0, 4, 0, 0, -32, 0, 44, 0, 0, 36, 28, 0, -112, -56, 0, 92, -16, 0, 24, 4, 0, -12, 4, 0, -16, 12, 0, 0, 60, 0, 124, 76, 0, 0, 0, 0, -176, -4, 0, -68, -40, 0, -200, -52, 0, -40, 20, 0, 0, -12, 0, 0, 80, 0, -32, 0, 0, 0, 96, 0, 0, 40, 0, 52, -160, 0, 0, -48, 0, 28, 0, 0, 24, 0, 0, 24, 48, 0, 0, -28, 0, 0, -12, 0, -24, 0, 0, 0, -8, 0, -64, 0, 0, 20, 0, 0, 0, 0, 0, -24, -12, 0, 24, 76, 0, -32, -16, 0, -44, 24, 0, -24, 24, 0, 68, 48, 0, 0, 0, 0, -20, 0, 0, 104, 0, 0, 16, -4, 0, -24, 0, 0, -8, 36, 0, 56, 108, 0, 32, 52, 0, -16, 32, 0, 0, 0, 0, 8, 0, 0, -72, 0, 0, -28, -96, 0, 76, 0, 0, -12, 140, 0, 132, 0, 0, 12, -76, 0, -48, 0, 0, -12, 0, 0, -56, 44, 0, 32, -36, 0, -24, 44, 0, -96, -8, 0, -24, 0, 0, 0, -112, 0, 16, -8, 0, 16, -124, 0, 108, -64, 0, 28, 8, 0, 0, 96, 0, -12, 0, 0, -36, -28, 0, 0, -16, 0, 0, -56, 0, -144, 112, 0, -132, 8, 0, -4, -48, 0, 100, 28, 0, 68, -8, 0, 20, 0, 0, 0, 4, 0, 108, 40, 0, -64, 56, 0, 32, -88, 0, -24, 32, 0, 0, -24, 0, 0, -76, 0, -104, 48, 0, 40, 76, 0, 76, 44, 0, 0, -92, 0, 64, 88, 0, 0, 76, 0, 0, -44, 0, 8, 0, 0, -108, 20, 0, 28, -8, 0, -92, 4, 0, 68, 88, 0, -80, -32, 0, 48, 80, 0, 0, -24, 0, -64, 148, 0, 0, 0, 0, -24, 48, 0, 184, -52, 0, -44, 20, 0, 40, -180, 0, -4, -168, 0, -16, -24, 0, -84, 0, 0, 0, -88, 0, 0, -16, 0, 64, 8, 0, 0, 8, 0, 76, 0, 0, -24, 0, 0, 0, 48, 0, 0, 136, 0, 0, 64, 0, -80, 0, 0, -128, -32, 0, -104, 0, 0, 88, 0, 0, 0, 76, 0, -120, 60, 0, -4, -120, 0, 184, -96, 0, 0, -204, 0, -112, -8, 0, -148, 0, 0, 0, 0, 0, -12, 76, 0, 12, 0, 0, 112, 32, 0, 96, 0, 0, -4, 0, 0, 64, 4, 0, -36, 160, 0, 44, -184, 0, 0, 28, 0, -88, 0, 0, -36, 0, 0, 84, 0, 0, -28, 0, 0, -28, -12, 0, -72, -72, 0, -52, 48, 0, -4, 0, 0, -12, 0, 0, -40, 40, 0, -56, -136, 0, 24, -152, 0, -32, 52, 0, 76, 0, 0, 0, 112, 0, -32, -52, 0, -40, -40, 0, 48, -80, 0, 48, 60, 0, -28, 104, 0, 88, 0, 0, -56, -56, 0, -32, -64, 0, 0, -48, 0, 112, -8, 0, 148, 52, 0, -44, 120, 0, 40, -192, 0, 92, -8, 0, 160, 0, 0, 0, -44, 0, 0, -104, 0, -32, 0, 0, 36, -100, 0, -56, 96, 0, 0, -116, 0, 0, -12, 0, -8, 28, 0, -40, -16, 0, 12, -80, 0, 0, -24, 0, 12, 24, 0, 0, 176, 0, 0, -60, 0, -40, 0, 0, 44, -128, 0, 44, -32, 0, 20, -20, 0, -24, -56, 0, -128, 16, 0, -144, 56, 0, 0, 140, 0, -16, 20, 0, 0, 0, 0, 0, 0, 0, 56, 188, 0, 88, -124, 0, -48, 68, 0, 84, -8, 0, 0, 88, 0, 132, 0, 0, 0, 32, 0, 0, 8, 0, -8, -52, 0, 0, 60, 0, 8, 0, 0, 44, 0, 0, 8, 64, 0, 0, -8, 0, 0, -4, 0, 8, 0, 0, -16, 132, 0, 8, 0, 0, -88, 0, 0, 0, 8, 0, -72, 132, 0, -56, 52, 0, 12, 52, 0, -80, 140, 0, -24, -12, 0, -84, -48, 0, 0, 0, 0, -16, 124, 0, -16, 0, 0, -12, -4, 0, 132, -8, 0, 88, 28, 0, 4, 84, 0, -8, -56, 0, 100, -68, 0, 0, 140, 0, 8, 0, 0, 56, 0, 0, 60, 64, 0, -72, 0, 0, 40, 24, 0, 128, -8, 0, -24, -24, 0, -116, 0, 0, 40, 0, 0, 32, -44, 0, 48, -144, 0, -48, -12, 0, -60, -76, 0, -28, 0, 0, 0, -184, 0, -84, -128, 0, -20, -184, 0, 32, 0, 0, 36, -216, 0, -156, -32, 0, -20, 0, 0, 8, -40, 0, 52, -48, 0, 0, -24, 0, 0, 288, 0, 124, -20, 0, 160, -96, 0, -264, -24, 0, -24, 100, 0, -276, 0, 0, 0, 88, 0, 52, -48, 0, 44, -124, 0, 168, 16, 0, -60, 180, 0, 0, -44, 0, 0, -116, 0, 104, 64, 0, 56, -44, 0, 108, 48, 0, 0, 32, 0, -72, -16, 0, 0, -236, 0, 0, 36, 0, -76, 0, 0, 56, 12, 0, 52, -80, 0, -124, -76, 0, -52, 72, 0, 92, 20, 0, 68, -64, 0, 0, -40, 0, 12, 16, 0, 0, 0, 0, 4, 124, 0, -104, -96, 0, -96, 216, 0, 40, -28, 0, -20, -4, 0, -40, -56, 0, 16, 0, 0, 0, -12, 0, 0, 224, 0, 84, 84, 0, 0, -60, 0, -104, 0, 0, -160, 0, 0, 164, 72, 0, 0, 92, 0, 0, 32, 0, -20, 0, 0, 100, -64, 0, -52, 0, 0, 24, 0, 0, 0, 0, 0, -56, 128, 0, 32, -40, 0, 24, -112, 0, -52, 208, 0, 120, -52, 0, -32, -60, 0, 0, 0, 0, 124, -60, 0, 40, 0, 0, -8, 140, 0, -76, 176, 0, -16, 120, 0, -32, -12, 0, 84, -28, 0, -124, 16, 0, 0, -32, 0, -16, 0, 0, 64, 0, 0, -88, -44, 0, 0, 0, 0, -24, 72, 0, -148, 176, 0, 64, -24, 0, -20, 0, 0, -108, 0, 0, 12, 88, 0, 32, -64, 0, 68, -192, 0, 208, 156, 0, 8, 0, 0, 0, 16, 0, 60, 136, 0, 168, -12, 0, 48, -148, 0, -88, 44, 0, 108, -132, 0, -12, 0, 0, -28, -344, 0, -24, -8, 0, 0, -48, 0, 0, -24, 0, 12, -24, 0, -48, 48, 0, -4, 104, 0, 52, -4, 0, 8, 0, 0, 0, 4, 0, -32, 72, 0, 104, 68, 0, -8, 8, 0, -156, 68, 0, 0, -120, 0, 0, 112, 0, 0, 36, 0, -248, 4, 0, -132, -88, 0, 0, -20, 0, -4, -112, 0, 0, -72, 0, 0, -12, 0, -16, 0, 0, 16, 44, 0, 52, 8, 0, 184, -84, 0, -72, -196, 0, -52, 148, 0, 36, -40, 0, 0, 104, 0, 148, -96, 0, 0, 0, 0, -168, 16, 0, -56, -40, 0, -176, -148, 0, -28, 336, 0, 128, 12, 0, 48, 84, 0, -44, 0, 0, 0, -32, 0, 0, 12, 0, 0, 48, 0, 0, 36, 0, -8, 0, 0, 4, 0, 0, -212, -176, 0, 0, -184, 0, 0, 60, 0, 36, 0, 0, 16, -120, 0, -12, 0, 0, -8, 0, 0, 0, -124, 0, 72, 0, 0, -76, -112, 0, 96, 32, 0, -16, 40, 0, -16, 16, 0, 20, -8, 0, 0, 0, 0, 224, 88, 0, -80, 0, 0, -120, -88, 0, 140, 96, 0, 32, -88, 0, -64, 24, 0, -156, 40, 0, -8, -60, 0, 0, 116, 0, -112, 0, 0, 172, 0, 0, 8, -220, 0, -128, 0, 0, 112, 208, 0, 16, -16, 0, -20, 20, 0, 16, 0, 0, -12, 0, 0, 180, -84, 0, 40, -88, 0, 40, 8, 0, -224, 196, 0, 140, 0, 0, 0, 220, 0, 120, -12, 0, 20, 200, 0, 160, -44, 0, 40, -204, 0, -56, -4, 0, -28, 0, 0, -176, 156, 0, 72, 260, 0, 0, 96, 0, -56, 20, 0, -160, 32, 0, 28, -40, 0, -80, 96, 0, 160, 48, 0, 320, 0, 0, 0, 124, 0, -196, -16, 0, 24, -148, 0, 128, 64, 0, 96, -112, 0, 0, 28, 0, 0, -112, 0, -36, 4, 0, -28, 16, 0, 40, -120, 0, 0, 136, 0, -156, 12, 0, 0, 48, 0, 0, 4, 0, -112, 0, 0, 92, 108, 0, -8, -280, 0, -88, -48, 0, 92, 136, 0, 184, -36, 0, -104, 16, 0, 0, -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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 91, 9, 1, 4, 0]], "char_orbit_index": 24, "prim_orbit_index": 9, "minimal_twist": "546.2.o.b", "char_is_minimal": true, "conrey_index": 307, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, -1, 1, 0, -1], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, -1, 0], [0, 1, 2, -1, 0, -1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 2, 0, 0, 1, -1, 0], [0, 1, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, -1, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 1, 1, 1], [0, 0, 0, 1, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 1, 1, -1, 0], [0, 1, -2, 2, 1, -1, 0, 5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 1, -1, 1, 0, -2], [-2, 0, -1, 2, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -1, 1, 1, 0, 1], [-4, 0, -2, -2, 2, 2, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 2, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 1, 1, 0, -1, 0, -1, -1], [2, -1, -1, -1, 1, 1, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, -1, 0, 0], [-2, 0, -2, -2, 1, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 1], [1, 1, 5, -1, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, 2, 0, 0, 0, 3], [0, -1, -1, 2, -1, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [3, -1, -4, 1, 0, 1, -1, 2], [0, 0, 0, -2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 4, 0, 2, -2, 0, 3], [0, 1, 1, -1, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 1, 0, 0, 3], [-6, 0, -2, -2, -1, -1, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 2, -2, 0, 0, 0, 3], [-1, -1, -2, 0, 0, 0, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -2, -2, 1, 1, 0, 2, -1], [-1, 4, 4, -2, 4, 0, -4, 5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 7, -7, 2, -2, 0, -1], [0, 0, -2, -2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 2, -4, -1, 1, 2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [5, 2, 2, 6, 0, 0, -2, -3], [0, 1, 1, -1, -1, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 2, -3, 0, -1, 1, -1], [4, 3, 3, 3, -2, 0, -3, -1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 4, 1, -1, 0, -4, 4], [-2, 0, 1, 1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, 0, 1, 0, 1, -1], [0, -3, -4, 6, 0, 2, 0, -5], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, -1, 1, 1, 4, 0], [0, 0, -1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-6, 0, -2, -2, 1, 1, 0, 0], [7, -1, 1, 1, 0, -2, -1, 6], [0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -3, 0, 0, 1, 0, 2], [2, 0, -3, 0, 0, 1, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, -1, 1, -1, 0, 3], [3, 2, 2, -4, 0, 0, -2, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, -2, 1, -4, 4, 2], [4, 0, -3, -3, -1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2], [0, -1, 4, -4, 2, -2, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, -4, -4, 0, -2, 4, 4], [-2, -2, -1, 6, 0, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, -2, -2, 1, 1, 1, 0]]}