# Stored data for newform 195.2.bb.a, downloaded from the LMFDB on 17 April 2026. {"Nk2": 780, "analytic_conductor": 1.5570828394149674, "analytic_rank": 1, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 28, "char_orbit_label": "bb", "char_order": 6, "char_parity": 1, "char_values": [195, 6, [131, 157, 106], [6, 6, 1]], "cm_discs": [], "conrey_index": 121, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[2, [4, 12, 14, 6, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 1855459426499, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 5, 1, 6, 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": "195.2.bb.a", "level": 195, "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": true, "level_primes": [3, 5, 13], "level_radical": 195, "minimal_twist": "195.2.bb.a", "nf_label": "4.0.144.1", "prim_orbit_index": 5, "qexp_display": "q+(-1+\\zeta_{12}-\\zeta_{12}^{2})q^{2}+(-1+\\zeta_{12}^{2}+\\cdots)q^{3}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "195.2.bb", "trace_display": [-6, -2, 0, -12], "trace_hash": 1128853727821196218, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.775", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "53.608", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1230.245", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.187", "prec": 17}, "traces": [0, 4, -6, -2, 4, 0, 6, -12, 0, -2, 2, -12, -8, 0, 20, 0, -16, -10, 0, -12, -12, 0, 12, -8, 12, -4, -4, 4, -12, 2, 2, 0, 48, 12, 0, 2, 4, 0, 16, 0, 24, -6, -10, -4, 0, 0, 36, 0, -16, 12, 6, 20, 36, 0, -6, 0, 12, 0, 0, -6, 0, -2, -22, 12, -64, 14, -24, -12, 8, -8, 0, -6, -12, 0, 8, 2, 0, 48, -10, -20, -24, -2, 20, 0, 12, -6, 0, 2, -24, 6, -4, -10, -80, 18, 28, 4, 0, -12, -12, 0, -4, 4, -24, -8, -84, -4, -24, -10, 4, 0, -12, 0, 0, -32, -8, -12, -16, 0, 48, 66, -12, 2, 0, 6, 60, 0, -10, 12, 48, 8, -24, 12, 24, 28, -6, 0, -24, -42, 0, 22, 20, -18, -32, 0, 32, -6, 26, 12, 0, 0, -6, 0, 0, -10, -60, 8, 12, 32, 54, 0, 16, 0, 6, -12, 0, 0, 24, -12, -24, -46, -8, 12, 20, 10, 0, 12, 96, 0, -12, -6, 12, 72, -6, 4, 120, 8, -22, 0, -96, -12, 0, 10, 32, -24, -28, -4, -48, -24, 12, -30, 0, 12, -36, 0, 8, 14, 30, 16, 96, 48, -6, -30, 48, 0, -12, 6, 0, 32, 26, -36, 48, 18, -16, -48, -80, 2, 0, 30, 0, 0, 20, -24, 24, -40, 14, -20, -120, 10, -44, 0, 24, -36, 0, -2, -20, -24, -40, -20, -120, -12, -2, 0, 0, 48, -6, 0, -32, 18, -18, -16, 20, -4, -24, 30, -24, 0, -48, -6, 0, -14, 2, -6, 112, 14, 96, 12, 40, -8, 0, -18, -60, 0, 28, -4, 120, -8, 36, -4, -48, -22, 4, 0, -12, 54, 0, -18, -48, -12, -16, 48, 8, 18, 40, 4, 0, -12, 24, 0, 24, 4, -30, -20, 24, -64, -42, 2, -68, 0, 24, -12, 0, -10, -52, 72, -8, 0, 60, -6, -96, -26, 0, 42, -96, 0, -16, -18, 72, -48, 90, 64, 48, -36, -8, 0, -60, 12, 0, -20, 8, 90, -20, 0, -192, -24, -24, 22, 0, -66, 60, 0, -12, -6, -120, -4, -40, 20, 6, 12, -112, 0, -24, 24, 0, 28, 48, 0, 192, 24, 20, -6, 16, 12, 0, -30, -48, 0, 50, -4, 132, -56, 18, 56, 72, -6, 32, 0, -24, 60, 0, 28, 16, -60, 12, -28, 112, 0, 4, 0, 0, 30, -48, 0, -44, -6, -36, -24, -80, -44, -48, 18, 20, 0, 102, 18, 0, 10, 16, 24, 128, 0, -20, -60, -16, 20, 0, 6, -132, 0, 26, 10, -72, -24, 28, -36, 48, -6, 52, 0, 144, -24, 0, 12, 40, -48, -48, -36, 0, -36, -20, -10, 0, 78, 60, 0, -8, -4, 12, 60, -48, 84, 48, -16, 120, 0, -54, 12, 0, 0, -8, -114, -32, -16, 120, 36, -4, 26, 0, 72, 60, 0, 12, -10, 96, -32, 0, 0, 192, 34, 24, 0, 12, 12, 0, 20, 12, 24, -144, 2, -72, 24, 4, -82, 0, -12, -48, 0, 20, 36, -24, -20, -12, -44, 0, 68, 24, 0, -120, -78, 0, -10, 24, 6, -32, -28, 24, 42, 84, -6, 0, -72, -12, 0, 2, -36, -192, -40, 24, -64, -120, -2, -12, 0, -120, 36, 0, 8, 4, -12, 44, -18, 64, -60, 24, 0, 0, -12, 18, 0, -120, -78, 0, -40, -168, -20, -72, 8, 32, 0, 6, 24, 0, -12, 14, 0, 24, -10, -72, -30, 24, 28, 0, 24, 96, 0, 12, 22, 48, 60, -100, -44, -12, -4, -26, 0, -48, 0, 0, -56, -64, -18, 20, 70, -16, 72, -62, 14, 0, -120, -30, 0, 44, -8, 12, -12, -72, 4, 114, -24, 20, 0, 6, 54, 0, -30, -16, -30, -96, 96, 0, 6, -48, 36, 0, -72, 168, 0, -40, 4, 12, 24, 4, -64, -132, 46, 26, 0, 216, 36, 0, 12, -24, 66, -100, 6, 192, -36, 8, -4, 0, 48, 42, 0, -80, -20, 6, -4, -88, 48, -84, 50, -48, 0, 132, -6, 0, -6, -34, 36, 112, -24, -40, -54, -32, -24, 0, 24, -24, 0, -82, 20, 12, -48, -4, -32, 192, 10, -36, 0, 120, -30, 0, 10, 48, 96, 88, -48, -192, 12, 20, 66, 0, 6, 66, 0, 96, -2, 6, 32, 180, 4, 6, -14, -20, 0, 6, 24, 0, 24, 20, 36, 32, 28, 48, 114, 60, 8, 0, 12, -48, 0, -2, -8, -264, 0, -20, 16, -12, -40, -30, 0, -48, -48, 0, 8, 136, 6, 128, 90, 64, 36, 12, 18, 0, 48, 18, 0, -132, 8, 72, -32, -28, 24, -120, 2, 0, 0, 24, 12, 0, 30, -34, 204, 48, 36, -92, -24, 60, -2, 0, 60, -48, 0, 64, 72, -84, 32, 120, 28, -168, -72, 2, 0, 48, 6, 0, -18, -56, 12, -84, -4, 80, -24, -48, 36, 0, -12, -84, 0, 40, -14, 48, 16, 48, -168, 42, -28, 0, 0, -156, 12, 0, 50, -38, -42, -168, 0, -56, -12, -96, -4, 0, 48, -120, 0, 2, 4, -192, 20, 12, -52, 36, 2, 48, 0, 48, -6, 0, -22, -76, 60, -8, 36, 264, 12, -32, -2, 0, -120, 6, 0, 48, 12, 12, -32, -192, 36, 96, -46, -48, 0, 24, 12, 0, -16, 8, -42, -96, -36, 120, -6, -4, 24, 0, -18, -120, 0, 40, -56, 24, -8, 70, 80, 48, 24, 46, 0, -24, -30, 0, 52, -72, 24, -200, -110, -48, 0, -110, 4, 0, -60, 30, 0, 56, 10, -60, 24, 60, 32, -6, 32, -56, 0, 42, 108, 0, 2, 36, 54, 136, -70, -16, -12, 0, 0, 0, 78, 0, 0, 108, 78, 48, 0, 72, 20, -216, 26, -52, 0, 12, -72, 0, -60, 4, -156, -144, 0, -64, -24, -30, -12, 0, 6, 72, 0, -96, 8, 12, 52, -32, 56, 12, -44, -176, 0, 36, 0, 0, 84, -56, 0, -24], "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], [-1, 1, -1, 0], [-1, 0, 1, 0], [0, -2, 2, -2], [0, 0, 0, -1], [2, -1, -1, 1], [-4, -1, 2, 1], [2, 0, -4, 6], [0, 0, -1, 0], [1, -1, -1, 2], [-2, 0, -2, 0], [-2, 4, 0, -2], [0, 1, 0, 3], [5, -2, 0, 1], [0, 1, 0, 0], [-8, 4, 8, -8], [0, -1, -5, -1], [-1, 0, 2, -1], [-4, -2, 2, 2], [-4, 2, 2, -2], [2, 0, -4, -1], [0, -2, 6, -2], [-4, 2, 4, -4], [2, -6, 2, 0], [-1, 0, 0, 0], [-3, 2, 4, -7], [1, 0, 0, 0], [-2, 10, -2, 0], [1, 1, -1, -2], [0, -1, 1, -1], [3, 0, -6, 2], [16, -8, -8, 8], [4, 0, -2, 0], [-4, 0, 8, -2], [0, 2, 1, 2], [2, -2, -2, 4], [0, 4, 0, 0], [4, 0, 0, 0], [0, -4, 0, 1], [6, -4, 0, 2], [-1, 7, -1, 0], [-5, 1, 5, -2], [0, 1, -2, 1], [4, 0, -8, 12], [0, -1, 0, 1], [12, -10, -6, 10], [-3, 0, 6, -5], [0, 4, -8, 4], [6, 4, -6, -8], [1, -1, 1, 0], [5, 2, 0, -1], [14, -6, -10, 8], [0, -8, 0, 4], [-1, 1, -1, 0], [0, -2, 0, 4], [0, -10, 6, -10], [2, 0, -4, -2], [0, -2, 0, 2], [-2, 9, 1, -9], [2, 0, -4, 2], [0, -2, -1, -2], [-11, 5, 11, -10], [2, 1, 2, 0], [-16, 16, 0, -8], [4, 0, -1, 0], [-6, 4, 0, -2], [-2, -9, -2, 0], [4, -8, -4, 16], [0, 2, -4, 2], [-1, 0, 2, -5], [-2, -11, 1, 11], [-4, 6, 2, -6], [-6, 0, 12, 5], [0, -4, 4, -4], [1, 0, -1, 0], [0, 8, 0, 0], [12, 4, 0, -2], [-1, 5, -3, 2], [-5, 8, 0, -4], [-4, 8, -4, 0], [-1, 0, 1, 0], [0, -8, 10, -8], [-2, 0, 4, -6], [4, -10, -2, 10], [-2, -5, 1, 5], [-3, 0, 6, -5], [0, 1, 1, 1], [-12, 12, 12, -24], [1, -3, 1, 0], [-1, 2, 0, -1], [-1, -10, -3, -4], [-20, 24, 0, -12], [3, -2, 3, 0], [14, -8, -14, 16], [0, 2, 2, 2], [-8, 0, 16, -8], [-4, -13, 2, 13], [-4, -6, 2, 6], [-2, 0, 4, 0], [0, 2, -2, 2]]}