# Stored data for newform 429.2.b.a, downloaded from the LMFDB on 10 May 2024.
{"label": "429.2.b.a", "space_label": "429.2.b", "level": 429, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 68753031597, "dim": 10, "is_polredabs": true, "trace_hash": 516438117882346963, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [1, 0, 21, 0, 74, 0, 54, 0, 13, 0, 1]]], "qexp_display": "q+\\beta _{1}q^{2}-q^{3}+(-1+\\beta _{2})q^{4}+(-\\beta _{5}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 13, "char_orbit_label": "b", "char_is_real": true, "Nk2": 1716, "analytic_conductor": 3.4255822467129287, "hecke_ring_index": 4, "level_radical": 429, "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": "0.513", "prec": 17}, "analytic_rank_proved": true, "char_values": [429, 2, [287, 79, 67], [2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [3, 11, 13], "conrey_indexes": [298], "field_disc": -16216793432064, "field_disc_factorization": [[-1, 1], [2, 14], [3, 2], [10487, 2]], "field_poly": [1, 0, 21, 0, 74, 0, 54, 0, 13, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8.756", "prec": 17}, {"__RealLiteral__": 0, "data": "0.839", "prec": 17}, {"__RealLiteral__": 0, "data": "431.135", "prec": 24}, {"__RealLiteral__": 0, "data": "291.693", "prec": 24}, {"__RealLiteral__": 0, "data": "33512.270", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "1.2.3.c2", "trace_display": [0, -10, 0, 0], "traces": [0, 10, 0, -10, -6, 0, 0, 0, 0, 10, 0, 0, 6, 12, -32, 0, 6, 20, 0, 0, 0, 0, -2, 8, 0, -14, -2, -10, 0, 8, 0, 0, 0, 0, 0, 0, -6, 0, 0, -12, -20, 0, 32, -24, 0, 0, 0, 0, -6, -26, 0, -20, -48, -4, 0, 4, 16, 0, 0, 0, 0, 36, 24, 0, 50, 28, 2, 0, -12, -8, 0, 0, 0, 0, 24, 14, 0, 12, 2, 36, 0, 10, -20, 0, 0, 0, 0, -8, -6, 0, 0, -24, -8, 0, -32, 44, 0, 0, 0, 0, 74, -60, 0, -64, 34, 0, 0, -36, 6, 0, 0, 0, 0, -20, 0, 0, -52, 12, 4, 0, 20, -10, 0, 0, 0, 0, -32, 68, 0, 24, 24, 16, 0, 8, -140, 0, 0, 0, 0, -32, 68, 0, 44, 2, 6, 0, -4, 26, 0, 0, 0, 0, -64, 20, 0, -32, 48, -28, 0, 4, -20, 0, 0, 0, 0, -4, 56, 0, -16, 30, 144, 0, 8, 16, 0, 0, 0, 0, -84, 48, 0, 44, -68, -36, 0, -48, -24, 0, 0, 0, 0, -32, -50, 0, 20, -28, 38, 0, -2, 32, 0, 0, 0, 0, 12, -4, 0, 8, 0, 0, 0, 56, 52, 0, 0, 0, 0, 32, -60, 0, -36, -16, -24, 0, -16, -14, 0, 0, 0, 0, 136, -12, 0, -44, -2, -40, 0, -36, 8, 0, 0, 0, 0, -10, -152, 0, 20, 72, -108, 0, -88, -48, 0, 0, 0, 0, -58, -36, 0, -92, 16, 8, 0, 60, 6, 0, 0, 0, 0, 60, 0, 0, -8, 24, 16, 0, 8, -64, 0, 0, 0, 0, 32, 36, 0, -44, -8, 8, 0, 38, 224, 0, 0, 0, 0, -64, 12, 0, -20, 104, -74, 0, 104, 60, 0, 0, 0, 0, -24, 64, 0, 72, -34, 68, 0, 0, 12, 0, 0, 0, 0, 36, 56, 0, -6, -76, -4, 0, 124, -132, 0, 0, 0, 0, 152, -72, 0, 72, -72, 20, 0, -44, 0, 0, 0, 0, 0, 24, 52, 0, -32, -12, 10, 0, -4, -32, 0, 0, 0, 0, -20, -106, 0, 10, 48, 40, 0, -48, 32, 0, 0, 0, 0, -68, -40, 0, 36, -16, 32, 0, -168, -68, 0, 0, 0, 0, -76, -24, 0, -44, -24, -12, 0, -16, 92, 0, 0, 0, 0, -8, 126, 0, 140, 4, -20, 0, -20, 52, 0, 0, 0, 0, 8, 104, 0, 116, 14, 32, 0, 48, -68, 0, 0, 0, 0, -120, -44, 0, 20, -2, -232, 0, -6, 4, 0, 0, 0, 0, 4, -32, 0, -26, 16, -8, 0, -136, -60, 0, 0, 0, 0, 36, -12, 0, -40, -56, 64, 0, 100, -20, 0, 0, 0, 0, 4, 32, 0, -64, -48, -88, 0, 28, 20, 0, 0, 0, 0, -4, -184, 0, 20, -48, 60, 0, 6, 184, 0, 0, 0, 0, 164, -68, 0, 240, 64, 4, 0, 132, -56, 0, 0, 0, 0, 28, 16, 0, -44, -30, 136, 0, -144, 64, 0, 0, 0, 0, -8, 28, 0, -16, -48, 68, 0, -36, -168, 0, 0, 0, 0, 74, -188, 0, -280, -4, 84, 0, 104, -48, 0, 0, 0, 0, 80, -44, 0, -48, 68, -96, 0, 36, 74, 0, 0, 0, 0, 48, 276, 0, 24, 0, 8, 0, -140, 20, 0, 0, 0, 0, -80, 96, 0, 80, -22, 32, 0, -72, 50, 0, 0, 0, 0, 120, -20, 0, 116, 28, -84, 0, -38, 60, 0, 0, 0, 0, 2, 128, 0, -32, -32, -64, 0, 208, -104, 0, 0, 0, 0, -196, -56, 0, -176, -48, -12, 0, 152, 4, 0, 0, 0, 0, 32, -8, 0, 28, 0, 42, 0, 0, 28, 0, 0, 0, 0, -56, -40, 0, -52, 48, -28, 0, 168, -20, 0, 0, 0, 0, -276, -40, 0, -36, -66, -32, 0, -196, 60, 0, 0, 0, 0, -92, 36, 0, -32, 16, 0, 0, 24, -40, 0, 0, 0, 0, 16, -120, 0, 14, -98, 12, 0, 156, -168, 0, 0, 0, 0, -160, 168, 0, 52, -76, -136, 0, -48, 12, 0, 0, 0, 0, 20, 44, 0, 168, 2, 124, 0, 40, 92, 0, 0, 0, 0, 36, 148, 0, -8, 44, -40, 0, 192, 192, 0, 0, 0, 0, -100, -112, 0, -256, 176, 10, 0, -288, 152, 0, 0, 0, 0, -16, -20, 0, 336, -72, 112, 0, 108, -168, 0, 0, 0, 0, 88, 8, 0, 48, -48, -36, 0, -164, -260, 0, 0, 0, 0, 168, 32, 0, 252, 4, 58, 0, -48, 36, 0, 0, 0, 0, 176, 92, 0, 48, -16, 8, 0, -8, -158, 0, 0, 0, 0, -60, -120, 0, -6, 64, 192, 0, -368, 196, 0, 0, 0, 0, -4, 0, 0, 60, 112, -60, 0, -96, 0, 0, 0, 0, 0, -264, 8, 0, -68, -24, 0, 0, -16, -240, 0, 0, 0, 0, -8, 84, 0, 64, 172, 32, 0, 192, 116, 0, 0, 0, 0, 86, 52, 0, 88, 64, -32, 0, -132, -36, 0, 0, 0, 0, -284, 44, 0, -112, 8, -64, 0, -8, 264, 0, 0, 0, 0, -38, -284, 0, -224, 56, -20, 0, -96, -20, 0, 0, 0, 0, 32, 76, 0, 0, -192, 64, 0, 168, -12, 0, 0, 0, 0, 124, 20, 0, -352, -104, -56, 0, 74, -20, 0, 0, 0, 0, -104, 80, 0, -60, 60, -112, 0, -68, 260, 0, 0, 0, 0, -48, -116, 0, -76, 140, 24, 0, 136, -64, 0, 0, 0, 0, 96, -72, 0, 24, 34, 84, 0, -68, 224, 0, 0, 0, 0, 0, 92, 0, -12, -44, 240, 0, -172, -308, 0, 0, 0, 0, 0, -124, 0, -106, 88, -36, 0, 208, -56, 0, 0, 0, 0, -16, 6, 0, -104, 76, -148, 0, 4, 20, 0, 0, 0, 0, -124, 92, 0, 132, 8, -76, 0, 32, -124, 0, 0, 0, 0, 64, 96, 0, 276], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "429.2.b.a", "char_is_minimal": true, "conrey_index": 298, "id": null, "nf_label": 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, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 1, -1, -1], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0, 1, 0], [0, -1, 0, 0, 0, 1, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 2, 2, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, 0, 0, 0, 1, -1, 1, 0], [-4, 0, 1, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, -1, 1, 1], [1, 0, 0, -1, 1, 0, 1, 0, 0, 0], [1, 0, 0, 2, 1, 0, -1, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 2], [0, 1, 0, 0, 0, 4, 0, -1, 0, 2], [0, -1, 0, 0, 0, 1, 0, 0, -1, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [2, 0, -1, 1, 1, 0, 3, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, -1, 0, 0], [-1, 0, 1, -3, 1, 0, 1, 0, 0, 0], [-1, 3, 1, 1, -1, 0, -1, -1, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -4, 0, 0, 0, 5, 0, 1, 2, 2], [0, 0, -1, 2, 2, 0, -1, 0, 0, 0], [0, 0, 1, -2, -2, 0, -1, 0, 0, 0], [0, -2, 0, 0, 0, 5, 0, 1, 1, -1], [0, -2, 0, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 5, 0, -1, 1, 3], [-1, 0, 1, 2, 1, 0, 0, 0, 0, 0], [-1, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -5, 0, 0, 1, -1], [2, 0, -1, -5, -1, 0, 1, 0, 0, 0], [-2, 0, 1, 0, 0, 0, -1, 1, -1, 0], [-1, 0, 0, -4, 1, 0, 1, 0, 0, 0], [0, 2, 0, 0, 0, -5, 0, -1, -2, 0], [4, 0, -1, -2, 0, 0, 0, 0, 0, 0], [-1, 0, 0, -4, -1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, -1], [0, 0, 0, 0, 0, -1, 0, 1, -1, -1], [0, 1, 0, 0, 0, 5, 0, -2, 1, 2], [0, 1, 0, 0, 0, -3, 0, 0, 1, -1], [-1, 0, 0, 1, -1, 0, -1, 0, 0, 0], [-3, 0, 0, 5, -1, 0, 1, 0, 0, 0], [0, -4, 0, 0, 0, -7, 0, 0, 1, -2], [-1, 0, 0, -2, -1, 0, 1, 0, 0, 0], [-5, -2, 2, 0, -1, 3, 1, 0, 1, 0], [-2, 0, 2, 1, -3, 0, -3, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, 1, 0, 0, 0], [4, 0, -3, -3, -1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, -1, 0, -1, 0, -2], [0, 3, 0, 0, 0, 4, 0, -3, 2, 4], [0, 0, 0, 0, 0, 2, 0, 0, -2, -2], [0, -1, 0, 0, 0, -4, 0, 1, 0, -2], [3, 0, -1, 0, -3, 0, -4, 0, 0, 0], [4, 0, -3, -2, 2, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, -1, 0, 0, 1, 0], [7, 0, -3, -1, 3, 0, 3, 0, 0, 0], [2, -1, 1, 2, -2, -5, -1, 2, -1, -2], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, -1, 0, 1, -3, -1], [-2, 0, 3, -6, -2, 0, -3, 0, 0, 0], [-2, 0, 1, -1, -1, 0, -3, 0, 0, 0], [0, -3, 0, 0, 0, 7, 0, 0, 1, 3], [0, -1, 0, 0, 0, -1, 0, 2, -3, 1], [0, -1, 0, 0, 0, 1, 0, 1, 0, 0], [0, 1, 0, 0, 0, -1, 0, -2, -1, 0], [1, 0, -1, 8, 1, 0, 0, 0, 0, 0], [1, 0, -1, 3, -1, 0, -1, 0, 0, 0], [0, 3, 0, 0, 0, -13, 0, 2, -1, -2], [1, 0, 0, -1, 0, 0, -1, 0, 0, 0], [1, -3, -1, -1, 1, 0, 1, 1, 0, 0], [1, 0, 2, 0, -1, 0, -5, 0, 0, 0], [0, 0, 0, 0, 0, -3, 0, -3, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 3, 3, -1, 0, -1, 0, 0, 0], [0, -3, 0, 0, 0, 8, 0, -3, 3, 0], [0, 4, 0, 0, 0, -5, 0, -1, -2, -2], [0, -6, 0, 0, 0, -3, 0, 3, -2, -4], [0, -2, 0, 0, 0, -11, 0, 1, -1, -5], [0, 0, 1, -2, -2, 0, 1, 0, 0, 0], [-1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 5, 0, 0, 0, -6, 0, 1, -6, -2], [0, 0, -1, 2, 2, 0, 1, 0, 0, 0], [-4, 3, 1, 2, 0, -1, -2, -2, -1, -3], [2, 0, 1, -6, -2, 0, 4, 0, 0, 0], [0, 2, 0, 0, 0, -5, 0, -1, -1, 1], [-5, 0, 1, 6, 1, 0, 0, 0, 0, 0], [5, 0, -3, 0, 3, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, -1, -1, 0], [0, 1, 0, 0, 0, -1, 0, -4, -1, 3], [0, -4, 0, 0, 0, 16, 0, 1, -1, 4], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [7, 0, -2, 6, 4, 0, 2, 0, 0, 0]]}