# Stored data for newform 136.2.h.a, downloaded from the LMFDB on 18 April 2024.
{"label": "136.2.h.a", "space_label": "136.2.h", "level": 136, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 481069891720, "dim": 16, "is_polredabs": true, "trace_hash": 1953647303704495608, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q-\\beta _{5}q^{2}+\\beta _{12}q^{3}-\\beta _{3}q^{4}-\\beta _{6}q^{5}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 136, "char_orbit_label": "h", "char_is_real": true, "Nk2": 544, "analytic_conductor": 1.0859654674894132, "hecke_ring_index": 2048, "level_radical": 34, "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": "0.766", "prec": 17}, "analytic_rank_proved": true, "char_values": [136, 2, [103, 69, 105], [2, 1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 4, "level_primes": [2, 17], "conrey_indexes": [101], "field_disc": 1558192657091181112459264, "field_disc_factorization": [[2, 28], [17, 2], [29, 4], [73, 4]], "field_poly": [64, 0, 136, 0, 268, 0, -156, 0, 240, 0, 36, 0, 20, 0, 8, 0, 1], "hecke_ring_index_factorization": [[2, 11]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.001", "prec": 17}, {"__RealLiteral__": 0, "data": "12.572", "prec": 20}, {"__RealLiteral__": 0, "data": "4.420", "prec": 17}, {"__RealLiteral__": 0, "data": "1647.072", "prec": 27}, {"__RealLiteral__": 0, "data": "2526.358", "prec": 27}, {"__RealLiteral__": 0, "data": "312152.530", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 16, "sato_tate_group": "1.2.3.c2", "trace_display": [-2, 0, 0, 0], "traces": [0, 16, -2, 0, -6, 0, 0, 0, -2, 8, 0, 0, 0, 0, 0, -8, -14, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -2, -8, 18, 0, -22, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, -24, 0, -8, 34, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, 0, 0, 0, -30, 0, -32, 0, 38, 0, 40, 0, 70, 0, 0, 0, 4, 0, 0, 0, 0, -24, 0, 0, 72, 0, 4, -40, 0, -24, 0, 0, 0, 0, -16, 0, 0, 0, 34, 0, -34, 0, -40, 64, 72, 0, -80, 0, 0, 0, -48, 56, 0, 0, 0, 0, 0, 0, -76, 8, -32, -8, 0, 0, 0, 0, 0, 80, -2, 0, 0, 0, 56, 0, 36, -80, -38, 40, -72, 0, -80, 0, 0, 0, -38, 16, 0, 0, 0, 0, 0, 80, -84, -40, 8, 0, 0, 0, 0, 0, 0, 24, -66, 0, 0, 0, -76, 0, 80, -16, 72, 0, -84, 0, 128, 0, 0, 0, 4, 0, 0, 0, 0, 56, 0, 0, 152, 0, -48, 0, 0, -56, 0, 0, 0, 0, -50, 0, 0, 0, -86, 0, -80, 0, 80, 0, 160, 0, 152, 0, 0, 0, 88, 0, 0, 0, 0, 40, 0, 0, 128, 0, -64, 24, 0, -104, 0, 0, 0, 0, 40, 0, 0, 0, 152, 0, -68, 0, -48, -120, 112, 0, -98, 0, 0, 0, -80, -80, 0, 0, 0, 0, 0, 0, -80, -72, -62, 56, 0, 0, 0, 0, 0, -64, 16, 0, 0, 0, 148, 0, 80, 56, -74, 80, -76, 0, -152, 0, 0, 0, -64, 64, 0, 0, 0, 0, 0, -64, -170, -48, -40, 0, 0, 0, 0, 0, 0, -16, -72, 0, 0, 0, -80, 0, 164, -16, 58, 0, -168, 0, 184, 0, 0, 0, 144, 0, 0, 0, 0, -136, 0, 40, 200, 0, -14, 0, 0, -8, 0, 0, 0, 0, -68, 0, 0, 0, -160, 0, -98, 0, 80, 0, 196, 0, 164, 0, 0, 0, 80, 0, 0, 0, 0, 80, 0, 0, 100, 0, -28, -120, 0, -16, 0, 0, 0, 0, 48, 0, 0, 0, 136, 0, -152, 0, -120, 144, 112, 0, -232, 0, 0, 0, -112, 224, 0, 0, 0, 0, 0, 0, -224, 88, -14, 8, 0, 0, 0, 0, 0, 240, 86, 0, 0, 0, 160, 0, 184, -200, -80, 16, -224, 0, -160, 0, 0, 0, -152, -56, 0, 0, 0, 0, 0, 168, -168, 0, 80, 0, 0, 0, 0, 0, 0, -40, -40, 0, 0, 0, -224, 0, 64, 32, 72, 0, -192, 0, 112, 0, 0, 0, 18, 0, 0, 0, 0, 224, 0, -56, 160, 0, 64, 0, 0, 16, 0, 0, 0, 0, -80, 0, 0, 0, -156, 0, -232, 0, 160, 0, 96, 0, 240, 0, 0, 0, 90, 0, 0, 0, 0, -88, 0, 0, 304, 0, 80, 24, 0, 104, 0, 0, 0, 0, 116, 0, 0, 0, 160, 0, -144, 0, -112, -176, 286, 0, -172, 0, 0, 0, -200, -200, 0, 0, 0, 0, 0, 0, -160, -72, -48, -56, 0, 0, 0, 0, 0, -232, 76, 0, 0, 0, 144, 0, 16, 248, -70, -96, -152, 0, -148, 0, 0, 0, -64, -24, 0, 0, 0, 0, 0, -144, -160, 40, 124, 0, 0, 0, 0, 0, 0, -80, -80, 0, 0, 0, -160, 0, 234, 40, 142, 0, -192, 0, 304, 0, 0, 0, 72, 0, 0, 0, 0, -296, 0, -160, 168, 0, -8, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, -164, 0, -168, 0, 38, 0, 308, 0, 256, 0, 0, 0, 224, 0, 0, 0, 0, -160, 0, 0, 232, 0, -40, -120, 0, 24, 0, 0, 0, 0, 32, 0, 0, 0, 168, 0, -88, 0, -116, 200, 94, 0, -224, 0, 0, 0, -48, 136, 0, 0, 0, 0, 0, 0, -220, 224, -12, 16, 0, 0, 0, 0, 0, 184, 160, 0, 0, 0, 146, 0, 224, -240, -160, 72, -224, 0, -316, 0, 0, 0, -20, 144, 0, 0, 0, 0, 0, 88, -352, -16, -80, 0, 0, 0, 0, 0, 0, -16, 28, 0, 0, 0, -184, 0, 84, 40, 152, 0, -316, 0, 208, 0, 0, 0, 210, 0, 0, 0, 0, 264, 0, 32, 304, 0, 112, 0, 0, 8, 0, 0, 0, 0, -64, 0, 0, 0, -224, 0, -80, 0, 96, 0, 80, 0, 64, 0, 0, 0, 96, 0, 0, 0, 0, 184, 0, 0, 32, 0, 0, 144, 0, -56, 0, 0, 0, 0, 68, 0, 0, 0, 224, 0, -144, 0, -128, -368, 62, 0, -280, 0, 0, 0, -40, -224, 0, 0, 0, 0, 0, 0, -240, -152, 122, 152, 0, 0, 0, 0, 0, -392, 56, 0, 0, 0, 80, 0, 208, 408, -144, 176, -204, 0, -288, 0, 0, 0, -144, -136, 0, 0, 0, 0, 0, -232, -296, -40, 80, 0, 0, 0, 0, 0, 0, 64, -80, 0, 0, 0, -144, 0, 24, 88, -18, 0, -232, 0, 200, 0, 0, 0, 72, 0, 0, 0, 0, -320, 0, 160, 36, 0, 72, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, -208, 0, -70, 0, 224, 0, 116, 0, 320, 0, 0, 0, -96, 0, 0, 0, 0, 224, 0, 0, 206, 0, 64, -16, 0, 64, 0, 0, 0, 0, 144, 0, 0, 0, 36, 0, -176, 0, -144, 184, 384, 0, -304, 0, 0, 0, -96, 96, 0, 0, 0, 0, 0, 0, -268, 152, -72, 128, 0, 0, 0, 0, 0, 384, 12, 0, 0, 0, 312, 0, -36, -424, -80, -296, -144, 0, -224, 0, 0, 0, -80, -216, 0, 0, 0, 0, 0, 168, -106, 144, 80, 0, 0, 0, 0, 0, 0, -208, 16, 0, 0, 0, -124, 0, 288, 0, 232, 0, 0, 0, 112, 0, 0, 0, 48, 0, 0, 0, 0, 400, 0], "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, 8, 2, 1, 2, 0], [1, 1, 17, 2, 1, 2, 0], [1, 1, 136, 8, 1, 2, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "136.2.h.a", "char_is_minimal": true, "conrey_index": 101, "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, 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, 0, -1, 0, 0, 0, 0, 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, -1, 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, 0, 0, 0], [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, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 0, 0, 0, 0, 1, 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, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0], [-1, 0, 1, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, -1, 0, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [-1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1], [0, 1, 0, 0, 0, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 1, 0], [0, -1, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0, 1, 1, -1, 0], [-1, 0, 1, 1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0], [1, 0, -2, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, -1, 0], [0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, -1, 1, 0, 0, -1, 0, -1, -1, 1, 0], [-1, 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 2, 0, -1, 0, 0, 0], [-1, 0, 2, 1, -1, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 0, -1, 1, -1, -1, 1, 1, 0, 0, -1, -1, 0, 1, 0], [0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 1], [-3, 0, 2, 0, 1, -1, 0, 0, -1, 0, 0, -2, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, -1, 0], [3, 0, -2, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 1, 0], [0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, -1, -1, -1, 0], [0, 2, 0, 0, 0, 0, 0, -1, 0, 2, -1, 0, 1, -1, -1, 0], [-2, 0, 2, 0, 2, -1, 0, 0, -2, 0, 0, -1, 0, 0, 0, -1], [1, 0, -1, -1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0, 0, 1, 0, 0, 1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, -1, 1, -1, 0], [-1, 0, -1, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, 0, 0, 1, -1, 0, -1, 1, -1, 0], [-1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [3, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 1, -1, -1, 1, 1], [-1, 0, 0, -1, 3, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 1, 0, -3, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, -1, 0, 2, 0, 0, -1, 0, -1, 0], [1, 0, -1, -3, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 3, 0, -1, -1, 1, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 2, 0], [1, 0, 1, -1, -1, -3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 1, -1, 1, 0], [0, -1, 0, 0, 0, 0, -2, 1, 0, 0, 0, 0, 3, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, 0, 1, 0, -2, 0], [-1, 0, -2, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 2, 0, 0, 0, 0, 0, -1, 0, -2, -3, 0, 1, 1, 1, 0], [-3, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0], [-1, 0, -1, 2, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [3, 1, 0, 0, -1, -1, -1, -1, 1, -1, 0, 0, 2, 0, 0, 1], [2, 0, 0, -2, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1], [2, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 2, 0], [6, 0, -2, 0, -2, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0], [0, 1, 0, 0, 0, 0, -2, -2, 0, 2, -2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 1, 0, 0, -1, 0, -2, -1, 1, 0], [0, 0, 2, 0, 0, -2, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0], [2, 0, -2, -2, -2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1], [0, 1, 0, 0, 0, 0, 3, -1, 0, 2, 0, 0, 3, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, 0, 1, 0, -2, 0], [0, -1, 0, 0, 0, 0, -1, 2, 0, 1, 1, 0, 1, -1, 1, 0], [-1, 0, 0, 1, -2, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -2, -2, 2, 0], [1, 0, 1, -1, -1, -3, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2], [5, 0, -2, -1, 1, -1, 0, 0, 1, 0, 0, -2, 0, 0, 0, -1], [-2, 0, 1, 1, 2, 1, 1, -1, 1, 0, 1, -1, -1, 1, -1, 0], [1, 0, 0, -1, 1, -1, 0, 0, 1, 0, 0, 2, 0, 0, 0, -1], [-5, 0, 3, -1, 3, -5, 0, 0, -3, 0, 0, -2, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 1, -1, -1, 0], [0, 0, -2, -3, 2, -1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 1, 0, 2, 1, -1, 0], [0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, -3, 2, -1, 0], [-2, 0, 2, -2, 2, 2, 0, 0, 1, 0, 0, -4, 0, 0, 0, -1], [-1, 0, 0, 1, -1, 3, 0, 0, -1, 0, 0, 2, 0, 0, 0, 1], [0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], [0, 1, 0, 0, 0, 0, -3, 0, 0, -1, 1, 0, -3, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 3, 0, -1, -1, 1, 0], [3, 0, 0, -1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, -2, -1, 0, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0]]}