# Stored data for newform 2646.2.h.b, downloaded from the LMFDB on 19 April 2024. {"label": "2646.2.h.b", "space_label": "2646.2.h", "level": 2646, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4504080697264726, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 995985428000831252, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [2, 1]], [11, [1, 1]], [13, [36, -6, 1]]], "qexp_display": "q+(-1+\\zeta_{6})q^{2}-\\zeta_{6}q^{4}-2q^{5}+q^{8}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "h", "char_is_real": false, "Nk2": 10584, "analytic_conductor": 21.12841637483079, "hecke_ring_index": 1, "level_radical": 42, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.014", "prec": 17}, "analytic_rank_proved": true, "char_values": [2646, 3, [785, 1081], [1, 2]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [361, 667], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "2.017", "prec": 17}, {"__RealLiteral__": 0, "data": "0.186", "prec": 17}, {"__RealLiteral__": 0, "data": "12.187", "prec": 20}, {"__RealLiteral__": 0, "data": "3.162", "prec": 17}, {"__RealLiteral__": 0, "data": "113.436", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [-1, 0, -4, 0], "traces": [0, 2, -1, 0, -1, -4, 0, 0, 2, 0, 2, -2, 0, 6, 0, 0, -1, -5, 0, 7, 2, 0, 1, -8, 0, -2, 6, 0, 0, -4, 0, 6, -1, 0, -5, 0, 0, -2, -14, 0, -4, 3, 0, 1, 1, 0, 4, 0, 0, 0, 1, 0, -12, 12, 0, 4, 0, 0, 8, -7, 0, 12, -12, 0, 2, -12, 0, -13, 10, 0, 0, 16, 0, -1, 4, 0, 7, 0, 0, 6, 2, 0, 3, 16, 0, 10, -2, 0, -2, -6, 0, 0, 4, 0, 0, -14, 0, 5, 0, 0, 1, 8, 0, 28, 6, 0, 12, 3, 0, 2, -2, 0, 0, -10, 0, 16, -4, 0, 14, 0, 0, -20, 12, 0, 6, 24, 0, -24, -1, 0, -12, 8, 0, 0, 26, 0, -5, 38, 0, 5, 0, 0, -8, -6, 0, 8, -1, 0, -2, 48, 0, 20, 7, 0, 0, -12, 0, -2, 6, 0, 2, 0, 0, 4, -6, 0, -32, 20, 0, -23, 10, 0, 1, 2, 0, 0, 1, 0, 12, 24, 0, 0, 0, 0, -8, 4, 0, 5, 0, 0, 28, 12, 0, -17, -10, 0, 0, -20, 0, -14, -2, 0, -4, 0, 0, -6, -14, 0, 6, -7, 0, 16, -24, 0, -6, -2, 0, 0, 2, 0, -2, 30, 0, 4, 0, 0, -10, -6, 0, -52, -8, 0, -4, -29, 0, 0, -7, 0, 0, 6, 0, 46, 10, 0, -24, 0, 0, 84, 6, 0, -12, -6, 0, 8, 12, 0, -1, 30, 0, 0, 24, 0, -4, -36, 0, -24, 0, 0, -13, 20, 0, 6, -5, 0, -19, 2, 0, 4, 5, 0, 0, 22, 0, -4, -8, 0, -6, 0, 0, -8, -16, 0, 2, 0, 0, 14, -2, 0, -24, -24, 0, 0, -10, 0, -14, -24, 0, 14, 0, 0, 24, 2, 0, 17, 4, 0, -12, -6, 0, 4, -4, 0, 0, -70, 0, -6, -8, 0, 3, 0, 0, -8, 16, 0, 20, 26, 0, 9, 46, 0, -20, -6, 0, 0, 1, 0, 2, -3, 0, 14, 0, 0, 1, 30, 0, -32, -6, 0, 24, 2, 0, -30, 0, 0, 0, 2, 0, -44, 4, 0, -8, 0, 0, 44, 5, 0, 0, -48, 0, -34, -14, 0, 12, -8, 0, 0, 34, 0, 5, -16, 0, 20, 0, 0, 10, -12, 0, -18, -14, 0, 1, -18, 0, 72, -4, 0, 0, 2, 0, -11, -6, 0, -14, 0, 0, -32, -12, 0, 14, -12, 0, 12, 16, 0, 12, 5, 0, 0, 3, 0, 4, 0, 0, -50, 0, 0, -4, -28, 0, 24, 4, 0, -60, 7, 0, 12, -8, 0, 0, -34, 0, -3, 20, 0, 3, 0, 0, -1, 26, 0, -8, 14, 0, 8, 8, 0, 58, -13, 0, 0, 0, 0, -7, -1, 0, -7, 0, 0, 6, 40, 0, -24, -23, 0, 10, -10, 0, 10, 12, 0, 0, 33, 0, 40, -42, 0, -12, 0, 0, -58, -12, 0, 3, -12, 0, -16, -4, 0, 12, -60, 0, 0, 2, 0, -15, -56, 0, 0, 0, 0, -12, -9, 0, 28, -4, 0, 18, -60, 0, -14, -24, 0, 0, -18, 0, -6, -13, 0, 20, 0, 0, 24, -12, 0, 10, -4, 0, 21, -19, 0, -1, 28, 0, 0, -2, 0, -10, -28, 0, 12, 0, 0, -44, 31, 0, 20, 8, 0, 16, -15, 0, 33, 12, 0, 0, 8, 0, 35, 16, 0, 8, 0, 0, -12, -1, 0, 0, -47, 0, -42, -28, 0, 4, -6, 0, 0, -24, 0, -24, 24, 0, 19, 0, 0, -10, 40, 0, -48, 7, 0, -24, 0, 0, -42, -7, 0, 0, -17, 0, 74, -12, 0, -4, 0, 0, -38, 17, 0, -2, 20, 0, 16, 6, 0, -6, 48, 0, 0, -8, 0, 2, -2, 0, 7, 0, 0, 35, 12, 0, 7, -6, 0, 4, 12, 0, -16, 3, 0, 0, 16, 0, -28, -8, 0, 16, 0, 0, 16, -40, 0, -52, -12, 0, -14, 9, 0, -23, 30, 0, 0, 10, 0, 12, 39, 0, -76, 0, 0, -2, -72, 0, -32, -4, 0, 6, -10, 0, 15, -28, 0, 0, -16, 0, 14, -2, 0, -15, 0, 0, 4, 16, 0, -6, -24, 0, 12, -48, 0, -4, 6, 0, 0, -30, 0, 0, 4, 0, 14, 0, 0, 2, -10, 0, -36, 22, 0, 4, 13, 0, 33, 4, 0, 0, -6, 0, -96, -22, 0, -10, 0, 0, -36, 0, 0, 24, -40, 0, -96, 17, 0, -14, -20, 0, 0, -24, 0, 4, -84, 0, -22, 0, 0, -17, -52, 0, -6, 5, 0, 8, 42, 0, -16, 20, 0, 0, 4, 0, 12, 10, 0, -12, 0, 0, -72, 36, 0, 28, -12, 0, 0, 1, 0, 9, 1, 0, 0, -36, 0, 8, -43, 0, 62, 0, 0, -4, -8, 0, -7, 22, 0, 12, 46, 0, -34, 28, 0, 0, -24, 0, -4, 64, 0, 6, 0, 0, -40, -7, 0, -12, -20, 0, 13, -24, 0, -32, 46, 0, 0, 12, 0, 5, 8, 0, -44, 0, 0, 3, -60, 0, 58, -2, 0, 0, 38, 0, -4, 25, 0, 0, -6, 0, -156, 2, 0, 56, 0, 0, 32, 24, 0, -2, -84, 0, 106, 30, 0, 7, 12, 0, 0, -24, 0, 4, 0, 0, -48, 0, 0, 17, 24, 0, 60, -3, 0, -10, 0, 0, -54, 3, 0, 0, 0, 0, -16, -1, 0, 26, 0, 0, -16, 16, 0, -28, 48, 0, 2, 8, 0, -4, -18, 0, 0, -29, 0, 26, -10, 0, 4, 0, 0, 0, 20, 0, -12, 14, 0, 2, -37, 0, 6, 14, 0, 0, 70, 0, -24, -12, 0, -20, 0, 0, -5, 12, 0, -23, 34, 0, -14, -20, 0, 20, -12, 0, 0, 10, 0, 12, -15, 0, 6, 0, 0, 33, 120, 0, 40, -20, 0, -42, -4, 0, 28, 6, 0, 0, 28, 0, 4, 29, 0, 24, 0, 0, 70, 3, 0, 6, 168, 0, 52, 8, 0, -4, -96, 0, 0, -24, 0, 30, 110, 0, 14, 0, 0, -1, -3, 0, -36, -15, 0, 28, 60, 0, -18, 0, 0, 0, 60, 0, 24, -12, 0, -9, 0, 0, 14, -56, 0, 8, -10, 0, 21, 18, 0, 30, -32, 0, 0, 7, 0, 48, 10, 0, 40, 0, 0, 36, -5, 0, -38, 12, 0, 26, -8, 0, -1, -40, 0, 0, 192, 0, 0, -48, 0, 6, 0, 0, -12, -5, 0, -4, -23, 0, -22, -42, 0, 38, -55, 0, 0, -1, 0, 28, -64, 0, -60, 0, 0, -2, 60, 0, -8, 5, 0, -28, -8, 0, -60, -6, 0, 0, 49, 0, 88, 22, 0, -62, 0, 0, -78, 20, 0, -4, -28, 0, 12, -8, 0, -15, 130, 0, 0, -66, 0, -6, 104, 0, 12, 0, 0, -4, -48, 0, -37, 35, 0, -8, -72, 0, 168, 8, 0, 0, 21, 0, 58, -12, 0, -1, 0, 0, 65, 0, 0, 94, 0, 0, -3, -42, 0, 14, -38, 0, 0, -2, 0, 12, 33, 0, -24, 0, 0, 48, -47, 0, -12, 48, 0, -48, -2, 0, -23, -38, 0, 0, -92, 0, -40, 20, 0, -20, 0, 0, 50, 24, 0, 7, 9, 0, -48, 48, 0, 0, 18, 0, 0, -42, 0, -7, 54, 0, -18, 0, 0, -17, -168, 0, 112, -37, 0, -12, -5, 0, 10, 2, 0, 0, 4, 0, 18, 19, 0, -34, 0, 0, 12, -2, 0, -10, 42, 0, 60, -8, 0, 6, -16, 0, 0, 12, 0, -24, 36, 0, 91, 0, 0, 4, -30, 0, -8, 2, 0, 1, 54, 0, -60, 7, 0, 0, -21, 0, 13, 35, 0, 12, 0, 0, 55, -14, 0, 12, -40, 0, -6, 4, 0, -6, -16, 0, 0, 8, 0, -6, 24, 0, 72, 0, 0, -32, 54, 0, 25, 56, 0, 16, -12, 0, -34, -32, 0, 0, 42, 0, -6, -32, 0, 20, 0, 0, 84, 26, 0, -12, 30, 0, -40, 28, 0, -18, 56, 0, 0, -23, 0, 30, -12, 0, 28, 0, 0, 10, 58, 0, 0, -6, 0, 39, -14, 0, 33, 38, 0, 0, 22, 0, -24, 1, 0, 144, 0, 0, 44, -32, 0, 2, -8, 0, -14, -3, 0, -10, 36, 0, 0, -30, 0, 14, 24, 0, 38, 0, 0, 8, -48, 0, -44, 14, 0, 1, 78, 0, -160, -15, 0, 0, 8, 0, -12, 4, 0, 16, 0, 0, 38, 12, 0, 48, -15, 0, 10, 12, 0, 24, -26, 0, 0, 2, 0, -12, 56, 0, -8, 0, 0, 60, 16, 0, -24, 0, 0, -8, 60, 0, 6, -28, 0, 0, 0, 0, 44, -4, 0, 5, 0, 0, 0, 18, 0, 22, 60, 0, 50, -8, 0, -26, 7, 0, 0, 33, 0, 4, -57, 0, 4, 0, 0, -6, -12, 0, -4, 48, 0, -22, 42, 0, 48, 5, 0, 0, -57, 0, 84, 18, 0, 0, 0, 0, -38, 24, 0, 20, 8, 0, 60, 48, 0, 17, -12, 0, 0, 28, 0, 10, -110, 0, -12, 0, 0, 12, -5, 0, 28, 4, 0, 42, -28, 0, -96, -22, 0, 0, 52, 0, -32, -17, 0, -52, 0, 0, -24, 12, 0, -10, -35, 0, -4, 8, 0, -21, -6, 0, 0, 8, 0, -40, -34, 0, -108, 0, 0, -8, 19, 0, -60, -24, 0, -20, -112, 0, -20, 24, 0, 0, -84, 0, 12, 144, 0, -18, 0, 0, 2, -14, 0, -12, -8, 0, 8, 0, 0, -2, 57, 0, 0, 9, 0, 1, 12, 0, -10, 0, 0, -36, -44, 0, 140, -4, 0, -43, -47, 0, 58, -31, 0, 0, 72, 0, -120, 2, 0, 16, 0, 0, -64, -7, 0, -11, -76, 0, -48, -6, 0, 46, 144, 0, 0, 68, 0, -14, -50, 0, -72, 0, 0, 12, 16, 0, -47, -4, 0, -32, -20, 0, -28, 6, 0, 0, -43, 0, 62, -40, 0, -7, 0, 0, 13, 24, 0, 40, 4, 0, 32, 13, 0, 12, -18, 0, 0, 16, 0, -92, 42, 0, 140, 0, 0, -24, 6, 0, -55, -10, 0, -16, 24, 0, 12, 88, 0, 0, -36, 0, -28, -6, 0, 30, 0, 0, -20, -29, 0, -2, -31, 0, 11, 0, 0, -76, 2, 0, 0, -4, 0, 25, 54, 0, 6, 0, 0, -6, 0, 0, -84, 78, 0, 2, -28, 0, 64, -28, 0, 0, -70, 0, 42, -16, 0, -48, 0, 0, -104, -2, 0, 42, 6, 0, -60, -53, 0, 30, -96, 0, 0, -14, 0, -6, -16, 0, 23, 0, 0, 12, 114, 0, 24, 4, 0, 0, -8, 0, 0, -48, 0, 0, -4, 0, -4, 17, 0, 24, 0, 0, 29, -120, 0, 6, 60, 0, -30, -10, 0, 0, 15, 0, 0, 27, 0, -6, -24, 0, -30, 0, 0, 0, 0, 0, 1, 32, 0, 2, 42, 0, -18, -52, 0, 0, 88, 0, -20, 32, 0, -8, 0, 0, -35, 14, 0, 48, -78, 0, 42, -4, 0, -16, 10, 0, 0, -4, 0, -18, 23, 0, -50, 0, 0, -29, -88, 0, -54, -13, 0, -10, 52, 0, 54, -2, 0, 0, -2, 0, -56, 0, 0, -40, 0, 0, 96, -12, 0, -7, 126, 0, 144, -1, 0, -37, 68, 0, 0, -12, 0, -7, 36, 0, -2, 0, 0, -35, -63, 0, -64, -24, 0, 6, -78, 0, 16, -20, 0, 0, 28, 0, -50, -5, 0, 12, 0, 0, 0, 46, 0, -68, 77, 0, -38, -14, 0, 10, 144, 0, 0, -10, 0, 24, -52, 0, 32, 0, 0, -20, 24, 0, -8, -24, 0, 30, -40, 0, 98, -12, 0, 0, -48, 0, 60, -66, 0, -60, 0, 0, -24, -20, 0, -20, 42, 0, -6, 84, 0, 8, -72, 0, 0, 28, 0, 6, 36, 0, 60, 0, 0, 28, 0, 0, 134, -2, 0, 29, -48, 0, -58, -12], "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, 63, 7, 1, 3, 0]], "char_orbit_index": 8, "prim_orbit_index": 7, "minimal_twist": "126.2.f.b", "char_is_minimal": false, "conrey_index": 361, "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], [1, 0], [-1, 1], [0, 0], [0, -1], [-2, 0], [0, 0], [0, 0], [1, 0], [0, 0], [2, -2], [-1, 0], [0, 0], [6, -6], [0, 0], [0, 0], [-1, 1], [-5, 5], [0, 0], [0, 7], [0, 2], [0, 0], [1, -1], [-4, 0], [0, 0], [-1, 0], [0, 6], [0, 0], [0, 0], [0, -4], [0, 0], [0, 6], [0, -1], [0, 0], [0, -5], [0, 0], [0, 0], [0, -2], [-7, 0], [0, 0], [-2, 0], [3, -3], [0, 0], [0, 1], [0, 1], [0, 0], [4, -4], [0, 0], [0, 0], [0, 0], [1, -1], [0, 0], [-6, 0], [12, -12], [0, 0], [2, 0], [0, 0], [0, 0], [4, 0], [0, -7], [0, 0], [12, -12], [-6, 0], [0, 0], [1, 0], [-12, 12], [0, 0], [0, -13], [5, 0], [0, 0], [0, 0], [8, 0], [0, 0], [-1, 1], [2, 0], [0, 0], [7, -7], [0, 0], [0, 0], [6, -6], [2, -2], [0, 0], [0, 3], [0, 16], [0, 0], [10, -10], [-1, 0], [0, 0], [-1, 0], [0, -6], [0, 0], [0, 0], [0, 4], [0, 0], [0, 0], [0, -14], [0, 0], [0, 5], [0, 0], [0, 0], [0, 1]]}