# Stored data for newform 2736.2.s.l, downloaded from the LMFDB on 28 May 2023.
{"level_primes": [2, 3, 19], "is_polredabs": true, "sato_tate_group": "1.2.1.d3", "rm_discs": [], "conrey_indexes": [577, 1873], "cm_discs": [-3], "trace_hash": 1335980907801655149, "level_radical": 114, "hecke_ring_index_proved": true, "self_twist_type": 1, "related_objects": [], "prim_orbit_index": 3, "is_cm": true, "hecke_orbit": 12, "analytic_conductor": 21.847069993022313, "inner_twist_count": 4, "field_disc_factorization": [[-1, 1], [3, 1]], "is_rm": false, "char_order": 3, "level_is_square": false, "weight_parity": 1, "label": "2736.2.s.l", "field_poly_is_real_cyclotomic": false, "is_self_twist": true, "is_twist_minimal": false, "minimal_twist": "684.2.k.c", "field_poly_is_cyclotomic": true, "dim": 2, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -77, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -62, 0, 0, 0, 0, 0, 86, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -94, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 98, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 98, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -42, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -74, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 55, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, -55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -91, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, -55, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -106, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, -182, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 74, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, -67, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 55, 0, 0, 0, 0, 0, -91, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -106, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 0, -29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -196, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, -35, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, 0, 0, -71, 0, 0, 0, 0, 0, 110, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -71, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -55, 0, 0, 0, 0, 0, 91, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, -73, 0, 0, 0, 0, 0, -71, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 154, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132, 0, 0, 0, 0, 0, -65, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, -77, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -158, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -140, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -73, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, -17, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, -154, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 0, 0, 0, -160, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -65, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, -59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, -161, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, -136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -74, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 130, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -143, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 85, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -76, 0, 0, 0, 0, 0, -104, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -130, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, -178, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, 89, 0], "hecke_ring_index_factorization": [], "nf_label": "2.0.3.1", "field_poly": [1, -1, 1], "has_non_self_twist": 1, "char_values": [2736, 3, [1711, 2053, 1217, 1009], [3, 3, 3, 1]], "Nk2": 10944, "field_poly_root_of_unity": 6, "analytic_rank": 0, "char_orbit_label": "s", "weight": 2, "trace_display": [0, 0, 0, 2], "analytic_rank_proved": true, "char_parity": 1, "level_is_squarefree": false, "hecke_ring_index": 1, "level_is_prime": false, "char_is_minimal": false, "qexp_display": "q+q^{7}+7\\zeta_{6}q^{13}+(-5+2\\zeta_{6})q^{19}+\\cdots", "self_twist_discs": [-3], "char_is_real": false, "field_disc": -3, "level_is_prime_power": false, "relative_dim": 1, "hecke_cutters": [[5, [0, 1]], [7, [-1, 1]], [11, [0, 1]], [13, [49, -7, 1]]], "space_label": "2736.2.s", "level": 2736, "is_self_dual": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 1, 57, 8, -1, 6, 0], [1, 1, 19, 3, 1, 3, 0]], "char_degree": 2, "char_conductor": 19, "char_orbit_index": 19, "hecke_ring_generator_nbound": 19, "hecke_orbit_code": 49540832885213872, "trace_moments": [{"__RealLiteral__": 0, "data": "0.017", "prec": 17}, {"__RealLiteral__": 0, "data": "2.030", "prec": 17}, {"__RealLiteral__": 0, "data": "0.312", "prec": 17}, {"__RealLiteral__": 0, "data": "18.591", "prec": 20}, {"__RealLiteral__": 0, "data": "4.397", "prec": 17}, {"__RealLiteral__": 0, "data": "228.435", "prec": 24}], "id": null, "projective_field": null, "embedded_related_objects": null, "projective_image_type": null, "artin_image": null, "atkin_lehner_string": null, "atkin_lehner_eigenvals": null, "artin_field": null, "projective_image": null, "artin_field_label": null, "projective_field_label": null, "fricke_eigenval": null, "artin_degree": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-5, 2], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-11, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [5, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-6, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 13], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [7, -7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-13, 13], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-14, 14], [0, 0], [0, 0], [0, 0]]}