# Stored data for newform 2736.2.s.c, downloaded from the LMFDB on 09 May 2024.
{"label": "2736.2.s.c", "space_label": "2736.2.s", "level": 2736, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9008436238879408, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 1312367657439430834, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [16, 4, 1]], [7, [-3, 1]], [11, [-2, 1]], [13, [49, -7, 1]]], "qexp_display": "q+(-4+4\\zeta_{6})q^{5}+3q^{7}+2q^{11}+7\\zeta_{6}q^{13}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "s", "char_is_real": false, "Nk2": 10944, "analytic_conductor": 21.847069993022313, "hecke_ring_index": 1, "level_radical": 114, "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": [2736, 3, [1711, 2053, 1217, 1009], [3, 3, 3, 1]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [577, 1873], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "1.969", "prec": 17}, {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, {"__RealLiteral__": 0, "data": "11.749", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "105.601", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.3.c3", "trace_display": [0, 0, -4, 6], "traces": [0, 2, 0, 0, 0, -4, 0, 6, 0, 0, 0, 4, 0, 7, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, -11, 0, 0, 0, 4, 0, -2, 0, 0, 0, -12, 0, 14, 0, 0, 0, 4, 0, 7, 0, 0, 0, -2, 0, 4, 0, 0, 0, -4, 0, -8, 0, 0, 0, 6, 0, 1, 0, 0, 0, -56, 0, 3, 0, 0, 0, -2, 0, 3, 0, 0, 0, 12, 0, 5, 0, 0, 0, -24, 0, 0, 0, 0, 0, 18, 0, 21, 0, 0, 0, -4, 0, -10, 0, 0, 0, 2, 0, -18, 0, 0, 0, 4, 0, -6, 0, 0, 0, -4, 0, -32, 0, 0, 0, 0, 0, -14, 0, 0, 0, 48, 0, 0, 0, 0, 0, 18, 0, 24, 0, 0, 0, -2, 0, 21, 0, 0, 0, 14, 0, -32, 0, 0, 0, -18, 0, -40, 0, 0, 0, 4, 0, -7, 0, 0, 0, 12, 0, -22, 0, 0, 0, -6, 0, -36, 0, 0, 0, 12, 0, -33, 0, 0, 0, -24, 0, 2, 0, 0, 0, -28, 0, 0, 0, 0, 0, -40, 0, 21, 0, 0, 0, 20, 0, -7, 0, 0, 0, 12, 0, 16, 0, 0, 0, 16, 0, 9, 0, 0, 0, 28, 0, -6, 0, 0, 0, 0, 0, 5, 0, 0, 0, 8, 0, -14, 0, 0, 0, 6, 0, 16, 0, 0, 0, 48, 0, -1, 0, 0, 0, -8, 0, 49, 0, 0, 0, -14, 0, 8, 0, 0, 0, -28, 0, 42, 0, 0, 0, 18, 0, 32, 0, 0, 0, 18, 0, -8, 0, 0, 0, -22, 0, -52, 0, 0, 0, 4, 0, -12, 0, 0, 0, 12, 0, 17, 0, 0, 0, 36, 0, 24, 0, 0, 0, -28, 0, 21, 0, 0, 0, -8, 0, 12, 0, 0, 0, 68, 0, -14, 0, 0, 0, -24, 0, 8, 0, 0, 0, 0, 0, 77, 0, 0, 0, -6, 0, -46, 0, 0, 0, -24, 0, -13, 0, 0, 0, -4, 0, -30, 0, 0, 0, -28, 0, 62, 0, 0, 0, 0, 0, -8, 0, 0, 0, 12, 0, 26, 0, 0, 0, 12, 0, 19, 0, 0, 0, -12, 0, -44, 0, 0, 0, -28, 0, 42, 0, 0, 0, 14, 0, -24, 0, 0, 0, -24, 0, 0, 0, 0, 0, 20, 0, 13, 0, 0, 0, 10, 0, -7, 0, 0, 0, 28, 0, -10, 0, 0, 0, 18, 0, 48, 0, 0, 0, 60, 0, -26, 0, 0, 0, 0, 0, 3, 0, 0, 0, -6, 0, -23, 0, 0, 0, 28, 0, 23, 0, 0, 0, -4, 0, -144, 0, 0, 0, -32, 0, 8, 0, 0, 0, -168, 0, 58, 0, 0, 0, -34, 0, -38, 0, 0, 0, -16, 0, 9, 0, 0, 0, 14, 0, -77, 0, 0, 0, -34, 0, 49, 0, 0, 0, -40, 0, -32, 0, 0, 0, -26, 0, 0, 0, 0, 0, -6, 0, -11, 0, 0, 0, 12, 0, -16, 0, 0, 0, -6, 0, 9, 0, 0, 0, 36, 0, -4, 0, 0, 0, -76, 0, 29, 0, 0, 0, 0, 0, 7, 0, 0, 0, 56, 0, -8, 0, 0, 0, 8, 0, 19, 0, 0, 0, -24, 0, -29, 0, 0, 0, 28, 0, 15, 0, 0, 0, 22, 0, 98, 0, 0, 0, -84, 0, 8, 0, 0, 0, -32, 0, 14, 0, 0, 0, 44, 0, 4, 0, 0, 0, -72, 0, -8, 0, 0, 0, 18, 0, -8, 0, 0, 0, 34, 0, 0, 0, 0, 0, -30, 0, 38, 0, 0, 0, 28, 0, -82, 0, 0, 0, 14, 0, 38, 0, 0, 0, 18, 0, 46, 0, 0, 0, 54, 0, -41, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 14, 0, 0, 0, 18, 0, 13, 0, 0, 0, -56, 0, 12, 0, 0, 0, 60, 0, 72, 0, 0, 0, 10, 0, -10, 0, 0, 0, -12, 0, -16, 0, 0, 0, 2, 0, -2, 0, 0, 0, 76, 0, -30, 0, 0, 0, 80, 0, 16, 0, 0, 0, 28, 0, -24, 0, 0, 0, -168, 0, 0, 0, 0, 0, 8, 0, 56, 0, 0, 0, 6, 0, 3, 0, 0, 0, -4, 0, -112, 0, 0, 0, -16, 0, -54, 0, 0, 0, 44, 0, 37, 0, 0, 0, 0, 0, 60, 0, 0, 0, 6, 0, 35, 0, 0, 0, -26, 0, -72, 0, 0, 0, 12, 0, -31, 0, 0, 0, 80, 0, 23, 0, 0, 0, 84, 0, -18, 0, 0, 0, 84, 0, 5, 0, 0, 0, 6, 0, 11, 0, 0, 0, 4, 0, -4, 0, 0, 0, -28, 0, -98, 0, 0, 0, -12, 0, -7, 0, 0, 0, -12, 0, 0, 0, 0, 0, 6, 0, -96, 0, 0, 0, -72, 0, 36, 0, 0, 0, 44, 0, 7, 0, 0, 0, 12, 0, 44, 0, 0, 0, -8, 0, 90, 0, 0, 0, 0, 0, 48, 0, 0, 0, 40, 0, 13, 0, 0, 0, -144, 0, -42, 0, 0, 0, 28, 0, 9, 0, 0, 0, -6, 0, 7, 0, 0, 0, -12, 0, 48, 0, 0, 0, 10, 0, -21, 0, 0, 0, 144, 0, -19, 0, 0, 0, 48, 0, -41, 0, 0, 0, -10, 0, 0, 0, 0, 0, -14, 0, 48, 0, 0, 0, -4, 0, 0, 0, 0, 0, -16, 0, 20, 0, 0, 0, -24, 0, -48, 0, 0, 0, 54, 0, -22, 0, 0, 0, -28, 0, -77, 0, 0, 0, 8, 0, 16, 0, 0, 0, 0, 0, 25, 0, 0, 0, 16, 0, 32, 0, 0, 0, -54, 0, 42, 0, 0, 0, -10, 0, 80, 0, 0, 0, -6, 0, -60, 0, 0, 0, 84, 0, -9, 0, 0, 0, -14, 0, 63, 0, 0, 0, -28, 0, 36, 0, 0, 0, -6, 0, -40, 0, 0, 0, 56, 0, -29, 0, 0, 0, 56, 0, 53, 0, 0, 0, 42, 0, 0, 0, 0, 0, -28, 0, -10, 0, 0, 0, 60, 0, -96, 0, 0, 0, 108, 0, 13, 0, 0, 0, -88, 0, 70, 0, 0, 0, -18, 0, 10, 0, 0, 0, 0, 0, -15, 0, 0, 0, -54, 0, -8, 0, 0, 0, -42, 0, -13, 0, 0, 0, 36, 0, -120, 0, 0, 0, -30, 0, 70, 0, 0, 0, -20, 0, 13, 0, 0, 0, 28, 0, -154, 0, 0, 0, -84, 0, 8, 0, 0, 0, 12, 0, 28, 0, 0, 0, -40, 0, -25, 0, 0, 0, -44, 0, -21, 0, 0, 0, 108, 0, 0, 0, 0, 0, 36, 0, 4, 0, 0, 0, 20, 0, -2, 0, 0, 0, 6, 0, 43, 0, 0, 0, 8, 0, -20, 0, 0, 0, -36, 0, -16, 0, 0, 0, 0, 0, -66, 0, 0, 0, 28, 0, -14, 0, 0, 0, 12, 0, -25, 0, 0, 0, -126, 0, 7, 0, 0, 0, 64, 0, 24, 0, 0, 0, -18, 0, -62, 0, 0, 0, -22, 0, 8, 0, 0, 0, -30, 0, -108, 0, 0, 0, -40, 0, 32, 0, 0, 0, -60, 0, -96, 0, 0, 0, -12, 0, -14, 0, 0, 0, 8, 0, 0, 0, 0, 0, 36, 0, -45, 0, 0, 0, -16, 0, 16, 0, 0, 0, 12, 0, -22, 0, 0, 0, 6, 0, -32, 0, 0, 0, -224, 0, -13, 0, 0, 0, 0, 0, -8, 0, 0, 0, 56, 0, 43, 0, 0, 0, -72, 0, 112, 0, 0, 0, -32, 0, -140, 0, 0, 0, -64, 0, 6, 0, 0, 0, -4, 0, 21, 0, 0, 0, 32, 0, 56, 0, 0, 0, 24, 0, 224, 0, 0, 0, 12, 0, 134, 0, 0, 0, -84, 0, 49, 0, 0, 0, 38, 0, -54, 0, 0, 0, -18, 0, 0, 0, 0, 0, -14, 0, 72, 0, 0, 0, -72, 0, -3, 0, 0, 0, -44, 0, 12, 0, 0, 0, -72, 0, -7, 0, 0, 0, -120, 0, -63, 0, 0, 0, 0, 0, 72, 0, 0, 0, -2, 0, 63, 0, 0, 0, -32, 0, 48, 0, 0, 0, 96, 0, 8, 0, 0, 0, -16, 0, 24, 0, 0, 0, -6, 0, 96, 0, 0, 0, 60, 0, 39, 0, 0, 0, 104, 0, 3, 0, 0, 0, 14, 0, -21, 0, 0, 0, 0, 0, -46, 0, 0, 0, -4, 0, -32, 0, 0, 0, 8, 0, 0, 0, 0, 0, -48, 0, -84, 0, 0, 0, 8, 0, 29, 0, 0, 0, 28, 0, 45, 0, 0, 0, -28, 0, 48, 0, 0, 0, -42, 0, 36, 0, 0, 0, -136, 0, -4, 0, 0, 0, 0, 0, -33, 0, 0, 0, 2, 0, -13, 0, 0, 0, 48, 0, -72, 0, 0, 0, -14, 0, 48, 0, 0, 0, -132, 0, 27, 0, 0, 0, 64, 0, -112, 0, 0, 0, -42, 0, 42, 0, 0, 0, 32, 0, -112, 0, 0, 0, 4, 0, 5, 0, 0, 0, 84, 0, -4, 0, 0, 0, 48, 0, 0, 0, 0, 0, 28, 0, -4, 0, 0, 0, 32, 0, 11, 0, 0, 0, 42, 0, 88, 0, 0, 0, 48, 0, 16, 0, 0, 0, -12, 0, 1, 0, 0, 0, 0, 0, 25, 0, 0, 0, 30, 0, -136, 0, 0, 0, 120, 0, 15, 0, 0, 0, 112, 0, -32, 0, 0, 0, -50, 0, -49, 0, 0, 0, -96, 0, 17, 0, 0, 0, 18, 0, 192, 0, 0, 0, 24, 0, 49, 0, 0, 0, -64, 0, -22, 0, 0, 0, -4, 0, -42, 0, 0, 0, -8, 0, -74, 0, 0, 0, 38, 0, 0, 0, 0, 0, 32, 0, 3, 0, 0, 0, 168, 0, 158, 0, 0, 0, 18, 0, -16, 0, 0, 0, 0, 0, -36, 0, 0, 0, 4, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, -19, 0, 0, 0, -80, 0, 1, 0, 0, 0, -42, 0, 15, 0, 0, 0, 144, 0, 33, 0, 0, 0, 24, 0, 25, 0, 0, 0, -52, 0, -3, 0, 0, 0, 126, 0, -63, 0, 0, 0, 18, 0, 130, 0, 0, 0, 252, 0, 8, 0, 0, 0, -72, 0, 48, 0, 0, 0, 60, 0, 0, 0, 0, 0, 24, 0, -19, 0, 0, 0, -14, 0, 147, 0, 0, 0, -48, 0, -112, 0, 0, 0, -14, 0, -18, 0, 0, 0, -124, 0, 64, 0, 0, 0, 0, 0, -42, 0, 0, 0, -42, 0, -112, 0, 0, 0, -28, 0, 0, 0, 0, 0, -4, 0, 24, 0, 0, 0, 44, 0, 79, 0, 0, 0, 14, 0, 57, 0, 0, 0, -132, 0, -55, 0, 0, 0, -44, 0, 48, 0, 0, 0, -84, 0, 5, 0, 0, 0, 44, 0, -147, 0, 0, 0, -78, 0, 28, 0, 0, 0, 40, 0, 0, 0, 0, 0, -48, 0, -66, 0, 0, 0, -6, 0, 136, 0, 0, 0, -152, 0, -12, 0, 0, 0, 54, 0, -10, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 96, 0, 0, 0, -72, 0, -66, 0, 0, 0, 88, 0, 16, 0, 0, 0, 72, 0, -102, 0, 0, 0, -72, 0, -5, 0, 0, 0, 54, 0, -112, 0, 0, 0, 140, 0, -1, 0, 0, 0, -84, 0, -24, 0, 0, 0, 36, 0, 24, 0, 0, 0, -96, 0, -48, 0, 0, 0, -78, 0, 56, 0, 0, 0, 14, 0, 0, 0, 0, 0, -66, 0, -16, 0, 0, 0, 76, 0, -59, 0, 0, 0, -252, 0, -156, 0, 0, 0, -12, 0, 192, 0, 0, 0, -100, 0, -28, 0, 0, 0, 0, 0, -72, 0, 0, 0, -28, 0, -140, 0, 0, 0, 12, 0, -48, 0, 0, 0, -58, 0, -110, 0, 0, 0, 74, 0, -36, 0, 0, 0, 52, 0, -78, 0, 0, 0, 4, 0, 2, 0, 0, 0, -46, 0, 55, 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, 19, 3, 1, 3, 0]], "char_orbit_index": 19, "prim_orbit_index": 3, "minimal_twist": "114.2.e.a", "char_is_minimal": false, "conrey_index": 577, "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], [0, 0], [0, 0], [0, 0], [-4, 4], [0, 0], [3, 0], [0, 0], [0, 0], [0, 0], [2, 0], [0, 0], [0, 7], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [5, -2], [0, 0], [0, 0], [0, 0], [0, 4], [0, 0], [0, -11], [0, 0], [0, 0], [0, 0], [0, 4], [0, 0], [-1, 0], [0, 0], [0, 0], [0, 0], [-12, 12], [0, 0], [7, 0], [0, 0], [0, 0], [0, 0], [4, -4], [0, 0], [7, -7], [0, 0], [0, 0], [0, 0], [0, -2], [0, 0], [2, 0], [0, 0], [0, 0], [0, 0], [0, -4], [0, 0], [-8, 8], [0, 0], [0, 0], [0, 0], [6, -6], [0, 0], [0, 1], [0, 0], [0, 0], [0, 0], [-28, 0], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [-2, 2], [0, 0], [3, -3], [0, 0], [0, 0], [0, 0], [6, 0], [0, 0], [5, -5], [0, 0], [0, 0], [0, 0], [-12, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 18], [0, 0], [0, 21], [0, 0], [0, 0], [0, 0], [-12, 20], [0, 0], [-10, 10], [0, 0], [0, 0], [0, 0]]}