# Stored data for newform 336.3.d.c, downloaded from the LMFDB on 18 April 2024. {"label": "336.3.d.c", "space_label": "336.3.d", "level": 336, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9007405463503184, "dim": 4, "is_polredabs": true, "nf_label": "4.0.65856.1", "trace_hash": 726932122408239805, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [84, 0, 56, 0, 1]]], "qexp_display": "q+(1-\\beta _{1}+\\beta _{3})q^{3}+(1-\\beta _{2}+2\\beta _{3})q^{5}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "d", "char_is_real": true, "Nk2": 3024, "analytic_conductor": 9.155336882505976, "hecke_ring_index": 1, "level_radical": 42, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [336, 2, [127, 85, 113, 241], [2, 2, 1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [113], "field_disc": 65856, "field_disc_factorization": [[2, 6], [3, 1], [7, 3]], "field_poly": [21, 0, 14, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.715", "prec": 17}, {"__RealLiteral__": 0, "data": "0.155", "prec": 17}, {"__RealLiteral__": 0, "data": "71.419", "prec": 20}, {"__RealLiteral__": 0, "data": "31.921", "prec": 20}, {"__RealLiteral__": 0, "data": "1900.063", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 2, 0, 0], "traces": [0, 4, 0, 2, 0, 0, 0, 0, 0, -20, 0, 0, 0, -36, 0, -28, 0, 0, 0, -12, 0, 14, 0, 0, 0, -12, 0, -10, 0, 0, 0, -136, 0, 28, 0, 0, 0, 16, 0, -4, 0, 0, 0, 160, 0, -140, 0, 0, 0, 28, 0, 84, 0, 0, 0, -56, 0, 64, 0, 0, 0, -156, 0, 28, 0, 0, 0, 24, 0, 168, 0, 0, 0, -32, 0, -146, 0, 0, 0, -128, 0, -68, 0, 0, 0, 168, 0, -28, 0, 0, 0, 28, 0, -96, 0, 0, 0, -8, 0, -112, 0, 0, 0, 352, 0, -112, 0, 0, 0, 256, 0, 204, 0, 0, 0, 0, 0, 208, 0, 0, 0, 372, 0, 532, 0, 0, 0, 104, 0, 164, 0, 0, 0, 140, 0, -196, 0, 0, 0, 260, 0, 0, 0, 0, 0, -280, 0, 14, 0, 0, 0, -536, 0, 168, 0, 0, 0, -396, 0, -588, 0, 0, 0, 432, 0, -56, 0, 0, 0, -324, 0, 200, 0, 0, 0, -280, 0, -336, 0, 0, 0, -36, 0, 20, 0, 0, 0, 0, 0, -238, 0, 0, 0, -136, 0, 140, 0, 0, 0, -304, 0, 124, 0, 0, 0, 280, 0, -168, 0, 0, 0, -120, 0, 84, 0, 0, 0, -56, 0, 348, 0, 0, 0, -552, 0, -220, 0, 0, 0, 68, 0, -140, 0, 0, 0, -672, 0, 440, 0, 0, 0, 920, 0, -538, 0, 0, 0, 248, 0, 0, 0, 0, 0, -336, 0, 336, 0, 0, 0, 392, 0, -392, 0, 0, 0, -1512, 0, -1036, 0, 0, 0, 1080, 0, -112, 0, 0, 0, -696, 0, 624, 0, 0, 0, 60, 0, -476, 0, 0, 0, 820, 0, 108, 0, 0, 0, 840, 0, -308, 0, 0, 0, 168, 0, -308, 0, 0, 0, -1308, 0, 8, 0, 0, 0, 320, 0, -308, 0, 0, 0, -224, 0, 1036, 0, 0, 0, -172, 0, 660, 0, 0, 0, 208, 0, 312, 0, 0, 0, 1464, 0, 812, 0, 0, 0, 0, 0, 168, 0, 0, 0, -876, 0, -148, 0, 0, 0, -1176, 0, 84, 0, 0, 0, -708, 0, 298, 0, 0, 0, -136, 0, -112, 0, 0, 0, 1640, 0, 504, 0, 0, 0, 944, 0, 108, 0, 0, 0, -56, 0, -632, 0, 0, 0, -336, 0, -896, 0, 0, 0, 628, 0, 28, 0, 0, 0, 1168, 0, 784, 0, 0, 0, -1264, 0, 0, 0, 0, 0, 1512, 0, 816, 0, 0, 0, 680, 0, -1008, 0, 0, 0, 196, 0, -392, 0, 0, 0, 552, 0, -448, 0, 0, 0, 800, 0, -140, 0, 0, 0, -616, 0, 2100, 0, 0, 0, -784, 0, -436, 0, 0, 0, -1272, 0, 84, 0, 0, 0, -288, 0, 1176, 0, 0, 0, 224, 0, -1276, 0, 0, 0, -1364, 0, -1680, 0, 0, 0, 248, 0, -336, 0, 0, 0, -1320, 0, 412, 0, 0, 0, 336, 0, 224, 0, 0, 0, 936, 0, 1288, 0, 0, 0, 1792, 0, -414, 0, 0, 0, 728, 0, -1160, 0, 0, 0, -672, 0, 532, 0, 0, 0, -348, 0, -182, 0, 0, 0, 772, 0, 1596, 0, 0, 0, 1624, 0, -2548, 0, 0, 0, -2056, 0, 1172, 0, 0, 0, 48, 0, 976, 0, 0, 0, 1008, 0, -1680, 0, 0, 0, -1272, 0, 168, 0, 0, 0, 2072, 0, -560, 0, 0, 0, -32, 0, 1876, 0, 0, 0, -2664, 0, -656, 0, 0, 0, -336, 0, 952, 0, 0, 0, 128, 0, -1204, 0, 0, 0, 504, 0, -96, 0, 0, 0, -2192, 0, 104, 0, 0, 0, -1496, 0, -364, 0, 0, 0, -1200, 0, 952, 0, 0, 0, -3132, 0, -840, 0, 0, 0, 36, 0, -784, 0, 0, 0, -176, 0, -116, 0, 0, 0, -252, 0, -1848, 0, 0, 0, -356, 0, -1792, 0, 0, 0, 1512, 0, -504, 0, 0, 0, 952, 0, 888, 0, 0, 0, -1740, 0, -672, 0, 0, 0, -336, 0, -80, 0, 0, 0, -888, 0, 2410, 0, 0, 0, 224, 0, -840, 0, 0, 0, -672, 0, -92, 0, 0, 0, 436, 0, 56, 0, 0, 0, -1344, 0, 1680, 0, 0, 0, 1912, 0, -1008, 0, 0, 0, 3712, 0, 1648, 0, 0, 0, 448, 0, 0, 0, 0, 0, -336, 0, -44, 0, 0, 0, -1952, 0, 1180, 0, 0, 0, 124, 0, -196, 0, 0, 0, 80, 0, -548, 0, 0, 0, 2520, 0, 2268, 0, 0, 0, 2616, 0, 2800, 0, 0, 0, 1520, 0, 336, 0, 0, 0, 1064, 0, -336, 0, 0, 0, -232, 0, -1988, 0, 0, 0, 968, 0, 252, 0, 0, 0, -1344, 0, -700, 0, 0, 0, -276, 0, 532, 0, 0, 0, 1600, 0, -2856, 0, 0, 0, 672, 0, 112, 0, 0, 0, 336, 0, -1596, 0, 0, 0, -1028, 0, -776, 0, 0, 0, 360, 0, -392, 0, 0, 0, -2944, 0, 1316, 0, 0, 0, 1508, 0, -628, 0, 0, 0, -224, 0, 816, 0, 0, 0, 2580, 0, 3472, 0, 0, 0, 224, 0, -2000, 0, 0, 0, -4012, 0, -1120, 0, 0, 0, 4636, 0, -644, 0, 0, 0, -560, 0, 74, 0, 0, 0, 8, 0, 264, 0, 0, 0, -1104, 0, 2548, 0, 0, 0, 3352, 0, 924, 0, 0, 0, 112, 0, 1232, 0, 0, 0, -4648, 0, -1848, 0, 0, 0, 2688, 0, 644, 0, 0, 0, 1816, 0, 2996, 0, 0, 0, 1512, 0, 308, 0, 0, 0, 1216, 0, -1928, 0, 0, 0, -3968, 0, -2096, 0, 0, 0, -84, 0, -672, 0, 0, 0, -3536, 0, -1100, 0, 0, 0, -3696, 0, -280, 0, 0, 0, 1016, 0, 2772, 0, 0, 0, -56, 0, -56, 0, 0, 0, 892, 0, 1400, 0, 0, 0, -2136, 0, 168, 0, 0, 0, 1372, 0, 1132, 0, 0, 0, 1456, 0, -216, 0, 0, 0, -952, 0, -1008, 0, 0, 0, -3392, 0, 1196, 0, 0, 0, 1284, 0, -3372, 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, 3, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "21.3.b.a", "char_is_minimal": false, "conrey_index": 113, "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [1, -1, 0, 1], [0, 0, 0, 0], [1, 0, -1, 2], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-4, 1, 0, 2], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [-9, 0, 1, 0], [0, 0, 0, 0], [-5, -1, -6, 4], [0, 0, 0, 0], [-2, 2, 2, -4], [0, 0, 0, 0], [-3, 0, 5, 0], [0, 0, 0, 0], [4, 2, 0, 1], [0, 0, 0, 0], [-2, 8, 2, -4], [0, 0, 0, 0], [-3, 0, -10, 0], [0, 0, 0, 0], [-2, 5, -9, 1], [0, 0, 0, 0], [2, 2, -2, 4], [0, 0, 0, 0], [-34, 0, -2, 0], [0, 0, 0, 0], [8, -2, -6, 2], [0, 0, 0, 0], [3, -2, -3, 6], [0, 0, 0, 0], [4, 0, 14, 0], [0, 0, 0, 0], [-5, 11, 0, -8], [0, 0, 0, 0], [-8, 22, 8, -16], [0, 0, 0, 0], [40, 0, 6, 0], [0, 0, 0, 0], [-37, -2, -9, -4], [0, 0, 0, 0], [4, 8, -4, 8], [0, 0, 0, 0], [7, 0, 0, 0], [0, 0, 0, 0], [18, 0, 6, -6], [0, 0, 0, 0], [16, -10, -16, 32], [0, 0, 0, 0], [-14, 0, -2, 0], [0, 0, 0, 0], [17, 13, 0, 2], [0, 0, 0, 0], [-1, -26, 1, -2], [0, 0, 0, 0], [-39, 0, 7, 0], [0, 0, 0, 0], [11, -5, -9, 8], [0, 0, 0, 0], [-6, -2, 6, -12], [0, 0, 0, 0], [6, 0, 8, 0], [0, 0, 0, 0], [42, -6, -12, 0], [0, 0, 0, 0], [6, 18, -6, 12], [0, 0, 0, 0], [-8, 0, 26, 0], [0, 0, 0, 0], [-43, -17, 0, -13], [0, 0, 0, 0], [2, -6, -2, 4], [0, 0, 0, 0], [-32, 0, 36, 0], [0, 0, 0, 0], [-19, -20, -18, -4], [0, 0, 0, 0], [-9, -18, 9, -18], [0, 0, 0, 0], [42, 0, 18, 0], [0, 0, 0, 0], [-2, -4, -18, 10], [0, 0, 0, 0], [16, -42, -16, 32], [0, 0, 0, 0], [7, 0, -9, 0], [0, 0, 0, 0], [-42, 30, 0, -36], [0, 0, 0, 0], [12, -10, -12, 24], [0, 0, 0, 0], [-2, 0, 8, 0], [0, 0, 0, 0], [-26, -16, 0, 4], [0, 0, 0, 0]]}