# Stored data for newform 432.3.q.d, downloaded from the LMFDB on 19 April 2024.
{"label": "432.3.q.d", "space_label": "432.3.q", "level": 432, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511898444071344, "dim": 4, "is_polredabs": true, "nf_label": "4.0.576.1", "trace_hash": 1125789905776912872, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [27, -9, 1]]], "qexp_display": "q+(3+3\\beta _{2})q^{5}+(\\beta _{1}-\\beta _{2}+\\beta _{3})q^{7}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "q", "char_is_real": false, "Nk2": 3888, "analytic_conductor": 11.771147420364827, "hecke_ring_index": 9, "level_radical": 6, "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": "0.173", "prec": 17}, "analytic_rank_proved": true, "char_values": [432, 6, [271, 325, 353], [6, 6, 5]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [17, 305], "field_disc": 576, "field_disc_factorization": [[2, 6], [3, 2]], "field_poly": [4, 0, -2, 0, 1], "hecke_ring_index_factorization": [[3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.997", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.297", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1464.431", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [0, 0, 18, -2], "traces": [0, 4, 0, 0, 0, 18, 0, -2, 0, 0, 0, 18, 0, -10, 0, 0, 0, 0, 0, 40, 0, 0, 0, 18, 0, 4, 0, 0, 0, -18, 0, -38, 0, 0, 0, 0, 0, 128, 0, 0, 0, 126, 0, 46, 0, 0, 0, 54, 0, -12, 0, 0, 0, 0, 0, 108, 0, 0, 0, 126, 0, 62, 0, 0, 0, -90, 0, 106, 0, 0, 0, 0, 0, -208, 0, 0, 0, 90, 0, -14, 0, 0, 0, -378, 0, 108, 0, 0, 0, 0, 0, -412, 0, 0, 0, 180, 0, 14, 0, 0, 0, 18, 0, -74, 0, 0, 0, 0, 0, -64, 0, 0, 0, -54, 0, 54, 0, 0, 0, -252, 0, -152, 0, 0, 0, 0, 0, 136, 0, 0, 0, 414, 0, -236, 0, 0, 0, -666, 0, 22, 0, 0, 0, 0, 0, -108, 0, 0, 0, -18, 0, -350, 0, 0, 0, -342, 0, 218, 0, 0, 0, 0, 0, 232, 0, 0, 0, -594, 0, -144, 0, 0, 0, -54, 0, 4, 0, 0, 0, 0, 0, 560, 0, 0, 0, 576, 0, -36, 0, 0, 0, -18, 0, -250, 0, 0, 0, 0, 0, -320, 0, 0, 0, 234, 0, 378, 0, 0, 0, -36, 0, -206, 0, 0, 0, 0, 0, -572, 0, 0, 0, -252, 0, 406, 0, 0, 0, 162, 0, -286, 0, 0, 0, 0, 0, 324, 0, 0, 0, -54, 0, -286, 0, 0, 0, -108, 0, 332, 0, 0, 0, 0, 0, 180, 0, 0, 0, 162, 0, -280, 0, 0, 0, 1386, 0, 540, 0, 0, 0, 0, 0, 136, 0, 0, 0, 36, 0, 98, 0, 0, 0, 630, 0, -290, 0, 0, 0, 0, 0, 436, 0, 0, 0, 522, 0, 378, 0, 0, 0, -306, 0, 370, 0, 0, 0, 0, 0, -440, 0, 0, 0, -558, 0, 794, 0, 0, 0, 990, 0, 18, 0, 0, 0, 0, 0, -40, 0, 0, 0, -810, 0, 490, 0, 0, 0, 954, 0, -670, 0, 0, 0, 0, 0, 260, 0, 0, 0, 1242, 0, -214, 0, 0, 0, 630, 0, 540, 0, 0, 0, 0, 0, -180, 0, 0, 0, -936, 0, 154, 0, 0, 0, -1260, 0, -226, 0, 0, 0, 0, 0, 1312, 0, 0, 0, -1098, 0, 270, 0, 0, 0, 234, 0, 36, 0, 0, 0, 0, 0, -496, 0, 0, 0, -1170, 0, -838, 0, 0, 0, 360, 0, 770, 0, 0, 0, 0, 0, -2268, 0, 0, 0, -918, 0, -538, 0, 0, 0, 72, 0, -586, 0, 0, 0, 0, 0, 1376, 0, 0, 0, -36, 0, -278, 0, 0, 0, 486, 0, -540, 0, 0, 0, 0, 0, 1188, 0, 0, 0, -1854, 0, -802, 0, 0, 0, 414, 0, -566, 0, 0, 0, 0, 0, -860, 0, 0, 0, 90, 0, 40, 0, 0, 0, 1674, 0, 112, 0, 0, 0, 0, 0, 760, 0, 0, 0, 2070, 0, 252, 0, 0, 0, 684, 0, 70, 0, 0, 0, 0, 0, 108, 0, 0, 0, -1170, 0, -544, 0, 0, 0, -666, 0, -90, 0, 0, 0, 0, 0, -1952, 0, 0, 0, 36, 0, -968, 0, 0, 0, -1926, 0, 1080, 0, 0, 0, 0, 0, -1096, 0, 0, 0, -288, 0, 82, 0, 0, 0, -612, 0, -554, 0, 0, 0, 0, 0, 836, 0, 0, 0, -1998, 0, -162, 0, 0, 0, 18, 0, -14, 0, 0, 0, 0, 0, -352, 0, 0, 0, 918, 0, -180, 0, 0, 0, -1746, 0, 268, 0, 0, 0, 0, 0, -1512, 0, 0, 0, -2898, 0, 1502, 0, 0, 0, -1368, 0, -1490, 0, 0, 0, 0, 0, 224, 0, 0, 0, 126, 0, -350, 0, 0, 0, 2556, 0, 1342, 0, 0, 0, 0, 0, 232, 0, 0, 0, 612, 0, 372, 0, 0, 0, 954, 0, 1186, 0, 0, 0, 0, 0, 1692, 0, 0, 0, 2250, 0, 1242, 0, 0, 0, -126, 0, -790, 0, 0, 0, 0, 0, 36, 0, 0, 0, 1206, 0, -274, 0, 0, 0, -198, 0, 1526, 0, 0, 0, 0, 0, -3996, 0, 0, 0, -1260, 0, 1414, 0, 0, 0, 198, 0, 324, 0, 0, 0, 0, 0, 2144, 0, 0, 0, 3870, 0, 698, 0, 0, 0, -666, 0, -918, 0, 0, 0, 0, 0, 2092, 0, 0, 0, -36, 0, -1286, 0, 0, 0, 1476, 0, 110, 0, 0, 0, 0, 0, -1088, 0, 0, 0, 1782, 0, -54, 0, 0, 0, 1368, 0, -482, 0, 0, 0, 0, 0, 3464, 0, 0, 0, 2214, 0, 1976, 0, 0, 0, -3438, 0, 314, 0, 0, 0, 0, 0, -152, 0, 0, 0, -36, 0, -828, 0, 0, 0, 1962, 0, 718, 0, 0, 0, 0, 0, -3212, 0, 0, 0, -378, 0, -828, 0, 0, 0, -1584, 0, -270, 0, 0, 0, 0, 0, -296, 0, 0, 0, 1044, 0, 1108, 0, 0, 0, -522, 0, -3158, 0, 0, 0, 0, 0, 3920, 0, 0, 0, 648, 0, -1782, 0, 0, 0, -162, 0, -1484, 0, 0, 0, 0, 0, 1600, 0, 0, 0, 360, 0, -154, 0, 0, 0, -2970, 0, 490, 0, 0, 0, 0, 0, -324, 0, 0, 0, 414, 0, -118, 0, 0, 0, -414, 0, -634, 0, 0, 0, 0, 0, 3352, 0, 0, 0, 522, 0, -716, 0, 0, 0, 2052, 0, 1728, 0, 0, 0, 0, 0, -3600, 0, 0, 0, 2520, 0, 670, 0, 0, 0, 594, 0, -954, 0, 0, 0, 0, 0, -152, 0, 0, 0, 2628, 0, 128, 0, 0, 0, -1674, 0, -552, 0, 0, 0, 0, 0, 3584, 0, 0, 0, -990, 0, 594, 0, 0, 0, -1350, 0, 1816, 0, 0, 0, 0, 0, -108, 0, 0, 0, -414, 0, 228, 0, 0, 0, -2250, 0, 1258, 0, 0, 0, 0, 0, 2764, 0, 0, 0, 90, 0, -252, 0, 0, 0, 90, 0, 432, 0, 0, 0, 0, 0, -2600, 0, 0, 0, -1440, 0, -550, 0, 0, 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, 9, 4, -1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 4, "minimal_twist": "18.3.d.a", "char_is_minimal": false, "conrey_index": 17, "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], [0, 0, 0, 0], [0, 0, 0, 0], [3, 0, 3, 0], [0, 0, 0, 0], [0, 1, -1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, 1, -3, -1], [0, 0, 0, 0], [-5, -2, 5, 4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [6, 0, -12, 2], [0, 0, 0, 0], [10, -4, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [3, 1, 3, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-6, 2, 3, -2], [0, 0, 0, 0], [-19, -3, 19, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [3, 0, -6, 9], [0, 0, 0, 0], [32, -4, 0, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [21, 6, 21, 0], [0, 0, 0, 0], [0, -3, 23, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [18, -7, -9, 7], [0, 0, 0, 0], [-6, 2, 6, -4], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [30, 0, -60, 10], [0, 0, 0, 0], [27, 6, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [21, 13, 21, 0], [0, 0, 0, 0], [0, 6, 31, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-30, -18, 15, 18], [0, 0, 0, 0], [53, -3, -53, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [30, 0, -60, -8], [0, 0, 0, 0], [-52, -12, 0, 6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [15, 8, 15, 0], [0, 0, 0, 0], [0, 5, -7, 5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-126, 5, 63, -5], [0, 0, 0, 0], [54, -6, -54, 12], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-30, 0, 60, -22], [0, 0, 0, 0], [-103, -6, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [30, -18, 30, 0], [0, 0, 0, 0], [0, -14, 7, -14], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}