# Stored data for newform 2352.3.f.f, downloaded from the LMFDB on 26 April 2024.
{"label": "2352.3.f.f", "space_label": "2352.3.f", "level": 2352, "weight": 3, "hecke_orbit": 6, "hecke_orbit_code": 22518341784570160, "dim": 4, "is_polredabs": true, "nf_label": "4.0.38025.4", "trace_hash": 2247751623731614571, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [1764, 0, 111, 0, 1]], [11, [-90, -15, 1]]], "qexp_display": "q+\\beta _{1}q^{3}+(2\\beta _{1}+\\beta _{2})q^{5}-3q^{9}+(8+\\cdots)q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "f", "char_is_real": true, "Nk2": 21168, "analytic_conductor": 64.08735817754183, "hecke_ring_index": 12, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [2352, 2, [1471, 1765, 785, 2257], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [97], "field_disc": 38025, "field_disc_factorization": [[3, 2], [5, 2], [13, 2]], "field_poly": [256, 16, 17, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.783", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "72.698", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1971.241", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -12, 0, 30, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 96, 0, -122, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -146, 0, -6, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, 36, 0, -198, 0, 0, 0, 162, 0, 0, 0, 0, 0, 0, 0, -204, 0, -14, 0, 0, 0, 204, 0, 0, 0, 0, 0, 0, 0, 112, 0, 36, 0, 0, 0, 444, 0, 0, 0, 0, 0, 0, 0, 96, 0, 48, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 174, 0, 82, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, 326, 0, 144, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 54, 0, -408, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, 612, 0, -490, 0, 0, 0, 1314, 0, 0, 0, 0, 0, 0, 0, -92, 0, 450, 0, 0, 0, 478, 0, 0, 0, 0, 0, 0, 0, 486, 0, -552, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, -12, 0, 424, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 996, 0, -288, 0, 0, 0, 716, 0, 0, 0, 0, 0, 0, 0, 90, 0, 408, 0, 0, 0, 366, 0, 0, 0, 0, 0, 0, 0, 888, 0, -120, 0, 0, 0, 348, 0, 0, 0, 0, 0, 0, 0, -114, 0, -126, 0, 0, 0, 720, 0, 0, 0, 0, 0, 0, 0, -18, 0, -948, 0, 0, 0, 396, 0, 0, 0, 0, 0, 0, 0, 840, 0, -34, 0, 0, 0, -528, 0, 0, 0, 0, 0, 0, 0, 268, 0, -102, 0, 0, 0, 534, 0, 0, 0, 0, 0, 0, 0, 36, 0, -2136, 0, 0, 0, 498, 0, 0, 0, 0, 0, 0, 0, -1062, 0, 630, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 1286, 0, 438, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, 0, -432, 0, 228, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, -336, 0, -938, 0, 0, 0, 1500, 0, 0, 0, 0, 0, 0, 0, -358, 0, 1854, 0, 0, 0, -430, 0, 0, 0, 0, 0, 0, 0, 210, 0, -624, 0, 0, 0, -1134, 0, 0, 0, 0, 0, 0, 0, -888, 0, 1218, 0, 0, 0, -1680, 0, 0, 0, 0, 0, 0, 0, 3126, 0, 102, 0, 0, 0, -58, 0, 0, 0, 0, 0, 0, 0, 540, 0, -1248, 0, 0, 0, 558, 0, 0, 0, 0, 0, 0, 0, -54, 0, 1764, 0, 0, 0, 1020, 0, 0, 0, 0, 0, 0, 0, -44, 0, -108, 0, 0, 0, -1154, 0, 0, 0, 0, 0, 0, 0, 576, 0, -2280, 0, 0, 0, 594, 0, 0, 0, 0, 0, 0, 0, -1518, 0, 1208, 0, 0, 0, -270, 0, 0, 0, 0, 0, 0, 0, -2830, 0, -180, 0, 0, 0, -3456, 0, 0, 0, 0, 0, 0, 0, -486, 0, -1788, 0, 0, 0, 1512, 0, 0, 0, 0, 0, 0, 0, -2628, 0, 188, 0, 0, 0, 852, 0, 0, 0, 0, 0, 0, 0, -2974, 0, -54, 0, 0, 0, -608, 0, 0, 0, 0, 0, 0, 0, 72, 0, 1698, 0, 0, 0, -900, 0, 0, 0, 0, 0, 0, 0, 768, 0, 1042, 0, 0, 0, -2928, 0, 0, 0, 0, 0, 0, 0, -2070, 0, 612, 0, 0, 0, -126, 0, 0, 0, 0, 0, 0, 0, -528, 0, -1248, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, -300, 0, 2132, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, 3436, 0, 1800, 0, 0, 0, 3814, 0, 0, 0, 0, 0, 0, 0, -612, 0, 888, 0, 0, 0, -1440, 0, 0, 0, 0, 0, 0, 0, -822, 0, 54, 0, 0, 0, -3180, 0, 0, 0, 0, 0, 0, 0, 144, 0, 1386, 0, 0, 0, -2156, 0, 0, 0, 0, 0, 0, 0, 882, 0, -1278, 0, 0, 0, -366, 0, 0, 0, 0, 0, 0, 0, -3552, 0, -1992, 0, 0, 0, -2286, 0, 0, 0, 0, 0, 0, 0, -248, 0, -336, 0, 0, 0, -360, 0, 0, 0, 0, 0, 0, 0, -1446, 0, 1572, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 2820, 0, 958, 0, 0, 0, -1068, 0, 0, 0, 0, 0, 0, 0, -460, 0, 882, 0, 0, 0, 1420, 0, 0, 0, 0, 0, 0, 0, -1332, 0, 48, 0, 0, 0, 648, 0, 0, 0, 0, 0, 0, 0, -1164, 0, 5040, 0, 0, 0, -3816, 0, 0, 0, 0, 0, 0, 0, -1752, 0, 306, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 1206, 0, -2340, 0, 0, 0, -222, 0, 0, 0, 0, 0, 0, 0, -2682, 0, -1880, 0, 0, 0, -1566, 0, 0, 0, 0, 0, 0, 0, -3000, 0, -288, 0, 0, 0, -2770, 0, 0, 0, 0, 0, 0, 0, 1002, 0, -3504, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 240, 0, -72, 0, 0, 0, 2010, 0, 0, 0, 0, 0, 0, 0, 2636, 0, 2178, 0, 0, 0, -3046, 0, 0, 0, 0, 0, 0, 0, 270, 0, -2820, 0, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, -2616, 0, 1598, 0, 0, 0, 1056, 0, 0, 0, 0, 0, 0, 0, 3842, 0, -318, 0, 0, 0, 2698, 0, 0, 0, 0, 0, 0, 0, 1152, 0, -180, 0, 0, 0, -1332, 0, 0, 0, 0, 0, 0, 0, 384, 0, 1410, 0, 0, 0, -3276, 0, 0, 0, 0, 0, 0, 0, -3944, 0, -522, 0, 0, 0, -5216, 0, 0, 0, 0, 0, 0, 0, 1938, 0, -2904, 0, 0, 0, -246, 0, 0, 0, 0, 0, 0, 0, -1680, 0, 3728, 0, 0, 0, 2328, 0, 0, 0, 0, 0, 0, 0, -1068, 0, 2988, 0, 0, 0, 416, 0, 0, 0, 0, 0, 0, 0, 1296, 0, 5334, 0, 0, 0, -2790, 0, 0, 0, 0, 0, 0, 0, 828, 0, -4600, 0, 0, 0, 4272, 0, 0, 0, 0, 0, 0, 0, -6660, 0, 1272, 0, 0, 0, 766, 0, 0, 0, 0, 0, 0, 0, 540, 0, 186, 0, 0, 0, 2592, 0, 0, 0, 0, 0, 0, 0, -804, 0, -3130, 0, 0, 0, 3252, 0, 0, 0, 0, 0, 0, 0, 460, 0, -978, 0, 0, 0, 542, 0, 0, 0, 0, 0, 0, 0, -1548, 0, 3840, 0, 0, 0, -432, 0, 0, 0, 0, 0, 0, 0, 8514, 0, -2384, 0, 0, 0, -6756, 0, 0, 0, 0, 0, 0, 0, 3128, 0, 576, 0, 0, 0, 3078, 0, 0, 0, 0, 0, 0, 0, -300, 0, -2304, 0, 0, 0, 3060, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 3624, 0, 0, 0, 498, 0, 0, 0, 0, 0, 0, 0, 4160, 0, 864, 0, 0, 0, 4230, 0, 0, 0, 0, 0, 0, 0, 666, 0, 906, 0, 0, 0, 2778, 0, 0, 0, 0, 0, 0, 0, -1140, 0, -674, 0, 0, 0, -1974, 0, 0, 0, 0, 0, 0, 0, 2948, 0, -162, 0, 0, 0, -4752, 0, 0, 0, 0, 0, 0, 0, -3036, 0, 4734, 0, 0, 0, 1224, 0, 0, 0, 0, 0, 0, 0, -3000, 0, -900, 0, 0, 0, -1860, 0, 0, 0, 0, 0, 0, 0, -5502, 0, 2268, 0, 0, 0, -1416, 0, 0, 0, 0, 0, 0, 0, -540, 0, -5832, 0, 0, 0, -4608, 0, 0, 0, 0, 0, 0, 0, 1074, 0, 5652, 0, 0, 0, 660, 0, 0, 0, 0, 0, 0, 0, 578, 0, -2262, 0, 0, 0, 1958, 0, 0, 0, 0, 0, 0, 0, 3888, 0, -3492, 0, 0, 0, 2250, 0, 0, 0, 0, 0, 0, 0, 4284, 0, -1594, 0, 0, 0, 7590, 0, 0, 0, 0, 0, 0, 0, -2286, 0, -1836, 0, 0, 0, 834, 0, 0, 0, 0, 0, 0, 0, -1260, 0, 2202, 0, 0, 0, 1470, 0, 0, 0, 0, 0, 0, 0, -9120, 0, 438, 0, 0, 0, -1608, 0, 0, 0, 0, 0, 0, 0, 3538, 0, -5184, 0, 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, -3942, 0, 750, 0, 0, 0, -1188, 0, 0, 0, 0, 0, 0, 0, 1548, 0, -6252, 0, 0, 0, 6768, 0, 0, 0, 0, 0, 0, 0, 7634, 0, -3186, 0, 0, 0, 5980, 0, 0, 0, 0, 0, 0, 0, 3348, 0, -3612, 0, 0, 0, -366, 0, 0, 0, 0, 0, 0, 0, 3912, 0, 946, 0, 0, 0, 900, 0, 0, 0, 0, 0, 0, 0, 5802, 0, 276, 0, 0, 0, 680, 0, 0, 0, 0, 0, 0, 0, -1116, 0, 1608, 0, 0, 0, -1350, 0, 0, 0, 0, 0, 0, 0, 1974, 0, -4896, 0, 0, 0, 3732, 0, 0, 0, 0, 0, 0, 0, -10080, 0, 864, 0, 0, 0, -3528, 0, 0, 0, 0, 0, 0, 0, -1434, 0, 504, 0, 0, 0, -1566, 0, 0, 0, 0, 0, 0, 0, 108, 0, -882, 0, 0, 0, -336, 0, 0, 0, 0, 0, 0, 0, -4076, 0, 2520, 0, 0, 0, 7188, 0, 0, 0, 0, 0, 0, 0, -1044, 0, -438, 0, 0, 0, -1794, 0, 0, 0, 0, 0, 0, 0, 5016, 0, 460, 0, 0, 0, -3228, 0, 0, 0, 0, 0, 0, 0, 4310, 0, -1458, 0, 0, 0, 1714, 0, 0, 0, 0, 0, 0, 0, 2142, 0, 84, 0, 0, 0, 1656, 0, 0, 0, 0, 0, 0, 0, -2550, 0, -4678, 0, 0, 0, 4632, 0, 0, 0, 0, 0, 0, 0, 4896, 0, -2124, 0, 0, 0, 3420, 0, 0, 0, 0, 0, 0, 0, 1152, 0, 3036, 0, 0, 0, 828, 0, 0, 0, 0, 0, 0, 0, -750, 0, -1418, 0, 0, 0, 1746, 0, 0, 0, 0, 0, 0, 0, 9202, 0, -1650, 0, 0, 0, 1876, 0, 0, 0, 0, 0, 0, 0, -1998, 0, -4176, 0, 0, 0, 4284, 0, 0, 0, 0, 0, 0, 0, 1188, 0, -90, 0, 0, 0, 2910, 0, 0, 0, 0, 0, 0, 0, 6912, 0, 36, 0, 0, 0, -3464, 0, 0, 0, 0, 0, 0, 0, -1524, 0, -5094, 0, 0, 0, -1272, 0, 0, 0, 0, 0, 0, 0, 2688, 0, -280, 0, 0, 0, 3576, 0, 0, 0, 0, 0, 0, 0, -820, 0, 1134, 0, 0, 0, 1200, 0, 0, 0, 0, 0, 0, 0, -180, 0, 4308, 0, 0, 0, -1620, 0, 0, 0, 0, 0, 0, 0, 4326, 0, -2054, 0, 0, 0, 5160, 0, 0, 0, 0, 0, 0, 0, -5858, 0, -2868, 0, 0, 0, -3654, 0, 0, 0, 0, 0, 0, 0, 7308, 0, 2688, 0, 0, 0, 756, 0, 0, 0, 0, 0, 0, 0, -2718, 0, -1436, 0, 0, 0, -8562, 0, 0, 0, 0, 0, 0, 0, 12, 0, -2988, 0, 0, 0, -906, 0, 0, 0, 0, 0, 0, 0, 150, 0, 4170, 0, 0, 0, 864, 0, 0, 0, 0, 0, 0, 0, 5712, 0, 4444, 0, 0, 0, 10758, 0, 0, 0, 0, 0, 0, 0, 864, 0, -144, 0, 0, 0, 12432, 0, 0, 0, 0, 0, 0, 0, -2148, 0, 10980, 0, 0, 0, -450, 0, 0, 0, 0, 0, 0, 0, 2364, 0, 9660, 0, 0, 0, -3996, 0, 0, 0, 0, 0, 0, 0, -600, 0, -7170, 0, 0, 0, -3706, 0, 0, 0, 0, 0, 0, 0, -2268, 0, 2904, 0, 0, 0, 4230, 0, 0, 0, 0, 0, 0, 0, 10656, 0, -9258, 0, 0, 0, 7812, 0, 0, 0, 0, 0, 0, 0, -4140, 0, -270, 0, 0, 0, 94, 0, 0, 0, 0, 0, 0, 0, -270, 0, 2412, 0, 0, 0, -1224, 0, 0, 0, 0, 0, 0, 0, 870, 0, 10738, 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, 7, 2, -1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 2, "minimal_twist": "84.3.m.b", "char_is_minimal": false, "conrey_index": 97, "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, 1, 0, 0], [0, 0, 0, 0], [0, 2, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, -1], [0, 0, 0, 0], [0, 1, 1, 0], [0, 0, 0, 0], [-4, 0, 0, -1], [0, 0, 0, 0], [0, -4, -2, 0], [0, 0, 0, 0], [0, -13, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [24, 0, 0, 0], [0, 0, 0, 0], [-29, 0, 0, -3], [0, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [2, 0, 0, -1], [0, 0, 0, 0], [0, -11, -6, 0], [0, 0, 0, 0], [0, 6, -3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-37, 0, 0, 1], [0, 0, 0, 0], [-1, 0, 0, -1], [0, 0, 0, 0], [0, -14, -4, 0], [0, 0, 0, 0], [-19, 0, 0, 3], [0, 0, 0, 0], [0, -6, -3, 0], [0, 0, 0, 0], [0, -14, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [8, 0, 0, 2], [0, 0, 0, 0], [-50, 0, 0, 1], [0, 0, 0, 0], [0, -36, 3, 0], [0, 0, 0, 0], [41, 0, 0, -1], [0, 0, 0, 0], [0, -40, 1, 0], [0, 0, 0, 0], [0, 36, 8, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-50, 0, 0, -2], [0, 0, 0, 0], [-1, 0, 0, -5], [0, 0, 0, 0], [0, 24, 0, 0], [0, 0, 0, 0], [54, 0, 0, -6], [0, 0, 0, 0], [0, -11, -7, 0], [0, 0, 0, 0], [0, -35, -9, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [29, 0, 0, -2], [0, 0, 0, 0], [9, 0, 0, 0], [0, 0, 0, 0], [0, 2, -17, 0], [0, 0, 0, 0], [108, 0, 0, 6], [0, 0, 0, 0], [0, 0, -3, 0], [0, 0, 0, 0], [0, -36, -6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [21, 0, 0, 6], [0, 0, 0, 0], [6, 0, 0, 12], [0, 0, 0, 0], [0, 12, 7, 0], [0, 0, 0, 0], [-24, 0, 0, 3], [0, 0, 0, 0]]}