# Stored data for newform 525.3.h.d, downloaded from the LMFDB on 23 April 2024. {"label": "525.3.h.d", "space_label": "525.3.h", "level": 525, "weight": 3, "hecke_orbit": 4, "hecke_orbit_code": 13511279968780813, "dim": 12, "is_polredabs": true, "trace_hash": 813423376902811329, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [21, -198, 103, 40, -21, -2, 1]]], "qexp_display": "q+\\beta _{5}q^{2}-\\beta _{3}q^{3}+(4+\\beta _{1})q^{4}-\\beta _{9}q^{6}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "h", "char_is_real": true, "Nk2": 4725, "analytic_conductor": 14.305213878915588, "hecke_ring_index": 36864, "level_radical": 105, "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": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [525, 2, [176, 127, 451], [2, 2, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [3, 5, 7], "conrey_indexes": [76], "field_disc": 574941798467136000000, "field_disc_factorization": [[2, 12], [3, 8], [5, 6], [37003, 2]], "field_poly": [441, -1638, 4950, -5472, 5613, -1074, 1704, -372, 295, -26, 21, -2, 1], "hecke_ring_index_factorization": [[2, 12], [3, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.075", "prec": 17}, {"__RealLiteral__": 0, "data": "10.753", "prec": 20}, {"__RealLiteral__": 0, "data": "11.154", "prec": 20}, {"__RealLiteral__": 0, "data": "664.924", "prec": 24}, {"__RealLiteral__": 0, "data": "1519.630", "prec": 27}, {"__RealLiteral__": 0, "data": "64907.521", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "2.2.3.c2", "trace_display": [4, 0, 0, 8], "traces": [0, 12, 4, 0, 44, 0, 0, 8, -4, -36, 0, -16, 0, 0, -40, 0, 92, 0, -12, 0, 0, 36, 88, 64, 0, 0, 0, 0, -88, 104, 0, 0, 228, 0, 0, 0, -132, -32, 0, -24, 0, 0, 60, -152, 192, 0, 200, 0, 0, 60, 0, 24, 0, -176, 0, 0, -368, 240, 400, 0, 0, 0, 0, -24, -20, 0, 0, -168, 0, 0, 0, 32, 12, 0, 184, 0, 0, -8, -456, 120, 0, 108, 0, 0, 108, 0, 400, 0, 536, 0, 0, 24, -192, -48, 0, 0, 0, 0, -884, 48, 0, 0, -432, 0, 0, 0, -952, -416, 0, -376, 0, 0, 456, 400, 168, 0, -648, 0, 0, -408, 0, 788, 0, 696, 0, 0, 120, 0, 1084, 0, 0, 0, 0, 240, -320, 0, 0, -176, 0, 0, 0, -264, 64, 0, -276, 0, 0, 48, -1232, -664, 0, 584, 0, 0, 344, 0, -120, 0, -1576, 0, 0, -760, 36, 408, 0, 0, 0, 0, 468, -324, 0, 0, -296, 0, 0, 0, 1264, 360, 0, 512, 0, 0, -96, -672, -152, 0, 720, 0, 0, -108, 0, 368, 0, 808, 0, 0, -244, 208, -264, 0, 0, 0, 0, -584, -840, 0, 0, -192, 0, 0, 0, -328, -2832, 0, -184, 0, 0, -1320, 2552, 672, 0, -912, 0, 0, -600, 0, -280, 0, 1152, 0, 0, 936, -208, 1360, 0, 0, 0, 0, -48, 1664, 0, 0, 4092, 0, 0, 0, -1128, 1296, 0, -432, 0, 0, 264, -848, -1712, 0, 508, 0, 0, -144, 0, -312, 0, -992, 0, 0, -744, 216, -2968, 0, 0, 0, 0, 600, -856, 0, 0, -2160, 0, 0, 0, 2408, 1152, 0, 2688, 0, 0, -96, -684, 876, 0, 384, 0, 0, 1032, 0, -1480, 0, -80, 0, 0, 792, -1768, -768, 0, 0, 0, 0, 504, -120, 0, 0, -2808, 0, 0, 0, -1640, -608, 0, -1216, 0, 0, 1600, 1248, 396, 0, -1520, 0, 0, -912, 0, -1240, 0, 96, 0, 0, 1092, 1288, -860, 0, 0, 0, 0, 1400, 944, 0, 0, 1552, 0, 0, 0, 72, 4728, 0, -1608, 0, 0, 624, 280, 944, 0, -1524, 0, 0, 2472, 0, -72, 0, -4192, 0, 0, -184, -288, -864, 0, 0, 0, 0, -180, 1784, 0, 0, -896, 0, 0, 0, 3736, 456, 0, 104, 0, 0, -2716, 552, 1688, 0, -576, 0, 0, 1104, 0, -184, 0, 2304, 0, 0, 2144, 2528, -1536, 0, 0, 0, 0, 216, -600, 0, 0, -2160, 0, 0, 0, -888, -1672, 0, -2168, 0, 0, 600, 3168, 1440, 0, 1856, 0, 0, -2664, 0, 392, 0, 2064, 0, 0, -180, -3888, -2192, 0, 0, 0, 0, -408, -40, 0, 0, 7920, 0, 0, 0, 456, -56, 0, -72, 0, 0, 2928, 1152, -4952, 0, 2024, 0, 0, -568, 0, -2088, 0, -2032, 0, 0, 792, 528, 448, 0, 0, 0, 0, -96, -716, 0, 0, -896, 0, 0, 0, -592, 1512, 0, 8112, 0, 0, -3776, -528, -2488, 0, -888, 0, 0, 1104, 0, -3568, 0, 704, 0, 0, -1560, 1220, -720, 0, 0, 0, 0, 3512, 1152, 0, 0, -1200, 0, 0, 0, 3320, -1344, 0, -1276, 0, 0, 0, -2496, 2328, 0, 1472, 0, 0, -3040, 0, 1656, 0, 48, 0, 0, -192, -312, 2352, 0, 0, 0, 0, 448, -1784, 0, 0, 3376, 0, 0, 0, 624, -1784, 0, -5160, 0, 0, 72, 3440, -2344, 0, -1176, 0, 0, 2520, 0, 60, 0, -2396, 0, 0, 1536, -1968, -3152, 0, 0, 0, 0, -2496, 2064, 0, 0, -6336, 0, 0, 0, -3432, 1200, 0, 1040, 0, 0, -4312, 504, 4808, 0, -1824, 0, 0, 168, 0, 1392, 0, -1632, 0, 0, -2264, 2080, 984, 0, 0, 0, 0, 240, -2520, 0, 0, -2928, 0, 0, 0, -24, -8888, 0, -4072, 0, 0, 288, -4208, -96, 0, -1000, 0, 0, -4392, 0, 3360, 0, -36, 0, 0, -648, -2296, 5728, 0, 0, 0, 0, -2712, 752, 0, 0, 6200, 0, 0, 0, -552, 6496, 0, -3720, 0, 0, 4092, -1544, -5864, 0, -2884, 0, 0, 3432, 0, 96, 0, 3376, 0, 0, 1592, -1536, 3816, 0, 0, 0, 0, 24, -5416, 0, 0, -3024, 0, 0, 0, -4504, 1368, 0, 12032, 0, 0, -1320, 3000, -376, 0, -360, 0, 0, 2592, 0, -432, 0, 5728, 0, 0, -816, 2884, -1872, 0, 0, 0, 0, 6144, -324, 0, 0, -7200, 0, 0, 0, -1944, -6160, 0, -984, 0, 0, 7600, -9248, 5712, 0, 5608, 0, 0, -1768, 0, -856, 0, -1032, 0, 0, -324, -4208, 872, 0, 0, 0, 0, -4560, 8016, 0, 0, 1536, 0, 0, 0, 2472, 4936, 0, -1200, 0, 0, 1224, 2368, -1680, 0, 2336, 0, 0, -628, 0, 4536, 0, 3216, 0, 0, -3160, -1608, 432, 0, 0, 0, 0, -4848, -3888, 0, 0, -2792, 0, 0, 0, -2688, 3792, 0, 872, 0, 0, -6792, 4512, 1456, 0, -1416, 0, 0, -72, 0, 1112, 0, -2352, 0, 0, -2544, 9664, 576, 0, 0, 0, 0, 432, -1992, 0, 0, 144, 0, 0, 0, -460, -8152, 0, -8104, 0, 0, 296, -8656, 1824, 0, 4624, 0, 0, 0, 0, 6376, 0, 960, 0, 0, 384, 880, 1888, 0, 0, 0, 0, -8808, -992, 0, 0, 14728, 0, 0, 0, 4848, -2736, 0, -1200, 0, 0, 2652, 1432, -7344, 0, -5032, 0, 0, 872, 0, -144, 0, -768, 0, 0, 800, -1056, 4888, 0, 0, 0, 0, -2064, 3880, 0, 0, 1528, 0, 0, 0, -736, 7056, 0, 7528, 0, 0, -2424, 1296, 13544, 0, -3072, 0, 0, 4872, 0, -1184, 0, -2832, 0, 0, -816, 7824, -1248, 0, 0, 0, 0, 6968, 192, 0, 0, -7080, 0, 0, 0, -4976, -5600, 0, -1248, 0, 0, 6048, -6848, 2856, 0, 9600, 0, 0, -4696, 0, 924, 0, 1248, 0, 0, -3408, 2016, 4740, 0, 0, 0, 0, 4704, 400, 0, 0, 5872, 0, 0, 0, 1128, 8920, 0, -6792, 0, 0, 3576, -4080, -4448, 0, 152, 0, 0, 2504, 0, 2928, 0, -4504, 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, 7, 2, -1, 2, 0]], "char_orbit_index": 8, "prim_orbit_index": 2, "minimal_twist": "105.3.h.a", "char_is_minimal": true, "conrey_index": 76, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [4, 1, 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, -1, 0, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1], [-1, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0], [-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 0, -1, 2, 0, 1, 1, 0, 0, 0], [0, 0, 1, -4, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0], [-4, -2, -1, 2, -1, -1, 0, 1, 0, 1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 4, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2], [0, 0, 1, 1, 0, 0, 0, 0, 0, -2, -1, 1], [0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0], [0, 0, -1, 7, -1, 0, -1, 0, -1, 2, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, -1, 0, 1, 0, 1, 1, 0, 0, 0], [9, 3, 0, 0, -2, 4, 0, 4, 2, 0, 1, 1], [3, -3, 0, 0, 0, 0, 0, -1, 0, 0, -2, -2], [0, 0, 1, 1, 0, 0, 1, 0, 0, -3, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, -14, 1, 0, 1, 0, 1, -2, -1, 1], [0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 3, -2, 3, 0, -4, -1, -2, 0, 2, -1, 4], [5, -5, 0, 0, 0, 2, 0, -1, 0, 0, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, 0, 0, -1, 0, 0, 2, -3, 3], [20, 4, 0, 0, -2, 5, 0, 6, 2, 0, 0, 0], [0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 2, -2], [0, 0, 1, -11, -1, 0, 1, 0, -1, -2, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-5, -5, 0, 0, -2, 2, 0, 0, 2, 0, -2, -2], [0, 0, 1, 1, 2, 0, -2, 0, 2, 6, -1, 1], [0, 0, 0, 0, -1, -4, 0, -1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, 20, 1, 0, 1, 0, 1, -6, 1, -1], [6, 3, -2, 4, -2, 5, 0, 2, 0, 2, 3, 0], [-13, 3, 0, 0, 2, 6, 0, -2, -2, 0, 3, 3], [17, 7, 0, 0, -1, 14, 0, 9, 1, 0, 4, 4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [17, 1, 0, 0, 2, 0, 0, -8, -2, 0, 2, 2], [0, 0, 3, -9, -2, 0, -1, 0, -2, 6, -2, 2], [0, 0, 4, -9, 2, 0, 2, 0, 2, -4, 2, -2], [8, -1, 3, -1, 1, -10, 1, 0, -1, 4, 3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, 0, 0, -1, -4, 0, 2, 1, 0, 0, 0], [0, 0, 2, 2, -2, 0, 1, 0, -2, -14, 4, -4], [-15, -9, 0, 0, 0, -12, 0, 3, 0, 0, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-35, -7, -7, 14, -1, -1, -3, 0, -2, 7, -5, -1], [21, 3, 0, 0, 2, 2, 0, -1, -2, 0, 3, 3], [35, 1, 0, 0, 2, -4, 0, -10, -2, 0, 2, 2], [0, 0, -4, 14, -3, 0, -4, 0, -3, -2, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, -19, -3, 0, -2, 0, -3, 4, 0, 0], [0, 0, -10, 26, -4, 0, -1, 0, -4, 0, -5, 5], [-3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3], [-4, 9, 0, 0, -4, 28, 0, 6, 4, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, -9, 1, 0, 0, 0, 1, 0, 6, -6], [-17, -9, 0, 0, 2, -6, 0, 4, -2, 0, -1, -1], [0, 0, 3, -21, 2, 0, 2, 0, 2, -14, -1, 1], [0, 0, -3, -3, -2, 0, -1, 0, -2, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 4, 0, 0, -1, -4, 0, 0, 1, 0, -6, -6], [3, -3, 0, 0, 0, -9, 0, -3, 0, 0, 0, 0], [0, 0, -6, 20, -4, 0, 1, 0, -4, 10, -1, 1], [21, -3, 0, 0, -2, -12, 0, -5, 2, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -15, 37, -3, 0, 3, 0, -3, 6, 3, -3], [-4, -2, -1, 23, 0, 0, 3, -6, 2, 8, -4, -6], [-42, -12, 0, 0, -2, -2, 0, 1, 2, 0, -3, -3], [12, -10, 0, 0, -2, -20, 0, -2, 2, 0, -4, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 8, -40, 0, 0, 3, 0, 0, 18, 6, -6], [0, 0, -8, -8, -4, 0, -2, 0, -4, 4, 2, -2], [9, 6, 3, 4, 0, 9, -2, 6, 3, 4, -2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [33, -3, 0, 0, 1, -20, 0, 3, -1, 0, -8, -8], [0, 0, -5, -5, -2, 0, -1, 0, -2, -2, -1, 1], [47, 25, 0, 0, 2, 24, 0, 10, -2, 0, 5, 5], [0, 0, -2, 4, 1, 0, 7, 0, 1, 6, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [7, 11, -5, 19, 1, 2, 4, 6, -1, -2, 6, 2], [-29, -19, 0, 0, 2, -4, 0, -3, -2, 0, -10, -10], [-6, 0, 0, 0, -2, 10, 0, 7, 2, 0, 0, 0], [0, 0, -1, 41, 1, 0, 2, 0, 1, -28, -6, 6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 4, -20, 0, 0, 2, 0, 0, -1, 8, -8], [0, 0, -2, 12, 2, 0, -3, 0, 2, -6, 7, -7], [-79, -11, 5, 29, 4, 1, 4, -1, 2, -12, 5, -7], [3, -3, 0, 0, 3, -6, 0, -3, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}