# Stored data for newform 232.4.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "232.4.a.d", "space_label": "232.4.a", "level": 232, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220584, "dim": 5, "is_polredabs": true, "trace_hash": 1069070613950640414, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1340, 1525, 128, -74, -4, 1]]], "qexp_display": "q+(1-\\beta _{1})q^{3}+(2+\\beta _{3})q^{5}+(6+\\beta _{2}+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3712, "fricke_eigenval": 1, "atkin_lehner_string": "--", "analytic_conductor": 13.688443121331822, "hecke_ring_index": 8, "level_radical": 58, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [232, 1, [175, 117, 89], [1, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [2, 29], "conrey_indexes": [1], "field_disc": 6001835520, "field_disc_factorization": [[2, 9], [3, 1], [5, 1], [19, 1], [41131, 1]], "field_poly": [-198, 94, 74, -34, -1, 1], "hecke_ring_index_factorization": [[2, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.107", "prec": 17}, {"__RealLiteral__": 0, "data": "4.784", "prec": 17}, {"__RealLiteral__": 0, "data": "1.489", "prec": 17}, {"__RealLiteral__": 0, "data": "64.360", "prec": 20}, {"__RealLiteral__": 0, "data": "31.293", "prec": 20}, {"__RealLiteral__": 0, "data": "1458.679", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[2, -1], [29, -1]], "trace_display": [0, 4, 10, 32], "traces": [0, 5, 0, 4, 0, 10, 0, 32, 0, 29, 0, 36, 0, 26, 0, 88, 0, 82, 0, 156, 0, 72, 0, 336, 0, 151, 0, 352, 0, 145, 0, 432, 0, 108, 0, 600, 0, -18, 0, 688, 0, 82, 0, 340, 0, -146, 0, 680, 0, -115, 0, 608, 0, -102, 0, 736, 0, -576, 0, 924, 0, -618, 0, 584, 0, -704, 0, 44, 0, -1056, 0, 1032, 0, -1078, 0, -468, 0, -888, 0, 200, 0, -1843, 0, 452, 0, -1700, 0, 116, 0, -1790, 0, -1128, 0, -1884, 0, 1024, 0, -2518, 0, -1500, 0, -1810, 0, 136, 0, -2760, 0, -2164, 0, -1486, 0, -296, 0, -246, 0, -2280, 0, 230, 0, 608, 0, -2667, 0, -2784, 0, 1728, 0, -1312, 0, -660, 0, -1748, 0, 848, 0, -152, 0, 1162, 0, -4084, 0, 2292, 0, 2648, 0, 290, 0, -4540, 0, 2402, 0, 1920, 0, 3370, 0, -1784, 0, 286, 0, 336, 0, 6960, 0, -3852, 0, 2260, 0, 5816, 0, -17, 0, -3996, 0, 5998, 0, 4472, 0, 3248, 0, 332, 0, 2194, 0, 4512, 0, 5876, 0, -2624, 0, 4200, 0, 6832, 0, 2090, 0, -6680, 0, 8486, 0, 6768, 0, 7328, 0, 928, 0, -236, 0, 936, 0, 4784, 0, 180, 0, 1624, 0, 9328, 0, -2024, 0, -11256, 0, 6876, 0, -16, 0, 3667, 0, 652, 0, -6330, 0, -312, 0, 11638, 0, -10544, 0, 764, 0, 8424, 0, 7062, 0, -13172, 0, 12058, 0, 2704, 0, -2928, 0, -2196, 0, -8304, 0, -5768, 0, 13462, 0, -3632, 0, 841, 0, 5208, 0, -9624, 0, -15808, 0, 3894, 0, 1200, 0, 10648, 0, -4300, 0, -8458, 0, -4368, 0, 3158, 0, -7460, 0, -5360, 0, 5488, 0, -12289, 0, -6608, 0, 8662, 0, 8624, 0, -1500, 0, 2856, 0, -16088, 0, -4504, 0, 4772, 0, -4292, 0, -15592, 0, 4888, 0, -8850, 0, -5712, 0, 6406, 0, 1044, 0, -5096, 0, -2008, 0, -23030, 0, 3880, 0, -21176, 0, 3820, 0, -15402, 0, -616, 0, -13262, 0, -33720, 0, 5436, 0, 14848, 0, -28800, 0, -3980, 0, -23758, 0, -3200, 0, 7194, 0, 10816, 0, 13840, 0, -8592, 0, -18391, 0, -4132, 0, 5756, 0, 6480, 0, -20126, 0, -5304, 0, -958, 0, 12144, 0, 754, 0, 2996, 0, -13664, 0, 1448, 0, -584, 0, -16508, 0, 17790, 0, 20304, 0, -6112, 0, 5952, 0, -23302, 0, -10096, 0, 12846, 0, -2544, 0, -1382, 0, 23752, 0, -23950, 0, 19624, 0, 32624, 0, 33504, 0, 1344, 0, -3556, 0, 9134, 0, 15200, 0, -11394, 0, 960, 0, -19588, 0, 36344, 0, 23314, 0, 2552, 0, 15984, 0, 15824, 0, -19291, 0, 21252, 0, -41036, 0, 25392, 0, -15670, 0, 7280, 0, 17672, 0, -32104, 0, -13998, 0, 6008, 0, -5778, 0, 20984, 0, 16876, 0, 15660, 0, -8864, 0, 39040, 0, 45044, 0, -5188, 0, 13326, 0, 5664, 0, 14692, 0, -7536, 0, -12428, 0, 976, 0, 4332, 0, 45364, 0, 2378, 0, 15520, 0, 24080, 0, -33164, 0, 40328, 0, -14136, 0, 16052, 0, 4444, 0, -15262, 0, 28144, 0, 16800, 0, -11664, 0, 12508, 0, -26904, 0, -7786, 0, 43940, 0, -14784, 0, -216, 0, 36557, 0, 38484, 0, 28900, 0, -1488, 0, 17656, 0, -9820, 0, -41066, 0, -24552, 0, 15080, 0, 44420, 0, 32814, 0, 4524, 0, 1464, 0, -10096, 0, -20098, 0, -8696, 0, -16160, 0, 9668, 0, -20732, 0, -25552, 0, -34158, 0, -39052, 0, 30448, 0, -5112, 0, -28638, 0, -32736, 0, 37040, 0, -18168, 0, -11540, 0, 15052, 0, 23040, 0, -59528, 0, 58222, 0, -19952, 0, 28408, 0, -71312, 0, -53566, 0, -12244, 0, -10226, 0, 50880, 0, 2088, 0, 16328, 0, -3414, 0, -91400, 0, 22314, 0, -56036, 0, 54576, 0, -60624, 0, -33527, 0, -4504, 0, -23844, 0, -6584, 0, 26508, 0, -27480, 0, -29590, 0, -19320, 0, -12750, 0, 15924, 0, 97684, 0, 1216, 0, -38880, 0, -968, 0, 7086, 0, -33552, 0, -23326, 0, -46460, 0, -2874, 0, 55720, 0, 37712, 0, 9744, 0, -32216, 0, -24736, 0, 16326, 0, 13272, 0, -32026, 0, -23056, 0, -79832, 0, -6844, 0, -73444, 0, -104032, 0, -3408, 0, 79196, 0, 17280, 0, -100176, 0, 11076, 0, -53864, 0, -10790, 0, 34776, 0, 111868, 0, -65424, 0, 6546, 0, -4384, 0, 31824, 0, -6736, 0, -76640, 0, -78512, 0, 7856, 0, 80984, 0, 4379, 0, 40824, 0, -27103, 0, -63168, 0, 90230, 0, -101768, 0, 43136, 0, -20988, 0, 3136, 0, -47048, 0, -67168, 0, 13724, 0, -41920, 0, 14640, 0, 70164, 0, 52344, 0, -16514, 0, -33144, 0, 64082, 0, 83352, 0, -33956, 0, -59840, 0, 14370, 0, 60896, 0, -6618, 0, 10184, 0, -28512, 0, 58328, 0, 26408, 0, 10208, 0, -6372, 0, 40284, 0, 16132, 0, 19168, 0, -61436, 0, 23496, 0, -93194, 0, 22344, 0, -29678, 0, -49000, 0, 75216, 0, 28560, 0, -105206, 0, 35740, 0, 101980, 0, -102504, 0, 35408, 0, 66480, 0, 75490, 0, -12760, 0, 53504, 0, 50460, 0, -64986, 0, 30232, 0, -27166, 0, 4592, 0, 42012, 0, 9264, 0, 4205, 0, 114760, 0, -43006, 0, -77240, 0, 57616, 0, -44304, 0, 142726, 0, -15992, 0, -54226, 0, 71956, 0, -50944, 0, -43152, 0, 27100, 0, 67020, 0, 14164, 0, 133496, 0, 458, 0, 11832, 0, 71234, 0, 21256, 0, -8406, 0, 50132, 0, 31424, 0, 29256, 0, -99408, 0, 41244, 0, -19184, 0, 160904, 0, 155856, 0, 12528, 0, 25548, 0, -10456, 0, -108784, 0, 81588, 0, -101386, 0, 23376, 0, -19264, 0, 108584, 0, -107024, 0, -114088, 0, 6956, 0, 74928, 0, -38894, 0, -28616, 0, 69754, 0, 48764, 0, 64336, 0, 9960, 0, 88818, 0, -87552, 0, -26926, 0, 120288, 0, 80760, 0, 668, 0, -96500, 0, -2848, 0, 38646, 0, 91544, 0, 3132, 0, -4304, 0, -68279, 0, -70444, 0, 80212, 0, -39248, 0, -400, 0, 99092, 0, -86704, 0, -6936, 0, -34106, 0, -25008, 0, 42758, 0, -62160, 0, 57468, 0, 121800, 0, -176976, 0, 29568, 0, 202652, 0, 50696, 0, -23218, 0, -12848, 0], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "232.4.a.d", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 0, 0, 0], [1, -1, 0, 0, 0], [0, 0, 0, 0, 0], [2, 0, 0, 1, 0], [0, 0, 0, 0, 0], [6, 0, 1, 0, 1], [0, 0, 0, 0, 0], [6, -3, 0, -1, 1], [0, 0, 0, 0, 0], [8, 0, -1, 2, -2], [0, 0, 0, 0, 0], [7, -5, 1, -1, -2], [0, 0, 0, 0, 0], [18, 0, -6, 2, -1], [0, 0, 0, 0, 0], [17, -5, 2, -4, 1], [0, 0, 0, 0, 0], [31, 5, 1, 2, -2], [0, 0, 0, 0, 0], [17, -11, -2, -4, -1], [0, 0, 0, 0, 0], [64, 6, 9, -8, 5], [0, 0, 0, 0, 0], [27, 6, -3, 3, 5], [0, 0, 0, 0, 0], [68, 8, 3, -2, 2], [0, 0, 0, 0, 0], [29, 0, 0, 0, 0], [0, 0, 0, 0, 0], [85, 13, -3, 0, -3], [0, 0, 0, 0, 0], [20, 6, -7, 5, 1], [0, 0, 0, 0, 0], [112, 26, 5, 8, 7], [0, 0, 0, 0, 0], [0, 6, -2, 14, -12], [0, 0, 0, 0, 0], [135, -9, 13, -20, 11], [0, 0, 0, 0, 0], [15, 17, 18, -2, -5], [0, 0, 0, 0, 0], [74, 14, -27, 30, -22], [0, 0, 0, 0, 0], [-25, -9, -15, 16, -6], [0, 0, 0, 0, 0], [144, -18, -24, -6, -11], [0, 0, 0, 0, 0], [-35, 36, 24, 8, 12], [0, 0, 0, 0, 0], [126, -40, 23, -24, 9], [0, 0, 0, 0, 0], [-21, -9, -3, -15, 6], [0, 0, 0, 0, 0], [149, -11, -11, 0, 1], [0, 0, 0, 0, 0], [-113, -7, -5, -4, -2], [0, 0, 0, 0, 0], [174, -12, 7, -8, 33], [0, 0, 0, 0, 0], [-125, -27, -20, 4, 17], [0, 0, 0, 0, 0], [130, -42, -2, -8, -12], [0, 0, 0, 0, 0], [-143, 29, -22, -11, -9], [0, 0, 0, 0, 0], [30, -50, 18, 0, -28], [0, 0, 0, 0, 0], [-193, -93, 42, -58, 1], [0, 0, 0, 0, 0], [210, -2, 36, 4, -8], [0, 0, 0, 0, 0], [-242, 72, 26, -2, 30], [0, 0, 0, 0, 0], [-78, -34, -36, 48, -22], [0, 0, 0, 0, 0], [-185, -1, -8, -4, 19], [0, 0, 0, 0, 0], [42, 0, -2, 10, -5], [0, 0, 0, 0, 0], [-358, 15, 9, 16, -34], [0, 0, 0, 0, 0], [68, 46, -19, 40, 33], [0, 0, 0, 0, 0], [-341, 31, -8, 14, -13], [0, 0, 0, 0, 0], [29, -29, 0, 0, 0], [0, 0, 0, 0, 0], [-367, 71, -36, -26, -13], [0, 0, 0, 0, 0], [-214, -96, -5, -56, 19], [0, 0, 0, 0, 0], [-364, -44, 6, 25, -10], [0, 0, 0, 0, 0], [189, 47, 29, 6, 16], [0, 0, 0, 0, 0], [-515, 27, -24, -6, 15], [0, 0, 0, 0, 0], [-313, -3, -13, 14, 34], [0, 0, 0, 0, 0]]}