# Stored data for newform 378.4.g.d, downloaded from the LMFDB on 19 April 2024.
{"label": "378.4.g.d", "space_label": "378.4.g", "level": 378, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13511211266081146, "dim": 8, "is_polredabs": true, "trace_hash": 440005215190458331, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [9144576, 1850688, 1263600, -155736, 85860, -48, 310, -4, 1]]], "qexp_display": "q+2\\beta _{1}q^{2}+(-4-4\\beta _{1})q^{4}+(-\\beta _{1}+\\cdots)q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "g", "char_is_real": false, "Nk2": 6048, "analytic_conductor": 22.302721982169952, "hecke_ring_index": 108, "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": 0, "analytic_rank_proved": true, "char_values": [378, 3, [29, 325], [3, 2]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [109, 163], "field_disc": 43876713991806864, "field_disc_factorization": [[2, 4], [3, 4], [7, 2], [831221, 2]], "field_poly": [209764, 1374, 29779, 721, 3770, 59, 66, -1, 1], "hecke_ring_index_factorization": [[2, 2], [3, 3]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.007", "prec": 17}, {"__RealLiteral__": 0, "data": "7.715", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "238.141", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12661.080", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c3", "trace_display": [-8, 0, 4, 25], "traces": [0, 8, -8, 0, -16, 4, 0, 25, 64, 0, 8, 56, 0, -18, -22, 0, -64, -118, 0, 37, -32, 0, -224, 200, 0, -104, 18, 0, -56, -524, 0, 276, -128, 0, 472, 290, 0, -185, 74, 0, 32, 60, 0, -1556, 224, 0, 400, 30, 0, -1159, 416, 0, 36, 480, 0, 1456, 200, 0, 524, -296, 0, 474, -1104, 0, 512, 1542, 0, 1319, -472, 0, -32, -1852, 0, -1423, -370, 0, -296, 1228, 0, 765, 64, 0, -60, -1660, 0, -584, 1556, 0, 448, -864, 0, -738, -1600, 0, 60, 1766, 0, 1088, 2704, 0, -416, 658, 0, 1615, -144, 0, -1920, 1842, 0, 1874, -1456, 0, -176, -2684, 0, -992, 1048, 0, 1184, 1510, 0, 400, 948, 0, 1104, -1512, 0, -6984, -512, 0, 3084, 322, 0, -4696, -5276, 0, -944, 448, 0, 182, -1096, 0, 1852, 2772, 0, 5720, 5692, 0, 1480, 4716, 0, 2582, 296, 0, 1064, -16776, 0, -2924, 1530, 0, -256, -398, 0, -2660, -120, 0, 1660, -356, 0, -6866, 584, 0, 3112, -9242, 0, -17554, -1792, 0, -1728, 6048, 0, 12294, -1722, 0, 1600, 12254, 0, 7556, -240, 0, -7064, 6780, 0, 5233, -1088, 0, -772, -10960, 0, -1262, -832, 0, -2632, 4154, 0, -3612, 3230, 0, 144, 17512, 0, 7432, 1920, 0, 3684, -4384, 0, -11586, -7496, 0, -2912, -3996, 0, 10744, -448, 0, 2684, 10080, 0, -1198, 3968, 0, -4192, -5638, 0, 2568, -1184, 0, -6004, -20640, 0, 5944, 800, 0, -3792, -7088, 0, 1554, 2208, 0, 1512, 11544, 0, -11200, 6984, 0, -1024, -894, 0, 65, -12336, 0, 644, -8040, 0, 22128, -4238, 0, 5276, 4888, 0, 4830, 3776, 0, -1792, 10396, 0, 3934, -182, 0, 2320, -31948, 0, -202, 3704, 0, -11088, 10422, 0, 2788, 11440, 0, -5692, 17424, 0, -28960, -1480, 0, 9432, -9006, 0, -18955, -10328, 0, 592, 10428, 0, 14804, -7040, 0, 16776, 24274, 0, 26471, 11696, 0, -6120, 9456, 0, 9616, 256, 0, 25160, -46844, 0, 2055, -5320, 0, 480, -26352, 0, -12989, 3320, 0, 356, 46636, 0, 13086, 6866, 0, 1168, -60, 0, -13496, -12448, 0, -18484, -828, 0, -19516, 11854, 0, 1792, 16896, 0, -24008, 6912, 0, -24192, 6622, 0, -17733, -12294, 0, 6396, -39692, 0, 22927, 3200, 0, -49016, -2244, 0, -8437, 15112, 0, 240, 25488, 0, 17618, 7064, 0, 13560, -8422, 0, 15608, -20932, 0, -2176, -4886, 0, 48728, -9272, 0, 10960, 66, 0, 5706, 5048, 0, 3328, 33792, 0, -13575, 2632, 0, 15664, -59504, 0, -17165, -7224, 0, -12920, 29708, 0, -15404, 288, 0, -17512, -36696, 0, 19638, -7432, 0, 3840, -1454, 0, -22719, -14736, 0, -8768, 25692, 0, 14176, 22626, 0, 7496, 50914, 0, 4968, 11648, 0, 15984, 32762, 0, -18744, -10744, 0, 1600, -82400, 0, 21612, 5368, 0, -40320, -24750, 0, -29116, -2396, 0, -3968, 36952, 0, 55034, 4192, 0, -11276, -32342, 0, 11617, -10272, 0, -2368, 5584, 0, 3194, 5968, 0, 20640, 32888, 0, -38241, -23776, 0, -3200, -5384, 0, -34793, 3792, 0, 36620, -14940, 0, 6028, 3108, 0, -8832, -3776, 0, -25390, 3024, 0, -11544, 54552, 0, 47648, 11200, 0, 13968, -27666, 0, 23401, 4096, 0, -1788, 7706, 0, 20976, 2458, 0, 12336, -14658, 0, 11827, -2576, 0, 32160, 30414, 0, -47204, -22128, 0, 27260, -42456, 0, -7572, 10552, 0, -19552, 67124, 0, -33171, 9660, 0, -3776, -53144, 0, -35904, 1792, 0, 20792, -17158, 0, -62511, -15736, 0, -364, 10624, 0, 10050, -256, 0, 31948, 20924, 0, 35012, 808, 0, -14816, 33534, 0, -15543, 11088, 0, 77256, -90224, 0, 28937, 5576, 0, -45760, -25148, 0, -54960, -11384, 0, -17424, -27856, 0, 137430, 28960, 0, -2960, -654, 0, 4652, -37728, 0, -18012, 3798, 0, 35680, 23470, 0, 10328, 22280, 0, -35505, -2368, 0, -41712, -19032, 0, -55158, -14804, 0, 9824, -31600, 0, 55691, 33552, 0, -97096, -1254, 0, -6056, 52942, 0, -11696, 75040, 0, -54020, 6120, 0, 18912, -5232, 0, 37428, -38464, 0, 512, 40982, 0, 15100, -48728, 0, 46844, -52620, 0, -28268, -8220, 0, 21280, 63588, 0, -56212, -480, 0, 75420, 43976, 0, 6383, -25978, 0, -13280, 118846, 0, 21268, 712, 0, -46636, -49440, 0, -17318, -13086, 0, 13732, -2460, 0, -11519, -4672, 0, -120, 11730, 0, 57200, -976, 0, 12448, 46170, 0, 24718, 73936, 0, 3312, -8090, 0, -1608, 19516, 0, 46508, -61340, 0, 15110, 3584, 0, -67584, -69562, 0, -37526, -48016, 0, -6912, -146352, 0, 74616, 24192, 0, 13244, -17322, 0, -20677, 70932, 0, -24588, -64066, 0, -80032, -5904, 0, 39692, -21710, 0, -35658, -91708, 0, -12800, -74752, 0, -36966, 49016, 0, 24996, 137748, 0, 44388, -16874, 0, -60448, -5958, 0, -5007, 480, 0, -25488, 156520, 0, -16932, -17618, 0, 14128, 20240, 0, -18404, -54240, 0, -16844, -26868, 0, -22198, -13736, 0, 20932, -101234, 0, -55500, 8704, 0, 19544, 26526, 0, -34744, -48728, 0, 21632, 124760, 0, -4620, 21920, 0, -264, 64844, 0, -67347, 11412, 0, -5048, -44088, 0, 22776, -3328, 0, 67584, 53516, 0, -118816, 54300, 0, 5264, 10, 0, 187544, -47944, 0, 59504, 81512, 0, 82457, 68660, 0, 28896, 4238, 0, -19414, 12920, 0, 33736, -80808, 0, -46123, -30808, 0, -1152, -90892, 0, -58228, -35024, 0, 36696, -19852, 0, 50872, -19638, 0, -14864, -30250, 0, -41023, -15360, 0, -2908, -34490, 0, 29770, 118512, 0, 14736, 24594, 0, -4520, 35072, 0, -102768, -120914, 0, -32596, -14176, 0, 1092, 144432, 0, 65673, 14992, 0, -203656, -68316, 0, -28966, 9936, 0, -11648, 160608, 0, -34694, -15984, 0, 65524, 88170, 0, -25527, 74976, 0, -21488, 2706, 0, 221856, -1408, 0, 82400, -137514, 0, 93396, -86448, 0, -21472, 29202, 0, 51303, 40320, 0, 76428, 25716, 0, -25240, -58232, 0, 9584, 76340, 0, -54820, -7936, 0, -36952, -138348, 0, 73070, -55034, 0, 8384, 50640, 0, -128615, 45104, 0, -64684, -16772, 0, 113278, -11200, 0, 10272, 40180, 0, 90660, 9472, 0, -22336, -78446, 0, -64632, -3194, 0, 12080, 110960, 0, 61812, 41280, 0, -131552, -225124, 0, -94628, -76482, 0, 23776, -188356, 0, -78578, 3200, 0, -10768, 43998, 0, -18512, 139172, 0, 7584, -58902, 0, 21480, -44888, 0, 14940, -15138, 0, 56104, -24112, 0, -12432, -144428, 0, 3403, 8832, 0, 57884, 328328, 0, 310, -50780, 0, -12096], "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, 3, 1, 3, 0]], "char_orbit_index": 7, "prim_orbit_index": 3, "minimal_twist": "378.4.g.d", "char_is_minimal": true, "conrey_index": 109, "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], [1, 0, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -4, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, -1, -1, 0, 0, -1], [8, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 0, 0, 0, 0, 0], [14, 14, 2, 1, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 3, 0, 0, 1, -3, 1], [0, 6, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 16, 0, 0, 0, 0, 0, 0], [-30, -30, -2, -1, 2, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -10, 0, -4, 3, 2, 0, 3], [-4, 0, -4, 0, 0, 0, 4, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-28, 0, -4, 2, 0, -4, 4, 0], [0, -48, 0, 0, -8, 0, 2, -8], [0, 0, 0, 0, 0, 0, 0, 0], [-24, -24, -3, -5, -8, 3, 0, 0], [0, -4, 0, 0, -2, 0, 6, -2], [0, 0, 0, 0, 0, 0, 0, 0], [-12, -12, 0, 4, 0, 0, 0, 4], [-67, 0, 11, -4, 0, 2, -11, -6], [0, 0, 0, 0, 0, 0, 0, 0], [71, 71, -12, -1, -8, 7, 0, 0], [-32, -32, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [60, 0, 4, -2, 0, 8, -4, 4], [26, -20, -14, -4, -6, 7, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 47, 0, 6, -3, -3, 24, -3], [20, 20, 0, 4, -6, 10, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -8, 0, 0, 0, 0, -8, 0], [2, 0, -2, -15, 0, 8, 2, -22], [0, 0, 0, 0, 0, 0, 0, 0], [-193, 0, 0, -4, 0, 14, 0, 6], [0, -56, 0, -8, 0, 4, -8, 0], [0, 0, 0, 0, 0, 0, 0, 0], [96, 96, -4, 0, 16, -16, 0, 0], [0, -3, 0, -20, -18, 10, 3, -18], [0, 0, 0, 0, 0, 0, 0, 0], [-209, -129, 0, -12, 1, 0, -21, 2], [48, 0, 6, -10, 0, 4, -6, -16], [0, 0, 0, 0, 0, 0, 0, 0], [8, 8, -12, 0, 4, -4, 0, 0], [122, 122, 28, 8, -8, 16, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [181, 0, 27, -1, 0, -2, -27, -4], [24, 0, 0, -8, -8, 0, 0, -8], [0, 0, 0, 0, 0, 0, 0, 0], [0, -134, 0, 16, 12, -8, 22, 12], [-76, -76, -12, 17, 8, 9, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -110, 0, -12, -34, 6, 27, -34], [-142, 0, 24, -2, 0, -12, -24, -16], [0, 0, 0, 0, 0, 0, 0, 0], [64, 0, 0, 0, 0, 0, 0, 0], [0, -382, 0, -22, -14, 11, 4, -14], [0, 0, 0, 0, 0, 0, 0, 0], [330, 330, 45, 9, -1, 10, 0, 0], [0, 120, 0, 8, -8, -4, 8, -8], [0, 0, 0, 0, 0, 0, 0, 0], [40, 92, 28, 10, 8, -14, -28, -4], [-235, 0, -39, -6, 0, -2, 39, -14], [0, 0, 0, 0, 0, 0, 0, 0], [-360, -360, -36, 2, 17, -15, 0, 0], [-94, -94, -48, -6, 6, -12, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-40, 0, 0, 8, 0, -28, 0, -12], [49, -193, 7, 14, 8, -28, 14, -28], [0, 0, 0, 0, 0, 0, 0, 0], [0, -185, 0, -54, -25, 27, -12, -25], [16, 16, 16, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 60, 44, -30, -4, 44], [-204, 0, -22, 4, 0, 6, 22, 14], [0, 0, 0, 0, 0, 0, 0, 0], [-77, 0, -27, -7, 0, -2, 27, -16], [0, -386, 0, 16, -12, -8, 0, -12], [0, 0, 0, 0, 0, 0, 0, 0], [112, 112, 16, 8, 0, 8, 0, 0], [0, 218, 0, -6, -8, 3, -32, -8], [0, 0, 0, 0, 0, 0, 0, 0], [7, 207, 0, 14, -8, 0, -21, -21], [-192, 0, 8, 0, 0, 32, -8, 32], [0, 0, 0, 0, 0, 0, 0, 0], [6, 6, -6, 20, 36, -16, 0, 0], [428, 428, -4, 30, 54, -24, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [132, 0, 9, -29, 0, 42, -9, -16], [258, -160, 42, -2, -4, 28, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 96, 0, 40, 32, -20, 12, 32]]}