# Stored data for newform 147.4.e.h, downloaded from the LMFDB on 29 September 2023.
{"label": "147.4.e.h", "space_label": "147.4.e", "level": 147, "weight": 4, "hecke_orbit": 8, "hecke_orbit_code": 31525472336609427, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 915200841208954215, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [9, -3, 1]], [5, [9, 3, 1]]], "qexp_display": "q+3\\zeta_{6}q^{2}+(3-3\\zeta_{6})q^{3}+(-1+\\zeta_{6})q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 2352, "analytic_conductor": 8.67328077084387, "hecke_ring_index": 1, "level_radical": 21, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "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": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [147, 3, [50, 52], [3, 2]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 2, "level_primes": [3, 7], "conrey_indexes": [67, 79], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.008", "prec": 17}, {"__RealLiteral__": 0, "data": "1.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.011", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "110.319", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [3, 3, -3, 0], "traces": [0, 2, 3, 3, -1, -3, 18, 0, 42, -9, 9, 15, 3, 128, 0, -18, 71, 84, 27, -16, 6, 0, 90, 84, 63, 116, 192, -54, 0, -594, -27, -253, -45, -45, 504, 0, 18, 316, 48, 192, -63, -720, 0, 52, 15, -27, -252, -30, 426, 0, 696, -252, -64, -363, -81, -90, 0, -96, -891, -15, 9, -118, -1518, 0, 866, -192, 135, 370, 84, 504, 0, -684, -189, 362, -948, -348, 32, 0, 1152, -467, 213, -81, -1080, -954, 0, -504, 78, -891, 315, 906, -162, 0, -168, 759, 90, -48, 135, -1006, 0, -270, 116, -1086, 756, 1736, 2688, 0, -2178, 1353, 27, 370, -135, 1896, 0, -1296, -144, 252, 297, -576, -90, 0, -378, 1106, 354, -1080, -253, -1446, 0, 754, 1659, 78, 576, -651, 90, 0, 2220, 81, 1764, 1770, 756, 3116, 0, -180, -1026, 960, 639, 891, 2172, 0, -632, -2454, 1044, -1259, -336, -1512, 0, 1518, 192, -196, 1401, 1089, 270, 0, -486, 1252, 360, -135, -1431, 5292, 0, 3798, -756, -144, -26, -786, -5346, 0, 2130, 45, -2718, -2892, -27, -2704, 0, -708, 1764, 948, -2277, -1260, 60, 0, -288, -3912, 1299, -1493, -1509, -1152, 0, -8172, -405, -3556, 2436, -1110, -6516, 0, 504, 1080, -5208, 756, 4544, -480, 0, 2500, -363, -1026, -4059, -78, -1134, 0, 2220, -1086, 45, 5376, 2844, -850, 0, -2088, -1944, 3855, 48, -2188, 1512, 0, -12474, -852, 1728, -90, -15, -2802, 0, 11016, -639, 791, -3318, 243, 236, 0, -6480, -1024, -5313, -1431, -2169, -10530, 0, 2520, 1131, -756, -1513, -6870, 468, 0, 384, 2673, 1953, 222, -945, 2178, 0, 5436, 370, 7851, -243, 5183, 11928, 0, 10620, -1740, -252, 4960, 4674, 4554, 0, -1548, -270, 3698, 342, 144, 5760, 0, 810, -2143, -2673, -1509, 362, 12546, 0, 90, 6636, -405, 7362, 5376, 696, 0, -7554, 3258, 1136, -354, -2268, 3368, 0, 10416, 2277, -1320, 4032, -8503, -1176, 0, 934, 2577, -3267, -4455, -1299, 8118, 0, -2688, -81, 7424, -3756, -1110, -15120, 0, -810, 484, 477, 2844, 7938, -2220, 0, -16718, 5697, -1944, 252, 3795, -864, 0, 1092, -756, 2358, 1860, -891, 3836, 0, -3456, 675, -3048, -135, 1026, -1812, 0, -17352, 30, -567, 6603, -4056, 6636, 0, -2172, -1062, -11311, -5964, 3240, 5688, 0, -1518, -1208, 3780, -2169, -630, -38016, 0, 15280, -48, 1131, 11736, 12750, 9954, 0, -8958, -234, 503, -3126, -1728, 14112, 0, -3906, -12258, -1401, 135, -5932, -21336, 0, 16472, -1608, 3330, -16192, -1086, 486, 0, 9480, -5292, -4465, -3240, -5310, -3472, 0, 4536, 1431, -2880, 4674, -720, 3168, 0, -2660, 3750, -270, -7623, -9744, -6156, 0, -2706, -2880, 234, -9588, -1917, -988, 0, 5346, 370, 1344, 3258, -16009, -1890, 0, 32256, -7773, -948, 2718, -1275, -14724, 0, 1728, -3132, -5400, 648, 3777, 23130, 0, -2016, -2519, 6564, -2268, 252, 684, 0, -8672, -21087, 2277, 2556, 18636, 1152, 0, -540, 588, -315, 390, -4203, -3712, 0, 6534, 16524, 15078, 405, 20224, 4746, 0, -2212, 1509, -729, -6221, -2478, 7512, 0, -14742, -1080, -24948, 3072, 405, -35926, 0, -8586, -4274, 723, 7938, -15795, 5040, 0, 6516, 3780, 5697, -377, -14277, -4536, 0, 17466, 432, 20610, 5208, 78, -900, 0, -4716, -4032, -6306, -8019, 8072, 1302, 0, 1332, 21252, 3195, 5111, 3267, 270, 0, -46080, 8154, 4059, 7770, 8676, 47106, 0, -162, 22858, -15549, -4056, 3780, -2220, 0, -49448, 1770, -1062, 5220, 4752, 10584, 0, 29760, -2844, -1558, 9843, 6831, 3328, 0, -7560, -2322, -13371, 90, 1944, 22188, 0, -14364, 5232, -432, 14398, 960, -23472, 0, 19488, -3897, 19871, 6429, 4479, -1782, 0, -9054, 5445, 7602, -1728, 18819, 32274, 0, 8096, 135, -12258, -22436, -21324, -2430, 0, 4908, 10668, -16128, 8646, -7308, -22390, 0, -6660, -1259, 3318, -9774, -8971, 1440, 0, -2124, -1920, 756, 12772, 5052, 6480, 0, 25524, 15624, 12842, -759, -2268, -7920, 0, 27264, -12331, 25509, -720, -196, 53088, 0, 42730, -9807, 3750, -7731, -1131, -2178, 0, -26730, 3078, 4977, -8274, 12177, -55996, 0, -468, -4032, -17466, -1701, 225, 44544, 0, -2504, -2157, 3330, -1953, -25560, -6516, 0, 39888, -135, 27506, -1452, -16128, -20034, 0, 17064, -24948, -2646, -1275, -3330, -3540, 0, -38246, -25077, -3132, -1899, 13857, -11664, 0, -10584, -11565, -11385, 22245, -144, -10620, 0, -13128, 1846, -23232, 2268, -640, 1572, 0, 11160, -4674, -18711, -30240, 5754, -5112, 0, -31122, -5184, 5056, 6495, 270, -18288, 0, -90, -5534, -3078, -4203, 19026, -42504, 0, -5760, -2892, 16524, -90, -21846, -3834, 0, 39618, -2373, 1352, -34452, 9954, 22178, 0, 1458, -3258, 2184, 354, 11762, -67866, 0, -7560, -5550, -9720, 22726, 948, -6144, 0, 13356, 15939, -7362, 3624, 4293, 2520, 0, -13014, 19987, 2130, -15795, -57024, 7554, 0, 628, 22920, 3780, -1008, -11496, 6786, 0, 7824, 2268, -38250, -960, 4539, -5530, 0, -41220, -1493, -14046, 702, 29348, -21126, 0, -18756, 5760, 576, -5130, 21168, 16038, 0, 1176, -5859, -18514, 4086, -666, -8406, 0, -5670, -7552, 17796, 3267, -3556, 54990, 0, -5040, 5220, 8154, 4824, -5430, 2220, 0, -97152, -23553, -22806, 7944, 729, 57884, 0, 31098, 14220, 3756, 17892, -416, -26790, 0, -2160, -8187, 15930, 280, 36456, -10440, 0, 50634, 756, 15320, -4293, -14880, 55424, 0, 28044, -7938, 240, 6831, 4752, -68184, 0, 127640, -3990, -2322, -1250, -5697, -1620, 0, -51546, -11094, 29232, -26544, -1026, 14756, 0, 864, 28413, -15594, 8640, -30538, 156, 0, -57528, 822, 1215, -2358, -1482, -12858, 0, -14010, 8019, 23680, 7770, 4527, 8064, 0, 2172, 41824, 48027, 18819, -3195, 92196, 0, 42016, 5376, 135, 23319, 24036, 39816, 0, 16308, 1215, 425, -480, -22086, 17352, 0, 32256, 2592, 75141, 1044, 30492, -32400, 0, -27216, 4056, -11331, -13292, 3855, 19548, 0, -18612, -3408, -7155, 7557, 1062, 4376, 0, -13608, -16496, 5292, 5052, 1026, -43776, 0, 73312, -13008, 15624, 13365, 14154, 13662, 0, 1704, 3960, -55908, -3780, -12096, 7562, 0, -51018, -90, -25863, -1764, -30240, -2130, 0, 2340, 42384, 1401, 23168, -5568, 15462, 0, 21060, 9801, -11736, -5508, 13365, 90468, 0, -7794, -34218, -60672, 12177, 791, 8958, 0, -76682, 23226, -4032, -4527, 1923, -486, 0, -37326, -22272, 8378, -57090, 11268, 27180, 0, -6660, -22113, 5484, -22680, 12258, -149688, 0, 2048, 2184, -1215, 22465, -11385, 2904, 0, 21336, -1431, 29366, 12822, -8532, -30366], "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": 5, "prim_orbit_index": 3, "minimal_twist": "21.4.e.a", "char_is_minimal": false, "conrey_index": 67, "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], [1, 0], [0, 3], [3, -3], [-1, 1], [0, -3], [9, 0], [0, 0], [21, 0], [0, -9], [9, -9], [15, -15], [0, 3], [64, 0], [0, 0], [-9, 0], [0, 71], [84, -84], [27, -27], [0, -16], [3, 0], [0, 0], [45, 0], [0, 84], [63, -63], [116, -116], [0, 192], [-27, 0], [0, 0], [-297, 0], [0, -27], [-253, 253], [-45, 45], [0, -45], [252, 0], [0, 0], [9, 0], [0, 316], [48, -48], [192, -192], [0, -63], [-360, 0], [0, 0], [26, 0], [0, 15], [-27, 27], [-252, 252], [0, -30], [213, 0], [0, 0], [348, 0], [0, -252], [-64, 64], [-363, 363], [0, -81], [-45, 0], [0, 0], [-48, 0], [0, -891], [-15, 15], [9, -9], [0, -118], [-759, 0], [0, 0], [433, 0], [0, -192], [135, -135], [370, -370], [0, 84], [252, 0], [0, 0], [-342, 0], [0, -189], [362, -362], [-948, 948], [0, -348], [16, 0], [0, 0], [576, 0], [0, -467], [213, -213], [-81, 81], [0, -1080], [-477, 0], [0, 0], [-252, 0], [0, 78], [-891, 891], [315, -315], [0, 906], [-81, 0], [0, 0], [-84, 0], [0, 759], [90, -90], [-48, 48], [0, 135], [-503, 0], [0, 0], [-135, 0], [0, 116]]}