# Stored data for newform 76.3.g.b, downloaded from the LMFDB on 13 May 2024. {"label": "76.3.g.b", "space_label": "76.3.g", "level": 76, "weight": 3, "hecke_orbit": 2, "hecke_orbit_code": 4504011994562636, "dim": 4, "is_polredabs": true, "nf_label": "4.0.14400.6", "trace_hash": 35283639712405692, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [49, -42, 5, 6, 1]]], "qexp_display": "q+2q^{2}+(-1+\\beta _{1}-\\beta _{2})q^{3}+4q^{4}+\\cdots", "char_order": 6, "char_parity": -1, "char_degree": 2, "char_conductor": 76, "char_orbit_label": "g", "char_is_real": false, "Nk2": 684, "analytic_conductor": 2.0708500091382565, "hecke_ring_index": 1, "level_radical": 38, "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": "0.170", "prec": 17}, "analytic_rank_proved": true, "char_values": [76, 6, [39, 21], [3, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [7, 11], "field_disc": 14400, "field_disc_factorization": [[2, 6], [3, 2], [5, 2]], "field_poly": [100, 0, -10, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.914", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "56.748", "prec": 20}, {"__RealLiteral__": 0, "data": "1.895", "prec": 17}, {"__RealLiteral__": 0, "data": "1264.046", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c6", "trace_display": [8, -6, -4, 0], "traces": [0, 4, 8, -6, 16, -4, -12, 0, 32, 8, -8, 0, -24, -12, 0, -48, 64, -32, 16, 42, -16, -44, 0, 12, -48, -18, -24, 0, 0, -4, -96, 0, 128, 106, -64, -12, 32, -96, 84, 0, -32, 26, -88, -72, 0, 208, 24, 0, -96, -36, -36, -24, -48, 124, 0, 288, 0, 124, -8, -78, -192, -44, 0, 216, 256, 48, 212, -102, -128, -384, -24, 204, 64, -26, -192, 0, 168, 248, 0, -360, -64, -38, 52, 0, -176, -184, -144, 0, 0, -16, 416, -144, 48, -80, 0, 24, -192, -234, -72, -624, -72, -28, -48, 0, -96, 212, 248, 0, 0, -32, 576, 444, 0, -196, 248, 0, -16, 48, -156, 264, -384, -528, -88, -318, 0, 352, 432, -204, 512, -128, 96, 282, 424, 356, -204, 120, -256, 310, -768, 438, -48, 280, 408, 36, 128, -104, -52, 534, -384, 112, 0, 0, 336, 224, 496, -540, 0, -160, -720, 0, -128, -228, -76, 0, 104, -148, 0, -720, -352, 266, -368, -624, -288, 324, 0, 24, 0, 58, -32, 0, 832, 136, -288, 0, 96, -204, -160, 504, 0, -760, 48, 0, -384, 224, -468, 288, -144, -288, -1248, 132, -144, 1044, -56, -108, -96, -188, 0, 1128, -192, -754, 424, 276, 496, 76, 0, 744, 0, 200, -64, 318, 1152, 384, 888, -180, 0, -408, -392, 0, 496, -832, 0, -1632, -32, 110, 96, 0, -312, 200, 528, 0, -768, 242, -1056, -816, -176, -444, -636, 36, 0, 494, 704, -42, 864, 912, -408, 0, 1024, 6, -256, 0, 192, 136, 564, -192, 848, -976, 712, 0, -408, -40, 240, -504, -512, 528, 620, -1146, -1536, 568, 876, 600, -96, -434, 560, 474, 816, -700, 72, -552, 256, -174, -208, 822, -104, 184, 1068, 216, -768, 380, 224, -72, 0, -88, 0, 0, 672, 296, 448, -138, 992, -668, -1080, 0, 0, 50, -320, 0, -1440, -532, 0, 312, -256, -792, -456, -528, -152, -108, 0, 816, 208, 140, -296, 0, 0, -792, -1440, 0, -704, 226, 532, 54, -736, 1280, -1248, 0, -576, -276, 648, 1554, 0, -1328, 48, -540, 0, -164, 116, -1248, -64, -104, 0, -228, 1664, -22, 272, 1392, -576, 188, 0, -1188, 192, 1168, -408, 1248, -320, 1120, 1008, -1008, 0, -24, -1520, 0, 96, 1448, 0, 1008, -768, 1012, 448, 0, -936, -800, 576, 0, -288, -622, -576, 1200, -2496, 368, 264, -1656, -288, -442, 2088, 360, -112, -196, -216, 0, -192, 506, -376, 0, 0, -292, 2256, 912, -384, 924, -1508, 0, 848, 864, 552, -840, 992, 1536, 152, -468, 0, -1272, 1488, -972, 0, 616, 400, 156, -128, 0, 636, -972, 2304, -1032, 768, 1134, 1776, 2704, -360, -156, 0, -2052, -816, 1278, -784, -80, 0, 0, 992, -644, -1664, 1320, 0, -612, -3264, 0, -64, -340, 220, 0, 192, 828, 0, 240, -624, -928, 400, -1146, 1056, -16, 0, 96, -1536, 288, 484, 0, -2112, -348, -1632, 0, -352, -1290, -888, -1104, -1272, -112, 72, 0, 0, 536, 988, -42, 1408, 320, -84, -804, 1728, -3128, 1824, -798, -816, 240, 0, 552, 2048, 950, 12, 336, -512, -700, 0, -252, 384, -1308, 272, 264, 1128, -1608, -384, -1800, 1696, 586, -1952, 0, 1424, -312, 0, -216, -816, -630, -80, 0, 480, -328, -1008, 0, -1024, 656, 1056, 216, 1240, 56, -2292, 312, -3072, -1280, 1136, 1452, 1752, -424, 1200, 0, -192, 976, -868, 0, 1120, 436, 948, 336, 1632, 2144, -1400, 0, 144, 560, -1104, 2052, 512, 876, -348, -552, -416, 1672, 1644, 828, -208, -624, 368, -3288, 2136, 440, 432, -468, -1536, 566, 760, -1008, 448, -2104, -144, 36, 0, 1972, -176, -2928, 0, -72, 0, 0, 1344, 776, 592, 0, 896, 1076, -276, 0, 1984, 330, -1336, 0, -2160, -360, 0, 1128, 0, 578, 100, 3264, -640, 168, 0, 1920, -2880, -1636, -1064, 0, 0, 108, 624, 0, -512, 658, -1584, -1566, -912, 752, -1056, 0, -304, -22, -216, 780, 0, -1024, 1632, 456, 416, -1168, 280, 2616, -592, 540, 0, 144, 0, 1528, -1584, -564, -2880, -360, 0, -168, -1408, 704, 452, -570, 1064, -136, 108, 2928, -1472, -266, 2560, 0, -2496, -2200, 0, 1728, -1152, 744, -552, 0, 1296, 3016, 3108, 0, 0, -64, -2656, -1530, 96, -332, -1080, -108, 0, 140, -328, -1956, 232, 152, -2496, 0, -128, -1140, -208, 0, 0, 992, -456, -252, 3328, -4144, -44, 0, 544, 204, 2784, -2808, -1152, 2156, 376, 2352, 0, 1792, -2376, 912, 384, -2202, 2336, 882, -816, -1164, 2496, -324, -640, 404, 2240, -2736, 2016, -4176, -2016, -3084, 0, 2284, -48, -540, -3040, -1300, 0, 0, 192, 1700, 2896, 1104, 0, -1664, 2016, 0, -1536, 1032, 2024, 0, 896, 436, 0, 2220, -1872, 2556, -1600, 1104, 1152, 1196, 0, -240, -576, -560, -1244, 0, -1152, -708, 2400, 0, -4992, -264, 736, -2736, 528, 1360, -3312, 0, -576, -2576, -884, -1278, 4176, -3648, 720, 2040, -224, -852, -392, -720, -432, 1804, 0, -3720, -384, -2032, 1012, -1296, -752, 380, 0, 252, 0, 972, -584, 1998, 4512, -2400, 1824, 1968, -768, -672, 1848, 0, -3016, 1520, 0, 1536, 1696, 1614, 1728, 0, 1104, 532, -1680, 0, 1984, 1306, 3072, -2988, 304, 1140, -936, 2184, 0, -690, -2544, 582, 2976, 1772, -1944, 0, 0, 1368, 1232, 0, 800, -440, 312, 612, -256, -2352, 0, 0, 1272, -1580, -1944, -2136, 4608, -156, -2064, 894, 1536, 1208, 2268, -864, 3552, 1336, 5408, 486, -720, 140, -312, 2160, 0, 1152, -4104, -300, -1632, -4928, 2556, -1416, -1568, 2696, -160, -594, 0, 3352, 0, 0, 1984, -4028, -1288, 996, -3328, 1468, 2640, 0, 0, -682, -1224, 0, -6528, -768, 0, 3072, -128, 1046, -680, 1062, 440, 2272, 0, -5448, 384, -610, 1656, 0, 0, -276, 480, 0, -1248, -380, -1856, 1704, 800, 312, -2292, 0, 2112, -2422, -32, -1920, 0, -1144, 192, 3240, -3072, 684, 576, 3888, 968, 568, 0, -2676, -4224, -560, -696, -1386, -3264, -852, 0, -1116, -704, -2636, -2580, -6552, -1776, -3136, -2208, 3168, -2544, 1188, -224, 0, 144, 3312, 0, 1008, 0, -422, 1072, 0, 1976, -620, -84, 0, 2816], "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, 76, 7, -1, 6, 0]], "char_orbit_index": 7, "prim_orbit_index": 7, "minimal_twist": "76.3.g.a", "char_is_minimal": true, "conrey_index": 7, "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], [2, 0, 0, 0], [-1, 1, -1, 0], [4, 0, 0, 0], [-2, -1, 2, 2], [-2, 2, -2, 0], [4, 0, -8, 1], [8, 0, 0, 0], [0, -2, 4, -2], [-4, -2, 4, 4], [-1, 0, 2, -5], [-4, 4, -4, 0], [0, 0, -6, 0], [8, 0, -16, 2], [-16, 1, 8, -1], [16, 0, 0, 0], [-16, -2, 16, 4], [0, -4, 8, -4], [6, 3, 9, -5], [-8, -4, 8, 8], [-22, 5, 22, -10], [-2, 0, 4, -10], [4, -9, -2, 9], [-8, 8, -8, 0], [0, -4, -9, -4], [0, 0, -12, 0], [15, 0, -30, 1], [16, 0, -32, 4], [0, 1, -2, 1], [-32, 2, 16, -2], [-10, 0, 20, 7], [32, 0, 0, 0], [53, -6, -53, 12], [-32, -4, 32, 8], [-2, 10, -2, 0], [0, -8, 16, -8], [-24, 10, 0, -5], [12, 6, 18, -10], [-6, 0, 12, -6], [-16, -8, 16, 16], [13, -4, -13, 8], [-44, 10, 44, -20], [-12, -10, -12, 0], [-4, 0, 8, -20], [52, 0, 0, 0], [8, -18, -4, 18], [0, 7, 0, -7], [-16, 16, -16, 0], [-9, 16, 0, -8], [0, -8, -18, -8], [-8, -10, 4, 10], [0, 0, -24, 0], [0, 4, 62, 4], [30, 0, -60, 2], [48, 7, 48, 0], [32, 0, -64, 8], [53, -2, -44, 16], [0, 2, -4, 2], [-13, -1, -13, 0], [-64, 4, 32, -4], [0, -1, -22, -1], [-20, 0, 40, 14], [72, -28, -36, 28], [64, 0, 0, 0], [12, 12, 0, -6], [106, -12, -106, 24], [-34, 21, 17, -21], [-64, -8, 64, 16], [-96, 22, 0, -11], [-4, 20, -4, 0], [34, 14, 34, 0], [0, -16, 32, -16], [-13, 4, 13, -8], [-48, 20, 0, -10], [31, 0, -62, 3], [24, 12, 36, -20], [62, -42, 0, 21], [-12, 0, 24, -12], [-60, -8, -60, 0], [-32, -16, 32, 32], [-19, -2, 19, 4], [26, -8, -26, 16], [-19, 0, 38, -19], [-88, 20, 88, -40], [0, -20, -92, -20], [-24, -20, -24, 0], [-12, 0, 24, -5], [-8, 0, 16, -40], [0, -22, -8, -22], [104, 0, 0, 0], [-48, 6, 24, -6], [16, -36, -8, 36], [-40, -3, 40, 6], [0, 14, 0, -14], [-40, -20, 92, 27], [-32, 32, -32, 0], [-117, 2, 117, -4], [-18, 32, 0, -16], [-208, 26, 104, -26], [0, -16, -36, -16]]}