# Stored data for newform 38.5.b.a, downloaded from the LMFDB on 25 April 2024. {"label": "38.5.b.a", "space_label": "38.5.b", "level": 38, "weight": 5, "hecke_orbit": 1, "hecke_orbit_code": 68803362854, "dim": 8, "is_polredabs": true, "trace_hash": 2133270297357950164, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta _{2}q^{2}+(\\beta _{1}+\\beta _{2})q^{3}-8q^{4}+(2-\\beta _{6}+\\cdots)q^{5}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "b", "char_is_real": true, "Nk2": 950, "analytic_conductor": 3.928058597186084, "hecke_ring_index": 32, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [38, 2, [21], [1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 19], "conrey_indexes": [37], "field_disc": 6973177926876578172518400, "field_disc_factorization": [[2, 14], [3, 2], [5, 2], [11, 2], [347, 2], [360323, 2]], "field_poly": [77475204, 0, 4001228, 0, 68229, 0, 450, 0, 1], "hecke_ring_index_factorization": [[2, 5]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.067", "prec": 17}, {"__RealLiteral__": 0, "data": "6.963", "prec": 17}, {"__RealLiteral__": 0, "data": "7.006", "prec": 17}, {"__RealLiteral__": 0, "data": "290.505", "prec": 24}, {"__RealLiteral__": 0, "data": "733.661", "prec": 24}, {"__RealLiteral__": 0, "data": "19023.732", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "4.2.3.c2", "trace_display": [0, 0, 18, -162], "traces": [0, 8, 0, 0, -64, 18, -32, -162, 0, -268, 0, -6, 0, 0, 0, 0, 512, 510, 0, -12, -144, 0, 0, -396, 256, 3458, -192, 0, 1296, 0, -2752, 0, 0, 0, 0, 1002, 2144, 0, -3216, -6588, 0, 0, 1376, -8654, 48, -10334, 0, 3210, 0, 9222, 0, 0, 0, 0, 9088, 17146, 0, -14076, -960, 0, 0, 1314, -15168, 29938, -4096, 0, 4928, 0, -4080, 0, 0, 0, 0, 23398, 13152, 0, 96, -44622, 0, 0, 1152, -20368, 16512, -10440, 0, 21274, 0, -14316, 0, 0, 0, 0, 3168, 19416, 0, -34686, -2048, 0, 0, -56798, -27664, 45792, -51712, 0, 1536, 0, 1152, 0, 0, 0, 0, 74472, -10368, 0, 28960, -23660, 0, 0, 34464, 9726, 22016, 33650, 0, -29304, 0, 51210, 0, 0, 0, 0, 26496, 59586, 0, -26822, 56352, 0, 0, -14250, -81184, -62838, -8016, 0, 59136, 0, -17152, 0, 0, 0, 0, -129318, -109728, 0, 25728, -66830, 0, 0, 52704, 77904, -48384, 162636, 0, -36888, 0, 35616, 0, 0, 0, 0, -11008, -52684, 0, 36908, 69232, 0, 0, -124960, -384, -126780, -134976, 0, 82672, 0, -178368, 0, 0, 0, 0, -79454, -25680, 0, 87456, 6294, 0, 0, 195840, 384144, -73776, 196560, 0, -300674, 0, 279708, 0, 0, 0, 0, 20352, -91640, 0, 7986, 439168, 0, 0, -34248, -183264, -17094, -72704, 0, 86208, 0, -137168, 0, 0, 0, 0, -321354, -119616, 0, 112608, -38622, 0, 0, 7680, 470154, -150816, 228442, 0, -221736, 0, -145914, 0, 0, 0, 0, -10512, 16716, 0, -4596, 121344, 0, 0, -115398, -239504, -143732, -282048, 0, 32768, 0, -270784, 0, 0, 0, 0, -282438, -39424, 0, 302016, -502464, 0, 0, 459584, 474700, 32640, 265980, 0, 79524, 0, 301722, 0, 0, 0, 0, 89984, 131074, 0, -472560, 549312, 0, 0, -267898, -616896, -74712, -187184, 0, 280800, 0, -105216, 0, 0, 0, 0, 119802, -139584, 0, -768, -253686, 0, 0, 356976, 277440, 46272, 485982, 0, -72996, 0, 718298, 0, 0, 0, 0, -9216, 370500, 0, -230214, 162944, 0, 0, -337692, -132096, 447522, -968768, 0, 83520, 0, -290496, 0, 0, 0, 0, 501720, -170192, 0, 349680, -704322, 0, 0, 432864, -395838, 114528, 131338, 0, -740940, 0, -345564, 0, 0, 0, 0, 483744, 751374, 0, -606976, 30240, 0, 0, -1341606, -898816, 438496, -25344, 0, 680448, 0, -155328, 0, 0, 0, 0, -248868, -477856, 0, 277488, -553488, 0, 0, 16384, 39758, 222336, -73310, 0, 769770, 0, 509224, 0, 0, 0, 0, 454384, 698266, 0, -229764, 221312, 0, 0, 149256, -366336, 1006834, -689088, 0, 413696, 0, -787008, 0, 0, 0, 0, 1039300, -12288, 0, 12192, -1528488, 0, 0, 555936, 286594, -9216, 836784, 0, -741286, 0, 613464, 0, 0, 0, 0, 285312, 90960, 0, -134496, 833600, 0, 0, -893754, -558048, -111654, -595776, 0, 204672, 0, 82944, 0, 0, 0, 0, 534504, 7776, 0, -231680, 457942, 0, 0, 189280, -298254, 165568, -206582, 0, -339744, 0, 572154, 0, 0, 0, 0, -275712, -486294, 0, -401978, -77808, 0, 0, 223632, -176128, -215880, 552000, 0, -269200, 0, -65696, 0, 0, 0, 0, -1317384, 234432, 0, 257568, -1124806, 0, 0, 28160, -32142, -409680, -784440, 0, 1087668, 0, 516292, 0, 0, 0, 0, -375296, 352278, 0, -188652, 772032, 0, 0, -158150, -617664, -1115976, -211968, 0, 49056, 0, -476688, 0, 0, 0, 0, -856084, 466752, 0, 214576, 333720, 0, 0, -450816, 2286216, -656352, 2429436, 0, -547166, 0, -1059720, 0, 0, 0, 0, 114000, -1395614, 0, 1626876, 649472, 0, 0, 2841504, 502704, 1445106, 189888, 0, 64128, 0, 310464, 0, 0, 0, 0, 433462, -473088, 0, 241280, 870400, 0, 0, -461184, 843552, 137216, -1171026, 0, -1790712, 0, -1286556, 0, 0, 0, 0, -575232, -58590, 0, -388152, -786048, 0, 0, -1348992, 1949504, -2958130, 1034544, 0, -723840, 0, 877824, 0, 0, 0, 0, -2739108, -278848, 0, -205824, 4259436, 0, 0, 534640, 583362, 95520, -834912, 0, 1754922, 0, -985704, 0, 0, 0, 0, -421632, -2366868, 0, 825240, -623232, 0, 0, 1088154, 387072, -1036884, 78720, 0, -1301088, 0, -205056, 0, 0, 0, 0, 1608874, 295104, 0, -666336, -565890, 0, 0, -260928, -945048, -284928, 482538, 0, -2672390, 0, 2363698, 0, 0, 0, 0, -1670688, 843900, 0, 1933194, -1985952, 0, 0, -573024, 2522304, -1128678, 88064, 0, -493632, 0, 421472, 0, 0, 0, 0, -2187828, -135744, 0, -295264, 3104698, 0, 0, -553856, -1778940, -549056, -11246, 0, 2853194, 0, -4456998, 0, 0, 0, 0, 999680, 373464, 0, 1000536, 3072, 0, 0, 2606412, 1014240, 1024504, 3624960, 0, 1079808, 0, 2692384, 0, 0, 0, 0, -340362, -661376, 0, -433824, 1245720, 0, 0, -2065056, -714866, 1426944, -1124080, 0, 1530666, 0, 1253128, 0, 0, 0, 0, 444672, 1328370, 0, -1804440, -3124224, 0, 0, 465610, 1246848, -2224616, 635632, 0, -1606976, 0, 205440, 0, 0, 0, 0, 1038546, 174048, 0, -699648, 767718, 0, 0, -50352, -4637878, 197760, -1782900, 0, 2677374, 0, -457680, 0, 0, 0, 0, -1566720, -5426280, 0, 1891224, -3073152, 0, 0, 3235908, 590208, 2874564, 1928384, 0, -1572480, 0, 2244672, 0, 0, 0, 0, 7827888, 2405392, 0, -2559040, -2606, 0, 0, -3268032, -3998094, -2237664, -4735036, 0, -3661128, 0, -3483162, 0, 0, 0, 0, 1559040, 2579940, 0, -854910, -2085312, 0, 0, -2259798, 2662976, 1359918, -162816, 0, -1863648, 0, 733120, 0, 0, 0, 0, -2542452, 4962752, 0, -63888, 2249976, 0, 0, -3513344, -1889836, 3706368, -3791424, 0, 8031906, 0, -222928, 0, 0, 0, 0, 273984, -2222264, 0, 2826754, 1466112, 0, 0, 1405026, 136752, 5132088, 1758720, 0, 581632, 0, 1044864, 0, 0, 0, 0, 5840916, -689664, 0, -2136960, -6357090, 0, 0, -1667712, -4309908, 1097344, -1233894, 0, -1304766, 0, 1510224, 0, 0, 0, 0, -2190912, 1364650, 0, -872526, -2744512, 0, 0, -336612, 1236288, 187560, 2570832, 0, -1630272, 0, 956928, 0, 0, 0, 0, 1490728, 2381376, 0, -900864, 6164932, 0, 0, 308976, -3504918, 106112, -299484, 0, 5349864, 0, -6711192, 0, 0, 0, 0, -61440, 2350404, 0, 1857870, -3761232, 0, 0, 7781310, 1206528, 2330566, 4159392, 0, -1827536, 0, 2708864, 0, 0, 0, 0, 1248408, 1773888, 0, -2776752, -3555324, 0, 0, -4900128, -3080534, 1167312, -7419720, 0, -840090, 0, 2983352, 0, 0, 0, 0, 1393216, -1798512, 0, -5289252, -3820032, 0, 0, -1535134, 1597824, 23484, 84096, 0, -1376896, 0, -133728, 0, 0, 0, 0, -3566588, -1544544, 0, 36768, 4742772, 0, 0, -970752, -1831212, -3892224, -2335926, 0, 2512698, 0, -5808120, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 2, -1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "38.5.b.a", "char_is_minimal": true, "conrey_index": 37, "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, 0, 1, 0, 0, 0, 0, 0], [0, 1, 1, 0, 0, 0, 0, 0], [-8, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, -1, 0], [-4, 0, 0, 0, -1, 0, 0, 0], [-20, 0, 0, 0, 0, 1, 0, 0], [0, 0, -8, 0, 0, 0, 0, 0], [-33, 0, 0, 0, -1, 1, 1, 0], [0, 3, 4, -1, 0, 0, 0, 0], [-2, 0, 0, 0, -2, -2, -3, 0], [0, -8, -8, 0, 0, 0, 0, 0], [0, 7, 6, 1, 0, 0, 0, 1], [0, -1, -21, 0, 0, 0, 0, 1], [0, 12, 50, -2, 0, 0, 0, -2], [64, 0, 0, 0, 0, 0, 0, 0], [64, 0, 0, 0, 7, 1, 0, 0], [0, -12, -40, 1, 0, 0, 0, 1], [-1, 14, 57, 2, -3, -1, 3, -1], [-16, 0, 0, 0, 0, 0, 8, 0], [0, -47, -46, 5, 0, 0, 0, -1], [0, -5, -2, -3, 0, 0, 0, -2], [-48, 0, 0, 0, 14, -1, 7, 0], [32, 0, 0, 0, 8, 0, 0, 0], [431, 0, 0, 0, 12, -2, -3, 0], [-28, 0, 0, 0, -11, -8, -8, 0], [0, 3, -143, 8, 0, 0, 0, 2], [160, 0, 0, 0, 0, -8, 0, 0], [0, 15, 24, -9, 0, 0, 0, 3], [-336, 0, 0, 0, -4, 16, 16, 0], [0, -30, 222, 0, 0, 0, 0, 0], [0, 0, 64, 0, 0, 0, 0, 0], [0, 66, -40, -14, 0, 0, 0, -2], [0, 55, 91, 0, 0, 0, 0, 1], [128, 0, 0, 0, -58, 2, 9, 0], [264, 0, 0, 0, 8, -8, -8, 0], [0, -76, -246, 8, 0, 0, 0, 2], [-404, -32, -18, 3, -19, 8, -16, -1], [-834, 0, 0, 0, 6, 3, -45, 0], [0, -24, -32, 8, 0, 0, 0, 0], [0, 42, -234, -12, 0, 0, 0, 0], [164, 0, 0, 0, 33, 8, -40, 0], [-1078, 0, 0, 0, 48, 0, 15, 0], [16, 0, 0, 0, 16, 16, 24, 0], [-1278, 0, 0, 0, -74, 20, 35, 0], [0, 92, -5, 7, 0, 0, 0, -1], [398, 0, 0, 0, -24, 18, -31, 0], [0, 64, 64, 0, 0, 0, 0, 0], [1137, 0, 0, 0, -57, -39, -24, 0], [0, 107, 487, -3, 0, 0, 0, -2], [0, 93, 857, -2, 0, 0, 0, -8], [0, -56, -48, -8, 0, 0, 0, -8], [0, -183, -114, 3, 0, 0, 0, 15], [1116, 0, 0, 0, -29, -16, -64, 0], [2160, 0, 0, 0, 144, 22, 45, 0], [0, 8, 168, 0, 0, 0, 0, -8], [-1758, -28, -470, 4, -69, -21, 27, 10], [-108, 0, 0, 0, 9, -24, 72, 0], [0, 159, -459, -6, 0, 0, 0, 6], [0, -96, -400, 16, 0, 0, 0, 16], [178, 0, 0, 0, 150, -20, 75, 0], [-1896, 0, 0, 0, 30, 0, 0, 0], [3714, 0, 0, 0, 34, -40, -73, 0], [-512, 0, 0, 0, 0, 0, 0, 0], [0, -408, -606, -30, 0, 0, 0, -18], [648, 0, 0, 0, -22, 16, 112, 0], [0, -275, -1017, 22, 0, 0, 0, -26], [-512, 0, 0, 0, -56, -8, 0, 0], [0, 21, 1280, -5, 0, 0, 0, 1], [0, -493, -124, 9, 0, 0, 0, 2], [0, 66, -912, 66, 0, 0, 0, 18], [0, 96, 320, -8, 0, 0, 0, -8], [2972, 0, 0, 0, -69, 39, 150, 0], [1624, 0, 0, 0, 50, -16, -64, 0], [0, 611, 2031, -28, 0, 0, 0, -16], [8, -112, -456, -16, 24, 8, -24, 8], [-5564, 0, 0, 0, 6, 60, -5, 0], [0, 180, -723, -45, 0, 0, 0, 3], [0, 218, 852, 50, 0, 0, 0, 2], [128, 0, 0, 0, 0, 0, -64, 0], [-2571, 0, 0, 0, 86, -2, -98, 0], [2088, 0, 0, 0, -6, 0, 96, 0], [-1362, 0, 0, 0, -64, -70, -158, 0], [0, 376, 368, -40, 0, 0, 0, 8], [2592, 0, 0, 0, -30, -110, -159, 0], [0, 339, -916, 15, 0, 0, 0, 0], [-1746, 0, 0, 0, 12, 159, 15, 0], [0, 40, 16, 24, 0, 0, 0, 16], [0, 480, 2346, -6, 0, 0, 0, 18], [0, -717, -1664, 35, 0, 0, 0, 20], [0, -389, 2595, 22, 0, 0, 0, -32], [384, 0, 0, 0, -112, 8, -56, 0], [2412, 0, 0, 0, -222, -30, -30, 0], [0, -117, 346, -31, 0, 0, 0, 18], [-4310, 582, -1050, -66, 10, 52, 51, -36], [-256, 0, 0, 0, -64, 0, 0, 0], [0, 194, -2946, -64, 0, 0, 0, -4], [0, -345, 996, -24, 0, 0, 0, -39], [-7062, 0, 0, 0, -146, 68, 83, 0], [-3448, 0, 0, 0, -96, 16, 24, 0]]}