# Stored data for newform 22.3.d.a, downloaded from the LMFDB on 25 April 2024. {"label": "22.3.d.a", "space_label": "22.3.d", "level": 22, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 206208761878, "dim": 8, "is_polredabs": true, "nf_label": "8.0.64000000.1", "trace_hash": 74740316312508475, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta _{1}q^{2}+(1-\\beta _{1}-2\\beta _{2}+\\beta _{3}+2\\beta _{4}+\\cdots)q^{3}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "d", "char_is_real": false, "Nk2": 198, "analytic_conductor": 0.5994565815926531, "hecke_ring_index": 1, "level_radical": 22, "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": "0.100", "prec": 17}, "analytic_rank_proved": true, "char_values": [22, 10, [13], [7]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 11], "conrey_indexes": [7, 13, 17, 19], "field_disc": 64000000, "field_disc_factorization": [[2, 12], [5, 6]], "field_poly": [16, 0, -8, 0, 4, 0, -2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.674", "prec": 17}, {"__RealLiteral__": 0, "data": "1.424", "prec": 17}, {"__RealLiteral__": 0, "data": "184.229", "prec": 24}, {"__RealLiteral__": 0, "data": "104.345", "prec": 24}, {"__RealLiteral__": 0, "data": "7091.831", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.3.c10", "trace_display": [0, -2, 2, -30], "traces": [0, 8, 0, -2, 4, 2, -20, -30, 0, -4, 0, -4, 24, 30, 16, 42, -8, 30, 40, -30, -4, 0, 24, -104, -40, -12, -96, -26, -40, -10, -60, 46, 0, -14, 112, 70, -12, 6, 108, 130, 80, 250, 56, 0, -12, -136, -160, -54, -8, -144, -80, -30, -40, -274, 0, -26, 48, -130, 64, 50, 116, 50, 20, -20, 16, 0, -136, 112, 60, 76, 4, 54, -80, -70, -40, 318, 0, 266, 104, 370, 48, 180, -96, -150, -120, -330, -72, 0, 72, 24, 160, -294, -112, -134, -20, -330, 0, -18, 0, -308, -136, 30, -108, -166, -208, -140, 120, -130, 52, 0, 376, -244, -80, 642, 248, 544, 360, 610, 200, -22, 0, 16, -320, -370, -32, -58, -148, 390, 0, 300, -104, 0, -152, 572, 40, -284, 96, -194, 80, 130, 140, -194, 0, -566, -16, -950, -280, -624, 48, -790, -420, 230, -216, 0, -408, 324, 260, -198, 124, 646, 0, 340, 280, 270, 0, 954, -576, 430, 208, -64, -72, 270, -280, -90, 124, 0, 184, 620, 480, 102, 212, -798, 840, -330, 160, 294, 0, 362, -152, -280, 292, 218, -64, -750, -240, -1080, 288, 0, -352, -704, -160, 152, 216, 486, -300, 950, -440, -588, 0, -722, -16, 730, -592, -186, 76, -100, 280, -410, -88, 0, -188, -188, 180, 502, 64, -834, -40, -770, -480, -74, 0, 436, 32, -90, 168, 294, 200, 490, -340, 950, -232, 0, 1136, 704, 100, 174, -356, 538, -120, -50, 160, 970, 0, 32, 608, 1070, -32, 410, -72, 90, 420, 500, 176, 0, 32, 244, -1120, -1176, 16, 270, -780, -1690, 80, -384, 0, -1684, 448, -1270, -144, -38, -128, -230, 560, 30, -108, 0, -652, -1084, -160, 128, -984, -158, -40, 790, 620, -1070, 0, 738, 576, -520, 684, 172, -76, 550, 120, 890, -96, 0, 248, -1156, 100, -42, -248, 290, -120, 450, 440, 174, 0, 674, 224, 490, 312, 614, 80, 2460, 1820, -440, 192, 0, -224, -560, -300, 92, 52, -472, -120, 510, -1680, 1022, 0, -238, -144, 590, -16, -576, 1048, 770, -640, -250, -24, 0, -224, -1024, -560, -754, -648, -312, -1860, -50, -160, -376, 0, -54, -352, 1030, -20, -786, -16, -450, -280, -690, 268, 0, 424, 52, -40, -186, 848, -1850, 500, -2870, -360, 126, 0, 574, 1472, 360, 56, 1442, 476, -1720, -400, 880, 472, 0, -44, 544, 360, 1602, -48, -30, 40, 1150, -800, -1020, 0, 482, 16, 1650, -704, 1406, 152, -1070, 0, 1950, 416, 0, -24, 1960, -280, -26, -436, 802, 240, -1750, 960, 190, 0, -1266, 752, -930, 56, -270, -168, 200, 520, -1620, -60, 0, 248, -108, -240, -814, -32, 756, 1660, 1710, -240, 366, 0, 314, 456, -290, 264, -416, 544, 50, -1520, -1100, -1088, 0, -548, -1488, 720, -696, -256, -1086, -500, -600, -340, -1278, 0, -792, -2656, -2830, -76, -78, -1084, -870, 240, -830, -584, 0, -172, 628, -480, 1642, 400, 1630, 320, 2850, 1560, 702, 0, 748, -496, 910, 704, -478, -604, -70, -340, 2850, 296, 0, 248, 1336, 780, 54, 1028, 290, 0, 610, 1240, 1386, 0, 622, -128, -2090, -512, -710, -792, 2610, 440, 610, -408, 0, -456, 680, 1680, -400, 976, 594, 720, 90, -480, 1562, 0, -68, -1032, 2370, -920, -2598, -32, -260, 280, -3330, 388, 0, 204, -52, 160, -2274, -160, -996, -560, -1370, 740, -1972, 0, -438, -1664, -2650, -392, -2602, -612, -2020, -760, -1670, 1232, 0, 1272, -1572, 500, 2636, -48, 2830, 1120, 1390, -140, 86, 0, 1082, -480, -490, 704, 558, -1052, 330, -660, -940, -96, 0, -248, 1532, -1580, -24, 1568, -306, 640, 390, 520, 984, 0, -1766, -1224, 470, -448, 886, -560, -2170, 260, 1770, -1568, 0, -784, 1672, 2000, -966, 492, 1388, 540, 1080, 520, 608, 0, -822, 1656, 530, -352, 2378, 712, 3490, -240, 1230, -1292, 0, 1368, 2248, 0, 2818, -704, -2506, 520, 1180, -60, -3638, 0, -1030, 144, 200, 1240, 262, 1032, -4620, -1000, -740, 152, 0, -548, 1336, -240, 152, -408, 788, 200, -2100, -160, 1362, 0, 2350, 384, -2970, -1096, 2604, -1052, -3210, -2460, 670, 144, 0, -1432, -1920, 540, -1686, -1364, -1494, 400, -2650, -2440, 2530, 0, 792, 320, 2630, -568, -298, 776, -1190, -140, -710, 1012, 0, 112, -1836, -1240, 914, 720, 750, -300, -2970, 720, -568, 0, 1216, -1064, 1230, -120, -2034, 696, 1650, 1160, -1600, 1596, 0, -204, 1280, 1680, -2986, 1320, 244, 60, 2850, 800, -2636, 0, -1536, 3088, 1490, 332, -1602, 832, 3050, 80, -1510, -144, 0, 756, -1036, -500, 2350, -216, -2710, -1240, 2750, -660, 1966, 0, 2972, 16, 2330, 968, -712, 744, 1590, 2500, 6650, 128, 0, -232, 4980, -1500, -1826, -504, -404, -160, 830, -920, -942, 0, -2542, -2336, -1100, 424, 618, 176, 1810, 1080, -940, 1436, 0, -616, -6180, -2200, 564, -1952, 658, -2960, 830, -960, -492, 0, -1610, 256, -2900, 1368, 670, 768, 3730, 1440, -3250, -972, 0, -32, -10620, -600, 516, 1160, -1528, -1100, -3470, -740, -2150, 0, 2246, 640, -2690, -104, 642, -4, 1170, 160, 1450, -2144, 0, -736, -52, 480, 150, -688, -1248, -1440, 2230, -840, 2884, 0, -1746, -176, 730, -1448, 12, -268, 1610, 1300, 1970, -152, 0, 1128, 3504, -200, -54, -2532, 3130, 480, -1090, 4000, 1318, 0, 1654, 5576, 2680, 496, -406, -704, 1420, 640, 4090, 736, 0, 976, 3984, -1360, -3562, -1324, 1780, 2100, -3090, -440, -1098, 0, -860, 696, 2810, 1036, 3578, 32, -3900, 0, -310, 1668, 0, -652, -1208, -80, -782, -2016, -194, -1640, -2670, -1140, -2210, 0, -1306, 2848, -950, -392, 4224, -644, 190, -640, -360, -1432, 0, 1968, 656, -2680, 1288, 256, -1026, -1720, -2420, 1720, -102, 0, -1442, -416, 3050, 424, -870, 1052, -5610, 1020, 140, -400, 0, 1496, -896, 980, 2090, 628, -446, -560, -290, -3080, 2202, 0, -4956, -160, -1170, -336, 1824, 288, -350, 120, -4450, 352, 0, -112, -1036, 520, -2698, 492, -826, -780, -3200, 560, -422, 0, 1128, 1632, 1700, -624, -3170, -1448, 740, 880, -810, -1076, 0, -88, -2688, -240, 1340, -672, -416, 1580, 510, -4120, 408, 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, 11, 4, -1, 10, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "22.3.d.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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0], [1, -1, -2, 1, 2, -1, -1, 2], [0, 0, 2, 0, 0, 0, 0, 0], [0, -2, -1, 0, -3, 0, -1, -2], [-4, 1, 2, -2, -2, 2, 2, -1], [-5, 1, 2, -1, 1, 0, 4, -2], [0, 0, 0, 2, 0, 0, 0, 0], [-1, 2, 1, -4, 0, 4, 1, 0], [4, 0, -8, -1, 4, -3, -4, -1], [-1, 2, 4, 3, -2, 4, -4, -3], [2, -4, 0, 2, -2, -2, 2, 2], [1, -4, 5, 0, -4, -10, 2, 10], [4, -5, -2, 2, 2, 1, -4, 4], [10, 3, -9, 9, 10, -6, 0, 3], [0, 0, 0, 0, 4, 0, 0, 0], [6, 8, -1, -6, 3, 6, -5, -8], [0, -1, 4, 1, -8, 0, 8, 1], [-3, 11, -4, -5, -4, 11, -3, 0], [2, 4, -2, -8, 0, 4, -8, -4], [-6, 0, 12, -8, -3, -2, 9, -8], [6, -1, -2, 4, 12, -2, 2, -4], [-16, -16, 0, 12, -6, -8, 6, 4], [-4, 2, -4, 0, 0, -2, 0, 2], [-8, -16, 9, 4, -9, 8, 8, 8], [-20, 1, 12, 5, -20, -4, 0, 2], [0, -7, -4, -6, 5, -6, -4, -7], [-8, 4, -2, -2, -4, 2, 10, -4], [17, 6, -18, -6, 19, 0, -36, -4], [-6, 10, 12, -9, 12, 10, -6, 0], [3, 1, -3, -2, 0, 4, 14, 2], [0, 0, 0, 0, 0, 4, 0, 0], [-9, -4, -8, 16, -18, -8, 19, 6], [16, 6, 0, -1, 4, 3, -4, -5], [14, 7, 0, 0, 14, -3, -7, 3], [-2, 0, 0, 4, 0, -8, 2, 8], [3, 2, -6, 6, 3, -4, 0, 2], [0, -3, 22, -4, -10, -4, 22, -3], [26, -1, 0, -14, 13, 14, -26, 1], [8, 2, 0, -2, -8, 0, 0, -8], [25, -8, -12, 8, -12, -8, 25, 0], [16, -6, -16, 12, 0, -3, -20, 9], [-14, 0, 28, 4, -24, -10, 4, 4], [8, 6, -10, -2, 16, 12, -12, 2], [-3, 16, 0, -12, 28, 8, -28, -4], [-8, -16, -24, 0, 16, -6, -8, 6], [-13, 9, 6, 1, -6, -11, 13, 2], [-4, -4, 8, -4, -4, 0, 0, 0], [0, 10, -25, 14, 22, 14, -25, 10], [-16, -8, -16, 9, -8, -9, 32, 8], [-18, -11, 15, 11, -12, 0, 30, 5], [-4, -20, 6, 12, 6, -20, -4, 0], [-57, 6, 57, -12, 0, 0, 34, -12], [14, 0, -28, -4, 2, 5, -26, -4], [-12, 13, 15, -41, -35, 15, -15, -25], [8, -8, 0, -2, 4, -4, -4, 10], [-37, 10, 11, 0, -48, 26, 24, -26], [8, 17, 4, -18, -4, 19, -8, -36], [15, -13, -20, -33, 15, 20, 0, -10], [0, -6, 20, 12, -18, 12, 20, -6], [10, -6, 9, 34, 5, -34, -19, 6], [-4, 3, 6, -3, -8, 0, 12, 14], [-2, -12, -1, 13, -1, -12, -2, 0], [0, 0, 0, 0, 0, 0, 8, 0], [21, 0, -42, 18, 51, 10, 9, 18], [-12, -9, 4, -8, 20, -18, -4, 19], [12, 4, 0, -14, -4, 2, 4, 10], [10, 16, 2, 0, 8, 4, -4, -4], [30, 26, -26, -4, 26, -18, -30, -8], [-6, 14, 20, 0, -6, 14, 0, -7], [0, 19, -3, -7, -33, -7, -3, 19], [-16, -2, 16, 0, -8, 0, 0, 2], [-9, -22, 2, 22, 5, 0, 4, 26], [-4, 3, 8, -6, 8, 3, -4, 0], [66, -21, -66, 42, 0, -37, -39, 5], [6, 0, -12, 22, -2, -10, -14, 22], [39, -34, -2, 4, 23, -24, 2, 40], [-2, 26, 0, 0, -30, 13, 30, -26], [59, -17, 15, 0, 44, 24, -22, -24], [16, 8, -12, 0, 12, -8, -16, 0], [22, -4, 24, -32, 22, 28, 0, -14], [0, 25, -16, -12, 16, -12, -16, 25], [-30, -39, -1, 33, -15, -33, 31, 39], [-18, 16, 6, -16, 6, 0, 12, -20], [-33, -22, -22, -26, -22, -22, -33, 0], [-8, -14, 8, 28, 0, -24, -12, 4], [-32, 0, 64, 8, -43, 47, 21, 8], [-4, 8, 16, -10, -8, 16, 28, -12], [-30, 48, 0, -6, -66, 24, 66, -42], [8, -3, 24, 0, -16, 28, 8, -28], [-47, 45, -3, -42, 3, 39, 47, -84], [-12, -8, -20, -24, -12, 16, 0, -8], [0, -2, -22, -10, 23, -10, -22, -2], [-4, -13, 22, 6, -2, -6, -18, 13], [-8, 29, -25, -29, 58, 0, -50, -15], [0, -4, -8, 8, -8, -4, 0, 0], [1, -12, -1, 24, 0, -8, -12, 16], [-20, 0, 40, -25, 8, 22, 48, -25], [-33, 0, 11, 22, 22, -33, -11, 33], [-16, -16, 0, -16, 2, -8, -2, 32]]}