# Stored data for newform 33.3.g.a, downloaded from the LMFDB on 25 April 2024. {"label": "33.3.g.a", "space_label": "33.3.g", "level": 33, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 412367192097, "dim": 16, "is_polredabs": true, "trace_hash": 1302043712537493967, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+(1+\\beta _{2}-\\beta _{5}+\\beta _{7}+\\beta _{8})q^{2}-\\beta _{14}q^{3}+\\cdots", "char_order": 10, "char_parity": -1, "char_degree": 4, "char_conductor": 11, "char_orbit_label": "g", "char_is_real": false, "Nk2": 297, "analytic_conductor": 0.8991848723889798, "hecke_ring_index": 1, "level_radical": 33, "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": "0.102", "prec": 17}, "analytic_rank_proved": true, "char_values": [33, 10, [23, 13], [10, 7]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [3, 11], "conrey_indexes": [7, 13, 19, 28], "field_disc": 308848428439056000000000000, "field_disc_factorization": [[2, 16], [3, 8], [5, 12], [11, 2], [4931, 2]], "field_poly": [83521, 0, -71672, 43316, 32427, -16804, -1619, 1868, 1520, 578, -577, 88, 77, -4, 3, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "15.599", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "808.554", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "68626.694", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "2.2.3.c10", "trace_display": [0, 0, -4, -30], "traces": [0, 16, 0, 0, 20, -4, 0, -30, -40, -12, 0, -10, -24, 30, -2, -24, 16, -10, -30, 0, 42, 0, 42, 132, 90, -2, 46, 0, -50, 160, 180, 10, 0, 12, -368, -320, 60, -126, -130, 0, 30, -120, -204, 0, -206, -12, 50, -150, -96, 210, 330, -60, 110, 342, 0, 244, 524, 60, 150, 110, 36, -90, 40, 90, -168, 0, 48, 36, 80, 210, 340, -236, -150, -350, -730, -408, 0, -390, -312, 210, -806, -36, 114, -190, -180, 110, 736, 0, 144, 76, 60, 306, -150, 144, -350, 430, 450, -354, 0, 180, -116, 330, 456, -232, -150, 240, -230, -240, -72, 0, 338, -336, -400, -108, 48, -298, 380, -30, 570, 582, 0, -150, 936, 60, 648, 572, 84, 180, 570, 180, -488, 0, 30, -708, -1250, -72, -690, -10, -540, 330, -860, -306, 0, -572, -132, 270, -796, -120, 288, -110, -330, 410, 176, 0, -536, -92, 300, -1020, -234, 168, 750, -160, 90, -328, 0, 492, 64, -600, -18, 402, 124, 210, 430, -50, 252, 0, 186, -204, 1630, 1000, 36, 194, 420, -60, 550, 652, 0, 1126, 428, 0, 686, 636, 156, 270, -330, -510, -270, 0, -384, 1660, -100, -480, -318, -472, -930, -1480, -520, 6, 0, -1146, -96, -340, 66, -318, -976, -740, 0, -820, -592, 0, -1276, -1104, 330, -480, 382, -126, -1730, -340, -180, 380, 0, 696, -1236, 840, 138, -622, 362, 1140, 910, 1590, 870, 0, 3264, 0, -1630, 1260, 852, -222, -170, 780, -50, -1318, 0, 230, -1112, -420, 264, -602, -30, 250, 680, -480, 708, 0, -1116, 1968, 1250, -414, 2010, 1468, 360, 1240, 640, 504, 0, -1402, 972, -280, -656, -90, 228, -960, 120, -600, -1686, 0, -1038, -316, -450, -384, -1976, -804, 1580, -1460, 60, 822, 0, 36, 512, 830, -372, -1386, -36, 480, -1970, 1750, 246, 0, 1142, 1104, -540, 568, 378, -298, 1760, 510, -1420, -846, 0, 386, -2316, -1950, -1524, -44, -90, 210, -1660, -1740, 1390, 0, -1770, -2232, 1490, -378, 994, 526, -240, 2500, 2080, 432, 0, 16, 840, -1300, 1084, -528, 1182, -1660, -150, -410, -2942, 0, 712, -1152, -720, -202, -1758, -702, 990, -260, -90, 1308, 0, 420, 1348, 2040, 84, 1610, -708, -450, 2550, 3530, 600, 0, 314, 1620, 1560, 1492, 558, 802, 160, 1500, -1600, -506, 0, 1382, 508, 750, -88, 2502, -336, -1220, -900, -900, 1334, 0, 42, 1632, -1060, -828, 364, 290, 450, -2610, 70, -36, 0, -1494, 936, -1040, 1858, 354, -2442, -3180, -240, -4480, -730, 0, -1618, -1948, 690, -204, -1732, 330, -4910, -1900, 300, -350, 0, 666, -2644, -530, -288, -2184, -442, 540, -1540, -130, 1044, 0, 4212, -420, -1810, 2072, -396, -942, 2480, 210, 2370, -2124, 0, -398, -856, 480, -386, 394, -558, 5120, 1140, 180, 1634, 0, -1464, 472, 1600, -1596, 2422, 2206, 120, 2380, 130, 456, 0, -1166, -1044, 3340, -1754, -834, 3466, 2390, 180, 850, 112, 0, -1230, 968, 0, -1438, -218, 456, -1030, 850, -300, -1096, 0, 102, 5532, -100, 432, -368, 1430, 1410, -1680, 340, 282, 0, -256, 48, -380, 714, 438, -2118, -1310, -720, -50, 696, 0, 886, 2740, 900, -944, 1992, -660, -380, 2090, 840, -664, 0, -708, -3200, -5320, 330, -2226, -2878, -1620, -1150, -3130, -960, 0, -1540, -1152, -3490, -1414, -192, -790, -2800, 210, 3550, -1082, 0, 1038, -1672, -900, 848, -1724, 498, 5310, -1790, -120, 550, 0, 1332, -1552, -450, 990, 1676, 292, 180, 2560, -860, -492, 0, -218, -996, 4450, -1814, 516, 2158, 690, -2040, 1780, 4014, 0, -678, -2496, -1680, 4116, -1784, 1440, -1090, 2600, -990, -3094, 0, 324, 1368, 450, 288, -2648, -924, -1350, 1750, -2110, 138, 0, -310, -600, 1580, 428, -1302, -1586, 1390, 870, -60, 2666, 0, 678, 3604, 1230, -886, 2758, -360, -6810, 2520, 1800, -2248, 0, 1692, -5408, 1730, 1020, -1508, 1006, 600, -1560, 1560, -1788, 0, 1688, 1932, -2760, -790, 1968, 1064, 3150, -210, 2500, 5058, 0, 734, 6360, 900, 3592, 4010, 1332, 2120, -1950, 1050, -842, 0, 1344, -500, 1900, 756, 780, -2894, -2100, -1380, -5540, -1548, 0, -3094, -2544, 1030, -6268, 756, -734, -3880, -1500, -3450, 2782, 0, -3826, 356, 1110, 208, 1482, -300, -950, -2470, 1980, -4604, 0, 180, 6732, -1350, 2208, 1474, -3376, -870, -5460, -4010, -666, 0, -116, -2976, 1540, -1172, 210, -3392, 1690, -1140, 250, 1330, 0, 2530, -600, -570, -2916, -3500, 2022, -520, -270, -1440, 456, 0, 348, -2148, -5030, -108, -4128, 4730, 0, 960, -3290, -750, 0, -2060, -1428, -110, -4204, -1980, 1942, 3410, 420, 6470, 3320, 0, -1516, 2548, 2040, 2100, 1492, 1458, 6440, 3900, 540, -2130, 0, 1344, 1180, 1410, 2016, 2940, 298, 1350, 3520, 550, -1008, 0, -1874, 336, 3940, 1856, -2322, 4916, 1640, 1140, 510, 1332, 0, 568, 1884, 1440, 2920, -1868, -1596, -1000, 6390, 3750, -1642, 0, -348, 1124, 1040, 660, 2576, -1652, 870, -2900, -60, -762, 0, 3008, -4824, -2350, -2756, 588, -142, -1080, -360, 410, 2596, 0, 6352, -1356, -2400, 1836, 4172, 18, -4970, 820, 2100, 1038, 0, -1104, -10128, -7880, -450, -5858, -3962, -4080, -750, -5560, -2352, 0, -4926, -1008, -3980, -4536, -1584, -1062, -1510, -4920, 4680, 1828, 0, -2592, 4916, -1020, -140, -3072, -756, 3630, 1170, -1290, -488, 0, 72, 376, -3070, 1266, 4286, -3232, 1080, 4920, -2740, -2028, 0, 1992, 852, 1330, 2876, 738, -80, -790, -60, 670, -1496, 0, -2160, 6024, -780, 764, -2018, 2016, -3670, 3600, 1410, -84, 0, 270, 4144, 590, 216, 1600, 2156, 0, -5380, 1680, -798, 0, -2022, 4032, 2850, 1450, -1086, -2018, 2910, 2940, -2590, 218, 0, 82, -3052, 5790, -5700, 5158, -972, -2470, -1630, 3540, 2832, 0, 2490, -11692, 4450, -696, -7878, 822, 4140, -20, 5140, 1476, 0, -1180, 2340, 200, 6078, 3168, 2388, -1930, -540, -2650, 878, 0, 8520, -2836, 4080, 984, -48, -2052, 4340, -240, 690, 3174, 0, -2412, -7760, -3810, -852, 1246, 1988, -690, 1540, -5940, -888, 0, 242, -1380, 6960, -2000, 324, 8528, 1380, -2520, -3630, -510, 0, 694, 4720, -300, 2154, 1200, 192, -4920, -10260, -60, 950, 0, -456, 7856, 780, -1512, 2446, -1304, -2190, -4500, 2130, 252, 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": 7, "prim_orbit_index": 4, "minimal_twist": "33.3.g.a", "char_is_minimal": true, "conrey_index": 7, "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, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, -1, 0, -1, 1, 2, -1, -2, -2, 0, 0, 0, 0, 0, 0, -1], [1, 0, 1, -1, 1, 0, -1, 1, 2, -1, 0, 0, -2, 1, -2, -3], [-1, 0, -1, 1, -1, 0, 1, -1, -1, 0, -1, 0, 0, -1, 1, 1], [-3, 2, 0, 0, 2, 0, -1, -1, -2, 0, 1, 2, 2, 0, 0, 0], [0, 0, -1, 0, -2, -3, 2, 5, 4, 1, 1, -1, 1, 0, 1, 3], [0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, 2, -2, 3, 2, 1, -2, 2, 0, -2, 0, 0, 6, 6], [-6, -1, -3, 4, -4, 2, 1, -10, -9, 0, 0, 0, 1, -2, 1, 0], [1, -1, 1, 0, -1, -3, 0, 3, 0, -1, 1, -1, -1, 1, -2, -1], [3, 1, 0, -1, 0, -1, 0, 0, 2, 0, -1, -2, 0, 2, 2, -2], [-4, 3, -3, 1, 0, 3, 3, -1, -2, 0, -6, 1, 2, -2, 4, 8], [1, 2, 1, -1, -1, -3, 2, 5, 5, 1, 0, 0, -1, 1, -1, -1], [3, -6, 0, -2, -1, -3, -4, -1, -4, -2, 2, 4, 0, 0, -4, -7], [-1, 0, 0, 3, 5, 0, 0, 1, 6, 3, -2, 0, 0, -1, 0, 3], [-3, 0, 0, 0, 0, 3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 5, -8, 6, 5, -3, -4, 2, -2, 5, 0, -2, 0, -5, -5], [4, -3, 3, -8, 2, 2, -8, -1, -9, -4, 8, 2, -2, 2, -12, -14], [3, 0, 6, 1, 6, 0, -1, 5, 5, -1, 1, 1, 0, 0, 2, 1], [10, 2, 3, 7, 3, -6, 7, 16, 20, 0, -2, -2, -4, 0, 1, -2], [8, -1, 1, 0, -1, 3, 0, -3, 0, -1, 5, -1, 0, 2, -6, -1], [2, -1, -4, -2, 0, 0, 0, -7, -4, 0, -2, 1, 2, -1, 3, -1], [0, -2, 0, 2, -5, -3, -3, -5, -5, 2, -11, 0, 2, -4, 2, 15], [3, 1, 4, -11, 3, 4, 0, 3, 2, 2, -2, -1, -1, 2, -1, -10], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3], [-1, 0, 1, 11, -7, -3, -1, 2, -7, 0, -6, 0, 0, 2, -7, 2], [17, -3, 1, 7, -2, -12, -1, 7, 2, -1, -8, 0, -1, 1, 15, 7], [0, -4, -6, -4, -4, 6, 0, -16, -22, 2, 3, 0, 2, 0, -1, 1], [-2, 3, -6, -7, -12, -7, 18, 1, 4, 0, 7, -2, 0, -2, -4, -4], [8, 0, 1, 6, 1, -17, 1, 0, 17, 1, 1, -1, 0, 0, 14, 13], [-1, 2, -1, 5, 2, 12, -4, 3, 0, 1, 1, -1, 2, -1, 4, 5], [-21, 4, 3, -1, 5, 1, -4, 3, 4, 0, 13, 0, 0, 0, -13, 0], [-23, 2, 3, 4, 0, 17, 0, 9, -7, 0, 4, 0, 2, 0, 8, -6], [3, 3, -3, 0, 0, 0, 3, 0, 6, 0, -3, 0, 0, 0, 3, 3], [-7, -11, -12, 1, -1, -9, -6, -6, -5, -2, -7, 0, 2, -2, 2, 1], [-23, 16, -2, 1, 5, 20, 4, -11, -6, 3, 0, 0, 6, -3, 4, 11], [-1, 0, -4, 1, 3, -3, 4, 9, -3, 1, -1, 0, 0, 2, -2, 0], [1, 7, -2, 9, 5, 14, 12, 9, 32, 2, -7, -4, -2, -2, 12, 5], [-1, -7, -5, -17, -7, -10, 0, 8, 4, -2, 12, 5, -2, 0, -12, -12], [-16, -1, 5, -5, 8, 3, -10, -18, -6, -2, 5, 2, -1, 2, -5, -6], [-17, -2, -11, 5, -11, 17, -6, -23, -40, -4, -1, 4, -2, 2, 5, 6], [-9, -8, -1, 2, -1, -20, -11, -8, -17, 2, 3, 0, -1, 5, -7, -12], [-3, 0, -3, 0, -3, -3, 3, 0, -3, 3, 0, 3, 3, -3, 3, 3], [6, 1, 5, -6, 0, -8, 0, 1, 5, 0, -6, 6, -2, -6, 5, -7], [-8, -1, 2, -4, 7, -3, 4, 10, 0, -1, -9, -3, -7, 8, -9, 1], [3, 9, 9, 2, 0, -6, 3, 15, 12, -3, -3, 0, 3, -3, 3, 2], [17, -8, -3, -3, -8, -15, 5, 0, -2, 4, -6, -12, -4, 2, 1, -1], [17, 0, 1, 15, -2, 17, -1, -25, 10, -13, -11, 0, 0, 0, -4, -1], [-4, -12, 2, 2, -10, 9, -4, -9, -9, -2, -1, -1, -3, 2, -1, -5], [8, 13, 9, 4, 11, 2, 2, 9, 10, 4, 2, -2, 4, 0, 5, 12], [25, 3, -4, -2, 8, 9, -2, 36, 10, 16, 2, -8, 8, -8, 10, 18], [0, 0, 0, 0, 0, 0, 3, 3, 3, 3, 0, -3, 0, 0, 3, 3], [15, 3, 7, -6, 3, 5, 1, 7, -8, -2, 23, 10, 12, 2, -15, -12], [13, -8, -10, -10, -10, 20, 10, -30, -10, 2, 5, 2, -3, -7, -3, 2], [18, -2, 3, 2, 0, -24, 0, 12, 18, 0, 2, -3, -8, 3, -4, -4], [39, -17, 25, -8, 13, -16, -20, 13, 27, -8, 6, 0, -8, 16, -9, -22], [0, 13, 7, 17, -6, 3, 6, -20, -3, -7, -8, 6, 1, -7, 1, 11], [25, 10, 7, -2, 4, -24, 9, 38, 44, 1, -2, -4, -2, 1, -1, 7], [2, 0, 17, -7, 6, 6, -17, 14, -12, 0, -2, 0, 0, -4, 13, 3], [0, -6, -4, 5, -10, -39, 0, -5, -49, 4, 8, 1, 5, -4, -11, -12], [3, -3, 3, 0, -3, 3, 0, -9, -9, -6, 0, 0, -6, 0, -3, -6], [-12, 4, 4, -8, 12, -4, -4, -6, 3, 4, 8, 6, 2, 6, -6, -4], [32, 2, 9, 2, 9, -27, -4, 33, 60, -6, -7, 6, 1, -1, -9, -2], [-4, -5, -4, -7, -9, 21, -7, -8, -17, -4, -1, 5, -5, 2, -11, -15], [-5, 13, -7, 0, 25, 9, -9, 0, 9, 4, -11, 4, 6, -2, 15, 4], [-21, -9, -20, -15, 0, 29, 0, -29, -26, 0, -15, 1, -7, -1, -9, 2], [15, 4, -3, 0, 3, 0, 5, 2, 20, -1, 4, 1, 1, 0, -10, -4], [-10, -13, -26, -17, -13, 28, 3, -34, -48, 6, 4, -2, -4, 6, -4, -15], [-43, -10, 4, -3, -8, 41, 10, -33, -40, 3, -1, -2, 4, -2, 0, -13], [-3, 0, 6, 3, 6, -6, -6, 9, -3, -3, 0, 0, 0, 3, -6, -3], [-29, 4, 6, 4, 10, 22, 7, -6, 10, -6, -13, -8, -14, 6, 12, 2], [1, 2, 5, 25, 6, -29, -4, 72, 76, -3, -11, -8, -3, 0, 15, 19], [-40, -3, -7, 10, -8, 6, 2, -40, -7, 6, -10, -7, 3, -7, 13, 16], [-29, 6, -11, -5, -11, 37, -2, -23, -60, -8, 11, 8, 10, -10, -7, -18], [-11, 22, 14, -10, 23, -21, -6, -8, 41, -9, 10, -3, -9, 9, -7, 5], [-8, -6, -5, -1, -9, -33, 7, 26, -7, 1, 5, 1, 0, -2, -4, 1], [31, -5, 1, 18, 0, -38, 0, 10, 16, 0, 18, -2, 4, 2, -1, 5], [-74, -7, 2, 1, -16, 30, -13, -12, -88, 5, 21, -4, -3, -2, 5, -19], [0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0], [14, 0, -21, 21, -10, -24, -1, 14, 4, 10, 0, 0, 20, -10, 31, 59], [-14, 0, -19, -28, -20, -24, 19, -30, 32, 12, 26, 0, 0, 10, -8, -12], [-26, 9, -8, 2, 1, 33, 13, -6, 21, 8, -2, 1, 9, -8, 13, 19], [-23, -4, -12, -4, -11, 15, 7, -49, -38, 8, -1, 8, 8, 0, -2, -5], [77, 3, -4, 19, -18, -19, 24, 75, 46, -10, -19, 7, -5, 7, 23, 18], [-26, 5, -2, 5, -2, 21, 5, -26, -47, 0, -12, 0, 2, -2, -2, 10], [8, -5, -4, -1, 8, 17, 11, 11, 31, 6, -40, -12, 0, -6, 36, 32], [26, 13, 17, 26, 3, -21, -10, 31, 10, 3, -19, 3, 8, 2, 22, 3], [9, 0, 0, 6, 0, -12, 0, 3, 3, 0, 6, 0, 6, 0, -6, 12], [-1, 14, -20, 6, -17, 33, 9, -17, 2, 6, 17, 0, 6, -12, 0, -5], [4, 5, 5, 8, 0, -10, 4, 21, 18, 3, 10, -11, 8, 3, 8, 19], [17, 8, -10, 0, 7, -21, -16, 5, 5, -3, 7, 14, 8, -4, -3, -6], [-26, 0, -15, -5, -13, -24, 15, 8, -25, -2, 4, 0, 0, -2, 3, -2], [48, -3, 5, -28, 2, -40, -16, 17, -6, -5, 2, -7, -12, 5, -16, 7], [3, -4, -3, 19, -4, 18, 0, -40, -46, -1, -17, 0, -1, 0, 9, 1], [-28, 1, 4, 23, -4, -3, 6, -33, -1, -12, -23, 0, -6, 0, -2, -8], [27, -1, 23, -26, 23, -27, 4, 31, 58, 5, 22, -5, -5, 5, -25, -47], [6, -6, 0, -15, 3, 15, 0, -3, -3, 3, 6, -6, -3, 3, -9, -9], [17, -13, 15, -12, -17, -26, 1, 25, -1, -12, -13, -12, -20, 4, 1, -12]]}