# Stored data for newform 882.4.g.t, downloaded from the LMFDB on 25 April 2024. {"label": "882.4.g.t", "space_label": "882.4.g", "level": 882, "weight": 4, "hecke_orbit": 20, "hecke_orbit_code": 85568805304009586, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 576988202834100095, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [36, -6, 1]], [11, [900, -30, 1]], [13, [-2, 1]]], "qexp_display": "q+2\\zeta_{6}q^{2}+(-4+4\\zeta_{6})q^{4}+6\\zeta_{6}q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "g", "char_is_real": false, "Nk2": 14112, "analytic_conductor": 52.039684625063224, "hecke_ring_index": 1, "level_radical": 42, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [882, 3, [785, 199], [3, 2]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [361, 667], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.011", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12.512", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "118.725", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.3.c3", "trace_display": [2, 0, 6, 0], "traces": [0, 2, 2, 0, -4, 6, 0, 0, -16, 0, -12, 30, 0, 4, 0, 0, -16, 66, 0, 52, -48, 0, 120, 114, 0, 89, 4, 0, 0, -144, 0, 196, 32, 0, 264, 0, 0, 286, -104, 0, -48, 756, 0, 328, 120, 0, -228, -228, 0, 0, 356, 0, -8, -348, 0, 360, 0, 0, -144, -348, 0, 106, 784, 0, 128, 12, 0, -596, 264, 0, 0, -1260, 0, 1042, -572, 0, -416, 0, 0, 88, 96, 0, 756, 2880, 0, 792, 328, 0, -240, 1374, 0, 0, -912, 0, 456, -312, 0, -68, 0, 0, 356, -438, 0, -1676, -32, 0, -1392, 2022, 0, 502, 360, 0, 0, -4032, 0, -684, 288, 0, -1392, 0, 0, 431, -212, 0, 784, 2568, 0, 3568, 128, 0, -24, 1608, 0, 0, -2384, 0, -528, -2580, 0, 4288, 0, 0, -1260, 60, 0, -432, 4168, 0, -2288, 1500, 0, 1240, -416, 0, 0, 2352, 0, -614, -176, 0, 384, 0, 0, -92, -1512, 0, 2880, 7848, 0, -4386, 792, 0, -656, -1902, 0, 0, -960, 0, -2748, -6, 0, -5756, 0, 0, -912, -1716, 0, -1980, 1824, 0, -1248, -354, 0, 4858, -68, 0, 0, 792, 0, -1712, -712, 0, -1752, 0, 0, 2268, 3352, 0, -32, 3120, 0, -1544, -1392, 0, -4044, 984, 0, 0, 2008, 0, -720, 132, 0, 1552, 0, 0, -4032, -1788, 0, -5402, -2736, 0, 1152, 3012, 0, 1368, -1392, 0, 0, -7092, 0, 3562, -862, 0, -848, 0, 0, 104, -1568, 0, 2568, -6696, 0, 6840, 3568, 0, -256, 366, 0, 0, -96, 0, -3216, 4170, 0, -4176, 0, 0, -2384, 6078, 0, -2468, -2112, 0, -10320, -2670, 0, 394, 4288, 0, 0, 792, 0, 1348, 2520, 0, 240, 0, 0, 557, 864, 0, 4168, -15012, 0, -4176, -2288, 0, -3000, 228, 0, 0, 4960, 0, 832, -636, 0, 3496, 0, 0, 2352, -1140, 0, -146, -2456, 0, -704, -8148, 0, -2160, 384, 0, 0, 6864, 0, 178, 184, 0, -6048, 0, 0, 9700, -5760, 0, 7848, -7152, 0, 16348, -4386, 0, -1584, -5880, 0, 0, -2624, 0, 3804, -4038, 0, 21532, 0, 0, -960, 3666, 0, -3780, -10992, 0, -24, -5106, 0, 4155, -5756, 0, 0, 12504, 0, 5776, 1824, 0, -6864, 0, 0, -8462, 3960, 0, 1824, -288, 0, 13720, -1248, 0, 708, -696, 0, 0, 19432, 0, 136, 11136, 0, 15048, 0, 0, 792, -528, 0, -10838, -6848, 0, -2848, -8364, 0, 392, -1752, 0, 0, 17160, 0, 1762, -4536, 0, 13408, 0, 0, 8640, 64, 0, 3120, -29160, 0, 17068, -1544, 0, 2784, -5874, 0, 0, -16176, 0, -1968, 5934, 0, -29516, 0, 0, 2008, -5928, 0, 11392, -2880, 0, 528, 7026, 0, -8244, 1552, 0, 0, 6768, 0, 11340, 8064, 0, -7152, 0, 0, 4282, 10804, 0, -2736, -33300, 0, -19328, 1152, 0, -6024, -12324, 0, 0, 5472, 0, 2784, 4920, 0, 9256, 0, 0, -7092, 18660, 0, 572, 14248, 0, -3448, -204, 0, 3400, -848, 0, 0, -5940, 0, -4752, -208, 0, -6272, 0, 0, 988, -5136, 0, -6696, -10368, 0, -5256, 6840, 0, -7136, 16854, 0, 0, -1024, 0, -732, 10056, 0, -13680, 0, 0, -96, -4398, 0, 10672, -12864, 0, 16680, -12936, 0, -829, -4176, 0, 0, 1512, 0, -12132, 4768, 0, 24312, 0, 0, -20702, 4936, 0, -2112, 6024, 0, -45752, -10320, 0, 5340, -3744, 0, 0, 1576, 0, -8576, -12876, 0, 656, 0, 0, 792, -6900, 0, -12096, 5392, 0, 10080, 14676, 0, -380, 240, 0, 0, 20292, 0, 11806, -1114, 0, 3456, 0, 0, 10440, -8336, 0, -15012, 38376, 0, 20384, -4176, 0, 4576, 690, 0, 0, -12000, 0, -456, -20490, 0, -23180, 0, 0, 4960, -2586, 0, 6424, 3328, 0, -2544, -456, 0, 9682, 3496, 0, 0, -10152, 0, -22664, -4704, 0, -4560, 0, 0, -3421, 292, 0, -2456, 37752, 0, -17168, -704, 0, 16296, 10704, 0, 0, -8640, 0, -768, 372, 0, 6376, 0, 0, 6864, -12732, 0, 10440, 712, 0, 736, -3576, 0, -9648, -6048, 0, 0, -22860, 0, -22646, -19400, 0, -23040, 0, 0, -8208, -15696, 0, -7152, 6360, 0, -27140, 16348, 0, 8772, -2838, 0, 0, -6336, 0, 11760, -6558, 0, -30960, 0, 0, -2624, -696, 0, 21832, 15216, 0, -16152, 12864, 0, 24948, 21532, 0, 0, -32400, 0, -14872, 1920, 0, 14664, 0, 0, -36722, 7560, 0, -10992, 44688, 0, 720, -24, 0, 10212, 13776, 0, 0, 16620, 0, 11512, -6408, 0, 68440, 0, 0, 12504, 10824, 0, 13750, 23104, 0, 7296, 17880, 0, -39836, -6864, 0, 0, -68940, 0, -9000, 16924, 0, 15840, 0, 0, -5240, -3648, 0, -288, 14880, 0, 37156, 13720, 0, 2496, 30534, 0, 0, 2832, 0, 1392, -696, 0, -79916, 0, 0, 19432, -3966, 0, -17444, 544, 0, 44544, 19656, 0, -18900, 15048, 0, 0, -7368, 0, 3760, -1584, 0, -2112, 0, 0, 212, 21676, 0, -6848, 48204, 0, -30096, -2848, 0, 16728, -31260, 0, 0, 1568, 0, 3504, 11712, 0, 74848, 0, 0, 17160, 552, 0, 8528, 7048, 0, -18144, 13452, 0, -20432, 13408, 0, 0, -48780, 0, 28510, -17280, 0, 256, 0, 0, 23544, -6240, 0, -29160, 73944, 0, -38410, 17068, 0, 3088, -13158, 0, 0, 11136, 0, 11748, -32604, 0, -28148, 0, 0, -16176, -8826, 0, 20500, -7872, 0, 23736, 7674, 0, 11412, -29516, 0, 0, 5280, 0, -1192, -4016, 0, -23712, 0, 0, 8890, -22784, 0, -2880, -1476, 0, 40, 528, 0, -14052, 39804, 0, 0, -32976, 0, -3104, 11856, 0, -72, 0, 0, 6768, -14112, 0, 22968, 45360, 0, 32256, -17268, 0, -29180, -7152, 0, 0, 96516, 0, 43200, -8564, 0, 43216, 0, 0, -25760, 5472, 0, -33300, -2520, 0, 50908, -19328, 0, -2304, -44778, 0, 0, -24096, 0, 24648, 11880, 0, -88988, 0, 0, 5472, -7458, 0, 43092, 11136, 0, 19680, 17790, 0, 2084, 9256, 0, 0, 11664, 0, 2124, 14184, 0, 74640, 0, 0, -8625, -1144, 0, 14248, 58296, 0, -26528, -3448, 0, 408, 3984, 0, 0, 13600, 0, 1696, -38940, 0, 82440, 0, 0, -5940, -8808, 0, 2376, -19008, 0, -832, 18696, 0, -18488, -6272, 0, 0, -20544, 0, 5002, -1976, 0, -20544], "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": 7, "prim_orbit_index": 3, "minimal_twist": "126.4.a.b", "char_is_minimal": false, "conrey_index": 361, "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, 2], [0, 0], [-4, 4], [0, 6], [0, 0], [0, 0], [-8, 0], [0, 0], [-12, 12], [30, -30], [0, 0], [2, 0], [0, 0], [0, 0], [0, -16], [66, -66], [0, 0], [0, 52], [-24, 0], [0, 0], [60, 0], [0, 114], [0, 0], [89, -89], [0, 4], [0, 0], [0, 0], [-72, 0], [0, 0], [196, -196], [32, -32], [0, 0], [132, 0], [0, 0], [0, 0], [0, 286], [-104, 104], [0, 0], [0, -48], [378, 0], [0, 0], [164, 0], [0, 120], [0, 0], [-228, 228], [0, -228], [0, 0], [0, 0], [178, 0], [0, 0], [-8, 8], [-348, 348], [0, 0], [180, 0], [0, 0], [0, 0], [0, -144], [-348, 348], [0, 0], [0, 106], [392, 0], [0, 0], [64, 0], [0, 12], [0, 0], [-596, 596], [0, 264], [0, 0], [0, 0], [-630, 0], [0, 0], [1042, -1042], [-572, 572], [0, 0], [-208, 0], [0, 0], [0, 0], [0, 88], [96, -96], [0, 0], [0, 756], [1440, 0], [0, 0], [396, 0], [0, 328], [0, 0], [-240, 240], [0, 1374], [0, 0], [0, 0], [-456, 0], [0, 0], [456, -456], [-312, 312], [0, 0], [-34, 0], [0, 0], [0, 0], [0, 356]]}