# Stored data for newform 1764.4.k.q, downloaded from the LMFDB on 23 April 2024.
{"label": "1764.4.k.q", "space_label": "1764.4.k", "level": 1764, "weight": 4, "hecke_orbit": 17, "hecke_orbit_code": 72058281299805924, "dim": 4, "is_polredabs": true, "nf_label": "4.0.335241.2", "trace_hash": 482792446397802574, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [324, -198, 139, 11, 1]], [11, [5560164, -11790, 2383, 5, 1]], [13, [-1200, 5, 1]]], "qexp_display": "q+(\\beta _{1}-6\\beta _{2})q^{5}+(1-7\\beta _{1}+6\\beta _{2}-7\\beta _{3})q^{11}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "k", "char_is_real": false, "Nk2": 28224, "analytic_conductor": 104.07936925012645, "hecke_ring_index": 1, "level_radical": 42, "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": "0.003", "prec": 17}, "analytic_rank_proved": true, "char_values": [1764, 3, [883, 785, 1081], [3, 3, 2]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [361, 1549], "field_disc": 335241, "field_disc_factorization": [[3, 2], [193, 2]], "field_poly": [2304, 48, 49, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.763", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "52.982", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1211.452", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [0, 0, -11, 0], "traces": [0, 4, 0, 0, 0, -11, 0, 0, 0, 0, 0, -5, 0, -10, 0, 0, 0, -100, 0, 67, 0, 0, 0, 76, 0, 93, 0, 0, 0, -550, 0, 362, 0, 0, 0, 0, 0, 5, 0, 0, 0, -324, 0, 1442, 0, 0, 0, 216, 0, 0, 0, 0, 0, 495, 0, 1406, 0, 0, 0, -173, 0, -532, 0, 0, 0, 510, 0, -111, 0, 0, 0, -3200, 0, 1215, 0, 0, 0, 0, 0, -1460, 0, 0, 0, -2818, 0, 328, 0, 0, 0, 1974, 0, 0, 0, 0, 0, 658, 0, -1122, 0, 0, 0, -188, 0, -1025, 0, 0, 0, 351, 0, -123, 0, 0, 0, -3268, 0, 2348, 0, 0, 0, 0, 0, -2079, 0, 0, 0, -1650, 0, 4720, 0, 0, 0, -347, 0, 0, 0, 0, 0, 554, 0, 366, 0, 0, 0, 3390, 0, 451, 0, 0, 0, -4614, 0, -1203, 0, 0, 0, -7842, 0, 1702, 0, 0, 0, 0, 0, -2872, 0, 0, 0, -9488, 0, -3938, 0, 0, 0, -134, 0, 0, 0, 0, 0, 1506, 0, -11074, 0, 0, 0, 4370, 0, 2452, 0, 0, 0, -6786, 0, 4784, 0, 0, 0, 5740, 0, -1124, 0, 0, 0, 0, 0, 2628, 0, 0, 0, -4388, 0, -7492, 0, 0, 0, -3676, 0, 0, 0, 0, 0, -1680, 0, -4610, 0, 0, 0, 11643, 0, 2493, 0, 0, 0, -6566, 0, -2286, 0, 0, 0, 3588, 0, -203, 0, 0, 0, 0, 0, -1615, 0, 0, 0, -1518, 0, -27400, 0, 0, 0, 8412, 0, 0, 0, 0, 0, 11502, 0, -7182, 0, 0, 0, 11743, 0, 3479, 0, 0, 0, -7198, 0, 10583, 0, 0, 0, 12916, 0, -1287, 0, 0, 0, 0, 0, 3282, 0, 0, 0, -2946, 0, -8326, 0, 0, 0, -9840, 0, 0, 0, 0, 0, -6786, 0, -18, 0, 0, 0, 16498, 0, -5376, 0, 0, 0, -7761, 0, -6743, 0, 0, 0, -4384, 0, 5075, 0, 0, 0, 0, 0, 71, 0, 0, 0, -13640, 0, -11156, 0, 0, 0, 14415, 0, 0, 0, 0, 0, 6252, 0, -3768, 0, 0, 0, 13206, 0, 13046, 0, 0, 0, -13666, 0, 10605, 0, 0, 0, -3136, 0, -1094, 0, 0, 0, 0, 0, 477, 0, 0, 0, -9240, 0, 10674, 0, 0, 0, -13834, 0, 0, 0, 0, 0, 1304, 0, 7840, 0, 0, 0, -14013, 0, -1465, 0, 0, 0, 7668, 0, -10555, 0, 0, 0, -60820, 0, 11164, 0, 0, 0, 0, 0, -1997, 0, 0, 0, 6420, 0, 12646, 0, 0, 0, 8896, 0, 0, 0, 0, 0, -714, 0, -24026, 0, 0, 0, -8336, 0, 959, 0, 0, 0, 8881, 0, 14910, 0, 0, 0, 12836, 0, 12564, 0, 0, 0, 0, 0, -19716, 0, 0, 0, -16292, 0, 29106, 0, 0, 0, -3566, 0, 0, 0, 0, 0, 224, 0, -138, 0, 0, 0, -13762, 0, -21725, 0, 0, 0, 287, 0, -15190, 0, 0, 0, -26850, 0, 17996, 0, 0, 0, 0, 0, -25137, 0, 0, 0, -15900, 0, 37580, 0, 0, 0, 17907, 0, 0, 0, 0, 0, 5074, 0, 47556, 0, 0, 0, -5994, 0, -6131, 0, 0, 0, 10380, 0, -17154, 0, 0, 0, 18180, 0, -18045, 0, 0, 0, 0, 0, 4969, 0, 0, 0, 7336, 0, 23488, 0, 0, 0, -6028, 0, 0, 0, 0, 0, -10501, 0, -710, 0, 0, 0, -26119, 0, -1628, 0, 0, 0, 25734, 0, -737, 0, 0, 0, -35392, 0, -5202, 0, 0, 0, 0, 0, 7317, 0, 0, 0, -25618, 0, 35834, 0, 0, 0, 19938, 0, 0, 0, 0, 0, 7998, 0, -13556, 0, 0, 0, -14812, 0, -33970, 0, 0, 0, 16830, 0, -16214, 0, 0, 0, 23896, 0, -18261, 0, 0, 0, 0, 0, 3624, 0, 0, 0, 34240, 0, -57910, 0, 0, 0, -2751, 0, 0, 0, 0, 0, 16978, 0, 37558, 0, 0, 0, -17796, 0, 35369, 0, 0, 0, 1407, 0, 30419, 0, 0, 0, -5576, 0, 11949, 0, 0, 0, 0, 0, 10780, 0, 0, 0, 56700, 0, 27944, 0, 0, 0, -15621, 0, 0, 0, 0, 0, -44697, 0, -5708, 0, 0, 0, -5580, 0, -10607, 0, 0, 0, 16460, 0, 1152, 0, 0, 0, 87266, 0, -13195, 0, 0, 0, 0, 0, 40748, 0, 0, 0, 104712, 0, -43080, 0, 0, 0, -35436, 0, 0, 0, 0, 0, -24464, 0, 77784, 0, 0, 0, -37208, 0, 34007, 0, 0, 0, 51736, 0, -32045, 0, 0, 0, 28872, 0, -17850, 0, 0, 0, 0, 0, 29440, 0, 0, 0, 71326, 0, 36568, 0, 0, 0, -5512, 0, 0, 0, 0, 0, -25140, 0, -15960, 0, 0, 0, 280, 0, 4397, 0, 0, 0, -10638, 0, 33722, 0, 0, 0, 58864, 0, -35050, 0, 0, 0, 0, 0, 20630, 0, 0, 0, -61038, 0, -49392, 0, 0, 0, -32764, 0, 0, 0, 0, 0, 65270, 0, -69348, 0, 0, 0, -25060, 0, 23285, 0, 0, 0, -29987, 0, 35256, 0, 0, 0, 47946, 0, -24411, 0, 0, 0, 0, 0, 25706, 0, 0, 0, 90800, 0, 1422, 0, 0, 0, 8417, 0, 0, 0, 0, 0, -87040, 0, 82582, 0, 0, 0, 48954, 0, -19202, 0, 0, 0, -13264, 0, -48022, 0, 0, 0, 91062, 0, -36875, 0, 0, 0, 0, 0, 35502, 0, 0, 0, 93996, 0, -91246, 0, 0, 0, -29910, 0, 0, 0, 0, 0, 3186, 0, 30912, 0, 0, 0, -28545, 0, 21276, 0, 0, 0, 50622, 0, -30533, 0, 0, 0, 105444, 0, -64703, 0, 0, 0, 0, 0, 40359, 0, 0, 0, 50460, 0, -95070, 0, 0, 0, 19128, 0, 0, 0, 0, 0, -19324, 0, -79748, 0, 0, 0, -8237, 0, -40896, 0, 0, 0, 12626, 0, 22535, 0, 0, 0, 33028, 0, -39060, 0, 0, 0, 0, 0, -44540, 0, 0, 0, -125578, 0, 31520, 0, 0, 0, 19617, 0, 0, 0, 0, 0, 67920, 0, -66612, 0, 0, 0, -56040, 0, -35278, 0, 0, 0, 21608, 0, 17666, 0, 0, 0, -13112, 0, -7475, 0, 0, 0, 0, 0, -29108, 0, 0, 0, 38376, 0, 42920, 0, 0, 0, -10761, 0, 0, 0, 0, 0, -37657, 0, 152352, 0, 0, 0, 11574, 0, 33565, 0, 0, 0, -5820, 0, -70658, 0, 0, 0, 22320, 0, 46016, 0, 0, 0, 0, 0, 35420, 0, 0, 0, 376, 0, 21118, 0, 0, 0, -15874, 0, 0, 0, 0, 0, -28853, 0, -148064, 0, 0, 0, -18187, 0, 50425, 0, 0, 0, 47080, 0, 36711, 0, 0, 0, -90420, 0, 61272, 0, 0, 0, 0, 0, -86246, 0, 0, 0, 36350, 0, 206646, 0, 0, 0, 12946, 0, 0, 0, 0, 0, 9908, 0, -27840, 0, 0, 0, -9465, 0, -124762, 0, 0, 0, -46091, 0, -41168, 0, 0, 0, 19096, 0, 37567, 0, 0, 0, 0, 0, -93932, 0, 0, 0, -144836, 0, -139074, 0, 0, 0, -35272, 0, 0, 0, 0, 0, 3386, 0, 175510, 0, 0, 0, -64662, 0, 57954, 0, 0, 0, -25200, 0, 29402, 0, 0, 0, -195690, 0, 5768, 0, 0, 0, 0, 0, 50256, 0, 0, 0, 96516, 0, 277902, 0, 0, 0, 104606, 0, 0, 0, 0, 0, 3825, 0, 6336, 0, 0, 0, 33074, 0, -69504, 0, 0, 0, -21248, 0, 32327, 0, 0, 0, -172046, 0, 63016, 0, 0, 0, 0, 0, 58368, 0, 0, 0, -70032, 0, 72360, 0, 0, 0, -82470, 0, 0, 0, 0, 0, 74979, 0, -17122, 0, 0, 0, -25770, 0, 78844, 0, 0, 0, 81208, 0, -70220, 0, 0, 0, -204644, 0, -8956, 0, 0, 0, 0, 0, -27381, 0, 0, 0, -221916, 0, -25180, 0, 0, 0, 105844, 0, 0, 0, 0, 0, -64062, 0, 37146, 0, 0, 0, 49719, 0, 5584, 0, 0, 0, 21009, 0, 78690, 0, 0, 0, -171024, 0, 39802, 0, 0, 0, 0, 0, -47545, 0, 0, 0, -71822, 0, -25250, 0, 0, 0, 40453, 0, 0, 0, 0, 0, 89250, 0, -116100, 0, 0, 0, 1404, 0, -2207, 0, 0, 0, -13464, 0, 14343, 0, 0, 0, 44370, 0, 124711, 0, 0, 0, 0, 0, -50995, 0, 0, 0, 98136, 0, -56026, 0, 0, 0, -66338, 0, 0, 0, 0, 0, 13827, 0, 191432, 0, 0, 0, 67304, 0, -67914, 0, 0, 0, -69806, 0, -94119, 0, 0, 0, -49832, 0, 77043, 0, 0, 0, 0, 0, -20673, 0, 0, 0, -40564, 0, 50718, 0, 0, 0, 99000, 0, 0, 0, 0, 0, 65703, 0, 141258, 0, 0, 0, 97416, 0, 34154, 0, 0, 0, -2532, 0, 109436, 0, 0, 0, 201560, 0, 15265, 0, 0, 0, 0, 0, -90279, 0, 0, 0, -136830, 0, -36556, 0, 0, 0, 10418, 0, 0, 0, 0, 0, 42818, 0, -450850, 0, 0, 0, 56651, 0, 15680, 0, 0, 0, -81678, 0, 84145, 0, 0, 0, -60768, 0, -14508, 0, 0, 0, 0, 0, -8979, 0, 0, 0, -97980, 0, -27240, 0, 0, 0, 64304, 0, 0, 0, 0, 0, -39408, 0, 78142, 0, 0, 0, 45978, 0, -110232, 0, 0, 0, -121569, 0, -77280, 0, 0, 0, -135744, 0, 66859, 0, 0, 0, 0, 0, 34, 0, 0, 0, -54236, 0, -164976, 0, 0, 0, -78570, 0, 0, 0, 0, 0, -33074, 0, 35444, 0, 0, 0, 121808, 0, 65011, 0, 0, 0, -13750, 0, -58509, 0, 0, 0, 288784, 0, -124556, 0, 0, 0, 0, 0, 147544, 0, 0, 0, -67744, 0, -218920, 0, 0, 0, -71088, 0, 0, 0, 0, 0, 21191, 0, -299584, 0, 0, 0, 116798, 0, 22085, 0, 0, 0, -17962, 0, 51368, 0, 0, 0, -189168, 0, -113613, 0, 0, 0, 0, 0, -11225, 0, 0, 0, -106282, 0, -53610, 0, 0, 0, 158118, 0, 0, 0, 0, 0, 130272, 0, 33666, 0, 0, 0, 27029, 0, 13600, 0, 0, 0, -105815, 0, 41453, 0, 0, 0, 111240, 0, -41431, 0, 0, 0, 0, 0, -145720, 0, 0, 0, -74918, 0, -82308, 0, 0, 0, -106965, 0, 0, 0, 0, 0, 39244, 0, 90490, 0, 0, 0, 52790, 0, 224275, 0, 0, 0, -206333, 0, 10299, 0, 0, 0, -205018, 0, 99351, 0, 0, 0, 0, 0, 86897, 0, 0, 0, -112240, 0, -186908, 0, 0, 0, 14853, 0, 0, 0, 0, 0, -78288, 0, -363462, 0, 0, 0, 215496, 0, 66525, 0, 0, 0, -160770, 0, 206373, 0, 0, 0, 221178, 0, 80047, 0, 0, 0, 0, 0, 61624, 0, 0, 0, 302500, 0, -4704, 0, 0, 0, -267296, 0, 0, 0, 0, 0, -149937, 0, -140568, 0, 0, 0, 155790, 0, -104929, 0, 0, 0, -8938, 0, -260866, 0, 0, 0, 188192, 0, -47998, 0, 0, 0, 0, 0, -97246, 0, 0, 0, -106380, 0, -257592, 0, 0, 0, 30690, 0, 0, 0, 0, 0, -27694, 0, 114354, 0, 0, 0, -420, 0, 53372, 0, 0, 0, 29101, 0, 12361, 0, 0, 0, 144056, 0, -106622, 0, 0, 0, 0, 0, 55959, 0, 0, 0, -77862, 0, 173750, 0, 0, 0, 93240, 0, 0, 0, 0, 0, 175140, 0, -194904, 0, 0, 0, -109458, 0, -112757, 0, 0, 0, -70977, 0, 244168, 0, 0, 0, -150086, 0, 9158, 0, 0, 0, 0, 0, -10398, 0, 0, 0, 19068, 0, 203550, 0, 0, 0, 5816, 0, 0, 0, 0, 0, -11965, 0, -302702, 0, 0, 0, -82586, 0, 48134, 0, 0, 0, 2254, 0, -140864, 0, 0, 0, 70114, 0, -95144, 0, 0, 0, 0, 0, -38280, 0, 0, 0, 255564, 0, -346984, 0, 0, 0, -45662, 0, 0, 0, 0, 0, -212622, 0, 662660, 0, 0, 0, 27933, 0, 141388, 0, 0, 0, -31302, 0, -49646, 0, 0, 0, -119132, 0, 124160, 0, 0, 0, 0, 0, 45036, 0, 0, 0, -148064, 0, -112594, 0, 0, 0, -26100, 0, 0, 0, 0, 0, 96998, 0, -306932, 0, 0, 0, 42945, 0, -81545, 0, 0, 0, 60272, 0, 2203, 0, 0, 0, 80640, 0, 148240, 0, 0, 0, 0, 0, -162408, 0, 0, 0, -303132, 0, -4154, 0, 0, 0, 110898, 0, 0, 0, 0, 0, -45210, 0, -171958, 0, 0, 0, 155022, 0, -228828, 0, 0, 0, 70971, 0, -166617, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 11, "prim_orbit_index": 3, "minimal_twist": "84.4.i.a", "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, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, -6, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, -7, 6, -7], [0, 0, 0, 0], [0, 0, 0, -5], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-52, 4, 48, 4], [0, 0, 0, 0], [0, -3, 35, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -20, 48, 0], [0, 0, 0, 0], [52, -11, -41, -11], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-143, 0, 0, 11], [0, 0, 0, 0], [171, 20, -191, 20], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -45, 25, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-72, 0, 0, -18], [0, 0, 0, 0], [362, 0, 0, -3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 36, 90, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [243, 9, -252, 9], [0, 0, 0, 0], [331, 0, 0, 41], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-113, 53, 60, 53], [0, 0, 0, 0], [0, 40, -286, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -30, 270, 0], [0, 0, 0, 0], [-94, 77, 17, 77], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-778, 0, 0, -44], [0, 0, 0, 0], [634, -53, -581, -53], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 62, -761, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-755, 0, 0, 101], [0, 0, 0, 0], [68, 0, 0, 28], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -42, 1008, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [304, 50, -354, 50], [0, 0, 0, 0], [-295, 0, 0, 29], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}