# Stored data for newform 2736.3.o.m, downloaded from the LMFDB on 18 April 2024.
{"label": "2736.3.o.m", "space_label": "2736.3.o", "level": 2736, "weight": 3, "hecke_orbit": 13, "hecke_orbit_code": 54044157651454640, "dim": 6, "is_polredabs": true, "nf_label": "6.0.219615408.1", "trace_hash": 2295970202310028157, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-24, -44, -1, 1]], [7, [-164, -64, -1, 1]]], "qexp_display": "q+\\beta _{3}q^{5}+\\beta _{2}q^{7}+(-4-\\beta _{2})q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "o", "char_is_real": true, "Nk2": 24624, "analytic_conductor": 74.55060032897723, "hecke_ring_index": 768, "level_radical": 114, "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": [2736, 2, [1711, 2053, 1217, 1009], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [721], "field_disc": -219615408, "field_disc_factorization": [[-1, 1], [2, 4], [3, 3], [23, 2], [31, 2]], "field_poly": [39, -93, 112, -39, 22, -3, 1], "hecke_ring_index_factorization": [[2, 8], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.422", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "166.154", "prec": 24}, {"__RealLiteral__": 0, "data": "63.423", "prec": 20}, {"__RealLiteral__": 0, "data": "7712.196", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "2.2.3.c2", "trace_display": [0, 0, 2, 2], "traces": [0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, -26, 0, 0, 0, 0, 0, 50, 0, 10, 0, 0, 0, 28, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 210, 0, 0, 0, 22, 0, -36, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 214, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102, 0, 0, 0, -266, 0, 0, 0, 0, 0, -404, 0, 370, 0, 0, 0, 0, 0, 0, 0, 0, 0, 358, 0, 0, 0, 0, 0, 164, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -172, 0, 0, 0, -238, 0, -356, 0, 0, 0, 310, 0, 0, 0, 0, 0, 166, 0, 6, 0, 0, 0, 98, 0, 242, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -644, 0, 0, 0, -764, 0, 164, 0, 0, 0, 0, 0, -570, 0, 0, 0, 0, 0, -760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 70, 0, 0, 0, 0, 0, 644, 0, 642, 0, 0, 0, 0, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, -286, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 934, 0, 0, 0, -334, 0, -874, 0, 0, 0, 118, 0, 0, 0, 0, 0, -360, 0, -48, 0, 0, 0, -74, 0, 652, 0, 0, 0, 0, 0, 0, 0, 0, 0, 550, 0, 0, 0, 0, 0, 0, 0, -876, 0, 0, 0, 648, 0, -362, 0, 0, 0, 0, 0, 642, 0, 0, 0, 0, 0, -356, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -190, 0, 0, 0, 790, 0, 0, 0, 0, 0, -842, 0, -452, 0, 0, 0, 0, 0, 0, 0, 0, 0, 790, 0, 0, 0, 0, 0, 1030, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1174, 0, 0, 0, 694, 0, 630, 0, 0, 0, -1996, 0, 0, 0, 0, 0, 2662, 0, -714, 0, 0, 0, 2518, 0, -204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, -1486, 0, 644, 0, 0, 0, 0, 0, 198, 0, 0, 0, 0, 0, 336, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -844, 0, 0, 0, -2612, 0, 0, 0, 0, 0, 1704, 0, 1878, 0, 0, 0, 0, 0, 0, 0, 0, 0, -316, 0, 0, 0, 0, 0, -3434, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, -3262, 0, -2142, 0, 0, 0, 550, 0, 0, 0, 0, 0, -650, 0, 748, 0, 0, 0, -1412, 0, 3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 652, 0, 0, 0, 0, 0, 0, 0, -382, 0, 0, 0, 1276, 0, 1276, 0, 0, 0, 0, 0, 310, 0, 0, 0, 0, 0, -1118, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -542, 0, 0, 0, 480, 0, 0, 0, 0, 0, -1128, 0, -1146, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 0, 0, 0, 1730, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 660, 0, 0, 0, 2088, 0, 1606, 0, 0, 0, -140, 0, 0, 0, 0, 0, 2614, 0, -2064, 0, 0, 0, 1940, 0, -1142, 0, 0, 0, 0, 0, 0, 0, 0, 0, -456, 0, 0, 0, 0, 0, 0, 0, -2858, 0, 0, 0, -4174, 0, 308, 0, 0, 0, 0, 0, -1310, 0, 0, 0, 0, 0, -3598, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -990, 0, 0, 0, -2378, 0, 0, 0, 0, 0, 2114, 0, 2870, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1418, 0, 0, 0, 0, 0, -2734, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1474, 0, 0, 0, -2208, 0, -2046, 0, 0, 0, 1874, 0, 0, 0, 0, 0, -3772, 0, 912, 0, 0, 0, -3796, 0, 540, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2666, 0, 0, 0, 0, 0, 0, 0, 786, 0, 0, 0, 1298, 0, 1308, 0, 0, 0, 0, 0, 2306, 0, 0, 0, 0, 0, 1618, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -506, 0, 0, 0, 338, 0, 0, 0, 0, 0, -7296, 0, -1130, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5568, 0, 0, 0, 0, 0, 4372, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2602, 0, 0, 0, -718, 0, 1508, 0, 0, 0, 2690, 0, 0, 0, 0, 0, 5036, 0, -362, 0, 0, 0, 2834, 0, 1490, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2280, 0, 0, 0, 0, 0, 0, 0, -1290, 0, 0, 0, -8686, 0, 3224, 0, 0, 0, 0, 0, -3684, 0, 0, 0, 0, 0, -2206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1920, 0, 0, 0, -674, 0, 0, 0, 0, 0, 8402, 0, -1870, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1726, 0, 0, 0, 0, 0, -2592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1756, 0, 0, 0, -4298, 0, 404, 0, 0, 0, 4224, 0, 0, 0, 0, 0, -748, 0, -756, 0, 0, 0, -338, 0, 2358, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1996, 0, 0, 0, 0, 0, 0, 0, 5894, 0, 0, 0, 4418, 0, -618, 0, 0, 0, 0, 0, 308, 0, 0, 0, 0, 0, 3954, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1700, 0, 0, 0, 2116, 0, 0, 0, 0, 0, -4414, 0, -4490, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2208, 0, 0, 0, 0, 0, 5858, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4848, 0, 0, 0, 604, 0, 5116, 0, 0, 0, 1414, 0, 0, 0, 0, 0, 4130, 0, -14, 0, 0, 0, 2402, 0, -2620, 0, 0, 0, 0, 0, 0, 0, 0, 0, -238, 0, 0, 0, 0, 0, 0, 0, -1626, 0, 0, 0, -8352, 0, 1048, 0, 0, 0, 0, 0, -2084, 0, 0, 0, 0, 0, -5454, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4812, 0, 0, 0, 646, 0, 0, 0, 0, 0, 6098, 0, 3140, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2496, 0, 0, 0, 0, 0, -3672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3180, 0, 0, 0, -1850, 0, -2928, 0, 0, 0, -1508, 0, 0, 0, 0, 0, -192, 0, 1794, 0, 0, 0, -5306, 0, 4114, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4728, 0, 0, 0, 0, 0, 0, 0, 2834, 0, 0, 0, 2092, 0, -2880, 0, 0, 0, 0, 0, 6998, 0, 0, 0, 0, 0, 534, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -996, 0, 0, 0, 2996, 0, 0, 0, 0, 0, -6218, 0, -4716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5280, 0, 0, 0, 0, 0, 5542, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2438, 0, 0, 0, 652, 0, -1344, 0, 0, 0, -820, 0, 0, 0, 0, 0, 8736, 0, -2016, 0, 0, 0, -286, 0, -8814, 0, 0, 0, 0, 0, 0, 0, 0, 0, -766, 0, 0, 0, 0, 0, 0, 0, -980, 0, 0, 0, -5020, 0, 2370, 0, 0, 0, 0, 0, 782, 0, 0, 0, 0, 0, 4262, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2988, 0, 0, 0, 1346, 0, 0, 0, 0, 0, 3670, 0, -1680, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 0, 0, 0, 0, -8836, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3738, 0, 0, 0, -3598, 0, -566, 0, 0, 0, 7148, 0, 0, 0, 0, 0, -6506, 0, 5138, 0, 0, 0, -10464, 0, -3166, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5140, 0, 0, 0, 0, 0, 0, 0, -4780, 0, 0, 0, 4802, 0, 1104, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 982, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3634, 0, 0, 0, 9432, 0, 0, 0, 0, 0, -2762, 0, -5018, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, 0, 0, 0, 5760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1150, 0, 0, 0, 7174, 0, 3990, 0, 0, 0, -5806, 0, 0, 0, 0, 0, 4012, 0, 5808, 0, 0, 0, 1754, 0, -4810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3360, 0, 0, 0, 0, 0, 0, 0, -2984, 0, 0, 0, -4922, 0, -1086, 0, 0, 0, 0, 0, 4032, 0, 0, 0, 0, 0, -4620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 662, 0, 0, 0, 1078, 0, 0, 0, 0, 0, 3364, 0, 1586, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2092, 0, 0, 0, 0, 0, -3146, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3292, 0, 0, 0, -9934, 0, -6138, 0, 0, 0, 2716, 0, 0, 0, 0, 0, -1150, 0, 6278, 0, 0, 0, -8180, 0, 6438, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5998, 0, 0, 0, 0, 0, 0, 0, -4138, 0, 0, 0, 6240, 0, 2510, 0, 0, 0, 0, 0, 8016, 0, 0, 0, 0, 0, -5348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1242, 0, 0, 0, 8326, 0, 0, 0, 0, 0, -2836, 0, -11706, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3072, 0, 0, 0, 0, 0, 1730, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8064, 0, 0, 0, -2, 0, 7660, 0, 0, 0, 9842, 0, 0, 0, 0, 0, 7388, 0, -4608, 0, 0, 0, -2542, 0, 1574, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5834, 0, 0, 0, 0, 0, 0, 0, 2662, 0, 0, 0, -3866, 0, 4082, 0, 0, 0, 0, 0, 1180, 0, 0, 0, 0, 0, 5356, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4340, 0, 0, 0, -3194, 0, 0, 0, 0, 0, -3836, 0, -1402, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3986, 0, 0, 0, 0, 0, 5206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4616, 0, 0, 0, -4224, 0, -460, 0, 0, 0, 10556, 0, 0, 0, 0, 0, 214, 0, 3840, 0, 0, 0, -3722, 0, -2772, 0, 0, 0, 0, 0, 0, 0, 0, 0, -554, 0, 0, 0, 0, 0, 0, 0, 2610, 0, 0, 0, -8714, 0, 5110, 0, 0, 0, 0, 0, 7010, 0, 0, 0, 0, 0, 9216, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6532, 0, 0, 0, 8036, 0, 0, 0, 0, 0, -6074, 0, -1160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2716, 0, 0, 0, 0, 0, 6384, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -426, 0, 0, 0, -4608, 0, 5026, 0, 0, 0, -3484, 0, 0, 0, 0, 0, 2692, 0, 5904, 0, 0, 0, 6240, 0, 1392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 434, 0, 0, 0, 0, 0, 0, 0, -4126, 0, 0, 0, -1082, 0, 530, 0, 0, 0, 0, 0, 2374, 0, 0, 0, 0, 0, -2478, 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": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 2, -1, 2, 0]], "char_orbit_index": 15, "prim_orbit_index": 2, "minimal_twist": "228.3.h.a", "char_is_minimal": false, "conrey_index": 721, "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], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 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, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [8, 0, -1, 2, 0, 0], [0, 0, 0, 0, 0, 0], [1, 0, 0, 2, -1, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [6, 0, -3, -1, 0, 0], [0, 0, 0, 0, 0, 0], [5, 0, -3, 2, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, -1, -4, 0, 0], [0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, -4], [0, 0, 0, 0, 0, 0], [36, 0, -1, -2, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [4, 0, 4, -5, 0, 0], [0, 0, 0, 0, 0, 0], [-7, 0, 5, -2, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 1, -2], [0, 0, 0, 0, 0, 0], [-2, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -4, 0, 0, 5, 2], [0, 0, 0, 0, 0, 0], [32, 0, 7, 4, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -6, 0, 0, 9, -4], [0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 4, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0], [12, 0, 1, 14, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-42, 0, -9, 2, 0, 0], [0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 8, -4], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-66, 0, 0, -4, 0, 0], [0, 0, 0, 0, 0, 0], [58, 0, -5, 16, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -11, 2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [60, 2, -6, 5, -7, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 7, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}