# Stored data for newform 1152.3.m.a, downloaded from the LMFDB on 25 April 2024.
{"label": "1152.3.m.a", "space_label": "1152.3.m", "level": 1152, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 824684053632, "dim": 6, "is_polredabs": true, "nf_label": "6.0.399424.1", "trace_hash": 1662862830297677564, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [8, 136, 1156, -64, 2, 2, 1]], [7, [136, -60, 2, 1]]], "qexp_display": "q+(-1+\\beta _{1}-\\beta _{2}-\\beta _{4})q^{5}+(\\beta _{2}+\\beta _{3}+\\cdots)q^{7}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 16, "char_orbit_label": "m", "char_is_real": false, "Nk2": 10368, "analytic_conductor": 31.389726454306203, "hecke_ring_index": 64, "level_radical": 6, "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": "0.249", "prec": 17}, "analytic_rank_proved": true, "char_values": [1152, 4, [127, 901, 641], [2, 1, 4]], "hecke_ring_generator_nbound": 25, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [415, 991], "field_disc": -399424, "field_disc_factorization": [[-1, 1], [2, 6], [79, 2]], "field_poly": [8, -8, 6, -6, 3, -2, 1], "hecke_ring_index_factorization": [[2, 6]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.012", "prec": 17}, {"__RealLiteral__": 0, "data": "5.767", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "116.847", "prec": 24}, {"__RealLiteral__": 0, "data": "11.907", "prec": 20}, {"__RealLiteral__": 0, "data": "3543.573", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "2.2.3.c4", "trace_display": [0, 0, -2, -4], "traces": [0, 6, 0, 0, 0, -2, 0, -4, 0, 0, 0, -18, 0, 2, 0, 0, 0, 4, 0, -30, 0, 0, 0, -60, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, -100, 0, -46, 0, 0, 0, 0, 0, 114, 0, 0, 0, 0, 0, -46, 0, 0, 0, 78, 0, 252, 0, 0, 0, 206, 0, -30, 0, 0, 0, -12, 0, 226, 0, 0, 0, 260, 0, 0, 0, 0, 0, -212, 0, 0, 0, 0, 0, 318, 0, 212, 0, 0, 0, 0, 0, -188, 0, 0, 0, 0, 0, -4, 0, 0, 0, 142, 0, -388, 0, 0, 0, -338, 0, -366, 0, 0, 0, -108, 0, -156, 0, 0, 0, -120, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, -226, 0, 244, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, -148, 0, 0, 0, -418, 0, 316, 0, 0, 0, 320, 0, 66, 0, 0, 0, 200, 0, 2, 0, 0, 0, -124, 0, 0, 0, 0, 0, 766, 0, 0, 0, 0, 0, 190, 0, -670, 0, 0, 0, 0, 0, 260, 0, 0, 0, 0, 0, 60, 0, 0, 0, -450, 0, 252, 0, 0, 0, -260, 0, 832, 0, 0, 0, -284, 0, 386, 0, 0, 0, 772, 0, 0, 0, 0, 0, -404, 0, 0, 0, 0, 0, -2, 0, -606, 0, 0, 0, 0, 0, -512, 0, 0, 0, 0, 0, 444, 0, 0, 0, 698, 0, -196, 0, 0, 0, -242, 0, -76, 0, 0, 0, 84, 0, -732, 0, 0, 0, -1532, 0, 0, 0, 0, 0, -1170, 0, 0, 0, 0, 0, -34, 0, 1106, 0, 0, 0, 0, 0, 786, 0, 0, 0, 0, 0, -686, 0, 0, 0, 958, 0, 380, 0, 0, 0, 188, 0, -1036, 0, 0, 0, 564, 0, 930, 0, 0, 0, 1604, 0, 0, 0, 0, 0, 526, 0, 0, 0, 0, 0, -292, 0, 786, 0, 0, 0, 0, 0, -1134, 0, 0, 0, 0, 0, 716, 0, 0, 0, -864, 0, -1160, 0, 0, 0, 206, 0, 274, 0, 0, 0, -748, 0, -860, 0, 0, 0, -2172, 0, 0, 0, 0, 0, 1616, 0, 0, 0, 0, 0, -36, 0, -1358, 0, 0, 0, 0, 0, 946, 0, 0, 0, 0, 0, -264, 0, 0, 0, -914, 0, -776, 0, 0, 0, -448, 0, 1394, 0, 0, 0, 580, 0, 64, 0, 0, 0, 1284, 0, 0, 0, 0, 0, -564, 0, 0, 0, 0, 0, -546, 0, -670, 0, 0, 0, 0, 0, -572, 0, 0, 0, 0, 0, -452, 0, 0, 0, 556, 0, 700, 0, 0, 0, 1134, 0, -48, 0, 0, 0, -124, 0, -1440, 0, 0, 0, -1208, 0, 0, 0, 0, 0, -1714, 0, 0, 0, 0, 0, 606, 0, 1460, 0, 0, 0, 0, 0, -114, 0, 0, 0, 0, 0, 2284, 0, 0, 0, 556, 0, -1412, 0, 0, 0, -818, 0, -1036, 0, 0, 0, -696, 0, 386, 0, 0, 0, 1604, 0, 0, 0, 0, 0, 670, 0, 0, 0, 0, 0, -1956, 0, 32, 0, 0, 0, 0, 0, 82, 0, 0, 0, 0, 0, -2030, 0, 0, 0, 64, 0, 1020, 0, 0, 0, 1514, 0, -30, 0, 0, 0, 2324, 0, -158, 0, 0, 0, 68, 0, 0, 0, 0, 0, 1630, 0, 0, 0, 0, 0, 2590, 0, -988, 0, 0, 0, 0, 0, -238, 0, 0, 0, 0, 0, 76, 0, 0, 0, -404, 0, -772, 0, 0, 0, -2002, 0, 160, 0, 0, 0, -1804, 0, 8, 0, 0, 0, 452, 0, 0, 0, 0, 0, -866, 0, 0, 0, 0, 0, -1536, 0, -478, 0, 0, 0, 0, 0, 146, 0, 0, 0, 0, 0, 1606, 0, 0, 0, -820, 0, 3772, 0, 0, 0, 2624, 0, 710, 0, 0, 0, 68, 0, 1634, 0, 0, 0, -1276, 0, 0, 0, 0, 0, -722, 0, 0, 0, 0, 0, 3006, 0, 866, 0, 0, 0, 0, 0, 772, 0, 0, 0, 0, 0, -3012, 0, 0, 0, 46, 0, -3336, 0, 0, 0, -4082, 0, 96, 0, 0, 0, 852, 0, 770, 0, 0, 0, 1284, 0, 0, 0, 0, 0, 1150, 0, 0, 0, 0, 0, -2212, 0, 178, 0, 0, 0, 0, 0, 1476, 0, 0, 0, 0, 0, 1848, 0, 0, 0, 1758, 0, 3900, 0, 0, 0, 700, 0, -846, 0, 0, 0, -4572, 0, 450, 0, 0, 0, -1404, 0, 0, 0, 0, 0, -404, 0, 0, 0, 0, 0, 2844, 0, -286, 0, 0, 0, 0, 0, -1276, 0, 0, 0, 0, 0, -196, 0, 0, 0, -562, 0, -384, 0, 0, 0, -1440, 0, -1292, 0, 0, 0, 3572, 0, 1218, 0, 0, 0, -376, 0, 0, 0, 0, 0, -1186, 0, 0, 0, 0, 0, -2816, 0, 1128, 0, 0, 0, 0, 0, -1838, 0, 0, 0, 0, 0, -2948, 0, 0, 0, -2034, 0, 444, 0, 0, 0, 2158, 0, 354, 0, 0, 0, 1292, 0, 228, 0, 0, 0, -1020, 0, 0, 0, 0, 0, 270, 0, 0, 0, 0, 0, 732, 0, -846, 0, 0, 0, 0, 0, 434, 0, 0, 0, 0, 0, 2316, 0, 0, 0, 384, 0, -1476, 0, 0, 0, -1856, 0, 1906, 0, 0, 0, -2444, 0, -862, 0, 0, 0, 2628, 0, 0, 0, 0, 0, 1568, 0, 0, 0, 0, 0, -64, 0, -780, 0, 0, 0, 0, 0, -1550, 0, 0, 0, 0, 0, -2052, 0, 0, 0, 3276, 0, 316, 0, 0, 0, 3452, 0, -2146, 0, 0, 0, 3972, 0, -1146, 0, 0, 0, -2424, 0, 0, 0, 0, 0, -1042, 0, 0, 0, 0, 0, 94, 0, 528, 0, 0, 0, 0, 0, 2624, 0, 0, 0, 0, 0, 1926, 0, 0, 0, 876, 0, -1796, 0, 0, 0, 718, 0, -2892, 0, 0, 0, -4092, 0, 1152, 0, 0, 0, 7108, 0, 0, 0, 0, 0, -1876, 0, 0, 0, 0, 0, -1764, 0, 2738, 0, 0, 0, 0, 0, 836, 0, 0, 0, 0, 0, 3388, 0, 0, 0, -4674, 0, -1352, 0, 0, 0, 878, 0, 818, 0, 0, 0, -1792, 0, -4800, 0, 0, 0, -3068, 0, 0, 0, 0, 0, 428, 0, 0, 0, 0, 0, 2204, 0, -908, 0, 0, 0, 0, 0, 3058, 0, 0, 0, 0, 0, -4424, 0, 0, 0, -1906, 0, 4220, 0, 0, 0, 2236, 0, 3938, 0, 0, 0, 4660, 0, 258, 0, 0, 0, 1988, 0, 0, 0, 0, 0, 1472, 0, 0, 0, 0, 0, 1022, 0, -1726, 0, 0, 0, 0, 0, -2492, 0, 0, 0, 0, 0, 2552, 0, 0, 0, 5214, 0, 2300, 0, 0, 0, -960, 0, -1982, 0, 0, 0, -3004, 0, -1726, 0, 0, 0, -884, 0, 0, 0, 0, 0, -1716, 0, 0, 0, 0, 0, -1444, 0, 1300, 0, 0, 0, 0, 0, 1472, 0, 0, 0, 0, 0, -1556, 0, 0, 0, 3472, 0, -836, 0, 0, 0, -2418, 0, -3664, 0, 0, 0, 2824, 0, 5986, 0, 0, 0, 4672, 0, 0, 0, 0, 0, -1426, 0, 0, 0, 0, 0, 382, 0, 960, 0, 0, 0, 0, 0, -1728, 0, 0, 0, 0, 0, -2676, 0, 0, 0, -6164, 0, -5512, 0, 0, 0, -1604, 0, 2562, 0, 0, 0, -1612, 0, -220, 0, 0, 0, -9212, 0, 0, 0, 0, 0, 2462, 0, 0, 0, 0, 0, -1380, 0, -1742, 0, 0, 0, 0, 0, -476, 0, 0, 0, 0, 0, 7468, 0, 0, 0, -788, 0, 1660, 0, 0, 0, -274, 0, 5012, 0, 0, 0, -824, 0, 1636, 0, 0, 0, -3328, 0, 0, 0, 0, 0, 1806, 0, 0, 0, 0, 0, -1986, 0, -2588, 0, 0, 0, 0, 0, -5294, 0, 0, 0, 0, 0, -6148, 0, 0, 0, 6814, 0, -3524, 0, 0, 0, -978, 0, -376, 0, 0, 0, 5460, 0, -732, 0, 0, 0, -4476, 0, 0, 0, 0, 0, -958, 0, 0, 0, 0, 0, -1344, 0, 736, 0, 0, 0, 0, 0, 2948, 0, 0, 0, 0, 0, -532, 0, 0, 0, -788, 0, -1544, 0, 0, 0, -2560, 0, -2668, 0, 0, 0, -4348, 0, -4352, 0, 0, 0, 1220, 0, 0, 0, 0, 0, -1714, 0, 0, 0, 0, 0, 412, 0, 2658, 0, 0, 0, 0, 0, -2432, 0, 0, 0, 0, 0, 5496, 0, 0, 0, -6560, 0, 3004, 0, 0, 0, -196, 0, 3184, 0, 0, 0, 1924, 0, -1180, 0, 0, 0, -892, 0, 0, 0, 0, 0, 906, 0, 0, 0, 0, 0, -290, 0, -462, 0, 0, 0, 0, 0, -1984, 0, 0, 0, 0, 0, -4516, 0, 0, 0, -1990, 0, -2436, 0, 0, 0, 2318, 0, 5074, 0, 0, 0, -1792, 0, 3554, 0, 0, 0, 3016, 0, 0, 0, 0, 0, 3932, 0, 0, 0, 0, 0, -706, 0, -3372, 0, 0, 0, 0, 0, 4338, 0, 0, 0, 0, 0, 6460, 0, 0, 0, 6078, 0, -1992, 0, 0, 0, 1838, 0, -2176, 0, 0, 0, -7864, 0, -1760, 0, 0, 0, 5764, 0, 0, 0, 0, 0, 1472, 0, 0, 0, 0, 0, 5630, 0, 242, 0, 0, 0, 0, 0, 2770, 0, 0, 0, 0, 0, 1420, 0, 0, 0, -660, 0, 3580, 0, 0, 0, -2760, 0, -5950, 0, 0, 0, 8244, 0, -3804, 0, 0, 0, -572, 0, 0, 0, 0, 0, -3584, 0, 0, 0, 0, 0, 3422, 0, -1186, 0, 0, 0, 0, 0, 2738, 0, 0, 0, 0, 0, -8020, 0, 0, 0, -5780, 0, 3836, 0, 0, 0, 2428, 0, 3410, 0, 0, 0, 3220, 0, 3300, 0, 0, 0, 7940, 0, 0, 0, 0, 0, 558, 0, 0, 0, 0, 0, 894, 0, 642, 0, 0, 0, 0, 0, -142, 0, 0, 0, 0, 0, 1016, 0, 0, 0, -1778, 0, -2052, 0, 0, 0, -2240, 0, 2240, 0, 0, 0, -3352, 0, -2752, 0, 0, 0, 3076, 0, 0, 0, 0, 0, 4108, 0, 0, 0, 0, 0, -3266, 0, -366, 0, 0, 0, 0, 0, 398, 0, 0, 0, 0, 0, 102, 0, 0, 0, 6588, 0, 9080, 0, 0, 0, 512, 0, -2222, 0, 0, 0, 6852, 0, 2338, 0, 0, 0, -4412, 0, 0, 0, 0, 0, -146, 0, 0, 0, 0, 0, 2872, 0, -1036, 0, 0, 0, 0, 0, -10894, 0, 0, 0, 0, 0, 3896, 0, 0, 0, -1042, 0, -4228, 0, 0, 0, 5120, 0, -2750, 0, 0, 0, -5484, 0, -542, 0, 0, 0, -9592, 0, 0, 0, 0, 0, -3316, 0, 0, 0, 0, 0, -5088, 0, 1956, 0, 0, 0, 0, 0, 2440, 0, 0, 0, 0, 0, 1068, 0, 0, 0, -5408, 0, -6724, 0, 0, 0, -1362, 0, 450, 0, 0, 0, -4092, 0, 3748, 0, 0, 0, 6408, 0, 0, 0, 0, 0, -3390, 0, 0, 0, 0, 0, -1954, 0, 3894, 0, 0, 0, 0, 0, 900, 0, 0, 0, 0, 0, -4144, 0, 0, 0, 3360, 0, -11908, 0, 0, 0, -6144, 0, -812, 0, 0, 0, 4296, 0, -2204, 0, 0, 0, -9660, 0, 0, 0, 0, 0, 2956, 0, 0, 0, 0, 0, -62, 0, -158, 0, 0, 0, 0, 0, 2482, 0, 0, 0, 0, 0, 2620, 0, 0, 0, 5582, 0, -2244, 0, 0, 0, 5628, 0, -924, 0, 0, 0, -4236, 0, -1728, 0, 0, 0, 3460, 0, 0, 0, 0, 0, 4334, 0, 0, 0, 0, 0, -5218, 0, -2316, 0, 0, 0, 0, 0, -4224, 0, 0, 0, 0, 0, -7112, 0, 0, 0, 12, 0, 6912, 0, 0, 0, 2286, 0, -1486, 0, 0, 0, -76, 0, -4700, 0, 0, 0, -3004, 0, 0, 0, 0, 0, -6850, 0, 0, 0, 0, 0, -264, 0, 4820, 0, 0, 0, 0, 0, -316, 0, 0, 0, 0, 0, 892, 0, 0, 0, -5922, 0, 9536, 0, 0, 0, -722, 0, 2516, 0, 0, 0, -2604, 0, 4386, 0, 0, 0, 3332, 0, 0, 0, 0, 0, -7394, 0, 0, 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, 16, 6, -1, 4, 0]], "char_orbit_index": 13, "prim_orbit_index": 6, "minimal_twist": "16.3.f.a", "char_is_minimal": false, "conrey_index": 415, "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], [-1, 1, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-4, -4, 0, -2, 0, -1], [0, 0, 0, 0, 0, 0], [1, 1, 0, -1, 0, 3], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-2, 0, -1, -1, -3, -3], [0, 0, 0, 0, 0, 0], [-4, 4, 2, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-8, 0, 1, 1, 2, 2], [0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 4, -4], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-1, -1, 0, -1, 0, 7], [0, 0, 0, 0, 0, 0], [0, -24, 2, -2, 2, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-16, 16, 4, 0, -2, 0], [0, 0, 0, 0, 0, 0], [-7, 7, -5, 0, 7, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -8, 6, -6, 6, -6], [0, 0, 0, 0, 0, 0], [16, 16, 0, -8, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -24, -2, 2, -10, 10], [0, 0, 0, 0, 0, 0], [-13, 0, -6, -6, -2, -2], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [15, -15, 1, 0, 5, 0], [0, 0, 0, 0, 0, 0], [48, 0, 1, 1, 8, 8], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [32, 32, 0, -4, 0, -3], [0, 0, 0, 0, 0, 0], [-7, -7, 0, -5, 0, -1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-10, 0, -6, -6, -6, -6], [0, 0, 0, 0, 0, 0], [44, -44, 14, 0, 5, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [56, 0, 1, 1, 18, 18], [0, 0, 0, 0, 0, 0], [0, -24, 11, -11, 13, -13], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-34, -34, 0, 4, 0, 0], [0, 0, 0, 0, 0, 0], [0, 64, 4, -4, -20, 20], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [56, -56, 0, 0, 9, 0], [0, 0, 0, 0, 0, 0], [42, -42, 4, 0, 16, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 8, -5, 5, 13, -13], [0, 0, 0, 0, 0, 0], [-24, -24, 0, 8, 0, 14], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 32, 7, -7, 0, 0], [0, 0, 0, 0, 0, 0], [2, 0, -11, -11, 15, 15], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]]}