# Stored data for newform 18.4.c.b, downloaded from the LMFDB on 18 April 2024. {"label": "18.4.c.b", "space_label": "18.4.c", "level": 18, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503737133432850, "dim": 4, "is_polredabs": true, "nf_label": "4.0.11025.3", "trace_hash": 877283348188569997, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [46656, 1944, 297, -9, 1]]], "qexp_display": "q-2\\beta _{1}q^{2}+(-\\beta _{1}-\\beta _{3})q^{3}+(-4-4\\beta _{1}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "c", "char_is_real": false, "Nk2": 288, "analytic_conductor": 1.062034380103331, "hecke_ring_index": 3, "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": 0, "analytic_rank_proved": true, "char_values": [18, 3, [11], [2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [7, 13], "field_disc": 11025, "field_disc_factorization": [[3, 2], [5, 2], [7, 2]], "field_poly": [81, -9, -8, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.953", "prec": 17}, {"__RealLiteral__": 0, "data": "0.150", "prec": 17}, {"__RealLiteral__": 0, "data": "58.765", "prec": 20}, {"__RealLiteral__": 0, "data": "3.866", "prec": 17}, {"__RealLiteral__": 0, "data": "1492.328", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [4, 3, 9, -19], "traces": [0, 4, 4, 3, -8, 9, 0, -19, -32, -51, 36, 24, -12, -61, 38, 171, -32, 6, 102, 266, 36, -315, -48, -69, -24, -263, -244, 0, 152, -237, -288, -211, 64, 630, 6, 774, 408, 524, 266, -249, -72, -468, -258, 86, -192, -459, -276, -483, 0, 33, 526, -153, -244, 300, 468, -1674, 152, 987, 474, -168, -1260, 1049, -844, -957, 256, 747, 558, 1166, -12, -261, 774, -624, 408, -622, 524, 2835, -532, 1173, 132, -349, -288, -1143, -1872, -1221, 744, 486, -172, -2205, -192, -984, -1404, 214, -276, -789, 966, -1764, 96, 128, 132, 1557, 2104, 1341, -630, -1453, 488, 1368, 300, 5826, 936, -1468, -1674, -1812, -304, 627, 3150, 783, 1896, 3111, -672, 444, -1368, 484, -2098, -1017, -844, -8622, -1938, 3932, 256, -7560, -1494, 2061, -1404, -3626, 4664, 2727, -48, -1272, 108, -1918, -1548, 4725, -624, 426, -816, 4482, -622, 3042, -1048, 1443, 3624, -1435, -2128, -549, 4692, 2367, 1260, -2659, 698, -1980, -288, 366, -4572, 3152, -1872, -1728, 2442, -2847, 2520, 2061, 1944, -1029, -688, 6051, -1494, 1754, 384, 63, -984, -12768, -972, -4192, 214, 4725, 552, 7794, 312, -909, 3864, 1557, -7056, -8127, 192, -1120, -256, -11025, 132, 996, 2448, -5188, 2104, -141, -2682, -5559, -648, 3051, -5812, 3519, 1952, 6321, 3150, 5429, -600, 4572, 5826, 23454, 0, 1174, -1468, 2841, 3348, -564, -8820, 3173, -1216, -2454, 2508, -2832, 2352, 4091, -1566, -3123, 1896, -9510, 4056, -18522, -672, 4095, -888, 951, 2304, -1072, 1936, -9747, -8392, -9126, -774, -1694, 1688, 6615, -8622, 6222, -48, 234, 3932, 1674, -512, -9282, -7818, 4126, -5976, -9351, 8244, -639, -5040, 7290, 7252, -7038, 4664, 1668, 15120, 19304, -48, 3468, 2544, -5349, 1260, 1247, -7672, 10761, -6192, 5271, 6174, -6079, 1248, 4284, 426, 7002, -3264, -18698, 4482, 6930, 1244, 12387, -5886, -189, -4192, -4752, 5772, -2577, -4092, -10523, 2870, 13545, -2128, -4734, -792, 6902, 4692, -14937, -4734, -7137, 1992, -11692, -10636, -7506, 2792, -4293, -8820, 9459, 576, 4527, 366, -4326, -4572, 24548, 3152, -3936, 3744, 2499, -1890, -5569, 9768, -13296, -11388, 423, 2064, -8038, -4122, 14643, 1944, 606, 11508, 4294, -688, -12285, -12102, 6162, 5832, 3293, 7016, 3357, 1536, 1194, -1134, -16524, 1968, 2520, -12768, 7380, 3672, 13878, -4192, 8286, -428, -11322, 1578, -9229, 2208, 23868, 31176, 5190, 3780, 1487, 1818, 936, 3864, 7842, -12006, 5474, -7056, -7446, 16254, -963, 0, 9369, -4480, -9147, -1024, 603, -13266, -576, -264, -6201, 996, -15426, -1332, -23428, -5188, -35910, -4208, -10440, 7278, -7853, -10728, 29241, -22236, -10086, 1224, 12536, -6102, -10710, -5812, 5082, 4464, -30834, 1952, 10983, -12642, 27933, 828, 1421, 21716, -5229, -2400, -4647, 20160, 17053, -11652, -7398, 23454, -7716, -3744, 31886, 1174, 17064, 2936, -2226, 13230, 19463, 13392, -1683, -2256, 15186, -10392, 16686, -6346, -20673, -1216, 12078, -26826, -7452, 2508, 50085, 5664, -9441, -7896, 1580, 16364, 7560, -6264, 17007, 13284, -19339, -3792, -37485, -9510, -35178, -4332, -33494, -18522, -4461, 1344, 21648, 5142, 3773, -3552, -10440, 3804, 5421, 10080, -14606, 2144, 4212, 1936, -19638, -19494, -27364, -8392, 4884, 18252, 21630, 2520, 2952, -6776, 19926, 6752, -12156, 10278, 24152, 17244, -21753, 6222, -17064, 7656, -28566, 234, 19215, -7864, -18675, -432, -6968, -2048, -37800, -37128, 44811, 14604, -8379, -8252, 10395, -5976, 4542, -24174, 66248, 8244, 9876, 1278, -1734, -4464, 21481, 29160, 8568, 29008, -15219, -25200, 12636, -9328, -18396, 1668, -35118, 19332, 15572, 19304, -21414, 96, 5202, 13230, 19130, 10176, 33837, -21396, -32298, 2088, 2827, -2494, 42246, -7672, 46392, 13596, -27926, -6192, -2835, -10542, -1902, -6552, -43929, -24316, 21717, 4992, -10764, -19152, -8740, -852, -9135, 7002, 26652, -3264, 12914, -18698, -40425, -8964, -1677, 6546, -11430, 4976, 2511, 49548, 6462, -23940, -6944, 378, 36972, -4192, -8760, 20736, -3564, 5772, -20586, 5154, -18519, -22680, -17086, -42092, -59466, 11480, -24858, 9522, -16111, 4256, 20799, -4734, 43638, 612, 29348, 6902, -76545, -9384, -43758, 21156, -3370, -18936, 4293, -28548, 23574, -1056, -8732, 23384, 60795, -10636, 14016, 24462, 67232, 2792, 39171, 8586, 40032, -9720, 9984, 37836, 23076, 2304, -17796, 630, -38488, -732, -6192, -4326, -16884, 9144, -7812, 24548, 13008, -6304, 3279, -11340, 18603, 14976, 17853, 9996, 5895, 3132, 2885, 11138, -5886, 9768, 75096, 132, 9738, -11388, -17955, -846, -26763, -5952, -39949, -32152, -64791, -16488, 26433, -25524, 11611, -3888, 28350, 606, -99558, 27132, 20682, 4294, -29301, 1376, -11190, -14634, -45697, -48408, -59823, 24648, -32949, 17640, -1647, -6586, -52335, 7016, 13872, -15120, -31304, 1536, 34776, -2388, 33057, -2520, 48161, -66096, -2757, 7872, -8697, 1188, 24111, 25536, 1899, 7380, 80856, 11232, -48938, 13878, 110250, 8384, -1398, -13668, -10831, -1712, 42228, -45288, 11469, -15744, 5639, 18458, 32130, 2208, 50664, 25758, -94510, 31176, 11004, -10380, 4515, 6312, 62019, 5948, -21213, 7272, -28146, 29610, 36053, -7728, 13329, 7842, -163170, -30240, 40400, 5474, -8802, 14112, -25797, -41580, 15478, 65016, -24786, -3852, -4179, -768, 27695, -18738, -30933, -4480, 31176, 8772, 81008, -1024, 630, -1206, -26397, 17568, 26496, -2304, -1269, -1056, 13383, 24768, -5719, -1992, -107415, -15426, 70302, -12456, -49814, -23428, 32670, 10376, 21777, -25032, -7812, -16832, -6354, -41760, 16113, 15120, -10989, 15706, 61416, -10728, -63570, 37908, -84970, -22236, 35268, 20172, -468, 5040, -50981, 50144, 7194, -24408, -3213, -6894, -19735, 11624, -32436, 5082, 24000, -5148, -87520, -30834, -31185, -3904, 9027, -33474, 65259, -50568, 13347, 111732, -6729, -10944, -2459, -2842, -58905, 21716, -39096, -49266, 36164, -2400, -19041, 9294, -15654, 22032, -21649, 68212, 89964, -46608, 5583, -30870, 8108, -46908, 39114, -7716, 114000, -7488, 23274, 31886, -14496, -2348, -8097, 54810, 29893, 11744, 13659, -8904, 18747, 15096, 34469, -38926, 14643, 13392, -53160, -19638, 78494, -2256, -23625, -30372, 21825, 14496, 12508, 66744, -27432, -25384, 3318, 50004, -2268, 2432, 20475, 12078, 30162, -43836, 13680, -7452, 13353, -5016, 45378, 54390, -26368, 22656, 54513, -37764, -37689, -25200, -5193, -3160, -75528, 16364, -94914, 8262, -44236, -6264, -66171, -34014, 24636, 39060, -93988, -77356, 74103, -15168, -9501, -44586, -42693, 19020, 11187, -35178, 324, -24888, 67304, -33494, 15750, 37044, -9843, -7032, -17091, 5376, -37800, 86592, 25446, -6096, 19408, -7546, -14805, -3552, -148194, -5580, -45738, 3804, -36369, -10842, -28149, 10944, 33069, -58424, -73809, 8576, 121275, 15750, -8293, -3872, -12537, -19638, 13032, 0, 119602, -27364, -45534, 16784, 53076, 10080, -43704, 73008, 10212, 86520, 12951, 8136, -106434, -5904, 19341, -6776, -28614, -45522, 55376, 6752, 15435, 24312, 38412, -5904, 35825, 96608, 105840, 68976], "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, 9, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "18.4.c.b", "char_is_minimal": true, "conrey_index": 7, "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, -2, 0, 0], [0, -1, 0, -1], [-4, -4, 0, 0], [6, 6, 0, 3], [-2, -2, -2, 0], [0, 8, 3, -3], [-8, 0, 0, 0], [-1, 25, -1, -1], [12, 0, 6, 0], [0, -9, -6, 6], [-4, 0, -4, 4], [-32, -32, 0, -3], [16, 16, 0, -6], [6, -78, 6, -3], [0, 16, 0, 0], [3, 0, 3, 0], [50, 52, -4, 2], [59, 0, -15, 0], [0, -24, 12, -12], [-70, 8, 11, -3], [-18, -18, 0, 12], [-36, -36, 0, -3], [0, 8, 0, 8], [0, 145, -27, 27], [-64, 0, -6, 0], [51, 78, 24, 0], [32, 0, -12, 0], [0, 108, 21, -21], [-156, -168, 6, -12], [-110, -110, 0, -9], [32, 32, 0, 0], [147, -9, -15, 6], [0, -6, 6, -6], [186, 0, -15, 0], [104, 4, -4, 8], [152, 0, 42, 0], [0, -118, -30, 30], [-32, 78, -32, 29], [-48, -48, 0, -24], [-237, -237, 0, -6], [16, 156, 16, -22], [0, -79, 72, -72], [-36, 0, 24, 0], [-234, -162, -72, -9], [-72, 0, -6, 0], [0, 264, -45, 45], [16, 16, 16, 0], [45, 45, 0, 57], [290, 290, 0, 54], [-78, -81, 3, -3], [0, 128, -12, 12], [96, 0, 42, 0], [156, 54, 48, -48], [-414, 0, 9, 0], [0, -64, -24, 24], [390, 331, -15, -59], [216, 216, 0, -42], [-81, -81, 0, 6], [-336, -24, -12, -12], [0, -502, -45, 45], [-220, 0, -18, 0], [-278, -130, 19, 67], [64, 0, 0, 0], [0, -426, 105, -105], [-18, -312, -18, 30], [565, 565, 0, -36], [-12, -12, 0, -12], [-36, 78, -36, 33], [0, -372, -30, 30], [-204, 0, -96, 0], [8, -200, 8, 8], [-187, 0, -63, 0], [0, -304, 84, -84], [847, 145, 118, 27], [-236, -236, 0, 60], [540, 540, 0, -93], [156, 220, -6, 64], [0, 194, -39, 39], [-96, 0, -48, 0], [-546, -597, 102, -51], [-474, 0, -12, 0], [0, 642, -63, 63], [312, 280, -12, -32], [252, 252, 0, 18], [-158, -158, 0, -144], [-438, 108, 129, -21], [0, 72, 48, -48], [-186, 0, 120, 0], [-324, 144, -162, 144], [22, 0, -63, 0], [0, 144, -12, 12], [-110, 234, -110, 101], [528, 528, 0, 90], [-816, -816, 0, 132], [32, 0, 32, -32], [0, -31, -66, 66], [90, 0, 114, 0], [381, 78, -24, -141], [580, 0, 108, 0]]}