# Stored data for newform 19.4.c.b, downloaded from the LMFDB on 24 April 2024. {"label": "19.4.c.b", "space_label": "19.4.c", "level": 19, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503737133432851, "dim": 4, "is_polredabs": true, "nf_label": "4.0.47961.2", "trace_hash": 1235832131792755144, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [324, -18, 19, 1, 1]]], "qexp_display": "q-\\beta _{1}q^{2}-\\beta _{2}q^{3}+(-11+\\beta _{1}+10\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 19, "char_orbit_label": "c", "char_is_real": false, "Nk2": 304, "analytic_conductor": 1.1210362901090716, "hecke_ring_index": 1, "level_radical": 19, "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": [19, 3, [2], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [19], "conrey_indexes": [7, 11], "field_disc": 47961, "field_disc_factorization": [[3, 2], [73, 2]], "field_poly": [324, 18, 19, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.708", "prec": 17}, {"__RealLiteral__": 0, "data": "0.134", "prec": 17}, {"__RealLiteral__": 0, "data": "48.880", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1095.750", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c3", "trace_display": [-1, -2, -19, 40], "traces": [0, 4, -1, -2, -21, -19, -1, 40, 78, 52, -46, -66, 42, -101, -156, -19, 39, 75, -52, 57, 472, -20, -93, -1, -39, 33, -264, -212, -356, 85, 92, 44, -143, 33, 804, -336, 546, 896, -722, 202, -480, -124, -156, 311, 237, -988, -1240, -411, 39, 196, 1354, 75, -878, -261, 53, 204, 1656, -57, 2908, -204, -236, -531, -230, 520, -1934, 1554, -93, -556, -3108, 2, -1920, -1563, 1014, 234, 1090, -66, 1387, 216, 132, 331, -104, -1298, 11, 2918, 712, 1479, 922, -170, -630, -601, 1196, -280, 610, -22, -2436, -1235, 286, 324, -2969, -858, -347, -587, -1608, -2572, -1422, -336, 7488, 2600, 1113, 65, -336, -448, -1508, 1290, 1387, -1222, -604, 2626, 3621, 3816, -480, -3578, 20, -124, -450, -3990, -8112, 3135, 3489, 311, -498, -2426, -474, -2204, -11270, 1007, 3762, -828, 620, -42, 10560, 822, -672, 2214, 2028, 1378, 3329, -98, -3390, -633, -677, 3852, -969, 3900, 1260, -428, -878, -1707, -966, 522, 16, 2472, -649, -7582, 2458, 204, 5147, -5067, -828, -1619, -18780, 0, -8064, 2863, -1454, -2444, -2067, -204, 6368, 11338, 6136, -4489, 11376, 1062, 1842, -2942, -230, 1062, -2892, -2120, 13870, -6792, 967, 4671, 10163, -777, -3949, 3080, -4836, 3975, -1437, 1112, -10436, -5136, 1554, -1105, 8746, 26, -8684, -3021, 3840, -6085, -6354, -1563, -3424, 3721, -4134, 2192, -11246, 234, -3408, 90, 1090, -75, 3972, -858, 5043, 14718, -95, 2116, 6182, -108, -2832, 1250, -3432, 4962, -3162, 331, 15048, 96, 208, 7336, 4508, -4160, -5320, -3851, -22, -6935, 2172, -1459, -426, -4428, 9256, 1878, -20728, -2958, 1783, -8474, -1844, -1552, -8268, -2210, 10759, -12081, 315, 12186, -12768, 1202, 75, 4893, 2438, 9427, 8502, 560, -10998, -2625, 610, -6060, 24278, 572, -11808, 5782, 1218, 4650, 32604, 1387, 14868, -948, 3718, -9083, -13010, 324, -11338, -13180, -2969, 1785, 9588, 3498, -12252, -3153, -347, 6176, 3782, 1174, -7904, 9578, -20904, -6566, 180, 1286, -2696, -6436, 2844, -256, -14614, -17472, -4688, 1647, -3744, -5892, 11048, -1300, -14736, 16701, 27258, 5134, -15515, 65, -2199, 1584, 672, 28162, -9443, 11648, 5724, -1262, -1508, -10990, 17623, -645, 24180, 588, 17290, 11600, 8364, 611, -1160, -16020, -604, 1356, 11496, 5353, 6411, -21326, -7242, -14739, -9194, 3816, -13967, 8393, -24960, -12635, -3176, 1789, -8488, 5435, -10, 851, -16172, -6448, 2836, -17064, 900, 10772, -8010, 1995, -3744, 11775, 8268, -5072, -7144, -6270, -5748, 9859, 3489, 288, 16388, 16172, -26806, -3243, -498, 25986, 21342, -2426, 7406, 2013, -6162, -18433, 23984, -3344, 19318, 2680, 5635, -16, -652, -12331, 22656, -22668, 3762, 16764, 4244, 1656, 21606, 12852, -16120, -7984, -13974, 84, 7752, -18848, -5280, 6767, -17606, 10686, -15930, -26652, 1344, -4288, -16424, -4428, -29636, 9015, -2067, 9663, -4344, -689, 21192, -23579, -6658, -21855, 2664, 2548, 31842, 13920, 6780, 17186, -10732, -633, -34232, 32990, 17602, 2265, -1407, -1926, -21309, 16416, -3192, -10322, 33708, -3975, 12292, -357, 1260, -10780, 42224, -428, 6173, 47186, -45656, 18092, 4782, -1707, 7191, -2832, 1932, 26353, -106416, 6786, 27132, 1849, -8, -29194, 35442, -4944, 22398, 13079, 4160, -60076, -9588, 3791, -31454, 5519, -1229, -56478, -37050, 10608, -2418, -15192, 5147, -14556, 19524, 10134, -23166, -5421, 21528, 130, 18708, -1619, 41714, -6419, 9390, 15188, -51298, -3021, 8182, 20320, 4032, 11052, -19176, 2863, 30960, 18454, 37804, -23815, 27002, 4888, -894, 5424, -2067, 13785, -42138, -10608, 72124, 13254, -3184, -15124, 6897, -5669, -10146, 14286, -25016, 7145, -10434, 8978, 45996, -10661, -5688, -5955, -2781, 13806, -23874, 56867, -3684, -1216, -6004, -2942, -12559, -14631, -11960, -23746, -16224, 1062, -48122, -29762, -2892, -762, -17677, -12980, -30150, -56112, -5624, -37030, 14706, 3396, -8796, 11806, -25142, 20434, 124058, 4671, -19900, -17832, -20326, -6534, 14199, 20202, 5996, 1579, 7898, -3534, -65076, -1540, 25818, 42450, 4929, 49392, 37164, -7950, 29850, 16167, 2874, 17826, 33456, 14456, -15478, 20609, 5218, 28504, -51319, 10272, -9658, -27873, -40404, -1457, -14817, 2210, -3672, -28262, 8746, 55376, 13952, 53, -59638, -17544, 4342, 13404, 106690, -1140, 63368, -10794, 49920, 7785, 3060, -6085, -107424, -77158, -6354, 9651, -52800, -81276, 40920, 1576, -3424, -21370, 32088, -7442, -66576, -19596, -25311, 14535, -35466, -1096, 22395, 8812, 22492, -11075, 3367, 12168, 29952, -20791, 1704, 24781, -19779, -45, 21642, -42864, 56680, 25483, -53532, -75, 46342, 9528, -7944, -19912, -25643, -1749, -2866, 83152, 5043, 43244, 54792, -7359, 2262, 48312, 33592, 3906, 10824, -1058, 3900, 4887, 6182, -55168, -54940, 2808, -29691, 25034, 5664, 3117, -46840, 1250, -30188, -33759, 13992, 37734, 20742, -2481, 29239, 16176, 1581, -31741, 69708, 17212, -20370, 3712, -30096, -24984, -70657, -48, 18176, -24979, 2704, -90544, 12635, -14672, -43302, -29836, 4508, 2027, -22104, -61772, -75004, -27759, -5320, 42936, 107992, -3851, -23030, 26913, -286, 48736, 53168, 6346, 127440, -49251, -1086, -17949, -30944, 37934, -5220, 48192, -426, 25755, -53040, 8856, -77442, -13552, 18868, 70391, 65508, -3756, -46968, 96430, 10364, -44464, 28212, -38454, 51394, 57834, -3566, 27751, 10656, 16948, -126196, 9201, -23972, -3798, 36321, 776, 65220, -2147, 16536, 26118, -29382, -4505, -36049, -29977, -21518, 41450, -7994, -12081, 7404, -30024, -8190, -28093, -31664, -6093, 27758, -118896, 16644, 28962, 28019, 15626, -80201, 5775, 75, -59232, 18120, 4893, 5088, -40874, 59708, -12571, -62688, 9427, -40542, 18604, -17004, 23427, -64798, 7280, -13172, 19131, 5499, -53865, -98772, 5250, 28764, -39776, 31720, -12220, 25208, 3030, 39526, 64995, -12139, 96930, 20805, -2332, -37628, -8529, -11808, -16191, 84304, -11564, 156912, 3052, -31668, -64688, 83772, 4650, 20022, -22562, -16302, -9189, 76704, 3952, 67344, 20916, -7434, 38000, 52028, -948, 77928, 21436, 7579, 24607, -97336, 18166, -15304, -8856, -13010, -57643, -32568, 16848, -12122, -28512, 5669, 48653, -51844, 6590, -9672, -26518, -154388, -29132, 31392, -3570, -14358, -13739, -4794, 66536, -42658, 21417, 22964, -54093, 24504, -64988, 65988, -3153, -21643, -8044, -18044, -171342, -6861, 6176, -7038, 77626, 3782, 26994, -94899, 15262, -61920, 3628, 18031, -83406, -37095, -4789, 23128, 23628, -42612, 143372, -59088, -6566, 3216, 158958, -360, 32358, 105406, -33436, 61448, -69388, 5392, -52687, -37346, 3218, -35923, 1548, 36972, 59966, -55176, 512, -20028, 18043, 29228, 2606, 52377, 17808, 2964, -49729, 2344, 8486, 24149, -3294, 113832, 68248, 97344, 24816, 26652, 11784, 156196, 15372, 11048, -116052, -185280, 33800, 55639, 58427, 7368, 29481, -91452, -29127, -214924, 14094, -43680, -48892, -11918, 5134, -27352, -73074, -15515, 1266, 139928, 3380, 74774, -21193, -2199, -6454, 37662, -3168, -23636, 25750, 8736, -50313, 6530, -14081, -120600, -47566, 18886, -17899, 14549, -47488, -69264], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 19, 3, 1, 3, 0]], "char_orbit_index": 3, "prim_orbit_index": 3, "minimal_twist": "19.4.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, -1, 0, 0], [0, 0, -1, 0], [-11, 1, 10, 1], [0, -1, -9, 0], [-1, 1, 0, 1], [12, 0, 0, -4], [21, 0, 0, -3], [26, 0, -26, 0], [-28, 10, 18, 10], [-15, 0, 0, -3], [11, 0, 0, -1], [-48, -5, 53, -5], [0, -12, -72, 0], [-10, 1, 9, 1], [0, -13, 26, 0], [0, 21, 27, 0], [-26, 0, 0, 26], [19, -19, 0, 0], [128, 0, 0, -20], [0, -4, -8, 0], [0, 15, -54, 0], [8, -17, 9, -17], [0, -3, -18, 0], [7, 19, -26, 19], [-42, 0, 0, -48], [-53, 0, 0, 0], [-204, 52, 152, 52], [22, 41, -63, 41], [28, 0, 0, -10], [14, 0, 0, -6], [-53, -37, 90, -37], [0, -3, 18, 0], [426, -48, -378, -48], [0, -48, -144, 0], [0, 26, 260, 0], [206, 0, 0, 36], [-361, 0, 342, 19], [48, 0, 0, 5], [0, -48, -216, 0], [0, 2, -63, 0], [-84, 12, 72, 12], [0, 21, 145, 0], [111, 15, -126, 15], [-260, 0, 0, 26], [-314, 0, 0, 8], [-186, -39, 225, -39], [13, 13, -26, 13], [89, 0, 0, -80], [335, 0, 0, 7], [48, -21, -27, -21], [0, 2, -440, 0], [-180, 99, 81, 99], [0, 53, 0, 0], [0, -12, 108, 0], [468, 0, 0, -108], [-19, 19, -19, 19], [716, 0, 0, 22], [0, 102, -153, 0], [0, -20, -108, 0], [-262, -7, 269, -7], [0, -14, -108, 0], [312, -104, -208, -104], [-509, 0, 0, 51], [390, 0, 0, -3], [-39, -15, 54, -15], [-197, -162, 359, -162], [-906, 0, 0, 258], [-8, 0, 0, 17], [-1056, 192, 864, 192], [0, 3, -783, 0], [546, -78, -468, -78], [0, 88, 73, 0], [0, -206, 648, 0], [-7, 0, 0, -19], [342, 19, 190, -190], [36, 0, 0, 36], [0, -48, 90, 0], [0, -31, 181, 0], [-104, 104, 0, 104], [0, 0, -649, 0], [-25, 61, -36, 61], [649, 0, 0, 161], [204, 0, 0, -52], [858, -237, -621, -237], [544, -166, -378, -166], [-22, 0, 0, -41], [-153, 0, 0, -9], [-340, 79, 261, 79], [0, 260, 468, 0], [-216, 152, 64, 152], [0, 178, 216, 0], [0, -6, -8, 0], [-516, 0, 0, -186], [-532, 171, 171, 190], [53, 0, 0, 37], [0, 274, 25, 0], [0, -89, -1440, 0], [-390, -78, 468, -78], [0, -183, -82, 0]]}