# Stored data for newform 23.4.a.b, downloaded from the LMFDB on 18 April 2024. {"label": "23.4.a.b", "space_label": "23.4.a", "level": 23, "weight": 4, "hecke_orbit": 2, "hecke_orbit_code": 4503599694479383, "dim": 4, "is_polredabs": true, "nf_label": "4.4.334189.1", "trace_hash": 902461727555289151, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [2, 61, -24, -2, 1]]], "qexp_display": "q+(1+\\beta _{3})q^{2}+(1+\\beta _{1}+\\beta _{2})q^{3}+(6+\\cdots)q^{4}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 368, "fricke_eigenval": 1, "atkin_lehner_string": "+", "analytic_conductor": 1.357043930132034, "hecke_ring_index": 1, "level_radical": 23, "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": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": 0, "analytic_rank_proved": true, "char_values": [23, 1, [5], [1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 1, "level_primes": [23], "conrey_indexes": [1], "field_disc": 334189, "field_disc_factorization": [[334189, 1]], "field_poly": [4, -5, -16, -2, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.042", "prec": 17}, {"__RealLiteral__": 0, "data": "3.720", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "35.170", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "488.046", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[23, 1]], "trace_display": [2, 7, 14, 16], "traces": [0, 4, 2, 7, 20, 14, -17, 16, -63, -33, -70, 8, -67, 111, -144, 10, 64, 98, 49, 96, 140, 180, 220, -92, -188, 184, -229, -155, 282, 21, -406, -193, -432, -418, 666, -752, -629, 170, 748, -291, -26, -125, 640, 2, 830, 168, -46, -677, 551, 1220, 414, -340, 2247, -230, 641, -972, -2174, 1322, -1835, -1140, -804, 754, 443, -1092, -805, 1318, -398, 488, 284, -161, -3820, -401, 1503, 1509, 1366, 1401, -3832, 736, -1907, -838, 2846, -932, -949, 142, 2614, 112, 918, 2223, -404, 2342, 1784, 292, -460, -509, 1567, -956, 799, 1062, 2478, -1498, -1608, -2612, -1324, 2480, -3448, -1976, -5862, 2908, 715, -2256, -264, -1826, 820, 1646, 2546, -322, -1503, -2580, -276, -2848, 354, -284, 2586, 201, -831, -5004, 2476, 1277, 2132, 1288, -1694, 1423, 1360, -1232, 4100, 1830, 2028, -1518, 391, 2641, 3692, -2577, 5671, 2814, -461, 3098, -3103, 231, 580, -4618, 3325, -289, 3854, -106, -1756, -4894, 735, 468, -5934, 1126, -3508, -368, -4954, -79, -621, -7868, -566, -1144, -3430, 2475, 3772, 4178, -6486, -3500, 2771, 6600, -6692, 776, 7650, 357, -6524, 1022, -18628, -350, 1449, 10100, 2587, 3516, -1555, -9676, 236, 7890, 1536, 8989, 12590, -1426, 9660, -4315, -2062, 2758, -3737, 4010, -2524, 5108, -5810, 4214, 5360, 759, 6627, -7856, -3740, -2264, 5862, -9621, 224, 3976, 8468, 4428, -18800, 6171, 9180, 2176, -9722, -152, 2726, -891, -7394, -2246, -10090, -6852, 1610, 12272, -7112, 3211, 9476, -14822, -11928, -2738, -4628, -2913, 13102, 3936, 4542, 952, 1890, -9610, -955, -17030, 1556, -1584, -2396, 9486, -7128, -184, 1225, -4560, -1832, -6221, 576, -26016, 21984, 2028, 10475, 1114, -3666, 13332, 28384, 5964, -12894, -1943, 16662, -112, -9182, 10220, -6122, -1112, 1541, 11457, 9485, -982, -936, -2098, 6319, 2812, 7425, 8012, 6878, -4484, 5925, -8032, -11602, 2200, 3473, -2116, -2053, -9728, 15626, 5922, 862, -2553, -1469, -13432, -11745, -11250, -8032, 4764, -8582, -14232, -14876, -2584, -2142, 5991, -7748, 15854, -16348, 1680, 11410, 2024, -3034, -19806, -22446, 11726, 3312, 4844, 12128, -9983, 15673, -768, 1764, 10764, -9848, -1275, 10776, 6856, -12512, -7076, -14260, 22782, -26675, -2220, 156, 8342, -18594, 15944, 13734, -230, -16052, -8236, 4569, -13735, 28904, 5583, -9158, 14069, 13256, -8646, -5774, 12304, 4577, 18270, 5808, 24196, -11550, 7439, 19170, 24842, -7606, -26804, -1472, 3396, 34440, 5288, 7659, 3382, 16896, -4948, 7300, -5011, -21200, 1950, -43576, -19143, -15662, 24956, 12733, -11800, -4667, 11474, -14408, -4880, -12706, -2254, -25411, -5185, 25061, 2532, 2914, 18391, -17930, -12792, -8072, -27612, 8630, -8867, 2204, -9514, 5524, -4244, -2810, -5583, 5418, -8388, 26118, 5152, -1127, -15072, -28323, -4887, 3240, -11330, 25796, -1320, 22032, -3422, -19516, 158, -12513, -14488, 7128, -3654, 16856, -30556, -11263, 9876, 24736, 30322, 23232, -2208, -9133, 10777, 11836, -22185, 38516, -577, -30252, -5312, -65564, -9214, 41566, -21288, -9581, -11138, 37512, 25891, 49270, 20832, 4232, 206, -17644, 13404, -3220, -4535, 26028, 2424, 40293, -17990, 21015, 20040, -39624, -3616, -742, 26872, 17144, -20044, -1714, 35848, -40472, -2368, 20567, -5016, 6332, 15266, 14024, -4140, -38652, -41416, -13424, 20957, 4844, -2299, -37334, 41789, -533, -27352, 41530, -6304, -21701, -22348, 3516, -44073, -35888, -26472, -28270, 40690, 42384, 8772, -5060, -16028, 48287, 12921, -15996, -9940, 28497, -22306, -43369, -18152, -23088, 30878, -61396, 23474, -44906, -51398, 26236, 19134, 11169, 7060, -7278, -1788, -21706, 2116, -13884, 13156, -25524, 779, 532, -14244, 14988, 10713, 10445, 41696, 7332, -6619, 9872, 16982, -19724, -1024, 8272, 3989, 9746, -268, 5900, 16094, 4324, 18808, -13863, 19772, 1159, 24892, -12298, -23244, 62284, -16712, -28698, 12078, 24223, 21808, 7656, 35704, 27920, -12492, -2164, 27370, 14640, 33446, -14396, -4232, -7839, -1943, 26710, 21927, -15360, 35528, 18736, -29468, -22952, -32204, -35780, 3859, -2155, -2758, 5480, -3969, 2178, -32272, 12158, -45880, -41866, 20130, 5267, 6296, -10696, 2037, 17960, 12082, -26503, 21734, -11214, 10124, 27024, -46148, 13668, -22527, 6754, -25820, -36584, 20718, -29016, -3696, -10972, -15662, -3012, 3565, 195, -2488, 21765, -36192, -30182, -43548, -21872, 37536, 62968, 37956, -23240, -25740, -18384, 44774, 27038, 36119, -40334, -7206, -18158, 1322, 13126, -42568, -6486, 30560, -30260, -28437, -29199, -13560, -13687, 13332, -54405, -25617, 12512, -32118, 23299, 2272, 65248, 9518, 28132, 40482, 57929, -32380, -29224, -110496, -12920, -483, 85516, 30496, 1048, 6196, -37142, 30167, 82170, -42613, 117619, 65762, -25220, 22160, 33992, -38032, -1030, -80439, 38314, 36288, 42232, -47868, 970, 34274, 9338, -27424, -46432, 4008, -75424, 70870, 3668, -10728, 58709, 47717, 16814, -50444, 78523, -500, 15932, -61614, 44721, -38968, 19220, 12364, 50674, -13496, -2382, 4439, 64636, 38644, -28497, -9933, -47122, -61144, -29704, 38864, -62158, -14934, -15816, 14123, 5715, 11554, -106078, 27900, -15754, 9884, -34762, 58768, -30260, -67774, 9936, -14416, 14100, -77531, -7132, -31186, -78432, 40640, 1114, 38556, 49434, -24786, 38272, 67856, 26724, 20272, -72817, 15264, -112551, -48742, -86230, -4262, 1658, 9614, 98932, -19895, -68335, 83264, 40432, 11688, 46004, -65056, 9465, 25000, -78920, 47665, 36321, -48252, -24738, 12369, 17812, -6776, -47528, -6766, 17316, 73294, -15318, -53067, -47044, 3776, -2849, 11006, -102947, 31714, -20036, 23792, 8306, 17198, 20723, 59764, 25060, -65742, 37056, -604, 17636, -1318, 436, -56630, -39944, 17296, 18329, 25067, 44378, -5496, -38110, 36011, 140430, -3640, 37800, 80246, 11696, 69628, -3723, -28568, -6280, 20292, -25812, 41583, -52086, 1754, 111464, -84370, 14467, 72744, -45308, 36731, -45516, 46042, -61055, -4848, 56228, -2807, 42754, 10424, 33328, 11939, 16308, 6620, -19700, 70404, -39442, -74696, 116706, -19582, -16970, -3910, -7421, 49712, -38664, 90992, -75598, 60643, -43514, -38977, -75096, -32892, -5572, -116435, -23863, -49492, 60076, -72479, -36210, 8596, 33682, -59734, -83648, -4634, -17204, -29296, -41139, 1604, -67591, -15928, -28936, -44786, -12895, 9392, 5118, 2496, 101031, 53051, 17358, -79020, -18312, 32432, 43148, -26782, -9998, -22490, 115796, 6693, 90396, -29425, 6057, -66576, -22730, -46544, -75144, 55956, 77887, -3640, -35824, 14554, -134260, 54122, 16594, 47356, -115874, -1892, 71892, 21308, 38988, -37308, 598, -40464, -92611, 28269, 3876, -70242, 43428, -51584, 38379, 2387, -738, 512, -97145, 9179, 23636, 6808, 95774, 77528, 109244, 6952, 2220, -86388, 49048, 2875, -28388, 49624, -3348, 130943, 64098, 41617, 47956, -35378, 1868, -80240, 104480, 23372, -40211, -33594, 93536, -57096, -52922, -80545, 158574, -33422, 62778, 95610, -14720, -116319, 79917, 40568, -23228, 120512, 63104, -161676, 74741, -5245, -18558, -56004, -44247, 3820, 88516, -35664, 8569, 27742, 13440, 2378, -79076, 49236, -186654, -46, 14488, 49128, 27195, -40291, -47256, 4628, 45754, 42908, -43117, 99218, 90724], "weight_parity": 1, "has_non_self_twist": 0, "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]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "23.4.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 1], [1, 1, 1, 0], [6, -3, -2, -2], [2, 2, -2, -2], [-5, 1, 3, 1], [4, -4, 4, -2], [-15, 4, -1, 5], [-10, 5, 1, 2], [-16, 4, -6, 4], [10, -12, -4, 2], [-16, -8, 1, -6], [31, -11, -11, -10], [-38, 10, 24, 18], [-10, 18, 2, -6], [3, 8, -2, -19], [32, -2, -6, 10], [6, -5, -5, -20], [14, 32, 24, 24], [46, -34, -20, -22], [64, -28, -8, 6], [68, -10, -8, 12], [-23, 0, 0, 0], [-51, 11, 0, 3], [43, 8, 28, 16], [-33, 19, -13, 61], [-25, -9, -29, 4], [34, 2, 18, -62], [-31, 35, 23, -26], [-116, 20, 2, -8], [-35, -19, 9, 12], [-122, 23, 30, 10], [-82, -54, 6, -6], [194, -36, -42, -2], [-212, -12, -48, -84], [-144, 15, 17, 50], [46, 30, -54, 10], [174, -48, 16, -66], [-85, -13, 11, -32], [22, 14, 46, 94], [-49, 21, -7, -18], [210, -26, -16, 66], [-24, 70, 14, 28], [194, 52, -14, 18], [36, 40, 48, 52], [-23, 0, 0, -23], [-119, -71, 13, 36], [105, 55, -25, -23], [365, -92, 8, 32], [103, -20, 72, 15], [-116, 32, 56, -2], [558, -108, -105, -168], [-118, 14, -26, -120], [181, -41, -115, -57], [-176, -120, -108, -40], [-560, 124, 2, 92], [270, 158, 70, 72], [-519, 101, 109, 35], [-304, 36, 60, 28], [-170, -118, -12, -62], [206, 14, -26, 36], [95, -27, 31, -43], [-248, 20, -52, 44], [-189, -64, 93, 7], [374, -134, -66, -78], [-136, 24, 90, -4], [110, 92, 84, 110], [158, -20, -80, 114], [-23, -23, -23, 0], [-1052, 204, -12, 4], [33, -143, -111, 68], [358, -93, -7, -132], [281, 127, -1, -66], [416, -84, -266, -68], [355, 35, 55, 72], [-828, -42, 52, 244], [84, 132, 208, 36], [-543, 107, 121, 35], [-214, -98, -50, -132], [632, 36, 142, -52], [-203, -156, -24, -108], [-269, 47, -13, -23], [96, -146, 6, -22], [662, 10, -106, -26], [60, 28, -96, 44], [200, -70, -70, -164], [517, 133, -71, 20], [-98, 12, -80, -22], [604, 82, 82, 160], [432, -108, 48, -112], [-116, 0, 56, -350], [-138, 69, 46, 46], [-19, -167, -39, 30], [355, -95, 51, -143], [-484, 540, 36, 68], [284, -44, -109, 70], [388, -38, 150, 282], [833, -88, 60, 369], [-340, -94, -46, -48], [-386, -37, 54, 22]]}