# Stored data for newform 1344.4.c.d, downloaded from the LMFDB on 18 April 2024.
{"label": "1344.4.c.d", "space_label": "1344.4.c", "level": 1344, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510936388175168, "dim": 6, "is_polredabs": true, "trace_hash": 511578628932982711, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [2085136, 0, 57348, 0, 444, 0, 1]], [23, [470448, -21186, 30, 1]]], "qexp_display": "q-3\\beta _{1}q^{3}+(\\beta _{1}-\\beta _{3})q^{5}+7q^{7}-9q^{9}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "c", "char_is_real": true, "Nk2": 21504, "analytic_conductor": 79.29856704771538, "hecke_ring_index": 16, "level_radical": 42, "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": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [1344, 2, [127, 1093, 449, 577], [2, 1, 2, 2]], "hecke_ring_generator_nbound": 13, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [673], "field_disc": -9778929528384, "field_disc_factorization": [[-1, 1], [2, 6], [3, 2], [29, 2], [4493, 2]], "field_poly": [127008, 54936, 11881, 722, 2, -2, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "5.787", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "173.550", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7362.229", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 42], "traces": [0, 6, 0, 0, 0, 0, 0, 42, 0, -54, 0, 0, 0, 0, 0, 24, 0, -16, 0, 0, 0, 0, 0, -60, 0, -138, 0, 0, 0, 0, 0, -552, 0, 168, 0, 0, 0, 0, 0, -36, 0, -272, 0, 0, 0, 0, 0, -1576, 0, 294, 0, 0, 0, 0, 0, -1632, 0, 432, 0, 0, 0, 0, 0, -378, 0, -664, 0, 0, 0, 0, 0, -2548, 0, 444, 0, 0, 0, 0, 0, -3528, 0, 486, 0, 0, 0, 0, 0, -336, 0, 16, 0, 0, 0, 0, 0, -4776, 0, 1548, 0, 0, 0, 0, 0, -2256, 0, 168, 0, 0, 0, 0, 0, -720, 0, 2156, 0, 0, 0, 0, 0, -112, 0, -4806, 0, 0, 0, 0, 0, -2280, 0, 900, 0, 0, 0, 0, 0, -216, 0, -4956, 0, 0, 0, 0, 0, -10600, 0, 1224, 0, 0, 0, 0, 0, -2064, 0, 144, 0, 0, 0, 0, 0, -1224, 0, -420, 0, 0, 0, 0, 0, -7656, 0, 3126, 0, 0, 0, 0, 0, -966, 0, -3000, 0, 0, 0, 0, 0, 2988, 0, 1000, 0, 0, 0, 0, 0, -15572, 0, -4764, 0, 0, 0, 0, 0, -5736, 0, 1908, 0, 0, 0, 0, 0, 540, 0, 24, 0, 0, 0, 0, 0, -9568, 0, -3864, 0, 0, 0, 0, 0, -2904, 0, 1242, 0, 0, 0, 0, 0, 1176, 0, 2988, 0, 0, 0, 0, 0, -23188, 0, 6348, 0, 0, 0, 0, 0, 6240, 0, -4248, 0, 0, 0, 0, 0, 4608, 0, 10512, 0, 0, 0, 0, 0, -10100, 0, 2760, 0, 0, 0, 0, 0, -14256, 0, -252, 0, 0, 0, 0, 0, 4968, 0, 23420, 0, 0, 0, 0, 0, -1904, 0, -17166, 0, 0, 0, 0, 0, 4272, 0, -1512, 0, 0, 0, 0, 0, -408, 0, -9992, 0, 0, 0, 0, 0, -15064, 0, 9708, 0, 0, 0, 0, 0, -6552, 0, -8712, 0, 0, 0, 0, 0, 16056, 0, -11032, 0, 0, 0, 0, 0, -37696, 0, 20004, 0, 0, 0, 0, 0, 2058, 0, -2016, 0, 0, 0, 0, 0, 324, 0, -6552, 0, 0, 0, 0, 0, -24396, 0, 4242, 0, 0, 0, 0, 0, -13560, 0, 2448, 0, 0, 0, 0, 0, 16200, 0, -8896, 0, 0, 0, 0, 0, -42384, 0, -11424, 0, 0, 0, 0, 0, 27624, 0, 15480, 0, 0, 0, 0, 0, 3024, 0, -26948, 0, 0, 0, 0, 0, 12952, 0, -25932, 0, 0, 0, 0, 0, 2064, 0, 288, 0, 0, 0, 0, 0, 14184, 0, -1000, 0, 0, 0, 0, 0, -52484, 0, 1332, 0, 0, 0, 0, 0, 55104, 0, -2646, 0, 0, 0, 0, 0, 14664, 0, 31636, 0, 0, 0, 0, 0, -4648, 0, -8892, 0, 0, 0, 0, 0, 8760, 0, -8328, 0, 0, 0, 0, 0, 36036, 0, -64, 0, 0, 0, 0, 0, -33944, 0, 9552, 0, 0, 0, 0, 0, 69408, 0, -1476, 0, 0, 0, 0, 0, 14688, 0, -17836, 0, 0, 0, 0, 0, 29904, 0, 58392, 0, 0, 0, 0, 0, 3108, 0, -3888, 0, 0, 0, 0, 0, 28080, 0, 14208, 0, 0, 0, 0, 0, -30664, 0, 13542, 0, 0, 0, 0, 0, 109920, 0, 6096, 0, 0, 0, 0, 0, 30996, 0, -37360, 0, 0, 0, 0, 0, 17808, 0, -24696, 0, 0, 0, 0, 0, 12504, 0, 36360, 0, 0, 0, 0, 0, 3402, 0, -23420, 0, 0, 0, 0, 0, -30228, 0, 39276, 0, 0, 0, 0, 0, 112296, 0, 5976, 0, 0, 0, 0, 0, 14544, 0, 25328, 0, 0, 0, 0, 0, 62892, 0, -16764, 0, 0, 0, 0, 0, 46536, 0, -2352, 0, 0, 0, 0, 0, 49248, 0, 55900, 0, 0, 0, 0, 0, 112, 0, -74370, 0, 0, 0, 0, 0, 114360, 0, -9540, 0, 0, 0, 0, 0, 22932, 0, -10516, 0, 0, 0, 0, 0, 55656, 0, -42480, 0, 0, 0, 0, 0, 2112, 0, -3996, 0, 0, 0, 0, 0, 32232, 0, -33432, 0, 0, 0, 0, 0, -72200, 0, 117612, 0, 0, 0, 0, 0, 10836, 0, 6408, 0, 0, 0, 0, 0, 41076, 0, 105456, 0, 0, 0, 0, 0, 55936, 0, -17016, 0, 0, 0, 0, 0, -192, 0, -27360, 0, 0, 0, 0, 0, 31752, 0, -78648, 0, 0, 0, 0, 0, -50240, 0, -15792, 0, 0, 0, 0, 0, 144288, 0, -4374, 0, 0, 0, 0, 0, 1176, 0, -71344, 0, 0, 0, 0, 0, -43180, 0, 6312, 0, 0, 0, 0, 0, -17280, 0, 10584, 0, 0, 0, 0, 0, 80712, 0, -29496, 0, 0, 0, 0, 0, -56752, 0, -93132, 0, 0, 0, 0, 0, 30552, 0, -5040, 0, 0, 0, 0, 0, 3024, 0, 95912, 0, 0, 0, 0, 0, 15092, 0, -52248, 0, 0, 0, 0, 0, -8256, 0, -144, 0, 0, 0, 0, 0, -13680, 0, 26508, 0, 0, 0, 0, 0, -108832, 0, -74112, 0, 0, 0, 0, 0, 64440, 0, -7968, 0, 0, 0, 0, 0, 35640, 0, -784, 0, 0, 0, 0, 0, -17736, 0, 133422, 0, 0, 0, 0, 0, -33642, 0, -64584, 0, 0, 0, 0, 0, 42984, 0, 131912, 0, 0, 0, 0, 0, -123612, 0, 12744, 0, 0, 0, 0, 0, -27288, 0, -13932, 0, 0, 0, 0, 0, -33888, 0, -30432, 0, 0, 0, 0, 0, 67224, 0, -15960, 0, 0, 0, 0, 0, -65856, 0, 84528, 0, 0, 0, 0, 0, 6300, 0, -18840, 0, 0, 0, 0, 0, -163844, 0, 89568, 0, 0, 0, 0, 0, 52176, 0, 11520, 0, 0, 0, 0, 0, 20304, 0, -146912, 0, 0, 0, 0, 0, -113480, 0, -54108, 0, 0, 0, 0, 0, -151176, 0, -1512, 0, 0, 0, 0, 0, -55848, 0, 185916, 0, 0, 0, 0, 0, -34692, 0, -37674, 0, 0, 0, 0, 0, 9576, 0, -5256, 0, 0, 0, 0, 0, -17028, 0, -23316, 0, 0, 0, 0, 0, -13712, 0, -147384, 0, 0, 0, 0, 0, -148176, 0, 25092, 0, 0, 0, 0, 0, 6480, 0, -74200, 0, 0, 0, 0, 0, -83184, 0, 181668, 0, 0, 0, 0, 0, 8568, 0, -19404, 0, 0, 0, 0, 0, -111864, 0, 141448, 0, 0, 0, 0, 0, -69300, 0, 192252, 0, 0, 0, 0, 0, -66000, 0, -92952, 0, 0, 0, 0, 0, 51876, 0, -148272, 0, 0, 0, 0, 0, -163600, 0, -14448, 0, 0, 0, 0, 0, -119304, 0, 61200, 0, 0, 0, 0, 0, 1008, 0, 4192, 0, 0, 0, 0, 0, 73344, 0, 20496, 0, 0, 0, 0, 0, -37752, 0, 43254, 0, 0, 0, 0, 0, -80208, 0, -195424, 0, 0, 0, 0, 0, -98484, 0, -99120, 0, 0, 0, 0, 0, 47568, 0, -8568, 0, 0, 0, 0, 0, -4608, 0, 96384, 0, 0, 0, 0, 0, -2940, 0, -27684, 0, 0, 0, 0, 0, -223056, 0, 11988, 0, 0, 0, 0, 0, 20520, 0, 60808, 0, 0, 0, 0, 0, -81776, 0, -265452, 0, 0, 0, 0, 0, -21648, 0, -8100, 0, 0, 0, 0, 0, -118944, 0, -53592, 0, 0, 0, 0, 0, -424, 0, 262872, 0, 0, 0, 0, 0, 21882, 0, -57408, 0, 0, 0, 0, 0, 8820, 0, 164112, 0, 0, 0, 0, 0, -84592, 0, -1548, 0, 0, 0, 0, 0, 1512, 0, -86976, 0, 0, 0, 0, 0, 1944, 0, -162600, 0, 0, 0, 0, 0, -57672, 0, -6762, 0, 0, 0, 0, 0, -116160, 0, 44604, 0, 0, 0, 0, 0, -21000, 0, 83376, 0, 0, 0, 0, 0, 35840, 0, 112260, 0, 0, 0, 0, 0, -108192, 0, 141144, 0, 0, 0, 0, 0, -87768, 0, -292296, 0, 0, 0, 0, 0, 128584, 0, -207792, 0, 0, 0, 0, 0, -105360, 0, 20916, 0, 0, 0, 0, 0, 95400, 0, 36468, 0, 0, 0, 0, 0, 7000, 0, -20844, 0, 0, 0, 0, 0, -41472, 0, -11016, 0, 0, 0, 0, 0, -99144, 0, -12184, 0, 0, 0, 0, 0, 80376, 0, -139140, 0, 0, 0, 0, 0, 32688, 0, -10656, 0, 0, 0, 0, 0, 24480, 0, -109004, 0, 0, 0, 0, 0, 2800, 0, 337272, 0, 0, 0, 0, 0, -33348, 0, -60840, 0, 0, 0, 0, 0, 18576, 0, 320488, 0, 0, 0, 0, 0, 196556, 0, 284286, 0, 0, 0, 0, 0, -100992, 0, -1296, 0, 0, 0, 0, 0, -210120, 0, -337448, 0, 0, 0, 0, 0, 123912, 0, -40152, 0, 0, 0, 0, 0, 80040, 0, 76152, 0, 0, 0, 0, 0, 13356, 0, 131460, 0, 0, 0, 0, 0, 118264, 0, 6288, 0, 0, 0, 0, 0, -196032, 0, 90432, 0, 0, 0, 0, 0, 11016, 0, -157704, 0, 0, 0, 0, 0, 137860, 0, -127248, 0, 0, 0, 0, 0, -58536, 0, 3780, 0, 0, 0, 0, 0, -159360, 0, 161312, 0, 0, 0, 0, 0, 168, 0, -123960, 0, 0, 0, 0, 0, 104688, 0, -136872, 0, 0, 0, 0, 0, 23688, 0, 220612, 0, 0, 0, 0, 0, 195312, 0, -336516, 0, 0, 0, 0, 0, -276288, 0, -59076, 0, 0, 0, 0, 0, 68904, 0, -66976, 0, 0, 0, 0, 0, 16336, 0, 214008, 0, 0, 0, 0, 0, -27048, 0, -28134, 0, 0, 0, 0, 0, -189288, 0, 440800, 0, 0, 0, 0, 0, 168712, 0, 94224, 0, 0, 0, 0, 0, -113760, 0, -88440, 0, 0, 0, 0, 0, -81504, 0, -59648, 0, 0, 0, 0, 0, 129640, 0, -20328, 0, 0, 0, 0, 0, 3984, 0, 213768, 0, 0, 0, 0, 0, 8694, 0, -41136, 0, 0, 0, 0, 0, 132268, 0, 225672, 0, 0, 0, 0, 0, 96, 0, 27000, 0, 0, 0, 0, 0, -101928, 0, -169488, 0, 0, 0, 0, 0, 244884, 0, -377940, 0, 0, 0, 0, 0, 83616, 0, 8232, 0, 0, 0, 0, 0, -123336, 0, 10128, 0, 0, 0, 0, 0, 20916, 0, -133152, 0, 0, 0, 0, 0, -260472, 0, -59940, 0, 0, 0, 0, 0, -26892, 0, -64064, 0, 0, 0, 0, 0, 48096, 0, -289236, 0, 0, 0, 0, 0, 58296, 0, -9000, 0, 0, 0, 0, 0, -274632, 0, -162316, 0, 0, 0, 0, 0, 413208, 0, 157314, 0, 0, 0, 0, 0, 44436, 0, -96264, 0, 0, 0, 0, 0, 26784, 0, 397224, 0, 0, 0, 0, 0, -77760, 0, 481200, 0, 0, 0, 0, 0, -79296, 0, -168372, 0, 0, 0, 0, 0, 140148, 0, -323320, 0, 0, 0, 0, 0, 400232, 0, 43680, 0, 0, 0, 0, 0, -7968, 0, 42876, 0, 0, 0, 0, 0, -29736, 0, -40328, 0, 0, 0, 0, 0, 177640, 0, -239364, 0, 0, 0, 0, 0, 268848, 0, 79176, 0, 0, 0, 0, 0, 13824, 0, -18320, 0, 0, 0, 0, 0, 230468, 0, 140004, 0, 0, 0, 0, 0, -290568, 0, 32256, 0, 0, 0, 0, 0, 51624, 0, 266480, 0, 0, 0, 0, 0, 73584, 0, -149772, 0, 0, 0, 0, 0, 385824, 0, -17172, 0, 0, 0, 0, 0, -367248, 0, 102048, 0, 0, 0, 0, 0, 262384, 0, -286068, 0, 0, 0, 0, 0, 203256, 0, -6864, 0, 0, 0, 0, 0, -21672, 0, -70700, 0, 0, 0, 0, 0, 366848, 0, 328218, 0, 0, 0, 0, 0, 19320, 0, -114696, 0, 0, 0, 0, 0, -4860, 0, 404784, 0, 0, 0, 0, 0, 579804, 0, -281508, 0, 0, 0, 0, 0, -2880, 0, -216, 0, 0, 0, 0, 0, -30216, 0, -131856, 0, 0, 0, 0, 0, 50032, 0, -99792, 0, 0, 0, 0, 0, 52464, 0, 261456, 0, 0, 0, 0, 0, -1764, 0, 92204, 0, 0, 0, 0, 0, 364440, 0, -33024, 0, 0, 0, 0, 0, -62784, 0, 156744, 0, 0, 0, 0, 0, 86112, 0, -217904, 0, 0, 0, 0, 0, 57008, 0, -44616, 0, 0, 0, 0, 0, 219816, 0, 34776, 0, 0, 0, 0, 0, -191160, 0, -122592, 0, 0, 0, 0, 0, 163940, 0, -216600, 0, 0, 0, 0, 0, -13272, 0, -231432, 0, 0, 0, 0, 0, 99396, 0, -370088, 0, 0, 0, 0, 0, 265272, 0, 89148, 0, 0, 0, 0, 0, 65016, 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, 8, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "1344.4.c.a", "char_is_minimal": true, "conrey_index": 673, "id": null, "nf_label": 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, -3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0], [7, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 9, 0, -2, 0, -1], [0, 0, 0, 0, 0, 0], [0, -2, 0, -1, 0, -1], [0, 0, 0, 0, 0, 0], [3, 0, -3, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 0, -2, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 22, 0, -5, 0, 1], [0, 0, 0, 0, 0, 0], [0, -21, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-9, 0, 0, 0, -3, 0], [0, 0, 0, 0, 0, 0], [-25, 0, -5, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 27, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -18, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0], [-92, 0, 3, 0, 3, 0], [0, 0, 0, 0, 0, 0], [27, 0, -6, 0, -3, 0], [0, 0, 0, 0, 0, 0], [0, 7, 0, -7, 0, 0], [0, 0, 0, 0, 0, 0], [0, -40, 0, 1, 0, 1], [0, 0, 0, 0, 0, 0], [-6, 0, -3, 0, -3, 0], [0, 0, 0, 0, 0, 0], [-53, 0, -18, 0, 5, 0], [0, 0, 0, 0, 0, 0], [0, 46, 0, -10, 0, 2], [0, 0, 0, 0, 0, 0], [0, -9, 0, 9, 0, 0], [0, 0, 0, 0, 0, 0], [-260, 0, 8, 0, 0, 0], [0, 0, 0, 0, 0, 0], [49, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 9, 0, 6, 0, 3], [0, 0, 0, 0, 0, 0], [0, -70, 0, 5, 0, 11], [0, 0, 0, 0, 0, 0], [-272, 0, 11, 0, 11, 0], [0, 0, 0, 0, 0, 0], [66, 0, -15, 0, 3, 0], [0, 0, 0, 0, 0, 0], [0, -164, 0, 2, 0, -6], [0, 0, 0, 0, 0, 0], [0, 164, 0, -11, 0, -5], [0, 0, 0, 0, 0, 0], [-63, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-112, 0, 6, 0, 10, 0], [0, 0, 0, 0, 0, 0], [0, 92, 0, -42, 0, 0], [0, 0, 0, 0, 0, 0], [0, 27, 0, 0, 0, 9], [0, 0, 0, 0, 0, 0], [-435, 0, -26, 0, 5, 0], [0, 0, 0, 0, 0, 0], [88, 0, 28, 0, -14, 0], [0, 0, 0, 0, 0, 0], [0, 75, 0, 15, 0, -3], [0, 0, 0, 0, 0, 0], [0, 63, 0, -14, 0, -7], [0, 0, 0, 0, 0, 0], [-582, 0, 16, 0, -2, 0], [0, 0, 0, 0, 0, 0], [81, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, -238, 0, 2, 0, 8], [0, 0, 0, 0, 0, 0], [0, 260, 0, 1, 0, -11], [0, 0, 0, 0, 0, 0], [-54, 0, 3, 0, -3, 0], [0, 0, 0, 0, 0, 0], [5, 0, -14, 0, -21, 0], [0, 0, 0, 0, 0, 0], [0, -14, 0, -7, 0, -7], [0, 0, 0, 0, 0, 0], [0, 276, 0, -9, 0, -9], [0, 0, 0, 0, 0, 0], [-802, 0, -22, 0, -4, 0], [0, 0, 0, 0, 0, 0], [280, 0, 62, 0, -4, 0], [0, 0, 0, 0, 0, 0], [0, -81, 0, 18, 0, 9], [0, 0, 0, 0, 0, 0]]}