# Stored data for newform 1728.4.c.a, downloaded from the LMFDB on 05 September 2025.
{"Nk2": 27648, "analytic_conductor": 101.95530048991978, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 12, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 2, "char_parity": 1, "char_values": [1728, 2, [703, 325, 1217], [1, 2, 1]], "cm_discs": [], "conrey_index": 1727, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[5, [432, 0, 1]], [7, [867, 0, 1]], [11, [36, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 137506064064, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 12, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "1728.4.c.a", "level": 1728, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "432.4.c.a", "nf_label": "2.0.3.1", "prim_orbit_index": 2, "qexp_display": "q-12\\beta q^{5}+17\\beta q^{7}-36 q^{11}-19 q^{13}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "3.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1728.4.c", "trace_display": [0, 0, 0, 0], "trace_hash": 374465060860945075, "trace_moments": [{"__RealLiteral__": 0, "data": "0.023", "prec": 17}, {"__RealLiteral__": 0, "data": "2.027", "prec": 17}, {"__RealLiteral__": 0, "data": "0.138", "prec": 17}, {"__RealLiteral__": 0, "data": "16.093", "prec": 20}, {"__RealLiteral__": 0, "data": "1.427", "prec": 17}, {"__RealLiteral__": 0, "data": "157.251", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "traces": [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, -38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 216, 0, -614, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1224, 0, 218, 0, 0, 0, 0, 0, 0, 0, 0, 0, 936, 0, -1048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 290, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1152, 0, -1618, 0, 0, 0, 0, 0, 0, 0, 0, 0, 720, 0, 4320, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 1910, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3096, 0, -428, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6120, 0, -70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1584, 0, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 8640, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3888, 0, -3532, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4392, 0, -3672, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2304, 0, -4430, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9144, 0, -1874, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12240, 0, -15552, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19440, 0, 5508, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6624, 0, 2020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5472, 0, 6014, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10224, 0, -7776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6048, 0, -5184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22104, 0, -5468, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22032, 0, -11774, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4104, 0, 27540, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17352, 0, -2666, 0, 0, 0, 0, 0, 0, 0, 0, 0, 360, 0, 11666, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13032, 0, 13862, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2592, 0, 19514, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16776, 0, 13712, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7344, 0, 362, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23328, 0, -44064, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20664, 0, 22676, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7848, 0, 13214, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17784, 0, -11414, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13176, 0, -9500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20304, 0, 11232, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23256, 0, -26284, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9000, 0, 18462, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4464, 0, -4142, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18216, 0, -43200, 0, 0, 0, 0, 0, 0, 0, 0, 0, -504, 0, 10368, 0, 0, 0, 0, 0, 0, 0, 0, 0, -79128, 0, -33696, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19440, 0, -1006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37728, 0, -5942, 0, 0, 0, 0, 0, 0, 0, 0, 0, 720, 0, 29274, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27216, 0, -57888, 0, 0, 0, 0, 0, 0, 0, 0, 0, -66312, 0, -20954, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1656, 0, -324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22032, 0, 14836, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17784, 0, -25054, 0, 0, 0, 0, 0, 0, 0, 0, 0, -15912, 0, 80498, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89424, 0, 19912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26928, 0, -2592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46800, 0, 30818, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10440, 0, -39386, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35712, 0, 16416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71352, 0, 77760, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14688, 0, -3206, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32688, 0, 112098, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97200, 0, -76172, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36072, 0, -89856, 0, 0, 0, 0, 0, 0, 0, 0, 0, -59544, 0, 81322, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1368, 0, -10082, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1296, 0, -41472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82008, 0, -5510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58248, 0, 132192, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11592, 0, -1620, 0, 0, 0, 0, 0, 0, 0, 0, 0, 87912, 0, 34450, 0, 0, 0, 0, 0, 0, 0, 0, 0, -45360, 0, -37622, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23544, 0, -71638, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9864, 0, -74304, 0, 0, 0, 0, 0, 0, 0, 0, 0, -222768, 0, 71642, 0, 0, 0, 0, 0, 0, 0, 0, 0, -53712, 0, -126684, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38880, 0, 25920, 0, 0, 0, 0, 0, 0, 0, 0, 0, -65808, 0, -25920, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21888, 0, -66926, 0, 0, 0, 0, 0, 0, 0, 0, 0, -155520, 0, -23978, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7560, 0, 30742, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23256, 0, 42086, 0, 0, 0, 0, 0, 0, 0, 0, 0, -66024, 0, -101082, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30168, 0, -76896, 0, 0, 0, 0, 0, 0, 0, 0, 0, -105048, 0, -6844, 0, 0, 0, 0, 0, 0, 0, 0, 0, -432, 0, -50650, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2448, 0, 110516, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54792, 0, -25306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127296, 0, 2592, 0, 0, 0, 0, 0, 0, 0, 0, 0, 94680, 0, 84354, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68760, 0, 52340, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13680, 0, 101088, 0, 0, 0, 0, 0, 0, 0, 0, 0, -67248, 0, -67964, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68544, 0, -82080, 0, 0, 0, 0, 0, 0, 0, 0, 0, -66096, 0, -93854, 0, 0, 0, 0, 0, 0, 0, 0, 0, -113184, 0, -32362, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65160, 0, 16422, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14760, 0, 99470, 0, 0, 0, 0, 0, 0, 0, 0, 0, 115920, 0, 34560, 0, 0, 0, 0, 0, 0, 0, 0, 0, -287352, 0, 111456, 0, 0, 0, 0, 0, 0, 0, 0, 0, -51192, 0, 155520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15408, 0, 117574, 0, 0, 0, 0, 0, 0, 0, 0, 0, 105264, 0, -95006, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127584, 0, 321736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1368, 0, -81038, 0, 0, 0, 0, 0, 0, 0, 0, 0, 194400, 0, -27898, 0, 0, 0, 0, 0, 0, 0, 0, 0, -128160, 0, -36290, 0, 0, 0, 0, 0, 0, 0, 0, 0, -69984, 0, -1086, 0, 0, 0, 0, 0, 0, 0, 0, 0, 161352, 0, -281664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 133416, 0, -94610, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96408, 0, 220320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113472, 0, 74446, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98352, 0, -87480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103320, 0, -83808, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132120, 0, 7776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12384, 0, -77544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 108936, 0, -70238, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58824, 0, 148818, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31320, 0, 53568, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104976, 0, 8132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 106200, 0, 150194, 0, 0, 0, 0, 0, 0, 0, 0, 0, -45144, 0, -57024, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18792, 0, -88598, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3672, 0, -146016, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22104, 0, -134130, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18936, 0, -189610, 0, 0, 0, 0, 0, 0, 0, 0, 0, -149328, 0, -1722, 0, 0, 0, 0, 0, 0, 0, 0, 0, -183600, 0, -56160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48096, 0, -89030, 0, 0, 0, 0, 0, 0, 0, 0, 0, -283824, 0, 51840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 116280, 0, -79270, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67176, 0, 93636, 0, 0, 0, 0, 0, 0, 0, 0, 0, -43344, 0, 1330, 0, 0, 0, 0, 0, 0, 0, 0, 0, -105552, 0, -433728, 0, 0, 0, 0, 0, 0, 0, 0, 0, -311040, 0, 15412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144648, 0, -193354, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12168, 0, 123010, 0, 0, 0, 0, 0, 0, 0, 0, 0, -48960, 0, 124416, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23328, 0, 572832, 0, 0, 0, 0, 0, 0, 0, 0, 0, -327816, 0, 121396, 0, 0, 0, 0, 0, 0, 0, 0, 0, -164808, 0, 201706, 0, 0, 0, 0, 0, 0, 0, 0, 0, -174744, 0, -142094, 0, 0, 0, 0, 0, 0, 0, 0, 0, 936, 0, -22462, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30096, 0, 139968, 0, 0, 0, 0, 0, 0, 0, 0, 0, -221544, 0, -51840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127152, 0, -1938, 0, 0, 0, 0, 0, 0, 0, 0, 0, 102024, 0, -256894, 0, 0, 0, 0, 0, 0, 0, 0, 0, 395640, 0, -72076, 0, 0, 0, 0, 0, 0, 0, 0, 0, -349920, 0, 362880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -353664, 0, -225148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197208, 0, 71348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 399024, 0, 32404, 0, 0, 0, 0, 0, 0, 0, 0, 0, -229680, 0, -114232, 0, 0, 0, 0, 0, 0, 0, 0, 0, -102744, 0, 496726, 0, 0, 0, 0, 0, 0, 0, 0, 0, 366696, 0, 158112, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144432, 0, -278386, 0, 0, 0, 0, 0, 0, 0, 0, 0, 132192, 0, -30598, 0, 0, 0, 0, 0, 0, 0, 0, 0, 161640, 0, 249374, 0, 0, 0, 0, 0, 0, 0, 0, 0, 118728, 0, -164160, 0, 0, 0, 0, 0, 0, 0, 0, 0, -443304, 0, 187170, 0, 0, 0, 0, 0, 0, 0, 0, 0, -246672, 0, 77760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 289440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137520, 0, -20236, 0, 0, 0, 0, 0, 0, 0, 0, 0, 130320, 0, -230688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 466560, 0, -6594, 0, 0, 0, 0, 0, 0, 0, 0, 0, -75888, 0, 82944, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33696, 0, -148716, 0, 0, 0, 0, 0, 0, 0, 0, 0, 159480, 0, -28010, 0, 0, 0, 0, 0, 0, 0], "weight": 4, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [0, 0], [0, 0], [0, 0], [0, -12], [0, 0], [0, 17], [0, 0], [0, 0], [0, 0], [-36, 0], [0, 0], [-19, 0], [0, 0], [0, 0], [0, 0], [0, 60], [0, 0], [0, -1], [0, 0], [0, 0], [0, 0], [108, 0], [0, 0], [-307, 0], [0, 0], [0, 0], [0, 0], [0, 120], [0, 0], [0, -54], [0, 0], [0, 0], [0, 0], [612, 0], [0, 0], [109, 0], [0, 0], [0, 0], [0, 0], [0, -216], [0, 0], [0, -270], [0, 0], [0, 0], [0, 0], [468, 0], [0, 0], [-524, 0], [0, 0], [0, 0], [0, 0], [0, -72], [0, 0], [0, 432], [0, 0], [0, 0], [0, 0], [36, 0], [0, 0], [145, 0], [0, 0], [0, 0], [0, 0], [0, 228], [0, 0], [0, -181], [0, 0], [0, 0], [0, 0], [576, 0], [0, 0], [-809, 0], [0, 0], [0, 0], [0, 0], [0, -612], [0, 0], [0, -287], [0, 0], [0, 0], [0, 0], [360, 0], [0, 0], [2160, 0], [0, 0], [0, 0], [0, 0], [0, 156], [0, 0], [0, -323], [0, 0], [0, 0], [0, 0], [-36, 0], [0, 0], [955, 0], [0, 0], [0, 0], [0, 0]]}