# Stored data for newform 144.4.a.d, downloaded from the LMFDB on 25 April 2024.
{"label": "144.4.a.d", "space_label": "144.4.a", "level": 144, "weight": 4, "hecke_orbit": 4, "hecke_orbit_code": 13510798949220496, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 1329435628791085473, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[5, [0, 1]]], "qexp_display": "q-20q^{7}-70q^{13}-56q^{19}-5^{3}q^{25}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 2304, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 8.496275040826648, "hecke_ring_index": 1, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [144, 1, [127, 37, 65], [1, 1, 1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [1], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.966", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.861", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.434", "prec": 17}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "3.2.1.d1", "atkin_lehner_eigenvals": [[2, -1], [3, 1]], "trace_display": [0, 0, 0, -20], "traces": [0, 1, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, -56, 0, 0, 0, 0, 0, -125, 0, 0, 0, 0, 0, -308, 0, 0, 0, 0, 0, 110, 0, 0, 0, 0, 0, 520, 0, 0, 0, 0, 0, 57, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 182, 0, 0, 0, 0, 0, 880, 0, 0, 0, 0, 0, 1190, 0, 0, 0, 0, 0, -884, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1400, 0, 0, 0, 0, 0, -1330, 0, 0, 0, 0, 0, -1820, 0, 0, 0, 0, 0, -646, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1331, 0, 0, 0, 0, 0, -380, 0, 0, 0, 0, 0, 1120, 0, 0, 0, 0, 0, -2576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1748, 0, 0, 0, 0, 0, -3850, 0, 0, 0, 0, 0, 3400, 0, 0, 0, 0, 0, 2703, 0, 0, 0, 0, 0, 2500, 0, 0, 0, 0, 0, 3458, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1150, 0, 0, 0, 0, 0, 5236, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6032, 0, 0, 0, 0, 0, 6160, 0, 0, 0, 0, 0, 3220, 0, 0, 0, 0, 0, 4466, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7378, 0, 0, 0, 0, 0, 3920, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -812, 0, 0, 0, 0, 0, -4030, 0, 0, 0, 0, 0, -5600, 0, 0, 0, 0, 0, -4913, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10400, 0, 0, 0, 0, 0, -10640, 0, 0, 0, 0, 0, 10010, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8750, 0, 0, 0, 0, 0, -992, 0, 0, 0, 0, 0, -4930, 0, 0, 0, 0, 0, 5720, 0, 0, 0, 0, 0, -11914, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3723, 0, 0, 0, 0, 0, -4340, 0, 0, 0, 0, 0, 12350, 0, 0, 0, 0, 0, 8584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1190, 0, 0, 0, 0, 0, 21560, 0, 0, 0, 0, 0, 8246, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17138, 0, 0, 0, 0, 0, -3640, 0, 0, 0, 0, 0, -2590, 0, 0, 0, 0, 0, -14924, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12710, 0, 0, 0, 0, 0, 19780, 0, 0, 0, 0, 0, -17600, 0, 0, 0, 0, 0, 7000, 0, 0, 0, 0, 0, -7700, 0, 0, 0, 0, 0, -20900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23800, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12040, 0, 0, 0, 0, 0, -12167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22678, 0, 0, 0, 0, 0, -1640, 0, 0, 0, 0, 0, 17680, 0, 0, 0, 0, 0, -36400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -23312, 0, 0, 0, 0, 0, -17710, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -29302, 0, 0, 0, 0, 0, 28420, 0, 0, 0, 0, 0, 17390, 0, 0, 0, 0, 0, 26656, 0, 0, 0, 0, 0, 15625, 0, 0, 0, 0, 0, -1892, 0, 0, 0, 0, 0, -3990, 0, 0, 0, 0, 0, -13160, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -20482, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24050, 0, 0, 0, 0, 0, 26600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16072, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6160, 0, 0, 0, 0, 0, 36146, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36400, 0, 0, 0, 0, 0, 10780, 0, 0, 0, 0, 0, 15050, 0, 0, 0, 0, 0, -31376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23452, 0, 0, 0, 0, 0, -41470, 0, 0, 0, 0, 0, 12920, 0, 0, 0, 0, 0, -4606, 0, 0, 0, 0, 0, 38500, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -43400, 0, 0, 0, 0, 0, -12740, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -39368, 0, 0, 0, 0, 0, -29120, 0, 0, 0, 0, 0, 12220, 0, 0, 0, 0, 0, 17066, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24389, 0, 0, 0, 0, 0, 26620, 0, 0, 0, 0, 0, -46690, 0, 0, 0, 0, 0, -31304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -61600, 0, 0, 0, 0, 0, 50150, 0, 0, 0, 0, 0, 20680, 0, 0, 0, 0, 0, 7600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -44840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2756, 0, 0, 0, 0, 0, -13750, 0, 0, 0, 0, 0, -3192, 0, 0, 0, 0, 0, -55510, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -83300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65073, 0, 0, 0, 0, 0, 50020, 0, 0, 0, 0, 0, 51520, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45628, 0, 0, 0, 0, 0, 28910, 0, 0, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "9.4.a.a", "char_is_minimal": false, "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], [1], [0], [0], [0], [0], [0], [-20], [0], [0], [0], [0], [0], [-70], [0], [0], [0], [0], [0], [-56], [0], [0], [0], [0], [0], [-125], [0], [0], [0], [0], [0], [-308], [0], [0], [0], [0], [0], [110], [0], [0], [0], [0], [0], [520], [0], [0], [0], [0], [0], [57], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [182], [0], [0], [0], [0], [0], [880], [0], [0], [0], [0], [0], [1190], [0], [0], [0], [0], [0], [-884], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [0], [1400], [0], [0], [0], [0], [0], [-1330], [0], [0], [0]]}