# Stored data for newform 1368.4.a.d, downloaded from the LMFDB on 17 March 2025.
{"Nk2": 21888, "analytic_conductor": 80.71461288785316, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1], [19, 1]], "atkin_lehner_string": "--+", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [1368, 1, [343, 685, 1217, 1009], [1, 1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 3, "field_disc": 7057, "field_disc_factorization": [[7057, 1]], "field_poly": [32, -22, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[5, [-608, -244, 7, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510798949221720, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "1368.4.a.d", "level": 1368, "level_is_powerful": false, "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, 19], "level_radical": 114, "minimal_twist": "152.4.a.c", "nf_label": "3.3.7057.1", "prim_orbit_index": 1, "qexp_display": "q+(-2-2\\beta _{1}-\\beta _{2})q^{5}+(2+\\beta _{1}+\\beta _{2})q^{7}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1368.4.a", "trace_display": [0, 0, -7, 7], "trace_hash": 740654562187612561, "trace_moments": [{"__RealLiteral__": 0, "data": "0.004", "prec": 17}, {"__RealLiteral__": 0, "data": "2.850", "prec": 17}, {"__RealLiteral__": 0, 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