# Stored data for newform 735.4.a.z, downloaded from the LMFDB on 21 December 2025.
{"Nk2": 11760, "analytic_conductor": 43.36640385421935, "analytic_rank": 1, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[3, 1], [5, 1], [7, -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": [735, 1, [491, 442, 346], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 5, "field_disc": 256639554384, "field_disc_factorization": [[2, 4], [3, 1], [5346657383, 1]], "field_poly": [-84, 153, 22, -30, -2, 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": [[2, [-60, 104, 70, -28, -3, 1]], [11, [35201580, 4542452, 74940, -3788, -43, 1]], [13, [125988247, -14427235, -566590, -1074, 123, 1]]], "hecke_orbit": 26, "hecke_orbit_code": 112589990751371999, "hecke_ring_generator_nbound": 11, "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": true, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "735.4.a.z", "level": 735, "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": [3, 5, 7], "level_radical": 105, "minimal_twist": "105.4.i.d", "prim_orbit_index": 1, "qexp_display": "q+(1-\\beta _{1})q^{2}-3q^{3}+(5+\\beta _{2})q^{4}-5q^{5}+\\cdots", "related_objects": [], "relative_dim": 5, "rm_discs": [], "sato_tate_group": "3.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "735.4.a", "trace_display": [3, -15, -25, 0], "trace_hash": 445388812152433472, "trace_moments": [{"__RealLiteral__": 0, 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