# Stored data for newform 4356.3.f.h, downloaded from the LMFDB on 16 September 2025.
{"Nk2": 39204, "analytic_conductor": 118.69240315534533, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 11, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 6, "char_orbit_label": "f", "char_order": 2, "char_parity": -1, "char_values": [4356, 2, [2179, 1937, 1333], [2, 2, 1]], "cm_discs": [], "conrey_index": 1693, "dim": 8, "field_disc": 1007567768715264, "field_disc_factorization": [[2, 16], [3, 4], [23, 2], [599, 2]], "field_poly": [902232, -56448, -106140, 5796, 5617, -84, -122, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[5, [792, -84, -59, 4, 1]], [7, [36, 0, 203484, 0, 11893, 0, 208, 0, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525541039313156, "hecke_ring_generator_nbound": 13, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 11, 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": "4356.3.f.h", "level": 4356, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 3, 11], "level_radical": 66, "minimal_twist": "1452.3.f.c", "prim_orbit_index": 2, "qexp_display": "q+(-1-\\beta _{3})q^{5}+(\\beta _{2}-3\\beta _{4}-\\beta _{6})q^{7}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "4356.3.f", "trace_display": [0, 0, -8, 0], "trace_hash": 1288273558173662815, "trace_moments": [{"__RealLiteral__": 0, "data": "0.025", "prec": 17}, {"__RealLiteral__": 0, "data": "7.262", "prec": 17}, {"__RealLiteral__": 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