# Stored data for newform 78.2.i.a, downloaded from the LMFDB on 16 April 2026.
{"Nk2": 312, "analytic_conductor": 0.622833135765987, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 9, "char_orbit_label": "i", "char_order": 6, "char_parity": 1, "char_values": [78, 6, [53, 67], [6, 1]], "cm_discs": [], "conrey_index": 43, "dim": 4, "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 12, "has_non_self_twist": 1, "hecke_cutters": [[5, [1, 0, 14, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 549789368398, "hecke_ring_generator_nbound": 2, "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, 13, 5, 1, 6, 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": true, "label": "78.2.i.a", "level": 78, "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": true, "level_primes": [2, 3, 13], "level_radical": 78, "minimal_twist": "78.2.i.a", "nf_label": "4.0.144.1", "prim_orbit_index": 5, "qexp_display": "q+\\zeta_{12}q^{2}+(-1+\\zeta_{12}^{2})q^{3}+\\zeta_{12}^{2}q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "78.2.i", "trace_display": [0, -2, 0, 6], "trace_hash": 161812522638456157, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.996", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "63.832", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", 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