# Stored data for newform 42.12.e.d, downloaded from the LMFDB on 17 September 2026.
{"Nk2": 6048, "analytic_conductor": 32.27041358350273, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 7, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [42, 3, [29, 31], [3, 2]], "cm_discs": [], "conrey_index": 25, "dim": 8, "field_disc": 13890808674581993069976797093236890000, "field_disc_factorization": [[2, 4], [3, 4], [5, 4], [83, 2], [1021, 2], [2539, 2], [19246631, 2]], "field_poly": [825509675429896900, 20250219160910620, 377283443578066, 2926931386118, 18152831051, 44838722, 131491, -2, 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, [572709007392976988192990250000, 475702305839835662956950000, 298712016882146605297500, 82233088098744307500, 17880676262704125, 1076271246300, 129418525, 1420, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511073961345066, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 813189888, "hecke_ring_index_factorization": [[2, 8], [3, 3], [7, 6]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 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": "42.12.e.d", "level": 42, "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, 7], "level_radical": 42, "minimal_twist": "42.12.e.d", "prim_orbit_index": 3, "qexp_display": "q+2^{5}\\beta _{1}q^{2}+(3^{5}-3^{5}\\beta _{1})q^{3}+(-2^{10}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "11.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": 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