# Stored data for newform 2008.1.c.b, downloaded from the LMFDB on 23 April 2024.
{"label": "2008.1.c.b", "space_label": "2008.1.c", "level": 2008, "weight": 1, "hecke_orbit": 2, "hecke_orbit_code": 4503737083103192, "dim": 3, "is_polredabs": true, "nf_label": "3.3.49.1", "trace_hash": 1745368109886232730, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [-1, -2, 1, 1]]], "qexp_display": "q+q^{2}+q^{4}-\\beta _{1}q^{7}+q^{8}+q^{9}+\\beta _{2}q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 2008, "char_orbit_label": "c", "char_is_real": true, "Nk2": 2008, "analytic_conductor": 1.0021225453670688, "hecke_ring_index": 1, "level_radical": 502, "projective_image": "D7", "projective_image_type": "Dn", "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 14, "artin_degree": 14, "artin_image": "14.1", "field_poly_is_real_cyclotomic": true, "artin_field_label": "7.1.8096384512.1", "projective_field_label": "7.1.8096384512.1", "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [2008, 2, [503, 1005, 257], [2, 1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 251], "conrey_indexes": [501], "field_disc": 49, "field_disc_factorization": [[7, 2]], "field_poly": [1, -2, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "-0.049", "prec": 20}, {"__RealLiteral__": 0, "data": "2.687", "prec": 17}, {"__RealLiteral__": 0, "data": "13.072", "prec": 20}, {"__RealLiteral__": 0, "data": "81.270", "prec": 20}, {"__RealLiteral__": 0, "data": "484.154", "prec": 24}, {"__RealLiteral__": 0, "data": "2906.500", "prec": 27}], "related_objects": ["ArtinRepresentation/2.2e3_251.7t2.1"], "self_twist_discs": [-2008], "cm_discs": [-2008], "rm_discs": [], "relative_dim": 3, "trace_display": [3, 0, 0, -1], "traces": [0, 3, 3, 0, 3, 0, 0, -1, 3, 3, 0, -1, 0, 0, -1, 0, 3, -1, 3, -1, 0, 0, -1, -1, 0, 3, 0, 0, -1, -1, 0, -1, 3, 0, -1, 0, 3, -1, -1, 0, 0, -1, 0, -1, -1, 0, -1, 0, 0, 2, 3, 0, 0, -1, 0, 0, -1, 0, -1, -1, 0, -1, -1, -1, 3, 0, 0, 0, -1, 0, 0, 0, 3, -1, -1, 0, -1, -2, 0, -1, 0, 3, -1, 0, 0, 0, -1, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 2, -1, 3, 0, 0, -1, 0, 0, -1, -1, 0, -1, 0, 0, -1, -1, 0, 0, -1, 0, -1, -2, 0, 2, -1, 0, -1, 0, -1, 0, 3, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 3, 0, -1, 0, -1, 0, 0, 0, -1, -1, -2, 0, 0, -1, -1, 0, 0, -2, 3, -1, -1, 0, 0, 0, 0, 3, 0, -1, -1, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 3, 0, 0, -2, 0, 0, -1, -1, 0, -2, 0, 0, -1, 0, -1, 0, 0, -2, -1, 0, 0, 0, 0, 0, -1, 3, -1, 0, 0, -1, 0, 0, -1, -1, 0, 0, -1, 0, -2, 0, 0, -1, 2, 0, -1, 0, 0, 0, -1, 0, 0, 3, -1, 5, 0, 0, 3, 0, 0, 5, 0, -1, 0, -1, 0, 0, -2, 0, 0, 6, 0, -1, -1, 0, 0, -1, 0, -1, -1, -1, 0, 0, 0, 6, 0, 0, 0, -2, 3, 2, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 5, 0, 0, -1, 0, -1, -1, -2, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, -2, 0, 0, -2, 5, 3, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 3, 0, 0, -2, -1, -2, -1, 0, 0, -1, 0, 6, -1, 0, -1, 0, 0, 0, -1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 0, -2, 0, 0, -2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -2, 2, 0, 0, 0, -1, -1, 0, 0, 3, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, -1, 5, -1, 0, 0, 0, -2, -1, 0, -1, 0, 0, -1, -1, 0, -2, -1, 0, 0, -1, 0, 0, -2, 0, -1, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -1, -1, 3, 5, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, -1, -1, 0, 0, 0, 0, -1, -2, 0, -1, -2, -1, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 5, 0, 0, -1, 0, 0, -1, 0, 0, 3, 6, -1, 0, 5, 0, 0, 0, 0, 5, 3, 0, 0, 0, 0, 0, 5, 0, 0, 0, -1, 0, 0, 0, -1, 5, 0, 2, 0, -1, -2, 0, 0, 0, 0, 0, 6, 4, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, -1, 5, 0, -2, -1, 0, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, 6, -1, 0, -1, 0, 0, 0, 0, -2, -1, 3, -1, 2, 0, 0, 0, 0, 5, -1, 0, -1, 0, 0, 5, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, -1, 0, 0, 0, -1, -1, -1, 0, -2, -1, 0, 0, 0, 0, -1, 5, 0, 3, 0, 0, -1, -2, 0, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 6, -2, 0, 5, 0, 3, -2, 0, 0, -1, -1, 0, 0, -1, -1, 0, -1, 0, -1, 0, 0, 0, 0, -1, -2, 0, 0, 0, 5, 0, 0, -1, 0, 3, 0, 0, 0, 0, 0, -2, 0, -1, 0, -2, 0, -1, 0, 0, 0, 0, -2, -1, 0, 0, -2, 6, 0, -1, 6, 0, -2, -1, 0, 0, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, 0, -1, -1, 0, -2, 2, 0, 0, -1, 0, 6, 0, 3, 0, -2, 0, -1, 0, 0, -1, 0, -1, 0, 0, 0, -2, -1, 0, 0, 0, 0, -2, -2, 0, -1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, -1, -2, 0, 0, -2, 0, 2, 0, 0, -1, 0, 0, 0, 5, -1, 0, -1, 0, 0, -1, 0, 0, 3, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, -1, 6, 0, 0, 0, -3, 0, 0, -2, 0, -1, -1, 0, 2, -1, 0, 0, 0, 0, -3, -1, 0, -1, -2, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, -2, -2, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 5, 3, -2, 5, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, -1, 0, 0, -3, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 5, -1, 0, -2, 0, 0, 0, -1, 0, -2, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, -1, 0, 0, -1, 2, 0, 0, 0, 0, 5, 0, 0, -1, 0, 0, -2, 0, -1, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -2, 3, 0, 6, -2, -1, -1, 0, 0, 5, 0, 0, 0, 0, -1, 0, 0, 0, 0, 5, 0, 3, -1, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 5, -2, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 6, -1, 0, 5, 0, 0, 0, 2, 0, 0, -1, -1, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -1, 6, 0, 4, 0, 0, 0, 0, 0, -1, 0, 0, -1, -1, 2, 0, -1, 0, 0, 0, 0, 0, -1, -1, -2, -1, 0, 5, 0, 0, 0, -2, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 4, 0, -1, 0, 0, 6, 5, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, -1, -1, 3, -1, -1, 0, 2, 0, 0, -2, 0, 0, 0, -1, 0, 0, 5, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, -2, 5, 0, 0, -1, 0, -1, -1, 0, -1, -1, 0, -2, 0, 0, 0, -1, 0, 0, 0, -2, 0, -2, 0, -1, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 5, 0, 0, 0, -1, -1, 2, -1, 0, -1, 0, 0, 6, -2, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, -2, -1, 0, 5, -2, 0, -1, 3, -1, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -2, 0, 0, 0, 5, 0, 0, 0, 3, 0, -2, 0, 0, -1, 0, -1, -1, 0, -1, 0, 0, 3, 0, 0, -1, 0, -1, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, -2, -1, -2, -2, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 0, -2, 0, 0, -1, -1, 2, 0, 0, -2, 0, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, -2, -2, -1, 0, 0, 0, 0, 0, -2, 0, 6, 0, 0, -1, -1, 0, 6, 5, 0, 0, -2, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0, -1, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -2, 0, 2, 0, 0, -1, 0, -2, -1, 0, 0, 0, 6, 0, 0, 0, 3, 0, 0, 0, -2, 3, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, -2, 0, -1, -1, 0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -2, -1, 0, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 6, -2, 0, -3, 0, 3, 0, 0, 0, -1, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 5, 0, -1, 0, 0, 0, -1, 0, 0, 5, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, -1, 5, 0, 0, -2, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -1, 0, 0, 0, 5, 0, 0, 0, -1, 0, 6, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -1, 0, 0, -2, 0, 0, 0, -1, 0, -1, -2, 0, 2, 2, -2, -1, 0, 0, -2, 0, 0, 0, -2, 0, -1, -3, 0, -1, 0, 0, -1, -1, 0, -2, 0, 0, 0, 0, 0, -2, 6, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 6, 5, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, -1, 0, 0, -1, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -2, 2, 0, -1, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, -1, 0, 0, -1, -2, 0, 0, -1, 0, 5, 0, 3, 0, -2, 0, 5, 0, 0, 0, -1, 0, 0, -1, 0, -3, 0, 0, 0, -2, 0, 5, 0, 0, 0, -1, 0, -1, 0, -2, 0, -2, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 2, -1, 0, 0, -2, -1, 0, -1, 0, 0, -1, 0, -1, -3, -1, -1, 0, 0, 0, -1, 0, 0, 6, 0, 0, 0, 0, 0, -1, 0, -1, 0, -2, -1, -2, 0, 0, 5, 0, -1, 0, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, -2, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, -1, 0, -1, 0, 0, 0, 0, 6, -1, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, -1, -1, -2, 0, 0, 0, -2, -2, 0, 0, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -1, 0, -1, 0, 0, -2, 0, 0, -2, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0], "projective_field": [-134, 82, -1, 15, -14, 6, -3, 1], "artin_field": [-134, 82, -1, 15, -14, 6, -3, 1], "weight_parity": -1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 2008, 3, -1, 2, -2008]], "char_orbit_index": 3, "prim_orbit_index": 3, "embedded_related_objects": [["ArtinRepresentation/2.2e3_251.7t2.1c3"], ["ArtinRepresentation/2.2e3_251.7t2.1c1"], ["ArtinRepresentation/2.2e3_251.7t2.1c2"]], "minimal_twist": "2008.1.c.a", "char_is_minimal": true, "conrey_index": 501, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "qexp": [[0, 0, 0], [1, 0, 0], [1, 0, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, -1, 0], [1, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 1], [0, 0, 0], [0, 0, 0], [0, -1, 0], [0, 0, 0], [1, 0, 0], [-1, 1, -1], [1, 0, 0], [-1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 1], [0, 0, 1], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, -1, 0], [-1, 1, -1], [0, 0, 0], [-1, 1, -1], [1, 0, 0], [0, 0, 0], [-1, 1, -1], [0, 0, 0], [1, 0, 0], [0, -1, 0], [-1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 1], [0, 0, 0], [0, -1, 0], [0, 0, 1], [0, 0, 0], [0, 0, 1], [0, 0, 0], [0, 0, 0], [1, 0, 1], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 1], [0, 0, 0], [0, 0, 0], [0, -1, 0], [0, 0, 0], [-1, 1, -1], [0, -1, 0], [0, 0, 0], [0, 0, 1], [-1, 1, -1], [0, -1, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, 0], [0, -1, 0], [0, -1, 0], [0, 0, 0], [-1, 1, -1], [-1, 0, -1], [0, 0, 0], [-1, 1, -1], [0, 0, 0], [1, 0, 0], [0, 0, 1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -1, 0], [0, 0, 0], [0, 0, 1], [0, -1, 0], [0, 0, 0], [0, 0, 0], [0, 0, 1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, 1], [0, 0, 1], [1, 0, 0]]}