# Stored data for newform 208.2.p.a, downloaded from the LMFDB on 21 January 2026. {"Nk2": 832, "analytic_conductor": 1.660888362042632, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 208, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 16, "char_orbit_label": "p", "char_order": 4, "char_parity": 1, "char_values": [208, 4, [79, 53, 145], [4, 3, 2]], "cm_discs": [], "conrey_index": 77, "dim": 8, "field_disc": 959512576, "field_disc_factorization": [[2, 16], [11, 4]], "field_poly": [81, 0, 0, 0, 7, 0, 0, 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": [[3, [25, 10, 2, -2, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 1030825705680, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 2, 1, 2, 0], [1, 1, 16, 5, 1, 4, 0], [1, 1, 208, 16, 1, 4, 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": "208.2.p.a", "level": 208, "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": [2, 13], "level_radical": 26, "minimal_twist": "208.2.p.a", "nf_label": "8.0.959512576.1", "prim_orbit_index": 16, "qexp_display": "q+(\\beta _{1}+\\beta _{4})q^{2}-\\beta _{3}q^{3}-2q^{4}-\\beta _{4}q^{5}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "208.2.p", "trace_display": [0, 4, 0, 0], "trace_hash": 1253747783842776276, "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "6.371", "prec": 17}, {"__RealLiteral__": 0, "data": "3.086", "prec": 17}, {"__RealLiteral__": 0, "data": "282.810", "prec": 24}, {"__RealLiteral__": 0, "data": "257.295", "prec": 24}, {"__RealLiteral__": 0, "data": "18695.485", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.634", "prec": 17}, "traces": [0, 8, 0, 4, -16, 0, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, 32, 24, 0, 0, 0, 0, -16, 0, 0, 0, 0, -44, 0, -24, 8, 0, 0, 0, 0, -12, 0, 0, 24, 0, -16, 0, 32, -4, 0, 0, 0, 0, 16, 24, 0, 12, 16, -24, 0, 0, 0, 0, 0, 0, 0, 32, -48, 0, -64, 0, -16, 0, -48, 56, 0, 0, 0, 0, -48, 16, 0, 24, 0, -8, 0, -16, 0, 0, 0, 0, 0, 0, 32, 0, 24, 44, 0, 0, 40, -24, 0, 0, 0, 0, 0, -24, 0, 0, 0, 0, 0, 24, 88, 0, 0, 0, 0, -48, 0, 0, 48, 24, 8, 0, -16, 0, 0, 0, 0, 0, 16, -56, 0, -136, -16, 36, 0, -8, 0, 0, 0, 0, 0, 20, 24, 0, 0, 0, 0, 0, 0, -120, 0, 0, 0, 0, -48, 0, 0, 24, 0, -16, 0, 152, 32, 0, 0, 0, 0, 8, 56, 0, -64, 0, 24, 0, 8, 96, 0, 0, 0, 0, 0, -12, 0, -64, 24, 0, 0, 0, -24, 0, 0, 0, 0, -144, -32, 0, -96, 44, -48, 0, -48, 0, 0, 0, 0, 0, -24, 0, 0, 160, -32, 48, 0, 92, 48, 0, 0, 0, 0, 0, 0, 0, 0, -24, -136, 0, 0, 96, 0, 0, 0, 0, -24, 0, 0, 0, 88, -20, 0, -136, 0, 0, 0, 0, 0, -8, -64, 0, 0, 0, 96, 0, -72, -24, 0, 0, 0, 0, 128, 120, 0, 28, 0, -16, 0, 0, 32, 0, 0, 0, 0, -48, 0, 0, 96, -88, 0, 0, -112, -40, 0, 0, 0, 0, 152, -88, 0, -56, 32, 0, 0, -64, -48, 0, 0, 0, 0, 0, 96, 0, 80, -24, -32, 0, 0, -112, 0, 0, 0, 0, -48, 96, 0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 200, -16, 0, 32, -32, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, -24, 0, -48, -160, 0, 0, 0, 0, -60, 0, 0, 96, 88, -64, 0, 272, 36, 0, 0, 0, 0, -48, 0, 0, 28, -88, 48, 0, 64, 0, 0, 0, 0, 0, 56, -48, 0, -80, 0, -88, 0, 48, 104, 0, 0, 0, 0, -144, -144, 0, 0, -8, 0, 0, 0, -112, 0, 0, 0, 0, -8, 0, 0, 0, 0, 48, 0, 160, 0, 0, 0, 0, 0, 0, 120, 0, -56, 0, -112, 0, 60, 0, 0, 0, 0, 0, 0, -96, 0, -48, -88, 0, 0, -176, 160, 0, 0, 0, 0, -40, 0, 0, 0, 0, 84, 0, 0, 24, 0, 0, 0, 0, 0, 96, 0, -16, 0, 0, 0, -72, -132, 0, 0, 0, 0, -96, 24, 0, 24, -48, 88, 0, 0, -16, 0, 0, 0, 0, 104, -56, 0, 32, -88, 144, 0, 0, 48, 0, 0, 0, 0, 24, 156, 0, -72, 0, 48, 0, -240, 0, 0, 0, 0, 0, 0, -32, 0, 48, 36, 112, 0, 24, -232, 0, 0, 0, 0, 272, 40, 0, 0, 32, 0, 0, 80, -72, 0, 0, 0, 0, 24, 0, 0, 16, 0, 264, 0, 0, 0, 0, 0, 0, 0, -24, -328, 0, 0, -64, -76, 0, -96, 64, 0, 0, 0, 0, 68, -40, 0, 0, 8, -48, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, -52, 0, -72, 0, -96, 0, 0, 0, 0, 0, -48, -48, 0, 0, 0, -64, 0, 240, 72, 0, 0, 0, 0, 0, -36, 0, 72, -88, 0, 0, 0, 120, 0, 0, 0, 0, 184, 96, 0, 64, 132, 0, 0, -168, 0, 0, 0, 0, 0, -48, 176, 0, 264, 0, -88, 0, 112, 32, 0, 0, 0, 0, 0, -16, 0, -304, -24, 96, 0, -64, 96, 0, 0, 0, 0, 72, 0, 0, 0, 0, 96, 0, 24, 0, 0, 0, 0, 0, -96, -16, 0, -72, 0, -112, 0, -232, 16, 0, 0, 0, 0, 128, -8, 0, 176, 0, 96, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, -16, 48, 0, 0, -192, 16, 0, 0, 0, 0, -72, -244, 0, -96, 88, 232, 0, -152, -32, 0, 0, 0, 0, 0, 0, 0, 96, -16, 24, 0, 0, -48, 0, 0, 0, 0, 128, -96, 0, 0, -48, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, -176, -248, 0, 48, 0, 0, 0, 0, 0, 0, -32, 0, 152, 0, 12, 0, 8, -168, 0, 0, 0, 0, -44, 288, 0, -56, 264, 64, 0, 48, 60, 0, 0, 0, 0, 192, 0, 0, 0, -88, -72, 0, 176, 96, 0, 0, 0, 0, -64, -8, 0, 96, 0, 48, 0, 0, -144, 0, 0, 0, 0, 16, -96, 0, 8, 48, 0, 0, 0, -16, 0, 0, 0, 0, -72, 48, 0, 0, 0, 0, 0, 264, 0, 0, 0, 0, 0, -320, -64, 0, -304, 64, 72, 0, 0, -96, 0, 0, 0, 0, 0, -72, 0, -184, 0, 0, 0, -96, -88, 0, 0, 0, 0, -96, 0, 0, 0, 16, 128, 0, 0, -8, 0, 0, 0, 0, -32, 0, 0, 64, 0, 0, 0, 160, -108, 0, 0, 0, 0, 0, 168, 0, -28, 48, -136, 0, 0, 272, 0, 0, 0, 0, -192, 80, 0, 0, -112, 208, 0, -192, -72, 0, 0, 0, 0, 56, -4, 0, -160, 0, -240, 0, 112, 0, 0, 0, 0, 0, 0, 48, 0, 128, -132, 0, 0, -144, 48, 0, 0, 0, 0, 0, 104, 0, 0, -176, 0, 0, 132, 40, 0, 0, 0, 0, 88, 0, 0, 272, -88, 96, 0, 0, 0, 0, 0, 0, 0, -104, 264, 0, 104, 96, 248, 0, 72, -8, 0, 0, 0, 0, -60, 16, 0, 0, -32, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 144, 0, 88, -192, 0, 0, 0, 0, 248, -144, 0, 144], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0], [-2, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 1, 0, 0, 1, -1, 0, 1], [0, -1, 0, 0, 2, 0, 0, 1], [0, -2, 0, 0, -2, 0, 0, 0], [-1, 0, 3, -1, 0, 0, 1, 0], [1, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 2, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0], [-1, 0, -1, 0, 1, -1, 0, 1], [1, 0, 3, 1, 0, 0, -1, 0], [0, 0, 0, 0, -1, 1, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0], [0, 4, 0, 0, -2, 0, 0, 2], [0, -3, 0, 0, -1, 1, 0, -1], [0, 0, 0, 0, 2, 0, 0, 0], [0, -1, 0, 0, -4, -1, 0, -1], [-2, 0, 2, 0, 0, 0, 0, 0], [1, 0, -3, 1, 0, 0, -1, 0], [0, -2, 0, 0, -2, 2, 0, -2], [0, 0, -4, 0, 0, 0, 0, 0], [1, -2, 1, 2, 0, 0, 0, 0], [-6, 0, 6, 0, 0, 0, 1, 0], [0, 2, 0, 0, -4, 0, 0, -2], [-4, 0, -4, -2, 0, 0, 0, 0], [1, 0, -1, -1, 0, 0, -1, 0], [0, 3, 0, 0, 3, 0, 0, 0], [0, 4, 0, 0, 4, 0, 0, 0], [0, 0, 0, 0, 2, -2, 0, 0], [0, 3, 0, 0, 3, 0, 0, 0], [-2, 0, -2, -1, 0, 0, 0, 0], [2, 0, -6, 2, 0, 0, -2, 0], [0, -1, 0, 0, 6, -1, 0, -1], [2, 0, 2, -2, 0, 0, 0, 0], [1, 6, -1, 1, -5, 0, -1, 1], [-2, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [3, 0, -3, 0, 0, 0, 2, 0], [-2, 0, 2, 0, 0, 0, 3, 0], [0, 0, 0, 0, -4, 0, 0, 0], [0, -3, 0, 0, -1, 1, 0, -1], [0, -4, 0, 0, 2, 0, 0, -2], [0, -1, 0, 0, -4, 3, 0, 0], [0, 0, 0, -4, 0, 0, 0, 0], [3, 0, 3, 3, 0, 0, 3, 0], [0, -4, 0, 0, 4, 0, 0, 0], [0, 0, 0, -3, 0, 0, 0, 0], [2, 0, 2, 0, -2, 2, 0, -2], [-1, 0, 1, 0, 0, 0, -4, 0], [0, 1, 0, 0, -11, 1, 0, 1], [0, 0, -2, 0, 0, 0, 0, 0], [-2, 0, -6, -2, 0, 0, 2, 0], [0, -9, 0, 0, 5, 0, 0, -4], [0, -6, 0, 0, 2, -2, 0, 2], [0, 3, 0, 0, -1, 3, 0, 3], [0, 0, 0, 0, 2, -2, 0, 0], [4, 0, 4, 0, 0, 0, 0, 0], [-6, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -1, 0, 0, 0], [-8, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, -1, 1, 0, -1, 0], [-2, 0, 2, 2, 0, 0, 2, 0], [0, 0, 0, 0, 2, -2, 0, 2], [-6, 0, 0, 0, 0, 0, 0, 0], [9, 0, -9, 0, 0, 0, -4, 0], [0, -3, 0, 0, 1, -1, 0, 1], [0, 3, 0, 0, -6, 0, 0, -3], [0, -8, 0, 0, 4, 0, 0, -4], [0, 5, 0, 0, -7, 0, 0, -2], [-7, 0, 7, 0, 0, 0, 2, 0], [4, 0, -4, 0, 0, 0, -4, 0], [0, 6, 0, 0, 2, -2, 0, 2], [4, 0, 4, 2, 0, 0, 0, 0], [1, -2, -11, 1, 0, 0, -1, -2], [-1, 0, 3, 3, 0, 0, 3, 0], [0, 0, 0, 0, -4, 0, 0, 0], [-2, 0, 3, 3, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -7, 0, 0, -3, 3, 0, -3], [0, 2, 0, 0, 8, 2, 0, 2], [0, 0, 0, 0, -3, 0, 0, 0], [0, 3, 0, 0, -1, 3, 0, 3], [2, 0, 8, 2, 0, 0, -2, 0], [4, 0, -4, 0, 0, 0, 0, 0], [0, 3, 0, 0, 3, 0, 0, 6], [2, 0, 2, -2, 0, 0, 0, 0], [4, -1, -4, 0, -3, -1, 3, -1], [-2, 0, 6, -2, 0, 0, 2, 0], [0, 3, 0, 0, 3, -3, 0, 3], [5, 0, -3, -3, 0, 0, -3, 0], [-3, 0, 1, 1, 0, 0, 1, 0], [0, 4, 0, 0, 4, -4, 0, 4], [0, 6, 0, 0, 6, 0, 0, 0], [0, 6, 0, 0, 0, 6, 0, 0], [0, 6, 0, 0, 2, -2, 0, 2], [0, 0, 8, 0, 0, 0, 0, 0]]}