# Stored data for newform 2100.2.bi.i, downloaded from the LMFDB on 25 April 2024. {"label": "2100.2.bi.i", "space_label": "2100.2.bi", "level": 2100, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36031133514729524, "dim": 2, "is_polredabs": true, "nf_label": "2.0.3.1", "trace_hash": 933870196250471209, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[11, [0, 1]], [13, [27, 0, 1]], [19, [75, -15, 1]], [37, [1, -1, 1]]], "qexp_display": "q+(1+\\zeta_{6})q^{3}+(3-\\zeta_{6})q^{7}+3\\zeta_{6}q^{9}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 21, "char_orbit_label": "bi", "char_is_real": false, "Nk2": 8400, "analytic_conductor": 16.76858442446888, "hecke_ring_index": 1, "level_radical": 210, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 6, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 1, "is_self_dual": false, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.590", "prec": 17}, "analytic_rank_proved": true, "char_values": [2100, 6, [1051, 701, 1177, 1501], [6, 3, 6, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 3, 5, 7], "conrey_indexes": [101, 1601], "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.009", "prec": 17}, {"__RealLiteral__": 0, "data": "1.863", "prec": 17}, {"__RealLiteral__": 0, "data": "0.108", "prec": 17}, {"__RealLiteral__": 0, "data": "16.699", "prec": 20}, {"__RealLiteral__": 0, "data": "1.606", "prec": 17}, {"__RealLiteral__": 0, "data": "186.083", "prec": 24}], "related_objects": [], "self_twist_discs": [-3], "cm_discs": [-3], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "1.2.1.d6", "trace_display": [0, 3, 0, 5], "traces": [0, 2, 0, 3, 0, 0, 0, 5, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 1, 0, 9, 0, 0, 0, 16, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, -27, 0, 12, 0, 0, 0, 5, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 13, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, -33, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, -11, 0, 0, 0, 0, 0, 38, 0, 24, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -19, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, -28, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 9, 0, 0, 0, -2, 0, 0, 0, 0, 0, -39, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, -54, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -27, 0, 0, 0, -45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 9, 0, 0, 0, 5, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 17, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, -66, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -57, 0, 0, 0, -1, 0, -3, 0, 0, 0, -68, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, -66, 0, 0, 0, 0, 0, -25, 0, 0, 0, 0, 0, -58, 0, 57, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 75, 0, 0, 0, -54, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, -38, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -69, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -57, 0, 0, 0, -41, 0, 0, 0, 0, 0, -46, 0, 0, 0, 0, 0, 5, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, -44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, -42, 0, 0, 0, 81, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, -78, 0, 0, 0, 0, 0, -23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -17, 0, 12, 0, 0, 0, 80, 0, -81, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, -47, 0, 0, 0, 0, 0, -24, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -180, 0, 0, 0, 0, 0, 0, 0, -39, 0, 0, 0, 0, 0, 30, 0, 0, 0, 9, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -87, 0, 0, 0, -45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 0, 0, 0, 0, 0, 0, 0, -33, 0, 0, 0, -74, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 53, 0, -39, 0, 0, 0, 0, 0, 0, 0, 0, 0, -66, 0, 3, 0, 0, 0, 0, 0, -54, 0, 0, 0, 93, 0, 0, 0, 0, 0, -53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -60, 0, 0, 0, 120, 0, 54, 0, 0, 0, 47, 0, 0, 0, 0, 0, 99, 0, 15, 0, 0, 0, 0, 0, 54, 0, 0, 0, 58, 0, 0, 0, 0, 0, -44, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -45, 0, 27, 0, 0, 0, 59, 0, 0, 0, 0, 0, -110, 0, 0, 0, 0, 0, 95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, -59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -52, 0, -54, 0, 0, 0, 0, 0, -99, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 122, 0, 0, 0, 0, 0, -39, 0, 0, 0, 0, 0, 0, 0, -114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 69, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, -102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117, 0, 57, 0, 0, 0, 5, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, -128, 0, 81, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, -4, 0, 33, 0, 0, 0, 44, 0, 0, 0, 0, 0, 117, 0, -66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 0, 0, -87, 0, 0, 0, 68, 0, 57, 0, 0, 0, 0, 0, 0, 0, 0, 0, 69, 0, 0, 0, 0, 0, -135, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -70, 0, 0, 0, 0, 0, 0, 0, -72, 0, 0, 0, 0, 0, 135, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, -162, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 117, 0, 0, 0, 0, 0, 0, 0, 0, 0, -54, 0, -57, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 0, -135, 0, 0, 0, 0, 0, 0, 0, 0, 0, -123, 0, 0, 0, 0, 0, -25, 0, 72, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0, -93, 0, 45, 0, 0, 0, 61, 0, 0, 0, 0, 0, -144, 0, 0, 0, 0, 0, 99, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -114, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74, 0, 0, 0, 0, 0, 270, 0, -69, 0, 0, 0, -117, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 171, 0, 0, 0, 0, 0, -20, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 6, 0, 0, 0, 0, 0, -65, 0, 0, 0, 0, 0, -90, 0, -132, 0, 0, 0, 0, 0, -51, 0, 0, 0, 152, 0, 0, 0, 0, 0, -145, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 195, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -144, 0, -42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 108, 0, 0, 0, 0, 0, 0, 0, 0, 0, -129, 0, 0, 0, 0, 0, -73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 0, -99, 0, 0, 0, 0, 0, -47, 0, 0, 0, 0, 0, 0, 0, -69, 0, 0, 0, 8, 0, 0, 0, 0, 0, -158, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26, 0, 0, 0, 0, 0, 111, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 0, -81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 39, 0, 0, 0, 5, 0, 0, 0, 0, 0, 141, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, -82, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -51, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -141, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, -180, 0, -24, 0, 0, 0, 0, 0, -12, 0, 0, 0, 15, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, -57, 0, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 0, 0, -270, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, -82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -73, 0, 75, 0, 0, 0, -234, 0, 45, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, -45, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, -141, 0, 0, 0, 0, 0, -65, 0, 0, 0, 0, 0, -69, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 324, 0, -3, 0, 0, 0, -60, 0, -87, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 87, 0, 0, 0, 170, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, -54, 0, 0, 0, -165, 0, 0, 0, 0, 0, 171, 0, 0, 0, 0, 0, 0, 0, -81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 117, 0, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, -96, 0, 0, 0, 0, 0, 37, 0], "weight_parity": 1, "has_non_self_twist": 1, "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, 3, 2, -1, 2, -3], [1, 1, 7, 4, -1, 6, 0], [1, 1, 21, 7, 1, 6, 0]], "char_orbit_index": 35, "prim_orbit_index": 7, "minimal_twist": "2100.2.bi.a", "char_is_minimal": true, "conrey_index": 101, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0], [1, 0], [0, 0], [1, 1], [0, 0], [0, 0], [0, 0], [3, -1], [0, 0], [0, 3], [0, 0], [0, 0], [0, 0], [3, -6], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [10, -5], [0, 0], [4, 1], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-3, 6], [0, 0], [0, 0], [0, 0], [-6, -6], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 1], [0, 0], [9, -9], [0, 0], [0, 0], [0, 0], [8, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [8, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [15, 0], [0, 0], [0, 0], [0, 0], [-18, 9], [0, 0], [3, 6], [0, 0], [0, 0], [0, 0], [5, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [9, 9], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 13], [0, 0], [-9, 9], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [3, -15], [0, 0], [0, -18], [0, 0], [0, 0], [0, 0], [3, -6], [0, 0], [0, 0], [0, 0]]}