# Stored data for newform 950.2.l.g, downloaded from the LMFDB on 24 April 2024. {"label": "950.2.l.g", "space_label": "950.2.l", "level": 950, "weight": 2, "hecke_orbit": 7, "hecke_orbit_code": 27022353712022454, "dim": 12, "is_polredabs": true, "trace_hash": 1437561795487548617, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [576, -864, 3600, -2064, -936, 210, 391, 189, 51, -4, 0, 3, 1]]], "qexp_display": "q+\\beta _{8}q^{2}+\\beta _{4}q^{3}+\\beta _{10}q^{4}+(\\beta _{6}-\\beta _{8}+\\cdots)q^{6}+\\cdots", "char_order": 9, "char_parity": 1, "char_degree": 6, "char_conductor": 19, "char_orbit_label": "l", "char_is_real": false, "Nk2": 3800, "analytic_conductor": 7.585788192021637, "hecke_ring_index": 1, "level_radical": 190, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "analytic_rank_proved": true, "char_values": [950, 9, [77, 401], [9, 7]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 5, 19], "conrey_indexes": [101, 251, 301, 351, 651, 701], "field_disc": 4824873170148249, "field_disc_factorization": [[3, 18], [3529, 2]], "field_poly": [5329, 0, -7788, 0, 4812, 0, -1511, 0, 264, 0, -24, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.060", "prec": 17}, {"__RealLiteral__": 0, "data": "11.889", "prec": 20}, {"__RealLiteral__": 0, "data": "2.278", "prec": 17}, {"__RealLiteral__": 0, "data": "505.427", "prec": 24}, {"__RealLiteral__": 0, "data": "136.423", "prec": 24}, {"__RealLiteral__": 0, "data": "47308.705", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c9", "trace_display": [0, -3, 0, 6], "traces": [0, 12, 0, -3, 0, 0, 3, 6, 6, 9, 0, -6, 0, 18, -6, 0, 0, -12, -24, 6, 0, -36, 9, -3, 3, 0, -3, -15, -3, 36, 0, -24, 0, -15, -6, 0, 9, -24, -15, -12, 0, -12, -18, 12, -9, 0, -18, 0, 6, 0, 0, -27, -18, 36, 9, 0, 12, 42, 0, -27, 0, 54, 24, 3, -6, 0, -39, -39, 15, -24, 0, 24, 18, 0, 15, 0, 9, -78, 6, -36, 0, -9, 12, 0, 12, 0, 24, -18, 6, 18, 0, 12, -12, -54, 18, 0, 0, 27, 18, 18, 0, 36, 0, -6, 0, 0, 12, -3, -9, 30, 0, -90, -3, 12, 57, 0, 36, 102, -27, -6, 0, 18, -12, -36, -6, 0, -54, 0, 0, -93, 0, -33, 30, 66, -12, 0, -6, 15, -12, -39, 0, 18, 48, -78, -12, 0, 0, -33, 3, 18, 0, 36, -6, -90, 12, 0, -42, -15, 36, 24, 0, -27, 0, 24, -12, 0, 42, 21, -18, 0, 0, 27, -18, 48, 18, 0, 0, -36, 33, 78, 0, 30, -12, 72, 12, 0, -18, -6, 0, -72, 0, 72, 6, 0, -18, 0, -18, 24, 45, 0, 0, 9, 12, 36, 45, 0, 15, 9, -6, 27, 0, -48, -9, -108, 72, 0, 15, -30, 24, 21, 0, 42, 90, 51, -6, 0, 51, 120, -36, -132, 0, 96, 0, 27, -102, 0, -9, 54, 42, -12, 0, 63, -27, 0, -18, 0, 54, 99, -48, -66, 0, 9, 12, 12, -24, 0, 0, -36, 36, -3, 0, 54, -12, 105, -39, 0, 45, 12, -39, 24, 0, -78, 6, -18, -24, 0, -42, 3, -15, 186, 0, -33, -108, -69, -12, 0, 12, -78, -9, 0, 0, 3, 12, 12, -48, 0, -12, -45, -18, 9, 0, -12, -30, -84, -3, 0, -27, 6, -21, 108, 0, -42, -6, -18, 15, 0, 0, 81, -60, 18, 0, -48, -78, -21, -12, 0, -15, -66, -15, -99, 0, 66, 39, 57, 12, 0, 18, 3, 0, 18, 0, -120, -60, 6, 24, 0, 15, -96, -18, 78, 0, -48, -9, 42, -45, 0, -9, -108, -63, -48, 0, -120, 36, 93, -69, 0, -30, -84, 18, 54, 0, -51, 24, 18, 6, 0, -18, 54, -6, -78, 0, 48, 0, -12, 3, 0, 0, 9, 18, 66, 0, -42, 0, 159, -27, 0, -36, 84, 96, 0, 0, 15, 39, -138, -36, 0, 0, 15, 18, 66, 0, 126, -15, 0, -27, 0, 0, 78, 69, -126, 0, -18, 21, 126, 9, 0, -36, 90, 72, 66, 0, 30, -9, -132, 108, 0, 48, 24, 30, 60, 0, 51, -24, -207, 12, 0, 66, 138, 6, -12, 0, -24, 21, 120, -15, 0, 12, -156, -36, 9, 0, -84, -96, -24, 0, 0, -18, -30, -27, 102, 0, 222, 0, -27, 48, 0, 48, 63, -90, -54, 0, -54, 33, 42, 27, 0, 15, -6, 18, 18, 0, -54, -36, -72, 66, 0, -6, -96, -123, 15, 0, -24, 63, -168, 15, 0, -27, 21, 9, -42, 0, -42, -12, 111, -120, 0, 69, 45, 24, -42, 0, -42, -18, 54, -36, 0, -105, 114, -15, 69, 0, -144, -30, -264, -12, 0, -78, -111, -24, -57, 0, -30, 24, 72, -15, 0, -114, -72, 51, -102, 0, -18, -48, 48, 60, 0, -30, 75, 18, -42, 0, -81, -12, -96, 108, 0, -75, -15, 48, 30, 0, 42, -78, -72, -21, 0, 9, -72, -3, 90, 0, -24, 3, -153, 45, 0, -39, -12, 84, 114, 0, 24, 12, 105, 0, 0, -42, 54, -27, 36, 0, 60, 12, 219, 12, 0, 138, -72, 9, -216, 0, -36, 36, 27, -6, 0, -39, -69, 126, -3, 0, 0, 66, 78, 48, 0, 24, -42, -36, 84, 0, 84, -18, -63, -18, 0, 96, -81, 36, 36, 0, -18, -33, 9, -27, 0, -6, 0, 0, 0, 0, 72, 15, 24, 42, 0, -3, -99, 0, 33, 0, 0, 21, -18, 0, 0, 36, -90, 3, -216, 0, 42, -12, 141, 6, 0, -9, -84, -18, -36, 0, 51, 6, -186, 27, 0, 21, -132, 12, 78, 0, 3, -30, -162, -75, 0, 18, 135, 36, -42, 0, 0, -72, -27, 12, 0, -93, 156, 63, 30, 0, -18, 9, -18, 54, 0, 63, -102, -186, -138, 0, 204, -9, 252, 30, 0, -39, 222, 69, 123, 0, 72, -6, 30, 45, 0, 3, 42, 72, -114, 0, -48, 120, -39, -36, 0, -72, 9, 30, 24, 0, -114, 9, 54, -54, 0, 24, -51, 36, 24, 0, -24, 54, 42, -18, 0, 12, 81, 0, -144, 0, -42, 27, -6, -12, 0, 45, 72, -60, -21, 0, -168, -30, 54, 9, 0, 48, 24, -36, -102, 0, -48, 36, 168, -21, 0, 0, 12, 18, -252, 0, 153, 93, 93, -39, 0, 30, -6, 0, 87, 0, 147, -18, -36, 54, 0, 0, 48, -120, 69, 0, -42, -18, -78, 6, 0, 9, 81, 54, 24, 0, -78, -18, -18, 90, 0, -9, 36, 21, -24, 0, 72, 18, 0, 51, 0, 180, 66, -12, 30, 0, 57, 90, -144, -120, 0, -6, -120, -192, -51, 0, 234, -12, 18, -18, 0, 84, 0, -108, 96, 0, -36, 24, -192, 30, 0, 21, 123, -78, 162, 0, -12, 30, 123, 42, 0, -72, -66, -90, 30, 0, 72, -48, -54, -264, 0, 3, 102, 6, -72, 0, -66, -102, 12, 6, 0, -120, 45, 6, 252, 0, -48, 78, -54, -15, 0, -72, 144, -9, 66, 0, 165, -24, -102, 60, 0, -39, -78, 36, -186, 0, 18, -60, 24, -57, 0, 42, -195, 0, 126, 0, -12, -54, 3, 0, 0, 27, 72, 54, -24, 0, -216, 42, 48, -126, 0, 90, -126, 18, 192, 0, -126, -72, 189, 27, 0, 48, -132, 36, 117, 0, 150, 99, 60, -84, 0, 12, 6, 135, 0, 0, -24, 54, 171, -117, 0, 90, 108, 42, 36, 0, 102, 24, 69, 96, 0, -21, 87, 84, 144, 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, 19, 5, 1, 9, 0]], "char_orbit_index": 12, "prim_orbit_index": 5, "minimal_twist": "190.2.k.c", "char_is_minimal": true, "conrey_index": 101, "id": null, "nf_label": 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, 0, 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, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 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, 0, 0, 0, 0, 1, 0, -1, -1, 0, 1], [0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, -1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0], [2, -1, 0, 0, 0, -1, 1, 1, -2, 0, 1, 0], [-1, 0, -1, 1, 0, 0, 1, 1, 0, -2, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0], [-2, 1, 0, 1, -1, -1, 1, 0, 3, 0, -2, 2], [-1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 2, -2], [0, 0, 1, 0, -2, -1, -1, 0, 0, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 0, 2, 2, 0, 0, 2, 0, -2, -2], [1, -1, 0, 0, 0, 0, 1, 1, -2, -2, 1, 0], [0, -1, 0, -1, 1, 1, 0, 0, -2, 0, -2, 0], [0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 1, 0, 1, 2, 2, 0, 0, 0], [-2, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2], [0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0], [4, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -2, 2, 0, -4, -2, 2, -2], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0], [0, -1, 0, 1, 0, 2, 0, 2, 0, -3, 0, -4], [-2, 1, -1, 1, -1, 0, 0, 0, 0, 0, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 1, -1, 0, 0, 0, -2, -3, 0, 0, -2], [-2, -1, 1, -1, -1, 1, 1, -3, 0, 0, -1, 0], [-2, 0, 1, 1, 0, 1, -1, -2, 2, 2, -1, 0], [0, 0, 0, 0, 2, 0, -2, -2, 4, 6, -4, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -2, -2, 1, 0, 1, 1, 0, 0, 3, -2], [-2, 0, 0, -2, 0, 0, 0, 0, -4, 0, 2, 2], [0, 1, -1, 0, 0, 1, 1, -2, 0, 1, 0, 2], [0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 0, -1, 1, 0, 0, 1, -2, -2, 0, 2], [4, 0, 3, -3, 3, 3, -3, -3, -2, 2, 0, -8], [0, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1], [1, 1, 0, -1, 1, 0, 0, -1, 0, 2, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 0, 0, 0, 0, 0, 3, 0, -1, -5, 0, 5], [-2, 1, -1, 0, 0, -1, 1, 2, 0, 0, 2, 2], [3, 1, 2, 0, -1, -3, 0, 0, 4, 4, 0, 1], [2, 0, -1, -1, 0, 0, 0, 2, -3, -3, 2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, -1, -1, 1, 0, 0, 0, -1, 2], [4, 2, -1, 0, 0, -2, 0, -6, 4, 5, -6, 0], [0, 0, 0, 0, 0, 0, 0, -4, 4, 2, -2, 0], [-4, 2, -1, 2, 0, 0, 1, 2, 0, 0, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, 2, 0, 0, 0, 0, 6, 4, -2, 0], [2, 0, -2, 2, 0, 0, 2, 0, 0, 2, -2, 0], [-1, 0, 1, 0, -1, 0, 2, 8, -2, -2, 8, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 0, -2, 1, 0, -2, -2, 1, 5, 0, -2], [0, -1, 1, 0, 0, 1, 0, 0, -7, 0, 0, -7], [2, 1, 0, 0, -1, -1, -1, 0, 0, 0, -2, -2], [0, 0, 4, 0, 0, 2, -2, 0, 0, 6, 2, -6], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 2, -2, 0, 0, -2, 2, -2, 0, 0, 0, 6], [2, -1, 0, 0, 1, 1, 0, 0, 1, 1, -1, -1], [-2, 3, -2, -2, -1, 0, -3, -2, 0, 0, -6, 3], [2, -1, -1, -1, 1, 1, -2, 1, -2, 0, 3, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 1, 1, -1, 0, 1, -1, 0, -1, 1, 0, -1], [-5, 2, -2, -1, 2, 1, -2, -1, 4, 4, -2, -3], [-2, 0, 2, 0, 0, 0, 2, 4, -2, 0, 2, 6], [-4, 2, 0, 0, -2, 0, -2, -4, 2, 2, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, -2, 0, 3, -2, -2, 0, 3, 0, -3], [2, -2, -1, 0, 1, -2, 1, 4, -2, -1, 4, 0], [0, 0, -2, 2, 2, -1, 3, -2, -3, -7, 0, 2], [2, -2, 0, 0, 0, 0, 0, 0, -4, -4, -2, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -1, -1, -1, -1, -1, 2, 0, -2, 0, 0], [0, 0, 0, -4, 2, -2, -2, 0, -2, 2, 0, 0], [0, 0, 0, 0, 0, -1, 1, 1, -1, 0, 1, 2], [1, -1, 1, 0, -1, -1, 0, -6, -2, 0, -6, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 1, 2, 0, -1, -3, 0, 0, -2, 6, -4, 9], [-1, -1, 0, 0, 1, 0, 1, -1, -4, -4, 0, 1], [-4, -2, -2, -2, -2, -2, -4, 0, 4, 0, -4, -2], [3, -3, 3, -3, 0, 3, 0, -4, -2, 2, -2, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 1, -1, 1, 0, 0, 0, 4, 4, 0, 4, 4], [1, -1, 0, 0, -1, 0, 1, 1, -1, -1, 0, 1], [1, 1, 1, -3, -1, -2, 0, 0, -1, 4, 6, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}