# Stored data for newform 1950.2.y.d, downloaded from the LMFDB on 23 April 2024.
{"label": "1950.2.y.d", "space_label": "1950.2.y", "level": 1950, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13512448183109534, "dim": 4, "is_polredabs": true, "nf_label": "4.0.144.1", "trace_hash": 4940182850765279, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [9, -3, 1]]], "qexp_display": "q-\\zeta_{12}^{2}q^{2}+(\\zeta_{12}-\\zeta_{12}^{3})q^{3}+(-1+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 65, "char_orbit_label": "y", "char_is_real": false, "Nk2": 7800, "analytic_conductor": 15.570828394149675, "hecke_ring_index": 1, "level_radical": 390, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 12, "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": "0.182", "prec": 17}, "analytic_rank_proved": true, "char_values": [1950, 6, [1301, 1327, 301], [6, 3, 5]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3, 5, 13], "conrey_indexes": [49, 199], "field_disc": 144, "field_disc_factorization": [[2, 4], [3, 2]], "field_poly": [1, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.037", "prec": 17}, {"__RealLiteral__": 0, "data": "3.918", "prec": 17}, {"__RealLiteral__": 0, "data": "0.144", "prec": 17}, {"__RealLiteral__": 0, "data": "55.417", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1161.258", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c6", "trace_display": [-2, 0, 0, 6], "traces": [0, 4, -2, 0, -2, 0, 0, 6, 4, 2, 0, -6, 0, 14, -12, 0, -2, 0, -4, -6, 0, 0, 6, 12, 0, 0, -4, 0, 6, -4, 0, 0, -2, -4, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -12, 12, 0, -4, 0, -16, -10, 0, 0, 0, 6, 16, -4, 12, 0, 8, -24, -6, 4, 0, 8, 4, 0, 0, 0, -24, 2, 0, -2, 0, 6, 0, 0, -40, 0, -2, 0, 24, 0, 0, 0, -12, -6, 42, 0, 30, 0, -4, -6, 0, 0, -4, -4, 0, 0, -4, 8, 0, 14, 0, 6, 24, 0, 0, 0, -24, -12, 0, -8, 0, 8, 10, 0, 0, 0, -8, -16, 8, 24, 0, -6, 30, -2, 24, 0, -12, -4, -18, 4, 0, 0, 20, 0, 2, 0, -12, 0, -24, -4, 0, 0, 0, 4, -72, 0, 0, -6, 0, 18, 0, 0, 0, 20, 4, 0, 0, -2, -8, 0, 0, -12, -6, 0, 46, 0, -6, 0, 42, 0, 0, 6, -32, -42, 32, 0, 40, -42, 0, 12, 0, -4, 32, -6, 0, 0, 0, 0, 8, 8, 0, 8, 2, 6, -36, 0, 12, -4, -24, 8, 0, -54, 0, -4, -20, 0, 30, -6, 24, -24, 0, 0, -72, -36, 24, 0, 0, 0, -10, 6, 0, 0, 20, -8, 0, 0, 12, -4, 0, -14, 0, -12, -24, 0, 0, 0, -18, 16, 0, 8, 0, -16, -18, 0, -12, 0, -46, 12, -12, -30, 0, -2, 12, -12, -12, 0, -8, 6, -78, -4, 0, 18, -4, -8, -48, 0, 36, 0, 0, -40, 0, 0, 54, -4, -24, 0, 0, 12, -36, 24, 0, 18, 0, 2, -2, 0, 0, 0, -10, 0, 0, -2, 4, 0, 48, 0, 0, -72, 36, 0, 0, 0, -16, -18, -8, 0, 48, 0, 0, -18, 0, 20, 108, 4, 36, 0, -12, -36, -32, 4, 0, 16, 0, 0, 18, 0, 36, -12, -4, -6, 0, 0, 0, -2, -48, 0, 32, 6, 60, 0, 0, 0, 36, 12, -12, 0, 0, 0, 36, 16, 0, 0, -24, 32, 0, 0, 0, -20, 0, 12, 0, -12, -60, -12, 0, 0, 18, 8, 24, -16, 0, 12, -8, 0, 6, 0, -8, 0, 32, 0, 0, 8, 0, -4, -16, 0, 0, -4, -60, 2, 0, -6, 2, 72, 24, 0, -42, 0, 24, 8, 0, 12, 54, -16, 66, 0, 0, 54, 36, -12, 0, -10, 0, 10, -8, 0, 0, 30, 6, 0, 0, -12, -24, 0, -20, 0, -48, 0, 72, 0, 0, 36, -24, -24, 8, 0, -8, 0, 0, 24, 0, -10, -8, 6, 42, 0, -16, 0, 4, -40, 0, 16, 8, -12, -8, 0, 36, 12, 80, -4, 0, 0, 0, 4, 24, 0, 32, 12, -48, 24, 0, 0, 6, -12, 84, 0, -4, 0, 0, -8, 0, 0, 42, 8, 0, 0, 10, 8, 0, -6, 0, -24, -72, 12, 0, 0, -12, 92, -6, -6, 0, 24, 0, 0, -60, 0, 0, 4, 8, -12, 0, -12, 6, 6, 40, 0, -68, 4, -96, 6, 0, 78, -16, 8, -22, 0, 12, 0, 0, 8, 0, 4, 24, 96, 12, 0, 0, -36, -24, 0, 0, 0, 0, 20, -8, 0, 0, 0, -60, 0, 0, 2, 66, 0, 0, 0, 24, 24, 60, 0, 0, 36, -12, -24, 2, 0, -12, 6, 0, 0, 0, 2, 32, -2, 48, 0, 36, 36, -14, 0, 0, 20, 4, 0, -8, 0, -36, -2, 96, 4, 0, 72, 0, -36, -88, 0, -6, 0, 8, 72, 0, 0, -102, 6, -36, 0, 42, 0, 90, 8, 0, 0, -64, -8, 0, 0, 0, -24, 0, 0, 0, -60, -12, 18, 0, 0, 0, -40, 24, -54, 0, -8, -8, 0, -24, 0, -22, 24, 16, 36, 0, -32, 6, -2, 40, 0, -24, -8, -54, 0, 0, 0, 0, -36, -24, 0, 36, 0, -56, 24, 0, 2, -24, 12, 48, 0, 0, 0, -72, 36, 0, -44, 0, 24, 12, 0, 0, 32, -48, 0, 0, -30, -16, 0, -6, 0, 66, -42, 18, 0, 0, -12, -64, 12, -36, 0, 24, 0, 0, -6, 0, 36, -24, 16, 60, 0, -20, 42, -48, 48, 0, -64, 0, -24, 32, 0, -162, 0, 80, -20, 0, -24, 0, 30, -4, 0, -48, 12, -28, 60, 0, 0, -36, 0, -138, 0, 56, 0, -8, -4, 0, 0, 12, -16, 0, 0, -20, -6, 0, -20, 0, 0, -6, -6, 0, 0, 90, 16, -108, 0, 0, -64, 36, 0, -96, 0, 36, -16, 86, 0, 0, -4, -72, 8, 64, 0, 0, 0, -12, -4, 0, 60, -4, -4, 4, 0, 0, 0, 40, -4, 0, -36, 48, -48, 48, 0, 0, 42, -48, -12, 0, -96, 0, -4, 28, 0, 0, 12, -28, 0, 0, 8, 48, 0, -12, 0, 60, 12, -54, 0, 0, -36, -8, 12, -44, 0, 16, 14, 0, -72, 0, 10, -8, -8, -108, 0, 26, 48, 0, -60, 0, -12, 24, 6, -8, 0, -12, -12, -40, -24, 0, 24, 0, 28, 52, 0, -24, 48, 16, 0, 0, 0, 0, 72, 108, 0, 8, 0, 4, 12, 0, 0, -12, 8, 0, 0, -2, 4, 0, 0, 0, -48, -6, -24, 0, 0, 6, 20, -66, 4, 0, -12, 0, 0, -72, 0, 16, 32, 36, 0, 0, 4, -24, 20, -8, 0, -32, -8, -12, 8, 0, 12, -18, 16, 8, 0, 84, 0, -72, -24, 0, -40, -54, 8, -48, 0, 0, 0, -24, -36, 0, 10, 0, -12, 32, 0, 0, 32, 0, 0, 0, 24, -48, 0, 0, 0, -12, 0, 60, 0, 0, 12, 40, -84, -60, 0, -84, -10, 0, 18, 0, 0, -60, -8, 24, 0, 62, 0, -6, -84, 0, -16, 4, 24, -34, 0, -36, 10, -60, 8, 0, 48, 0, 24, 0, 0, -16, 24, -16, 72, 0, 0, 90, -60, -24, 0, -18, 0, 64, -46, 0, 0, -10, -6, 0, 0, -32, -12, 0, 0, 0, 30, 0, 60, 0, 0, -72, 0, 60, -2, 0, -16, -140, 0, 0, 0, -12, 24, -96, -6, 0, 6, -48, -20, 24, 0, 24, 34, -216, 4, 0, 96, -28, -12, -6, 0, -36, 0, -4, 32, 0, -4, -216, 44, 36, 0, 0, -12, 12, -18, 0, 0, 0, -4, -16, 0, 0, 4, -52, 0, 0, -48, -12, 0, 84, 0, 36, 72, -48, 0, 0, 24, 112, 0, 8, 0, -28, 0, 0, 60, 0, 20, 16, -8, -54, 0, 8, -36, -30, 0, 0, 120, -8, -54, 36, 0, -60, 2, 24, 66, 0, 24, 0, 0, 64, 0, -76, -24, 104, -24, 0, 0, -24, -12, 30, 0, -36, 0, 70, 6, 0, 0, -16, 2, 0, 0, 24, 6, 0, -24, 0, 60, -72, 0, 0, 0, 24, -4, -192, -16, 0, 4, 168, 0, 24, 0, 12, -72, -28, -36, 0, -14, 48, 0, -36, 0, -156, -10, -48, 4, 0, 0, 0, 16, -6, 0, -24, 0, 132, 4, 0, -48, -12, -8, -48, 0, 0, -72, 24, -24, 0, -12, 0, 44, 36, 0, 0, -6, 20, 0, 0, -4, -48, 0, -8, 0, 126, -36, 78, 0, 0, -6, 48, 36, 12, 0, 56, -12, 0, 0, 0, 90, -80, 8, -12, 0, -32, 18, -20, 128, 0, 16, 52, -78, -48, 0, -96, 0, 96, -24, 0, -126, 0, 0, -84, 0, -2, 60, 192, 12, 0, 0, -48, 96, -90, 0, -20, 0, -16, 20, 0, 0, 60, -54, 0, 0, -16, 4, 0, -20, 0, -36, 48, 24, 0, 0, -36, 44, -12, -12, 0, -32, -6, 0, 150, 0, -98, 64, 0, -6, 0, -2, -84, -20, 48, 0, -48, 12, -6, -8, 0, 54, -68, 0, 48, 0, 48, 0, -8, 0, 0, 18, 60, 48, -24, 0, 0, -36, 0, -36, 0, 16, 0, -12, 12, 0, 0, 2, 24, 0, 0, -6, 0, 0, 54, 0, -72, 48, 96, 0, 0, 72, 24, -36, 72, 0, 48, 46, 0, -24, 0, 24, 48, 12, -72, 0, -26, -12, 12, -64, 0, 96, 74, -6, -24, 0, -12, -30, 132, -16, 0, 0, 0, 24, 12, 0, 44, -66, 88, 42, 0, 0, 96, -36, -72, 0, 96, 0, 108, 32, 0, 0, -14, -36, 0, 0, 28, -12, 0, 0, 0, -90, 36, 6, 0, 0, 48, -72, -18, 12, 0, -32, 36, 0, -36, 0, -8, 40, 40, -42, 0, -48, 60, -24, 120, 0, 8, 32, 12, 0, 0, 24, 4, -64, -20, 0, 138, 0, -72, 0, 0, -40, 84, 40, -36, 0, 0, 24, 78, 30, 0, -42, 0, 2, 82, 0, 0, -48, -30, 0, 0, 14, 8, 0, 0, 0, -108, 12, 36, 0, 0, 0, 180, 138, 16, 0, -20, -16, 0, -18, 0, -8, -140, -4, 0, 0, 36, -24, -60, -24, 0, 32, 32, -72, -34, 0, -36, -20, -12, -6, 0, 12, 0, 28, 8, 0, 68, 0, 32, 6, 0, 0, -96, 24, -48, 0, 44, 0, 4, -8, 0, 0, 24, 0, 0, 0, 32, 32, 0, 12, 0, 0, 36, 96, 0, 0, 24, -72, -78, 8, 0, -172, 0, 0, -72, 0, 0, 8, 84, 72, 0, 8, 42, -32, -72, 0, -60, 0, -36, 0, 0, 12, -32, 8, 28, 0, 30, 0, -40, 8, 0, 2, -84, -8, -126, 0, 0, 0, -18, 6, 0, -56, 0, 2, -60, 0, 0, -36, -16, 0, 0, 24, 36, 0, 40, 0, 66, -42, -36, 0, 0, 48, 36, 12, 52, 0, 64, 72, 0, 24, 0, -4, 16, 28, 42, 0, -40, 54, 12, -24, 0, 56, -32, -54, 20, 0, 0, 8, -96, 48, 0, -66, 0, -30, 160, 0, 24, -60, 64, -12, 0, 0, -12, -54, 144, 0, 120, 0, -4, 4, 0, 0, -4, -44, 0, 0, 64, -8, 0, -4, 0, 0, -96, 72, 0, 0, 36, -20, -36, 4, 0, 16, 84, 0, 0, 0, -50, -52, 16, -48, 0, 0, -54, 30, 8, 0, -116, 6, -24, 24, 0, -6, 12, 16, -16, 0, 0, 0, -42, 24, 0, 20, 60, 48, -12, 0, 0, -24, -48, 24, 0, -8, 0, -26, 0, 0, 0, -24, -4, 0, 0, -8, -46, 0, -72, 0, 60, -72, 48, 0, 0, -72, 16, -108, 42, 0, 168, 20, 0, -36, 0, 4, 136, 12, -24, 0, -32, 24, -28, 24, 0, -16, 138, -84, 44, 0, -24, -2, 96, 4, 0, -60, 0, 0, -80, 0, 36, 48, 4, 6, 0, 0, -72, -90, -72, 0, 100, 0, 40, -10, 0, 0, 84, 4, 0, 0, 36, 6, 0, 0, 0, -42, 24, 72, 0, 0, 96, -32, 96, -16, 0, -72, 10, 0, 12, 0, -8, -8, -4, 24, 0, 20, -120, 4, 96, 0, -32, 16, -30, -8, 0, 12, -12, -16, 16, 0, -36, 0, -48, 36, 0, -8, 42, -16, 0, 0, 0, -84, -132, -36, 0, -24, 0, 12, -14, 0, 0, -40, 0, 0, 0, -4, -40, 0, -90, 0, -72, 12, -12, 0, 0, 24, 112, 36, 12, 0, 144, -14, 0, 96, 0, -12, 52, 32, -12, 0, -10, -168, 144, -64, 0, 0, 8, -12, -134, 0, -120, 24, 32, -48, 0, -24, 0, 0, 60, 0, 56, 12, -164, 0, 0, 0, 24, -6, 72, 0, 0, 0, 64, -20, 0, 0, 12, -60, 0, 0, 96, 42, 0, 14, 0, -24, -48, -18, 0, 0, -102, 0, -192, 30, 0, 16, -216, 0, 162, 0, -68, -124, 32, 0, 0, -6, 24, 42, -40, 0, -8, 8, -72, 4, 0, -24, -22, 68, -28, 0, 54, 0, 72, -20, 0, 30, 72, -16, -144, 0, 0, -48, 66, 36, 0, -18, 0, 0, -16, 0, 0, -16, 64, 0, 0, 8, -52, 0, 0, 0, -12, -12, -24, 0, 0, 60, 56, 24, 0, 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, 65, 12, 1, 6, 0]], "char_orbit_index": 25, "prim_orbit_index": 12, "minimal_twist": "390.2.bb.a", "char_is_minimal": false, "conrey_index": 49, "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, 0, 0], [1, 0, 0, 0], [0, 0, -1, 0], [0, 1, 0, -1], [-1, 0, 1, 0], [0, 0, 0, 0], [0, -1, 0, 0], [3, 0, -3, 0], [1, 0, 0, 0], [1, 0, -1, 0], [0, 0, 0, 0], [-2, -2, 1, 2], [0, 0, 0, 1], [3, 0, 1, 0], [-3, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, -4, 0, 0], [-1, 0, 0, 0], [-1, 4, -1, 0], [0, 0, 0, 0], [0, 0, 0, -3], [1, 2, 1, 0], [4, 0, -2, 0], [0, 1, 0, -1], [0, 0, 0, 0], [1, 0, -4, 0], [0, 0, 0, -1], [0, 0, 3, 0], [0, -2, -2, -2], [0, 0, 0, 0], [4, 0, -8, -2], [-1, 0, 1, 0], [-2, -1, 2, 2], [0, 0, 0, 4], [0, 0, 0, 0], [0, 0, 1, 0], [0, -4, -1, -4], [-1, 0, 2, -4], [0, 4, 0, -3], [0, 0, 0, 0], [0, 4, 0, -4], [0, -3, 0, 3], [0, 6, 0, 0], [1, 0, -2, -2], [0, 0, 0, 0], [-2, 0, -2, 0], [3, -4, 0, 2], [0, -1, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [-4, 0, 3, 0], [-1, 0, 2, 2], [0, -1, 0, 1], [0, 0, 0, 0], [3, 0, -3, 0], [4, -2, 0, 1], [-2, -2, 2, 4], [2, -8, 2, 0], [0, 0, 0, 0], [4, 2, -4, -4], [-8, -2, 4, 2], [0, 0, -3, 0], [1, 0, 0, 0], [0, 0, 0, 0], [2, 2, 0, -1], [0, 2, 2, 2], [0, 4, 0, -4], [0, 2, 0, -4], [0, 0, 0, 0], [-4, 6, -4, 0], [1, 0, -1, 0], [0, 8, 0, -4], [-1, -4, 1, 8], [0, 0, 0, 0], [2, -4, -1, 4], [-3, 0, 6, 6], [0, -3, 0, -1], [-10, -8, 0, 4], [0, 0, 0, 0], [0, 0, -1, 0], [0, -4, 0, 0], [6, -4, 0, 2], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, 0, -6], [-2, -2, -2, 0], [-2, -2, 1, 2], [14, -2, -7, 2], [0, 0, 0, 0], [12, 0, -9, 0], [-2, 0, 4, 0], [0, -4, -2, -4], [0, 2, -3, 2], [0, 0, 0, 0], [0, 0, 0, 1], [-2, -6, 2, 12], [-2, 0, 2, 0], [-1, 0, 2, 2], [0, 0, 0, 0]]}