# Stored data for newform 950.2.l.i, downloaded from the LMFDB on 10 May 2024.
{"label": "950.2.l.i", "space_label": "950.2.l", "level": 950, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36029552966763446, "dim": 18, "is_polredabs": true, "trace_hash": 1589820901285462470, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [64, 288, 46512, -244544, 501912, -488322, 206005, 15876, -36531, 4636, 2925, -1422, 788, -216, 36, -6, 9, 0, 1]]], "qexp_display": "q+\\beta _{9}q^{2}+\\beta _{7}q^{3}-\\beta _{11}q^{4}+\\beta _{5}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": "0.012", "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": -6952040952870353428436830912512, "field_disc_factorization": [[-1, 1], [2, 18], [3, 27], [1864873, 2]], "field_poly": [64, 1824, 50640, 45584, 132588, -39408, 178501, -24822, 77397, -12862, 22809, -2478, 3518, -222, 393, -12, 24, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "17.524", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "985.613", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "88354.349", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 3, "sato_tate_group": "1.2.3.c9", "trace_display": [0, 0, 0, 0], "traces": [0, 18, 0, 0, 0, 0, 0, 0, -9, -18, 0, -12, 0, 6, 6, 0, 0, 0, 42, 0, 0, 12, 3, -9, 0, 0, -9, 18, -3, -6, 0, -6, 0, -66, 18, 0, -18, 12, 6, 48, 0, -21, -42, -18, 3, 0, 18, 54, 0, -39, 0, 42, -12, 24, -54, 0, 0, 18, 0, -30, 0, 48, 30, 57, -9, 0, 24, 6, 6, -30, 0, 30, 0, -6, -3, 0, -21, -30, 24, 30, 0, 18, -21, -6, 6, 0, 36, -24, -12, 30, 0, -60, 18, 12, 6, 0, 0, 12, 18, 171, 0, -60, -48, -12, 6, 0, 0, 24, -54, 66, 0, 96, -3, 36, -66, 0, -6, 78, -30, -78, 0, -63, -18, 78, -6, 0, -12, 90, 0, -18, 0, -51, 12, -96, 0, 0, -18, 24, -66, -42, 0, 48, 48, -108, -21, 0, -6, -186, 15, -24, 0, -96, 0, 84, -108, 0, 6, -111, 30, 6, 0, -39, -108, -12, 0, 0, -12, -15, 30, 108, 0, 30, -36, -30, 0, 0, 3, 30, -18, -60, 0, -18, -60, 120, 18, 0, -24, -30, 54, 48, 0, 84, 0, 24, 48, 0, 18, 42, -54, -30, 0, -30, 6, -48, 6, 0, -27, 51, 18, 117, 0, -24, 15, 24, 6, 0, 18, -42, -6, -30, 0, -24, 96, -81, 6, 0, 48, 36, 54, 36, 0, -84, 12, 30, 78, 0, 21, 132, -24, -60, 0, -18, 24, 162, -60, 0, 36, 3, 12, -12, 0, 18, 30, 90, 6, 0, 0, -78, -12, -87, 0, 12, 93, -129, 24, 0, -63, -84, 6, -12, 0, 132, -18, -42, 24, 0, 78, -63, -39, -24, 0, -48, 6, -72, -36, 0, -84, -162, 18, 48, 0, -114, -36, -48, 102, 0, -6, -6, -24, 9, 0, 66, 24, -216, 6, 0, -138, -30, 27, -162, 0, -12, -24, -48, 87, 0, -6, -27, -42, -18, 0, 108, 6, -108, 138, 0, -18, 84, 33, 21, 0, 0, -30, -39, 6, 0, 30, 18, -72, -144, 0, 36, 96, 210, 36, 0, -39, 102, 0, -54, 0, -72, -6, -18, -6, 0, 39, -12, 18, 6, 0, 120, -60, 66, 39, 0, 24, -30, 18, -108, 0, 33, 0, 60, -30, 0, -36, -6, 120, 162, 0, -276, 90, 150, 0, 0, 24, 42, -18, 174, 0, 6, -39, -114, -93, 0, -63, -6, 96, -66, 0, 78, 66, 150, -6, 0, 108, 57, -48, -219, 0, -36, -27, 162, 51, 0, 6, -132, 39, 252, 0, 42, 57, -120, 15, 0, 24, 18, -12, -156, 0, 6, 54, 72, -108, 0, -48, -54, 108, -138, 0, 9, 18, 48, 18, 0, 108, -36, 0, 0, 0, 144, 12, -72, 66, 0, 36, 60, 0, 246, 0, -18, -84, -42, 0, 0, 84, -12, -69, 0, 0, 198, 60, 0, 120, 0, 84, -171, -108, -30, 0, 66, 51, 42, 33, 0, 114, -48, -60, -240, 0, 48, 78, 48, -60, 0, -6, 84, -66, -90, 0, 84, -51, -24, -87, 0, -9, 174, -81, -36, 0, -30, 18, -162, 24, 0, -90, 87, -48, 102, 0, -78, 30, -30, -60, 0, -129, 60, -66, -135, 0, -102, 24, 60, -114, 0, -12, 12, -12, -39, 0, -30, -66, -96, 6, 0, -234, 30, -12, 168, 0, -72, 60, -96, 54, 0, -24, -39, -6, -72, 0, -210, -24, -6, 6, 0, 18, -315, 48, 60, 0, -150, -108, -12, 153, 0, 18, -36, -33, 84, 0, 36, 42, 99, -42, 0, 57, 96, 84, 18, 0, 18, -12, 168, -156, 0, 6, -24, 63, -30, 0, 60, 66, 102, -12, 0, 156, 120, -3, 24, 0, 156, 186, -27, -30, 0, 15, 18, 72, -66, 0, 228, -6, 198, -30, 0, 192, -42, 12, 54, 0, -138, -24, 84, 30, 0, 12, 183, 6, 150, 0, 24, -162, -72, -39, 0, 96, -180, -108, 201, 0, 84, -18, 96, -96, 0, -12, -18, -36, -33, 0, 42, 3, 24, 12, 0, -204, 54, -33, 276, 0, -198, 6, -36, 36, 0, -18, -114, -144, -102, 0, 42, -186, -60, -30, 0, 105, 60, -18, -54, 0, 18, 6, -120, -42, 0, -24, 12, 60, 324, 0, -168, -120, -3, 24, 0, 0, 96, -96, 156, 0, 6, -69, -30, -24, 0, 18, 192, 78, -6, 0, -108, -15, 336, -18, 0, -186, -204, 39, -183, 0, 72, 96, -180, 27, 0, -9, -180, -105, -9, 0, 12, 216, -111, 12, 0, 0, 30, -60, -114, 0, 24, -3, 60, -6, 0, -168, 45, 192, -12, 0, -144, 66, -126, -90, 0, 150, 51, 0, 120, 0, 12, -66, -96, -78, 0, -60, 60, 228, -219, 0, 126, 60, 372, -63, 0, 18, 6, 6, -366, 0, 174, -63, -84, 57, 0, -30, 252, -42, 96, 0, 96, 6, -144, 66, 0, -6, 156, 66, -45, 0, 3, 42, -264, 84, 0, 96, 216, 0, -135, 0, -198, -228, 18, -12, 0, -63, 18, 42, 42, 0, 30, -12, 6, 156, 0, 66, 192, -57, -90, 0, 84, 42, -294, -18, 0, 6, -114, 0, -12, 0, -99, -84, 78, 48, 0, -48, -198, -78, -18, 0, -84, -24, -162, 0, 0, 78, -108, -108, -132, 0, 12, -6, -60, 0, 0, -30, -207, -66, 66, 0, -48, 69, -108, -72, 0, 12, -174, -30, 438, 0, -516, -60, -144, -48, 0, -3, -222, 21, 120, 0, -42, -189, -192, -18, 0, -72, -264, 48, -84, 0, -108, 24, 540, 60, 0, 0, 192, 246, 30, 0, 18, -72, -18, 60, 0, -141, 174, -6, 69, 0, 36, -36, -72, 54, 0, -48, -108, 132, -144, 0, -42, 18, -75, 60, 0, -18, -60, 132, 48, 0, 192, -24, 186, 108, 0, -108, -120, 30, 132, 0, 75, 36, -48, -18, 0, 24, 60, 126, -30, 0, 276, -72, 210, -54, 0, -18, 6, 174, -117, 0, 156, 48, 183, 6, 0, -72, 204, -6, 276, 0, 24, 30, 24, 84, 0, 66, -141, 189, -168, 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.d", "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, 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, 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, 0, 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, 0, 0, 0, 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, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, 1, -1, -1, -1, -2, -1, -1, 0, 0, -1, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 1, 0], [0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 1, 0, 1, 1, 0, -1, 1, 0, 1, 1, 0, 1, 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, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, 0, 2, 0, -1, 0, -1, -1, 0, -1, -1, 0, -1, 0, 1, 0], [2, 0, 1, 0, -1, 0, 1, 0, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 1, 1, 0, 0, 1, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, -1, -1, 2, 1, 1, 3, 0, 0, 1, 0, 1, 3, 0, 0, -1], [0, 1, -1, 0, -1, 1, 1, 0, 0, -1, -1, 0, 0, -1, 0, 0, -1, -1], [-1, -1, 1, 0, 1, -1, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, -1, -1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, -1], [0, -2, -2, 0, -1, 1, 0, -2, 4, 2, -2, 2, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [-1, -1, 0, -1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0, 0, -1, -2, -1, 1, 1, -1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-3, 2, -1, 1, -2, 2, 0, -2, -3, 0, 1, -4, 0, -1, -1, 0, 0, -1], [1, 1, 1, -1, -2, 0, 1, 0, 0, 0, -1, 1, 1, 0, -1, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, -1, 1, 1, -1, -1, 0, 1, 2, 0, 1, -1, 0, 1, 0, 1, 0], [1, -1, 0, -1, 0, 1, 0, 1, 0, 0, 1, -1, -1, -1, 0, 0, 0, 0], [0, -1, 0, 0, 1, -1, 0, 1, 1, 0, 0, -1, -1, 0, 1, 0, 0, 0], [3, 1, 0, 2, 1, 1, 0, 2, -2, 2, 1, -1, 1, 1, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, 1, -3, -2, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -2, -2], [-3, 1, -1, 0, -1, 0, -1, -1, 0, 2, 3, 0, -1, 0, 1, -1, 0, 0], [-2, 1, -2, -1, -1, 1, 0, -1, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0], [0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 1, 0, 0, -1, 0, 1, -1, 0, 1, 0, 0, 0, 2, 0, 0, 0], [4, -1, 1, -1, 1, -1, -1, 0, 0, -1, 3, 0, 0, -1, -1, 1, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 1, 0, -1, -3, -1, 0, -3, -4, -1, -4, 0, 1, -4, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -3, 0, 2, -1, 1, 0, -1, 5, 3, 1, 5, -1, 2, -1, -1, 2, 1], [-1, 1, -1, 0, -1, 1, 0, -1, -1, 0, 1, -1, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, -1, 0, 0, -1, 0, -2, 0, 0, 0, 0, 2, 0, -1, 0], [-4, 2, -1, 1, 0, -1, 0, 2, 2, 2, 2, -2, 0, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 2, -1, 1, -2, 3, 2, 1, 3, -3, 1, 0, 1, 0, 3, 0, -1, 0], [0, 0, 1, 0, -1, -1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0], [-3, 1, 1, 0, 1, -1, -1, -1, 3, -3, 0, 3, 0, -1, 3, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -1, -3, 2, 3, 1, -2, 0, 0, -2, -4, -3, -2, 0, -2, -1, 1, 1], [1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 2, 0, 1, 1, -1, 1, 0], [5, 3, 0, 1, 3, 0, 0, 2, 1, 5, 4, 1, -1, 0, -4, -1, 0, 1], [-1, 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, 0, 0], [3, 1, -2, -1, 1, 1, 1, 0, -1, -4, -1, 0, 0, 0, -4, -1, 0, 0], [0, -1, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0], [0, -1, -1, 1, 1, 0, -1, -1, 1, 0, -1, 0, -1, 0, 1, -1, 1, 1], [-4, 0, 0, 3, 0, 0, 0, 0, 5, 2, 5, 3, -1, 1, 4, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, -2, -2, 0, 0, -1, -1, 0, 0, -1, 4, 0, -2, 4, 1, -1, -1], [-1, 1, 0, 0, -1, 1, 1, 1, 0, 0, 1, -2, 1, 0, 1, 0, -1, -1], [1, 0, 0, 0, 0, 0, 0, 1, 2, -4, -4, 3, -1, 0, -3, -1, 0, 0], [0, 0, 0, -2, -2, 2, 1, 0, -1, 1, 0, 0, 0, 0, -1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 1, 0, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, -1, 0], [-1, -2, 0, 0, 2, 0, 1, 2, 7, -7, -3, 3, 2, 2, 0, 2, 2, 0], [2, 0, 0, 0, 2, 1, 0, 1, -1, 3, 0, -2, 0, 1, -1, 0, 1, -1], [2, -2, 0, 2, 2, 2, 0, 2, -2, -2, -2, 0, -2, 0, 0, -2, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, 4, -1, 4, 3, 5, 1, 4, 4, 0, 7, -3, 0, 1, -7, -2, 1, 0], [-1, -1, 0, 0, 0, 1, -1, 0, -1, -1, 1, -1, -1, 1, -1, -2, 1, 2], [0, 0, 2, 0, 1, -3, 0, -1, 0, 2, 0, -2, 0, -2, 0, 2, -2, 0], [0, 1, -1, -1, -1, 1, 0, -2, -3, -2, 1, -2, 1, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, -1, 1, -1, 0, 0, -2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 3, 4, -1, -2, 1, 4, 7, 3, 7, -3, 2, -1, -1, 3, 2], [-1, 0, 1, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0], [4, 1, 0, 0, 0, -2, -1, -2, 2, 4, 5, 2, 2, -1, -5, 1, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, 0, -4, -3, -1, -1, -5, 0, 3, 4, -7, -1, 0, 1, 0, -1, 1], [1, -1, 0, 0, 0, 1, 0, 1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0], [0, -3, -3, -1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, -1, 1, -1, -1, 1, 1, 1, -3, 3, -1, 1, 1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 2, 2, 2, -2, -1, 2, 1, -4, 3, 0, -2, 1, 1, -4, 0, -1, -1], [3, -1, -1, 1, 0, 1, -1, 1, 1, -4, -4, 4, 1, 1, -4, 1, 0, 0], [8, -2, 2, -5, -3, 0, 2, -3, 0, -9, -8, -5, 2, 0, 1, 1, -3, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}