# Stored data for newform 1638.2.r.y, downloaded from the LMFDB on 25 April 2024. {"label": "1638.2.r.y", "space_label": "1638.2.r", "level": 1638, "weight": 2, "hecke_orbit": 25, "hecke_orbit_code": 108087559321552486, "dim": 4, "is_polredabs": true, "nf_label": "4.0.2601.1", "trace_hash": 975302685997421926, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-4, -1, 1]], [11, [16, -4, 5, 1, 1]], [17, [1, -8, 65, 8, 1]]], "qexp_display": "q+(1-\\beta _{2})q^{2}-\\beta _{2}q^{4}+(1+\\beta _{3})q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "r", "char_is_real": false, "Nk2": 6552, "analytic_conductor": 13.079495851085728, "hecke_ring_index": 1, "level_radical": 546, "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": "0.009", "prec": 17}, "analytic_rank_proved": true, "char_values": [1638, 3, [911, 703, 379], [3, 3, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7, 13], "conrey_indexes": [757, 1387], "field_disc": 2601, "field_disc_factorization": [[3, 2], [17, 2]], "field_poly": [16, 4, 5, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.903", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "59.373", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1564.086", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [2, 0, 2, -2], "traces": [0, 4, 2, 0, -2, 2, 0, -2, -4, 0, 1, -1, 0, -2, -4, 0, -2, -8, 0, 1, -1, 0, 1, 6, 0, -2, -1, 0, -2, -4, 0, 0, 2, 0, -16, -1, 0, 9, 2, 0, -2, -6, 0, 16, 2, 0, -6, 26, 0, -2, -1, 0, 1, -28, 0, 8, 2, 0, 4, 2, 0, 6, 0, 0, 4, -1, 0, -10, -8, 0, -2, 2, 0, -18, -9, 0, 1, 2, 0, -18, -1, 0, 6, 4, 0, -21, 32, 0, 1, 11, 0, 1, -12, 0, 13, -8, 0, 10, 2, 0, 1, 9, 0, -8, 2, 0, -14, -1, 0, -16, -8, 0, 4, -1, 0, 20, 8, 0, 4, -8, 0, 13, 12, 0, 0, 6, 0, 8, 2, 0, 25, -24, 0, 1, 10, 0, 8, 29, 0, 15, -1, 0, 4, 26, 0, 15, -9, 0, -18, -27, 0, -30, -1, 0, 1, 0, 0, -30, -9, 0, 1, -12, 0, -16, 12, 0, 2, -8, 0, -50, -42, 0, 16, -36, 0, 1, -1, 0, -11, -20, 0, 20, 2, 0, -6, 13, 0, -26, -13, 0, -16, -2, 0, 8, 20, 0, 4, 21, 0, 32, 2, 0, -9, 8, 0, 31, -4, 0, 1, -18, 0, -2, 14, 0, 1, 8, 0, 0, -8, 0, -16, 55, 0, -36, 2, 0, -2, -30, 0, -6, -20, 0, 4, 44, 0, 64, 2, 0, 8, -28, 0, 21, 26, 0, 6, -1, 0, 25, 0, 0, 3, 14, 0, -14, -8, 0, -2, -24, 0, -18, 26, 0, -12, 2, 0, -14, -1, 0, 20, 46, 0, -4, 16, 0, 58, 9, 0, 35, 30, 0, 1, 6, 0, 40, 2, 0, 25, 12, 0, -32, -15, 0, 9, 15, 0, -16, -9, 0, -54, 48, 0, 16, -15, 0, -2, -31, 0, 18, -1, 0, 0, -30, 0, -24, -15, 0, 9, -58, 0, -19, 2, 0, -6, -13, 0, 1, -32, 0, 6, -13, 0, -14, -2, 0, 8, 12, 0, 12, -25, 0, -21, 0, 0, 4, -16, 0, -72, -7, 0, 36, 2, 0, -2, -47, 0, 52, -22, 0, 20, 40, 0, 29, 10, 0, 1, -26, 0, 14, 6, 0, -13, 14, 0, 35, -13, 0, -26, 53, 0, -34, -8, 0, -4, -5, 0, -16, -8, 0, 10, 46, 0, -116, 2, 0, -21, 8, 0, -27, 64, 0, 1, 17, 0, 0, -18, 0, 4, -4, 0, 19, -31, 0, 4, 2, 0, -32, -1, 0, -9, 22, 0, 18, 2, 0, 28, -13, 0, 6, 2, 0, 16, 14, 0, 55, 0, 0, 8, -28, 0, 36, -8, 0, 8, 34, 0, 14, 36, 0, -2, -38, 0, -37, -1, 0, -60, 26, 0, -29, -3, 0, -40, -25, 0, 74, -4, 0, 22, 16, 0, 20, 32, 0, -2, -16, 0, -9, 16, 0, -14, 25, 0, 21, 42, 0, 13, 22, 0, -35, -6, 0, 1, 0, 0, -36, -1, 0, 0, 2, 0, 88, -3, 0, 28, -24, 0, 47, -28, 0, -16, -63, 0, 9, -4, 0, 24, -72, 0, 19, -9, 0, 1, -120, 0, 13, 12, 0, -2, 0, 0, -6, -7, 0, -2, 105, 0, -60, 10, 0, 92, -1, 0, -14, 4, 0, 8, 60, 0, -52, 29, 0, -9, -38, 0, 9, 70, 0, 15, 16, 0, -8, 2, 0, 3, -28, 0, -9, -40, 0, -2, -44, 0, -68, -1, 0, 6, 14, 0, -134, 32, 0, -30, -2, 0, 7, 18, 0, 30, -12, 0, 0, -32, 0, 9, 4, 0, -21, -27, 0, 54, 20, 0, -3, -16, 0, 15, 15, 0, 32, -1, 0, -62, -13, 0, -39, 9, 0, -2, 1, 0, 66, 0, 0, -15, -22, 0, -72, -12, 0, 15, -106, 0, 49, 18, 0, -29, 72, 0, 1, -38, 0, 1, 21, 0, -83, 6, 0, 13, -55, 0, -36, 26, 0, -16, 37, 0, 56, -6, 0, -26, 33, 0, 3, -28, 0, -4, -8, 0, -22, 16, 0, -12, -74, 0, 22, 6, 0, 25, 0, 0, 10, 21, 0, 0, 48, 0, 23, 2, 0, -32, 14, 0, 0, -36, 0, -14, 16, 0, -88, -36, 0, 1, 50, 0, -8, -1, 0, 47, -18, 0, 23, 104, 0, -11, 0, 0, -4, 40, 0, 20, -19, 0, 4, -29, 0, -10, 19, 0, 160, -1, 0, -13, 64, 0, 0, -14, 0, 12, -22, 0, -6, -26, 0, 28, 24, 0, -5, 70, 0, 13, 2, 0, 61, -13, 0, 49, 104, 0, -56, 34, 0, 8, 36, 0, 8, -2, 0, -10, 50, 0, -18, -8, 0, -16, -8, 0, 0, -10, 0, 23, -74, 0, 100, -58, 0, -2, -66, 0, -45, -42, 0, 4, -1, 0, 99, -54, 0, 32, 68, 0, -103, -1, 0, -17, -4, 0, -40, 0, 0, -9, -11, 0, 96, -4, 0, -8, 60, 0, -8, 38, 0, -62, 1, 0, 60, 8, 0, -2, -104, 0, -24, -16, 0, -2, 16, 0, -72, 9, 0, -22, 20, 0, 16, 9, 0, 4, -25, 0, 13, 14, 0, -26, -44, 0, 72, -6, 0, 1, -74, 0, 14, 8, 0, -14, -148, 0, -18, 110, 0, 0, 13, 0, 56, 16, 0, -14, -3, 0, -13, -36, 0, 8, 77, 0, -80, -47, 0, 17, -55, 0, -16, -14, 0, 72, -19, 0, -44, -4, 0, -76, 0, 0, 56, -74, 0, 1, -58, 0, -6, -30, 0, 1, 28, 0, -18, 29, 0, 3, 12, 0, 63, -20, 0, -50, -154, 0, 4, 37, 0, -8, -22, 0, -2, -22, 0, 8, -64, 0, -146, 10, 0, -32, 92, 0, -50, -4, 0, -8, 113, 0, 9, -18, 0, 8, 34, 0, 16, 14, 0, -25, 29, 0, -124, 30, 0, 21, 21, 0, -48, -13, 0, 44, 42, 0, 15, -70, 0, -12, -37, 0, -3, 2, 0, 0, 24, 0, 2, -18, 0, -26, 96, 0, -21, 0, 0, -2, 16, 0, 18, 44, 0, -6, -1, 0, -26, 14, 0, -48, -7, 0, 128, -47, 0, -14, 66, 0, -30, -8, 0, 63, 62, 0, -80, 18, 0, -2, 37, 0, 9, 48, 0, -36, 50, 0, -49, -19, 0, 9, -44, 0, 96, -25, 0, -60, -27, 0, 8, -13, 0, 24, -42, 0, 30, -4, 0, 0, 16, 0, 15, -12, 0, 7, -108, 0, -22, -1, 0, 99, 24, 0, -105, 60, 0, -10, 1, 0, -8, 46, 0, -2, -2, 0, 90, -7, 0, 8, 0, 0, 48, -8, 0, 30, 0, 0, 186, -26, 0, -29, 142, 0, 15, -18, 0, -19, 8, 0, 138, 18, 0, 35, -25, 0, -38, -15, 0, -16, -52, 0, 40, -16, 0, 1, -18, 0, -158, -3, 0, -56, 6, 0, 27, -18, 0, -80, -32, 0, -32, -4, 0, 44, 12, 0, -16, -34, 0, -26, -156, 0, 0, -6, 0, -14, -47, 0, -29, -67, 0, 64, 20, 0, -37, -15, 0, -4, -32, 0, 124, -7, 0, 9, 16, 0, -36, 15, 0, 12, 38, 0, 59, 0, 0, -16, -50, 0, 25, 18, 0, 2, 24, 0, -80, 21, 0, 27, 125, 0, 88, 6, 0, 10, 38, 0, -152, 3, 0, -32, 53, 0, 110, 30, 0, 30, -36, 0, -65, 64, 0, 1, -178, 0, -42, -31, 0, 70, 42, 0, 1, 39, 0, -9, 4, 0, 34, -1, 0, 2, 4, 0, 87, 33, 0, 0, 53, 0, -16, 15, 0, -11, -64, 0, -38, -36, 0, 12, 40, 0, 92, 30, 0, -53, 44, 0, -56, 98, 0, 9, -24, 0, -10, 29, 0, -72, 0, 0, -44, -1, 0, -19, 41, 0, -120, -1, 0, 42, 36, 0, 39, -166, 0, 12, 57, 0, 25, 26, 0, 55, -26, 0, 10, -18, 0, 25, 104, 0, -121, 16, 0, -37, 20, 0, 13, 28, 0, -12, 123, 0, -16, -13, 0, 66, 29, 0, -50, -3, 0, -14, 14, 0, 18, -2, 0, 8, -18, 0, 0, -44, 0, 8, -2, 0, 4, -24, 0, -37, 19, 0, 6, -22, 0, -6, 50, 0, -16, 50, 0, 0, -104, 0, -56, -10, 0, 42, 28, 0, 25, 0, 0, 96, 86, 0, 25, 46, 0, -2, -258, 0, -44, -16, 0, 7, -42, 0, -83, 0, 0, 36, 9, 0, 4, -7, 0, 32, -178, 0, 32, -44, 0, -72, -64, 0, -100, -1, 0, 25, -100, 0, 122, -4, 0, 1, -82, 0, 26, 94, 0, -9, 20, 0, 8, 46, 0, 52, -4, 0, 1, 11, 0, 0, 64, 0, -58, 4, 0, 20, -100, 0, -62, -20, 0, -38, 34, 0, 40, 8, 0, -58, -152, 0, 54, -20, 0, -19, 16, 0, -25, 80, 0, -2, 0, 0, 87, 13, 0, -64, 9, 0, 67, 0, 0, -28, 26, 0, 3, 6, 0, -44, -18, 0, 4, 6, 0, -13, 106, 0, -10, 14, 0, -24, 166, 0, -60, -10, 0, 35, 36, 0, 92, 26, 0, 1, 76, 0, -13, -61, 0, 13, 8, 0, -12, -4, 0, 52, 15, 0, -122, 56, 0, 68, -7, 0, 0, 16, 0, 72, 9, 0, -37, 16, 0, 2, 2, 0, 9, -5, 0, -2, 128, 0, 28, 18, 0, 8, -4, 0, -66, -8, 0, -16, -47, 0, 61, 0, 0, -20, -16, 0, 104, -23, 0, -37, -94, 0, 72, 50, 0, 58, -12, 0, 26, -4, 0, -33, 4, 0, -32, -90, 0, -21, 18, 0, -62, -4, 0, 1, 66, 0, -46, -6, 0, -27, -30, 0, 144, -32, 0, 136, 16, 0, 70, -206, 0, -2, 17, 0, 3, -34, 0, 4, 20, 0, -19, -20, 0, 0, -184, 0, -32, 9, 0, 11, -63, 0, 18, 48, 0, -8, -3, 0, -32, -4, 0, 120, -22, 0, 216, 8, 0, 19, -16, 0, 44, -31, 0, -1, 0, 0, -32, 120, 0, 4, 74, 0, 200, -4, 0, -52, 44, 0, 77, 24, 0, 16, 67, 0, 18, -1, 0, 8, -43, 0, -200, 72, 0, 18, 14, 0, 22, -44, 0, 40, -44, 0, -72, 32, 0, -9, 142, 0, 21, 2, 0, -38, -6, 0, -18, -13, 0, -14, -68, 0, 20, -13, 0, -88, 12, 0, 0, 36, 0, -12, 31, 0, -76, -1, 0, -37, 2, 0, -242, 7, 0, -8, -146, 0, 18, -28, 0, -74, -18, 0, -26, -36, 0, 55, -86, 0, -80, 0, 0, -13, 84, 0, 10, 46, 0, 8, 18, 0, -192, 14, 0, -6, 84, 0, -11, -26, 0, -72, 14, 0, -113, 16, 0, -77, -96, 0, 19, -40, 0, -55, -160, 0, -14, -17, 0, 55, 50, 0, 38, -8, 0, -28, -40, 0, 78, 36, 0, -38, 89, 0, -138, 44, 0, -2, 152, 0, 88, -38, 0, 0, 48, 0, 50, 112, 0, -37, 23, 0, -33, 2, 0, -29, -102, 0, 9, 6, 0, 30, -10, 0, 246, -25, 0, 14, -32, 0, -8, 18, 0, 58, 0, 0, 108, 6, 0, 24, 92, 0, 64, 126, 0, 20, -4, 0, 12, -25, 0, -2, 110, 0, -42, -4, 0, -37, -36, 0, 7, -4, 0, -44, -13, 0, -78, -1, 0, -44, 77, 0, 96, -8, 0, -32, -148, 0, 236, -73, 0, -10, 56, 0, 38, -64, 0, 46, 46, 0, -33, -100, 0, -2, 73, 0, 0, 8, 0, -113, 68, 0, 8, -21, 0, -9, -25, 0, 36, -8, 0, 68, 100, 0, -28, 32, 0, 28, -23, 0, 40, -50, 0, -29, -76, 0, -21, -62, 0, 9, -18, 0, 63, -21, 0, -21, 18, 0, 38, -24, 0, -26, -12, 0, 35, 22, 0, 84, -54, 0, 74, -15, 0, -35, 2, 0, -176, -6, 0, 37, -296, 0, 32, -6, 0, 1, -63, 0, 15, 0, 0, 12, -3, 0, 24, -2, 0, 18, 41, 0, 26, -25, 0, 48, -62, 0, -80, 21, 0, 0, 46, 0, -57, -4, 0, 32, -39, 0, 41, 36, 0, -44, -172, 0, 1, -3], "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, 13, 3, 1, 3, 0]], "char_orbit_index": 18, "prim_orbit_index": 3, "minimal_twist": "546.2.l.l", "char_is_minimal": true, "conrey_index": 757, "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], [1, 0, -1, 0], [0, 0, 0, 0], [0, 0, -1, 0], [1, 0, 0, 1], [0, 0, 0, 0], [0, 0, -1, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [1, 1, -1, 1], [0, 1, 0, 1], [0, 0, 0, 0], [-1, -2, 1, -1], [-1, 0, 0, 0], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 2, -5, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 1, -1, 0], [0, 0, 0, 0], [0, 1, 0, 0], [4, 2, -4, 2], [0, 0, 0, 0], [0, 0, 0, 1], [0, -1, 1, 1], [0, 0, 0, 0], [-1, 0, 1, 0], [-1, 2, 1, 2], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-5, 0, 0, -2], [0, 1, -1, 0], [0, 0, 0, 0], [5, 1, -5, 1], [0, 0, 0, -1], [0, 0, 0, 0], [-1, 0, 0, -1], [-1, 4, 1, 4], [0, 0, 0, 0], [0, 0, 8, 0], [0, 0, 0, -1], [0, 0, 0, 0], [0, 2, -4, 0], [8, 0, 0, 3], [0, 0, 0, 0], [-1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 0, 0], [1, 1, 0, 2], [-7, 0, 0, 0], [0, 0, 0, 0], [4, 0, -4, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 2, 1, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 4, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [-5, -1, 9, -1], [0, 0, 0, 0], [-4, 2, 4, 2], [-5, -2, 5, -2], [0, 0, 0, 0], [-1, 0, 0, -1], [0, -6, 4, 0], [0, 0, 0, 0], [-5, 0, 0, -1], [0, 1, -5, 0], [0, 0, 0, 0], [0, -1, 0, -1], [0, 0, 0, -1], [0, 0, 0, 0], [-4, 0, 0, 1], [-1, -1, 1, -1], [0, 0, 0, 0], [0, 4, 1, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 5, -13, 0], [8, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, -1], [6, 1, -6, 1], [0, 0, 0, 0], [1, 1, 0, 2], [-4, 0, 0, -2], [0, 0, 0, 0], [8, 3, -8, 3], [0, 0, -4, 0], [0, 0, 0, 0], [0, -2, 6, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 1, 0, 0]]}