# Stored data for newform 525.2.r.h, downloaded from the LMFDB on 19 April 2024. {"label": "525.2.r.h", "space_label": "525.2.r", "level": 525, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31526365656252941, "dim": 16, "is_polredabs": true, "trace_hash": 1309049093328355418, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [256, 0, -1296, 0, 5489, 0, -4947, 0, 3258, 0, -843, 0, 158, 0, -15, 0, 1]], [11, [107584, 59040, 29776, 6688, 1832, 296, 72, 8, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{12}q^{3}+(1+\\beta _{3}+2\\beta _{5}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 35, "char_orbit_label": "r", "char_is_real": false, "Nk2": 2100, "analytic_conductor": 4.19214610611722, "hecke_ring_index": 4, "level_radical": 105, "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": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [525, 6, [176, 127, 451], [6, 3, 4]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 4, "level_primes": [3, 5, 7], "conrey_indexes": [424, 499], "field_disc": 20264347788313541194285056, "field_disc_factorization": [[2, 20], [3, 8], [53, 4], [139, 4]], "field_poly": [256, 0, -1296, 0, 5489, 0, -4947, 0, 3258, 0, -843, 0, 158, 0, -15, 0, 1], "hecke_ring_index_factorization": [[2, 2]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.046", "prec": 17}, {"__RealLiteral__": 0, "data": "15.176", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2051.120", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "554088.839", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 8, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 14, 0, -4, 0, 0, 8, 0, -16, 0, 0, 24, 0, -34, 0, 0, 6, 0, 4, 0, 0, -6, 0, 38, 0, 0, -64, 0, -18, 0, 0, -56, 0, 28, 0, 0, 14, 0, 16, 0, 0, 52, 0, 12, 0, 0, 42, 0, -12, 0, 0, -2, 0, -42, 0, 0, 20, 0, 40, 0, 0, -84, 0, -24, 0, 0, 8, 0, 88, 0, 0, -42, 0, -92, 0, 0, 16, 0, -8, 0, 0, 36, 0, -24, 0, 0, -20, 0, 42, 0, 0, 44, 0, 34, 0, 0, -32, 0, -28, 0, 0, 20, 0, 168, 0, 0, 42, 0, -32, 0, 0, -54, 0, -56, 0, 0, -140, 0, -72, 0, 0, 12, 0, 30, 0, 0, -10, 0, -40, 0, 0, 12, 0, -156, 0, 0, 128, 0, -24, 0, 0, 34, 0, -108, 0, 0, 52, 0, -12, 0, 0, 56, 0, -70, 0, 0, 12, 0, -64, 0, 0, 116, 0, 76, 0, 0, -140, 0, -6, 0, 0, 16, 0, 328, 0, 0, 16, 0, 60, 0, 0, -84, 0, 88, 0, 0, 2, 0, 60, 0, 0, -78, 0, -40, 0, 0, -36, 0, 2, 0, 0, 32, 0, -34, 0, 0, 136, 0, 120, 0, 0, -100, 0, -12, 0, 0, -8, 0, -56, 0, 0, -150, 0, -60, 0, 0, 66, 0, 44, 0, 0, -38, 0, 80, 0, 0, 56, 0, -48, 0, 0, 140, 0, 32, 0, 0, -4, 0, -200, 0, 0, 34, 0, 38, 0, 0, -118, 0, -32, 0, 0, -56, 0, -118, 0, 0, -4, 0, -112, 0, 0, 88, 0, -132, 0, 0, -36, 0, 152, 0, 0, -88, 0, 16, 0, 0, 16, 0, -24, 0, 0, 14, 0, 22, 0, 0, 84, 0, 96, 0, 0, -6, 0, -28, 0, 0, -80, 0, 52, 0, 0, -268, 0, 156, 0, 0, 64, 0, 80, 0, 0, 14, 0, 6, 0, 0, -116, 0, 80, 0, 0, -204, 0, 98, 0, 0, -16, 0, -28, 0, 0, 160, 0, -44, 0, 0, 64, 0, 28, 0, 0, 36, 0, -144, 0, 0, 92, 0, -14, 0, 0, 270, 0, -10, 0, 0, 8, 0, -4, 0, 0, 232, 0, -52, 0, 0, -148, 0, -16, 0, 0, 252, 0, -88, 0, 0, 104, 0, -160, 0, 0, -8, 0, -52, 0, 0, 58, 0, -16, 0, 0, 12, 0, -96, 0, 0, -94, 0, -4, 0, 0, 24, 0, 254, 0, 0, -104, 0, -128, 0, 0, 68, 0, 240, 0, 0, -76, 0, -4, 0, 0, 256, 0, -106, 0, 0, 4, 0, 24, 0, 0, -154, 0, 162, 0, 0, 48, 0, 8, 0, 0, -384, 0, -164, 0, 0, 12, 0, 80, 0, 0, 136, 0, 0, 0, 0, 38, 0, 0, 0, 0, -94, 0, -240, 0, 0, -24, 0, 50, 0, 0, 52, 0, 2, 0, 0, 72, 0, -56, 0, 0, -186, 0, 432, 0, 0, -58, 0, 16, 0, 0, 120, 0, 112, 0, 0, -4, 0, 140, 0, 0, -128, 0, -76, 0, 0, -96, 0, -8, 0, 0, -696, 0, -496, 0, 0, 96, 0, 40, 0, 0, 36, 0, 42, 0, 0, -252, 0, -138, 0, 0, 116, 0, -10, 0, 0, -40, 0, -24, 0, 0, 268, 0, 110, 0, 0, 152, 0, -96, 0, 0, -136, 0, -180, 0, 0, 92, 0, -22, 0, 0, 264, 0, -42, 0, 0, 78, 0, -88, 0, 0, 94, 0, -128, 0, 0, -400, 0, -4, 0, 0, -48, 0, -248, 0, 0, 216, 0, 172, 0, 0, -46, 0, -24, 0, 0, -16, 0, 216, 0, 0, 96, 0, 280, 0, 0, 46, 0, 4, 0, 0, -140, 0, 332, 0, 0, 24, 0, -104, 0, 0, -204, 0, 64, 0, 0, 44, 0, -116, 0, 0, -180, 0, 172, 0, 0, 120, 0, 174, 0, 0, 14, 0, -76, 0, 0, 16, 0, 176, 0, 0, 392, 0, -84, 0, 0, 92, 0, -160, 0, 0, -156, 0, 84, 0, 0, -146, 0, 20, 0, 0, -46, 0, 30, 0, 0, -152, 0, -8, 0, 0, 520, 0, 24, 0, 0, 248, 0, 264, 0, 0, -60, 0, 304, 0, 0, 0, 0, -16, 0, 0, 132, 0, 224, 0, 0, 68, 0, -42, 0, 0, -32, 0, -54, 0, 0, -16, 0, 124, 0, 0, 32, 0, -600, 0, 0, -56, 0, 68, 0, 0, -256, 0, 106, 0, 0, -136, 0, 104, 0, 0, -152, 0, -30, 0, 0, 40, 0, -128, 0, 0, 344, 0, -180, 0, 0, -180, 0, -272, 0, 0, 24, 0, -452, 0, 0, -132, 0, -152, 0, 0, -198, 0, 36, 0, 0, 100, 0, 52, 0, 0, 164, 0, 70, 0, 0, 32, 0, 20, 0, 0, -132, 0, -672, 0, 0, 76, 0, -456, 0, 0, -128, 0, 120, 0, 0, 84, 0, -124, 0, 0, 222, 0, 28, 0, 0, -40, 0, 34, 0, 0, 260, 0, 212, 0, 0, -64, 0, -208, 0, 0, -110, 0, 88, 0, 0, -6, 0, 244, 0, 0, 150, 0, 316, 0, 0, 272, 0, 64, 0, 0, -34, 0, 92, 0, 0, -96, 0, -42, 0, 0, 328, 0, -124, 0, 0, -92, 0, 488, 0, 0, -200, 0, 252, 0, 0, 58, 0, -16, 0, 0, -136, 0, 24, 0, 0, 72, 0, -8, 0, 0, 152, 0, -94, 0, 0, -56, 0, 88, 0, 0, -342, 0, 756, 0, 0, 14, 0, -2, 0, 0, -228, 0, 50, 0, 0, -48, 0, 170, 0, 0, -116, 0, 10, 0, 0, -124, 0, 56, 0, 0, 64, 0, -192, 0, 0, 194, 0, -16, 0, 0, 84, 0, -64, 0, 0, -220, 0, -138, 0, 0, -346, 0, -240, 0, 0, -16, 0, -164, 0, 0, -48, 0, 170, 0, 0, 224, 0, 84, 0, 0, 72, 0, 224, 0, 0, 192, 0, 158, 0, 0, 64, 0, 96, 0, 0, -16, 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, 5, 2, 1, 2, 0], [1, 1, 7, 3, 1, 3, 0], [1, 1, 35, 10, 1, 6, 0]], "char_orbit_index": 18, "prim_orbit_index": 10, "minimal_twist": "525.2.i.i", "char_is_minimal": false, "conrey_index": 424, "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], [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, 1, 0, 0, 0], [1, 0, 0, 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, 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, 1, 1, 0, 0, 0, 1], [0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 1, -1, 1, -1, 1, 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], [-3, 0, 1, 0, -1, -3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 1, -1, -1], [0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 1, -1], [2, 0, 0, 0, -1, 2, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, -1, 1, 5, 2, -1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, -1, 2, 3, 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], [1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, 0, 0, 0, 0, 0, -3, 0, -1, 2, 3, 1, -1, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 2, 2], [-1, 0, 1, 0, 2, -1, 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, 3, 3, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0], [0, 4, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, 4, -1, 0, 0], [-4, 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, 0, 0], [-3, 0, 1, 1, 3, -2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -3, 4, 0, -2, 0], [0, -1, 0, 0, 0, 0, 0, 0, -3, 0, 1, 1, 0, 0, 1, 1], [-2, 0, -2, -1, 3, 0, 1, -3, 0, 3, 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, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2, 0, -2, 2, 2], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -7, -1, 2, -1], [0, 0, 1, 1, -1, 1, 1, 1, 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, 2, 1, -1, 0, 1, 1, 0, -1, 0, 0, 0, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, -2, -1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 0, 2, -1, -1], [1, 0, 3, -1, -4, -7, -3, -1, 0, -4, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, -2, 0, -4, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, 0, -2, 1, 1], [0, -1, 0, 0, 0, 0, 0, 0, 5, 0, -2, -1, -5, 2, -1, -1], [1, 0, 1, -1, -3, -1, 1, 1, 0, 1, 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, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -10, 2, 1, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -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, 0, 0, 0], [4, 0, -2, -4, 1, 12, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -3, 0, 1, 0, -1], [0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [5, 0, -1, -2, 1, 3, -2, -2, 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, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 12, 0, -4, -4, -12, 4, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [-3, 0, -1, -7, 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, 0, 0, 0], [-3, 0, -1, 0, -3, -3, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0], [0, -7, 0, 0, 0, 0, 0, 0, 1, 0, -1, -1, 0, 0, -1, -1], [2, 0, -2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [8, 0, -2, -6, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 1, 0, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, 2, 0, 2], [-4, 0, -2, -2, -7, -6, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, -1, 6, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0, 0, 0, 3, 0, -1, 5, -2, -4, 3, 1], [0, 3, 0, 0, 0, 0, 0, 0, -4, 0, 0, -3, 4, 0, 0, 0], [-1, 0, 1, 3, 2, -2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 1, -1, 0, 2, -1, -1], [0, -3, 0, 0, 0, 0, 0, 0, -1, 0, 1, 4, 1, -1, -1, 2], [1, 0, 1, -2, 2, -4, -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], [-2, 0, 2, 2, 0, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0], [0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 9, -5, 1, -2, 1], [1, 0, -1, -1, 0, 3, 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], [5, 0, 2, -1, -2, 4, -5, 1, 0, -2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, -18, 0, 4, 2, 18, -4, 2, 2], [0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 1, 0, 0], [5, 0, -1, 0, -5, 5, 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, 2, 3, 1, -4, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0], [0, 2, 0, 0, 0, 0, 0, 0, -3, 0, 2, 0, 3, -2, 0, 2], [0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 2, -1, 12, 0, -2, 0], [-2, 0, 0, 1, 1, 0, 1, -1, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}