# Stored data for newform 825.2.bx.h, downloaded from the LMFDB on 16 April 2024. {"label": "825.2.bx.h", "space_label": "825.2.bx", "level": 825, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31528564679508793, "dim": 16, "is_polredabs": true, "trace_hash": 427812742734190661, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [14641, 0, -15609, 0, 9087, 0, -3647, 0, 2730, 0, -473, 0, 57, 0, -6, 0, 1]], [13, [1, 0, -13, 0, 75, 0, -103, 0, 2874, 0, 683, 0, 665, 0, -42, 0, 1]]], "qexp_display": "q+(-\\beta _{8}+\\beta _{13}-2\\beta _{15})q^{2}-\\beta _{14}q^{3}+\\cdots", "char_order": 10, "char_parity": 1, "char_degree": 4, "char_conductor": 55, "char_orbit_label": "bx", "char_is_real": false, "Nk2": 3300, "analytic_conductor": 6.587658166755632, "hecke_ring_index": 1, "level_radical": 165, "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": "0.511", "prec": 17}, "analytic_rank_proved": true, "char_values": [825, 10, [551, 727, 376], [10, 5, 4]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [3, 5, 11], "conrey_indexes": [49, 124, 499, 724], "field_disc": 11316496000000000000, "field_disc_factorization": [[2, 16], [5, 12], [29, 4]], "field_poly": [1, 0, -1, 0, 15, 0, -59, 0, 104, 0, -59, 0, 15, 0, -1, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.208", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1713.151", "prec": 27}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "328477.827", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c10", "trace_display": [0, 0, 0, 0], "traces": [0, 16, 0, 0, 4, 0, 0, 0, 0, 4, 0, -6, 0, 0, 20, 0, -40, 0, 0, -12, 0, -8, 0, 0, 40, 0, -16, 0, 0, 0, 0, 6, 0, 0, -100, 0, -4, 0, 0, -12, 0, -50, 0, 0, -14, 0, -12, 0, 0, -42, 0, -20, 0, 0, -20, 0, 40, 0, 0, -70, 0, 42, 0, 0, 154, 0, 50, 0, 0, 10, 0, 50, 0, 0, 58, 0, -28, 0, 0, -60, 0, -4, 0, 0, 68, 0, -68, 0, 0, -64, 0, 74, 0, 0, 78, 0, 20, 0, 0, 6, 0, -20, 0, 0, -6, 0, -102, 0, 0, 0, 0, -28, 0, 0, -54, 0, 20, 0, 0, -10, 0, -14, 0, 0, 84, 0, 30, 0, 0, -62, 0, 12, 0, 0, 40, 0, 50, 0, 0, 38, 0, 10, 0, 0, -60, 0, 28, 0, 0, 32, 0, -20, 0, 0, 50, 0, 2, 0, 0, -14, 0, -20, 0, 0, -60, 0, 96, 0, 0, 32, 0, -18, 0, 0, -46, 0, 190, 0, 0, -40, 0, -78, 0, 0, 48, 0, -48, 0, 0, -2, 0, -92, 0, 0, 50, 0, 42, 0, 0, 84, 0, -2, 0, 0, 70, 0, 90, 0, 0, -58, 0, -118, 0, 0, -196, 0, 10, 0, 0, -92, 0, 60, 0, 0, 30, 0, 42, 0, 0, -70, 0, 88, 0, 0, 16, 0, -110, 0, 0, 22, 0, -16, 0, 0, 8, 0, -136, 0, 0, 88, 0, 132, 0, 0, 132, 0, 244, 0, 0, 56, 0, 0, 0, 0, 30, 0, -12, 0, 0, 94, 0, -42, 0, 0, -240, 0, 0, 0, 0, 4, 0, 20, 0, 0, -230, 0, 16, 0, 0, 32, 0, 10, 0, 0, 70, 0, -412, 0, 0, 26, 0, -76, 0, 0, -240, 0, 0, 0, 0, 52, 0, -38, 0, 0, 302, 0, -130, 0, 0, 0, 0, 2, 0, 0, 14, 0, -54, 0, 0, 200, 0, -104, 0, 0, -48, 0, 170, 0, 0, 86, 0, 84, 0, 0, -108, 0, 150, 0, 0, 92, 0, 12, 0, 0, 38, 0, 14, 0, 0, -50, 0, 112, 0, 0, -64, 0, -20, 0, 0, -10, 0, 28, 0, 0, -100, 0, -12, 0, 0, -6, 0, 42, 0, 0, -120, 0, 332, 0, 0, 42, 0, 100, 0, 0, 100, 0, -106, 0, 0, -144, 0, -24, 0, 0, 50, 0, -268, 0, 0, -144, 0, -38, 0, 0, 2, 0, 58, 0, 0, 176, 0, 42, 0, 0, -292, 0, -14, 0, 0, 2, 0, -152, 0, 0, 26, 0, 10, 0, 0, 188, 0, 32, 0, 0, 88, 0, 6, 0, 0, -14, 0, 140, 0, 0, 66, 0, -224, 0, 0, 20, 0, -88, 0, 0, -180, 0, -50, 0, 0, -326, 0, -30, 0, 0, 16, 0, -340, 0, 0, -282, 0, -50, 0, 0, 254, 0, 0, 0, 0, 44, 0, -134, 0, 0, -136, 0, -280, 0, 0, 212, 0, -80, 0, 0, -100, 0, 92, 0, 0, 114, 0, -86, 0, 0, 26, 0, 92, 0, 0, -8, 0, 166, 0, 0, -142, 0, -84, 0, 0, 260, 0, 70, 0, 0, 2, 0, 310, 0, 0, -38, 0, 64, 0, 0, 400, 0, 98, 0, 0, 28, 0, 248, 0, 0, -114, 0, 212, 0, 0, 20, 0, -30, 0, 0, -160, 0, 82, 0, 0, -108, 0, -316, 0, 0, -28, 0, 56, 0, 0, -24, 0, -86, 0, 0, -92, 0, 44, 0, 0, -18, 0, -62, 0, 0, -20, 0, -172, 0, 0, 124, 0, 202, 0, 0, -80, 0, -152, 0, 0, -160, 0, -34, 0, 0, 50, 0, 20, 0, 0, 160, 0, 20, 0, 0, -40, 0, -392, 0, 0, -260, 0, 142, 0, 0, 68, 0, 224, 0, 0, 100, 0, -6, 0, 0, 20, 0, 270, 0, 0, 0, 0, -18, 0, 0, -160, 0, -230, 0, 0, 208, 0, -96, 0, 0, 176, 0, 72, 0, 0, 124, 0, 158, 0, 0, 34, 0, 158, 0, 0, -60, 0, 172, 0, 0, 128, 0, 250, 0, 0, 48, 0, 60, 0, 0, -292, 0, 134, 0, 0, -72, 0, 66, 0, 0, 256, 0, 58, 0, 0, 308, 0, -60, 0, 0, 100, 0, 20, 0, 0, 42, 0, 6, 0, 0, 298, 0, 120, 0, 0, 4, 0, -290, 0, 0, 0, 0, -84, 0, 0, -154, 0, -104, 0, 0, 132, 0, -82, 0, 0, -84, 0, -30, 0, 0, -2, 0, -68, 0, 0, 50, 0, -86, 0, 0, -428, 0, -166, 0, 0, -392, 0, 124, 0, 0, -92, 0, 220, 0, 0, -2, 0, -40, 0, 0, -20, 0, -252, 0, 0, -74, 0, 88, 0, 0, 370, 0, -254, 0, 0, -150, 0, -56, 0, 0, 332, 0, 78, 0, 0, -38, 0, 162, 0, 0, -398, 0, -200, 0, 0, 26, 0, 174, 0, 0, -160, 0, -296, 0, 0, 248, 0, 66, 0, 0, -92, 0, -322, 0, 0, -176, 0, 48, 0, 0, -212, 0, -68, 0, 0, -112, 0, 32, 0, 0, 310, 0, 244, 0, 0, -460, 0, -10, 0, 0, 80, 0, 54, 0, 0, 20, 0, 46, 0, 0, -6, 0, 202, 0, 0, 60, 0, 36, 0, 0, -60, 0, 230, 0, 0, 56, 0, -6, 0, 0, -56, 0, 370, 0, 0, -154, 0, 120, 0, 0, 222, 0, -32, 0, 0, -30, 0, -48, 0, 0, 608, 0, 290, 0, 0, 182, 0, -66, 0, 0, 312, 0, 490, 0, 0, -222, 0, -126, 0, 0, -572, 0, -104, 0, 0, -4, 0, -96, 0, 0, 140, 0, -122, 0, 0, 272, 0, 12, 0, 0, 102, 0, 108, 0, 0, -54, 0, 98, 0, 0, 176, 0, -34, 0, 0, -60, 0, -228, 0, 0, 242, 0, -30, 0, 0, 4, 0, -10, 0, 0, -116, 0, -20, 0, 0, 148, 0, -388, 0, 0, 138, 0, 182, 0, 0, -52, 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, 11, 3, 1, 5, 0], [1, 1, 55, 10, 1, 10, 0]], "char_orbit_index": 50, "prim_orbit_index": 10, "minimal_twist": "165.2.m.a", "char_is_minimal": false, "conrey_index": 49, "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, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [-1, 0, -2, 4, 0, -1, -2, 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, -2, 0, 0, -1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, -1], [0, 3, 0, 0, 1, 0, 0, 0, -3, 3, 0, 3, 0, 0, -4, 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, 0, -1, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, -2, 0, 0, 0, 1, -4, 0, -3, 0, -2, -3, 4], [0, 2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 1, 1, 0], [1, 0, -5, 3, 0, -2, 0, 3, 0, 0, -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, -5, 0, -5, -5, -10, 0, 0, -5, 0, 5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0], [-1, 0, 5, -2, 0, 2, 0, -2, 0, 0, 2, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 0, 0, -3, -2, -1, 0, 0, -2, 0, 1, 0, 0, 0], [0, 5, 0, 0, 2, 0, 0, 0, -3, 4, 0, 6, 0, 3, -1, -4], [0, 0, 0, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 0, 1], [3, 0, 3, -3, 0, 0, 1, 0, 0, 0, 3, 0, -4, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -2, 0, 0, -2, -2, 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, 5, 0, 0, 5, 0, 0, 0, -5, 5, 0, 9, 0, 5, 0, -9], [0, 0, 4, -1, 0, 3, 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], [2, 0, 0, -2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -4, 0, 0, 0, 8, -16, 0, -7, 0, -4, -7, 16], [0, 2, 0, 0, -1, 0, 0, 0, 0, -2, 0, 0, 0, -1, -1, 1], [-10, 0, 0, 0, 0, 0, -5, 0, 0, 0, -5, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 1, 4, 0, 2, 0, 4, 0, 0, 2, 0, -3, 0, 0, 0], [0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, -5], [0, -10, 0, 0, -7, 0, 0, 0, 7, -5, 0, -9, 0, -10, 0, 9], [0, 0, 0, -1, 0, -1, -1, 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], [-6, 0, 3, 1, 0, -1, 0, 1, 0, 0, -1, 0, -6, 0, 0, 0], [0, 5, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 2, -4, 3], [0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, -3, 0, 1, -3, -3], [4, 0, -5, -3, 0, -7, -6, -14, 0, 0, -7, 0, 10, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, -1, 0, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0], [0, 1, 0, 0, -4, 0, 0, 0, -1, -3, 0, -3, 0, 0, -6, 0], [0, -5, 0, 0, -5, 0, 0, 0, 0, 0, 0, -5, 0, 0, 5, -5], [0, 0, 0, -4, 0, -1, -1, 0, 0, 0, 2, 0, 4, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0], [0, -3, 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 3, 5, -4], [-2, 0, 0, 0, 0, 0, -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], [6, 0, -4, 0, 0, -4, -8, -15, 0, 0, -8, 0, 15, 0, 0, 0], [0, -5, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, -2, 3, -2], [0, -4, 0, 0, 3, 0, 0, 0, 4, -1, 0, -1, 0, 0, 6, 0], [-6, 0, 1, 1, 0, 0, 1, 6, 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, 2, 0, -6, -6, -1, 0, 0, -3, 0, -2, 0, 0, 0], [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 7, -7], [0, 1, 0, 0, -2, 0, 0, 0, -1, -1, 0, -1, 0, 0, 0, 0], [16, 0, 2, -16, 0, 0, 11, 0, 0, 0, 2, 0, -8, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, -4, 0, -3, -1, -4, 0, 0, 2, 0, -1, 0, 0, 0], [0, 0, 0, 0, 5, 0, 0, 0, 5, 4, 0, 5, 0, 5, 5, -4], [0, -5, 0, 0, 0, 0, 0, 0, 10, -5, 0, 0, 0, -10, -5, 20], [0, 0, 0, 1, 0, -1, 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, 4, 0, -2, -2, 8, 0, 0, 3, 0, -4, 0, 0, 0], [0, -2, 0, 0, 1, 0, 0, 0, -1, 7, 0, 3, 0, -2, 0, -3], [0, 5, 0, 0, 5, 0, 0, 0, 0, 0, 0, -2, 0, 8, 4, -4], [-1, 0, -4, 12, 0, 5, 0, 12, 0, 0, 5, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9, 0, 12, 0, 0, 12, 11, 19, 0, 0, 11, 0, -19, 0, 0, 0], [0, -3, 0, 0, 1, 0, 0, 0, 1, 6, 0, 11, 0, -2, 7, -9], [0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, -2, 1, 0], [-7, 0, -2, 7, 0, 0, -2, 0, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -7, 0, 0, -3, 0, 0, 0, 3, -3, 0, -14, 0, -7, 0, 14], [0, 3, 0, 0, 5, 0, 0, 0, -5, -2, 0, 8, 0, 3, 0, -8], [9, 0, 0, -5, 0, -5, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-12, 0, -4, 12, 0, 0, -8, 0, 0, 0, -4, 0, -5, 0, 0, 0], [0, 0, 0, 0, 4, 0, 0, 0, -1, 1, 0, 1, 0, 4, 1, -1], [0, 7, 0, 0, -2, 0, 0, 0, 8, -23, 0, -8, 0, -4, -18, 18], [-2, 0, 2, 0, 0, 2, 2, -3, 0, 0, 2, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 7, -2, 0, 5, 0, -2, 0, 0, 5, 0, 6, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 3, -3], [0, 3, 0, 0, 3, 0, 0, 0, -3, 2, 0, 2, 0, 3, 0, -2], [0, 0, 0, 10, 0, -8, -8, -3, 0, 0, 1, 0, -10, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7, 0, -4, 16, 0, 4, 0, 16, 0, 0, 4, 0, -7, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, -3, -3, 4], [0, 0, 0, 0, -3, 0, 0, 0, 3, 1, 0, 7, 0, -3, 7, -1], [0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 3, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}