# Stored data for newform 225.3.d.a, downloaded from the LMFDB on 14 June 2025. {"Nk2": 2025, "analytic_conductor": 6.13080594810668, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 15, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": -1, "char_values": [225, 2, [101, 127], [1, 1]], "cm_discs": [], "conrey_index": 224, "dim": 4, "field_disc": 256, "field_disc_factorization": [[2, 8]], "field_poly": [1, 0, 0, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 8, "has_non_self_twist": 1, "hecke_cutters": [[2, [-2, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 206208762081, "hecke_ring_generator_nbound": 11, "hecke_ring_index": 2, "hecke_ring_index_factorization": [[2, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 1, 15, 4, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "225.3.d.a", "level": 225, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [3, 5], "level_radical": 15, "minimal_twist": "225.3.c.a", "nf_label": "4.0.256.1", "prim_orbit_index": 4, "qexp_display": "q+\\beta_{3} q^{2}-2 q^{4}+9\\beta_1 q^{7}-6\\beta_{3} q^{8}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "225.3.d", "trace_display": [0, 0, 0, 0], "trace_hash": 549794360885045897, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.539", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "109.620", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4297.296", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.761", "prec": 17}, "traces": [0, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -156, 0, 0, 152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, -128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 292, 0, 0, 224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 0, 0, -184, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 544, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -868, 0, 0, 312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -912, 0, 0, -416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -68, 0, 0, -936, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 264, 0, 0, 672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 476, 0, 0, -144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, -700, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -196, 0, 0, 672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1660, 0, 0, -584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1088, 0, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -704, 0, 0, -120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -104, 0, 0, 1732, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 828, 0, 0, 400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -192, 0, 0, -1976, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 1440, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -984, 0, 0, -2272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1056, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1104, 0, 0, 188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 456, 0, 0, -1272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1368, 0, 0, 412, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2240, 0, 0, -3264, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -200, 0, 0, 668, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 416, 0, 0, 736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 864, 0, 0, 2268, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 1736, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 624, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4896, 0, 0, -1536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1184, 0, 0, -2044, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1956, 0, 0, 3040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 832, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1508, 0, 0, 288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 3900, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 932, 0, 0, 136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5616, 0, 0, -4124, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2980, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3800, 0, 0, 728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1760, 0, 0, -1584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1344, 0, 0, -252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -728, 0, 0, 2168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 744, 0, 0, -2428, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3960, 0, 0, -952, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 3200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2816, 0, 0, -152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2112, 0, 0, -5348, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4576, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1400, 0, 0, -3496, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4380, 0, 0, 3328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, -600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 476, 0, 0, 392, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4032, 0, 0, 5144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, -600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -960, 0, 0, -2880, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10336, 0, 0, -1536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -696, 0, 0, -1372, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3200, 0, 0, 3352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2392, 0, 0, -544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2240, 0, 0, -3320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1168, 0, 0, 7488, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3844, 0, 0, -3168, 0, 0, 0, 0, 0, 0], "weight": 3, "weight_parity": -1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0], [-2, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 9, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 13, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 9, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [0, 0, 0, 19], [0, 0, 0, 0], [-25, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 26, 0, 0], [0, 0, 0, 3], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, -18, 0, 0], [0, 0, 19, 0], [0, 0, 0, 0], [-39, 0, 0, 0], [0, 0, 0, 20], [0, 0, 0, 0], [38, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -32, 0, 0], [0, 0, 0, -25], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -4, 0], [0, 0, 0, 0], [0, -23, 0, 0], [0, 0, -26, 0], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, 0, -23], [0, 0, 0, 0], [-32, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 68], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -54, 0], [0, 0, 0, 0], [0, 38, 0, 0], [0, 0, -7, 0], [0, 0, 0, 0], [73, 0, 0, 0], [0, 0, 0, -39], [0, 0, 0, 0], [56, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -63, 0, 0], [0, 0, 0, -38], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 44, 0], [0, 0, 0, 0], [0, 136, 0, 0], [0, 0, -32, 0], [0, 0, 0, 0], [50, 0, 0, 0], [0, 0, 0, -117], [0, 0, 0, 0], [24, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -8, 0, 0], [0, 0, 0, 33], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -23, 0], [0, 0, 0, 0], [0, -156, 0, 0], [0, 0, -72, 0], [0, 0, 0, 0], [-9, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [-46, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 7, 0, 0], [0, 0, 0, -32], [0, 0, 0, 0], [0, 0, 0, 0]]}