# Stored data for newform 425.2.e.e, downloaded from the LMFDB on 14 January 2025. {"Nk2": 1700, "analytic_conductor": 3.3936420859044163, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 17, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 4, "char_parity": 1, "char_values": [425, 4, [52, 326], [4, 1]], "cm_discs": [], "conrey_index": 251, "dim": 12, "field_disc": 3763724161024000000, "field_disc_factorization": [[2, 18], [5, 6], [30313, 2]], "field_poly": [1, 0, 278, 0, 519, 0, 364, 0, 119, 0, 18, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [1, 0, 278, 0, 519, 0, 364, 0, 119, 0, 18, 0, 1]], [3, [25, 40, 32, -112, 271, 70, 16, -26, 43, 10, 2, -2, 1]]], "hecke_orbit": 5, "hecke_orbit_code": 18014673420943785, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 17, 3, 1, 4, 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": "425.2.e.e", "level": 425, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [5, 17], "level_radical": 85, "minimal_twist": "425.2.e.c", "prim_orbit_index": 3, "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{4}q^{3}+(-1+\\beta _{2})q^{4}+(1+\\cdots)q^{6}+\\cdots", "related_objects": [], "relative_dim": 6, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "425.2.e", "trace_display": [0, 2, 0, 0], "trace_hash": 2244987963507253176, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.814", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "554.851", "prec": 24}, {"__RealLiteral__": 0, "data": "27.759", "prec": 20}, {"__RealLiteral__": 0, "data": "46132.251", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.248", "prec": 17}, "traces": [0, 12, 0, 2, -12, 0, 6, 0, 0, 0, 0, -4, 4, -12, 14, 0, 4, -6, 4, 0, 0, 8, -10, -12, -8, 0, 0, -22, 34, -6, 0, -6, 0, -4, 30, 0, 0, -18, 12, 16, 0, 6, 0, 0, 32, 0, 30, -36, 10, 0, 0, -40, 64, 0, 16, 0, -56, 18, 6, 0, 0, -8, 22, 30, -44, 0, 0, -20, -10, -72, 0, -20, 92, 18, -26, 0, 0, 0, -38, -14, 0, -8, 10, 0, 36, 0, 84, 0, -66, -24, 0, 12, 32, 0, 0, 0, 22, 52, -76, 30, 0, -8, -60, 32, 0, 0, -32, -30, -24, -34, 0, 0, -136, 8, -54, 0, -2, 0, 12, 30, 0, 0, -124, -4, 60, 0, 64, 0, 0, 46, 0, -10, 20, -10, 0, 0, -82, 112, 0, 44, 0, -76, 26, -2, 0, 0, -70, 22, 10, -8, 0, 0, -32, 4, -136, 0, -42, 44, -64, 12, 0, 0, 0, -24, 42, 0, 32, -8, 0, -8, 0, 104, 0, -14, -4, 0, 0, 98, 0, 0, 0, 54, 36, 44, -2, 0, -24, -76, 136, 0, 0, 96, -104, 50, -16, 0, 0, -60, 58, 16, 0, 8, 0, 0, 34, 0, 0, -102, 48, 12, 0, 26, 0, 0, 96, 0, 142, 48, 66, 0, 0, -2, 196, 0, 146, 0, -60, 52, 46, 0, 0, -28, 54, 86, 0, 0, 0, -112, -104, -104, 0, -108, 100, -54, -52, 0, 0, 0, 52, -52, 0, -12, -74, 0, 48, 0, 100, 0, -86, -68, 0, -8, 116, 0, 0, 0, -14, 54, 92, -56, 0, 32, -78, 44, 0, 0, -12, -62, -64, -52, 0, 0, -168, -84, -54, 0, -28, 0, -40, 40, 0, 0, -150, -156, 44, 0, 86, 0, 0, 62, 0, -14, 20, -64, 0, 0, -44, 84, 0, 132, 0, 20, 0, 50, 0, 0, -68, -38, -100, 52, 0, 0, -76, -16, -64, 0, -112, 28, -46, 80, 0, 0, 0, -120, -46, 0, -120, 4, 0, -52, 0, 80, 0, 60, -136, 0, 42, -12, 0, 0, 0, 94, 62, -16, 26, 0, -44, -30, 72, 0, 0, 76, -162, 108, -94, 0, 0, -100, 56, 0, 0, 58, 0, -96, -30, 0, 0, -58, 264, 78, 0, 22, 0, 0, 32, 0, 62, 132, -100, 0, 0, -76, 372, 0, -16, 0, -54, 40, 94, 0, 0, -86, 28, 68, 4, 0, 0, 120, -90, 0, 0, -84, 128, -150, -82, 0, 0, 0, -52, -52, 0, -28, 60, 0, 156, 0, 128, 0, -92, -108, 0, -66, 130, 0, 0, 0, 62, 104, 28, 16, 0, -148, -126, 100, 0, 0, -64, -22, 50, -22, 0, 0, 12, -120, -204, 0, -58, 0, 140, 120, 0, 0, -130, -44, -50, 0, -58, 0, 0, 72, 0, -36, -132, -52, 0, 0, 100, 68, 0, 8, 0, -66, -36, -24, 0, 0, -82, 40, 52, 152, 0, 0, 20, 62, -84, 0, -18, -108, -4, 30, 0, 0, 0, 24, -116, 0, 92, -110, 0, 16, 0, 12, 0, 98, 192, 0, 54, 52, 0, 0, 0, -76, 0, 124, -24, 0, 12, -60, -32, 0, 0, 204, -46, 38, 6, 0, 0, -122, 16, 170, 0, 102, 0, -40, 114, 0, 0, -30, 4, 44, 0, 4, 0, 0, 158, 0, 38, -52, 106, 0, 0, -132, 104, 0, -12, 0, 78, 80, -16, 0, 0, 26, -6, 102, -96, 0, 0, -160, -204, 44, 0, -60, 136, 80, -186, 0, 0, 0, -126, -30, 0, 28, -34, 0, 60, 0, 32, 0, -116, -156, 0, -116, -90, 0, 0, 0, -10, 26, -124, -66, 0, 116, -116, -48, 0, 0, 56, -126, -64, -24, 0, 0, -44, 42, -124, 0, -58, 0, -44, -86, 0, 0, -6, -44, 86, 0, 30, 0, 0, -66, 0, -46, -8, -90, 0, 0, 20, 92, 0, 12, 0, 10, -70, 6, 0, 0, -170, 48, -232, -64, 0, 0, 88, 142, -52, 0, 112, 24, -20, 104, 0, 0, 0, -88, 172, 0, 40, 100, 0, -188, 0, 64, 0, 106, 84, 0, 296, -130, 0, 0, 0, 112, 18, 24, 82, 0, 12, 94, 84, 0, 0, 136, 42, 136, 128, 0, 0, 96, 26, -8, 0, -38, 0, -68, -42, 0, 0, 44, 336, -44, 0, 120, 0, 0, -150, 0, 120, -12, 170, 0, 0, -24, -132, 0, 44, 0, 74, 4, 48, 0, 0, 34, 168, 130, 176, 0, 0, 44, 32, -76, 0, -16, -172, 120, 38, 0, 0, 0, 272, -74, 0, -12, 66, 0, -32, 0, -60, 0, -106, -116, 0, -42, 54, 0, 0, 0, -224, 78, -24, 32, 0, 44, -102, -92, 0, 0, -272, 176, -196, -172, 0, 0, 14, -52, 84, 0, -140, 0, 24, 148, 0, 0, 98, -400, 92, 0, -122, 0, 0, 20, 0, -96, -96, -14, 0, 0, 84, -120, 0, -32, 0, 8, -70, -102, 0, 0, -34, -56, -154, 48, 0, 0, 44, 164, 56, 0, 20, -100, 118, 60, 0, 0, 0, -114, 132, 0, -32, -158, 0, -48, 0, -68, 0, 58, 148, 0, -78, 66, 0, 0, 0, 22, -62, -180, -28, 0, -344, 54, -204, 0, 0, -4, -46, 120, 88, 0, 0, 10, 234, 0, 0, 46, 0, -76, -106, 0, 0, 82, 328, 86, 0, -178, 0, 0, -78, 0, -176, 60, 78, 0, 0, 30, -184, 0, -152, 0, -20, 72, -134, 0, 0, 92, -30, 72, -96, 0, 0, -108, 6, -80, 0, 24, 148, -92, -40, 0, 0, 0, -62, 74, 0, 44, 98, 0, -4, 0, -160, 0, -180, 84, 0, -42, 12, 0, 0, 0, -128, -80, -4, -114, 0, 204, 282, 112, 0, 0, 156, 68, -218, 116, 0, 0, 222, -42, 108, 0, -54, 0, 124, 50, 0, 0, 142, -60, -146, 0, 104, 0, 0, -128, 0, 12, 44, 12, 0, 0, 94, -204, 0, -4, 0, -104, -142, -68, 0, 0, 116, -76, -70, -244, 0], "weight": 2, "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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 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, 0, 0], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 1, -1, 1, 0, 0, -1], [0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1], [0, 1, 0, 1, 1, 0, 0, 1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 1, 1, 0, 0, -1, 1, -1, 1, 0, 0], [1, 1, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0], [-2, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 1], [0, -1, -1, 0, 1, 0, 0, 0, -1, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 1, -1, 1, -1, 0, -4, 0, 2, 2], [-1, -1, -1, 0, 1, -1, 1, 0, 1, 0, 0, -1], [1, 0, 1, -1, 1, 0, 0, 0, 1, 0, -1, -1], [0, -2, 0, -1, -1, 0, 0, -2, 0, -1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, 1, 0, 0, 0, 2, 0, 0, 0], [-1, -2, 0, 0, -2, 1, 0, -2, -2, 0, 1, 0], [-1, 1, 1, 3, 0, 0, -1, 2, -1, 1, 0, 2], [0, 0, 1, -1, 0, 0, -1, 1, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, 1, 1, -1, -1, 1, 0, 0, 0, 0], [-3, 0, -1, 0, 0, 0, 1, 2, 0, -1, 0, 2], [2, 2, -2, 0, 0, 0, -1, -1, -2, -2, 0, 2], [0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, -1, 1, 0, 1, 0, 0, -1, -1, -1, 0, 0], [0, 1, 0, 0, 0, -1, -1, -2, 0, -2, -1, 1], [1, 0, 1, 0, 0, 1, -1, 0, -1, 0, -1, -1], [3, 0, -1, 2, 1, 1, -1, -1, -1, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, 1, 0, 0, 1, 0, 2, 0, 0], [0, 1, 0, 0, 1, 2, 0, -2, 1, 0, -1, 0], [2, 0, -1, 1, -1, 0, 0, 0, 2, 0, 0, 0], [2, 2, -1, 0, -1, -1, 0, 3, 2, 1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, -1, 0, 0, 2, -2, 1, 0, 0, -1], [0, 1, 0, 0, 0, -1, -1, 6, 0, 2, 0, 0], [0, -2, 0, -1, -1, -1, -1, 2, 0, 1, 0, 0], [2, 2, 0, 1, 0, 0, -1, -1, -2, 0, 0, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, -1, 0, 0, 0, 1, 0, 2, -1, 0, -1, 0], [-4, 0, 2, 2, -2, -1, 1, 0, -2, 0, 0, 0], [1, -1, -1, 0, -3, 0, 0, 1, -1, 1, 0, 0], [0, 1, 0, -1, -1, 1, 1, -1, 0, -3, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 2, 0, 1, -1, 0, 0, 2, 0, 1, 2, 1], [6, 0, 0, 2, -2, 1, -1, 0, -1, 0, 1, 1], [0, -2, 0, -1, -1, 0, 0, -5, 0, -3, 1, -1], [1, 1, 1, 0, 4, -2, 0, 3, 1, -1, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 6, 2, 0, 2, -2, 0, -1, 6, -2, -3, 0], [1, 1, 1, -3, 0, 0, 0, -1, -1, 1, 0, -1], [0, -1, 0, -1, 0, 0, 2, -2, 1, 0, 0, -1], [0, -2, 0, -3, -3, 1, 1, -4, 0, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 2, -1, -2, 0, 0, 2, 0, -2, -1, 0, -2], [4, -3, 0, 0, 0, 0, -1, -3, 3, 0, 0, -2], [2, -2, 0, 0, 0, 1, 0, 1, -2, 0, 1, 0], [-1, 0, 3, 3, -3, 1, -1, 0, 2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, -3, -3, 1, 1, -5, 0, 0, 1, -1], [0, 0, 0, -1, 1, 0, 0, 0, 4, 0, -1, -1], [0, 4, -2, -1, 0, 0, 0, 1, 2, -2, -2, 1], [-7, 0, -1, 3, -3, -1, 1, 0, -1, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 1, 1, 0, -2, 0, 1, -1, 0], [7, 0, -1, -2, 2, 1, -1, 0, -3, 0, 0, 0], [2, 5, -4, 0, 3, -2, 0, 4, 5, 4, -1, 0], [-3, -1, 1, -5, 0, 0, 0, 3, 1, 1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, -2, -2, 1, 1, 2, 0, -1, 1, -1], [0, 5, 0, 2, 2, -2, -2, 5, 0, 0, 0, 0], [-5, 3, 1, 1, 0, 0, 2, 3, -3, 1, 0, 0], [-1, 1, -1, 2, 0, 0, 1, 0, -1, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3, 1, -1, -2, 2, 0, 5, 0, -1, -1], [-1, -1, -1, 0, 3, 0, 0, -1, -1, 1, 3, 0], [0, -4, 0, 0, 0, 1, 1, -8, 0, -2, 2, -2], [1, 0, -1, 0, 0, 0, 0, 0, -4, 0, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, -3, 2, -2, -1, 1, 0, -2, 0, 0, 0], [0, -2, 0, -1, -1, 1, 1, -6, 0, -1, 1, -1], [-4, 0, 2, 0, -4, 1, 0, -5, 0, -2, -1, 0], [-2, 0, -3, -3, 3, -1, 1, 0, 4, 0, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -2, -2, 0, 0, 0, -1, 2, -2, 0, 1], [1, 4, 1, 3, 0, 0, -1, 0, -4, 1, 0, 4], [0, 3, 0, 1, 1, 1, 1, 6, 0, 0, -2, 2], [0, -8, 0, 2, 2, 2, 2, -8, 0, 0, 3, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 3, 0, -2, 0, 0, 1, -1, -3, 0, 0, 0], [4, -1, 0, 0, -2, 2, 0, 2, -1, 0, 4, 0], [-5, 0, 4, -3, 3, -2, 2, 0, 7, 0, -3, -3], [3, 1, -1, 0, 5, 0, 0, 3, 1, 1, -3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}