# Stored data for newform 325.2.e.a, downloaded from the LMFDB on 13 June 2025. {"Nk2": 1300, "analytic_conductor": 2.5951380656916125, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 3, "char_parity": 1, "char_values": [325, 3, [27, 301], [3, 2]], "cm_discs": [], "conrey_index": 126, "dim": 4, "field_disc": 1521, "field_disc_factorization": [[3, 2], [13, 2]], "field_poly": [9, 3, 4, -1, 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, [9, -3, 4, 1, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 274911461701, "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, 13, 3, 1, 3, 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": false, "label": "325.2.e.a", "level": 325, "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, 13], "level_radical": 65, "minimal_twist": "65.2.e.b", "nf_label": "4.0.1521.1", "prim_orbit_index": 3, "qexp_display": "q-\\beta _{1}q^{2}+(1+\\beta _{2})q^{3}+(-1+\\beta _{1}+\\beta _{2}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "325.2.e", "trace_display": [-1, 2, 0, -2], "trace_hash": 796380913956496086, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.976", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "58.433", "prec": 20}, {"__RealLiteral__": 0, "data": "10.423", "prec": 20}, {"__RealLiteral__": 0, "data": "1468.566", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.018", "prec": 17}, "traces": [0, 4, -1, 2, -3, 0, 1, -2, 12, 4, 0, 4, -6, 0, 2, 0, 3, 8, -4, 4, 0, -4, -11, -6, 6, 0, -13, 20, -3, -2, 0, -16, 7, -4, -34, 0, 6, 0, -30, 0, 0, -6, 1, -6, 14, 0, -3, -8, -3, 12, 0, 16, -13, -16, -5, 0, -6, 8, 25, 0, 0, 2, 4, 4, -8, 0, -22, -14, 25, 6, 0, 12, 12, 32, 13, 0, 19, -8, 13, -8, 0, -2, -3, 8, 3, 0, 58, 2, 12, -2, 0, 0, 18, -8, 28, 0, 14, -24, 6, 16, 0, 18, -17, 16, 0, 0, -22, -2, -15, -48, 0, 0, -6, 4, -15, 0, -46, 0, -78, 8, 0, -12, -2, 6, 12, 0, 2, 6, 27, -12, 0, -56, 7, 4, -7, 0, 24, 4, -6, -20, 0, -4, 66, -26, 12, 0, 18, -12, -26, -6, 0, 24, 12, -16, -11, 0, -26, -16, -24, -8, 0, 12, -1, -22, 18, 0, -28, 18, -12, 52, 0, -8, -35, -12, 50, 0, -19, 0, 25, -24, 0, -16, 26, 4, -18, 0, -4, -20, 32, -10, 0, -12, -4, 24, -2, 0, -36, 24, 22, -4, 0, 14, 9, 4, -25, 0, -4, -24, -13, -36, 0, 40, -14, 24, 25, 0, 60, 8, 38, 16, 0, 26, 26, 6, 7, 0, 22, -26, -19, 56, 0, -4, -6, -32, -52, 0, 39, -4, 17, 0, 0, -18, -92, 32, 3, 0, -6, 26, -48, 4, 0, 36, -12, 12, -23, 0, 25, -40, 29, 0, 0, -8, 40, 38, -12, 0, 15, 2, 42, 18, 0, 20, -2, 0, 22, 0, 9, 48, -6, -16, 0, -24, -28, 10, -21, 0, 13, 12, -14, -24, 0, -48, 2, 28, 12, 0, 0, 20, 6, 0, 0, -6, 20, -18, -14, 0, -34, 64, -7, 8, 0, -8, 0, -56, 30, 0, -20, -24, 22, 56, 0, 2, -3, -42, 6, 0, -30, -24, -18, 4, 0, 16, -32, 0, 9, 0, -3, 16, -13, 8, 0, -16, -30, -52, -18, 0, -66, 26, -23, 22, 0, 0, 2, 12, -39, 0, -46, -8, -51, 16, 0, 4, -74, -24, -13, 0, -1, -6, 9, -24, 0, 8, 24, -48, 31, 0, -24, 52, 10, -12, 0, -6, 90, -6, -27, 0, 25, 12, -23, -32, 0, -48, 36, -28, -27, 0, 14, 8, 82, -4, 0, -10, -14, 0, -54, 0, 25, 26, 48, -2, 0, 8, -12, 0, 6, 0, 13, -40, 9, 16, 0, 72, 33, -8, -48, 0, 33, 2, -46, 26, 0, -8, 15, 0, -8, 0, 62, -24, -18, 4, 0, 48, -130, 32, -13, 0, -23, -12, 4, -18, 0, 12, -7, 12, 130, 0, 24, -32, -14, 40, 0, -58, 11, 80, 29, 0, 34, -40, 26, 28, 0, -8, 0, 80, 24, 0, -50, -16, 0, 36, 0, 26, -34, 6, 34, 0, -32, -2, 6, -44, 0, 12, 9, 88, -78, 0, -12, 12, 28, -48, 0, -18, 42, 6, 12, 0, 66, 26, 34, -6, 0, -16, 44, 20, -7, 0, 35, 44, 13, -24, 0, 72, -50, 26, 68, 0, -7, -32, -38, 28, 0, 0, -38, 0, 50, 0, -42, 24, -18, -24, 0, -16, 49, -8, -41, 0, 13, -16, -7, -4, 0, 96, 18, 4, -74, 0, -17, 4, 16, -52, 0, -10, 6, -10, 64, 0, 5, 4, 36, 26, 0, -32, 26, -24, -3, 0, -8, -32, -116, -24, 0, -4, -1, -68, 96, 0, -2, -38, -18, -16, 0, -24, 13, -112, -55, 0, -9, -8, -39, -56, 0, -42, -29, -56, 8, 0, 18, -54, -27, 2, 0, -104, 100, -4, -16, 0, -24, -12, 4, 0, 0, -30, 28, 4, 13, 0, 14, -18, 38, 52, 0, 36, -24, -40, 6, 0, -28, 0, 74, -24, 0, 10, 50, -38, -9, 0, -99, 50, -6, -156, 0, 16, -7, -36, -38, 0, 9, 32, -56, 48, 0, -34, 114, 52, 24, 0, -26, -6, -54, -6, 0, 8, -7, -28, -82, 0, -39, -48, 11, -24, 0, -52, 44, 58, 76, 0, 13, 28, 34, 104, 0, 24, 21, -8, 26, 0, 6, -48, -15, -16, 0, -88, -65, 52, 70, 0, 45, -36, -39, -30, 0, -8, -6, 24, 34, 0, 150, 0, -56, 44, 0, -8, -50, -36, -66, 0, -46, -112, 0, 52, 0, 76, -3, 72, 49, 0, -42, 28, 6, 64, 0, 52, 44, 30, -24, 0, 22, 8, 41, 4, 0, -28, 20, 72, 13, 0, -15, -20, -19, 24, 0, 6, -46, 24, -57, 0, 162, 78, 50, -22, 0, 40, -98, 52, 58, 0, -72, 0, 34, -24, 0, 204, 51, -10, -18, 0, -40, -14, 6, -38, 0, 4, 48, 0, -138, 0, -45, 36, 30, -68, 0, -8, -31, 84, 21, 0, 52, 36, 54, 38, 0, -128, 23, -20, 26, 0, -1, 64, 54, 0, 0, -14, 11, 10, 48, 0, 39, 112, 18, -30, 0, 96, -156, 96, -3, 0, 27, -80, -83, 4, 0, -48, -70, -12, -146, 0, 112, -12, -38, -10, 0, 0, 21, -160, 1, 0, -6, -24, 26, 72, 0, 6, -95, -144, 35, 0, -26, 24, 12, -60, 0, 0, -144, 48, 45, 0, 4, -40, 93, 56, 0, -14, -12, 40, 91, 0, 44, -2, 0, -12, 0, 4, 34, -60, 3, 0, -54, 0, 174, 8, 0, 20, 66, 6, 12, 0, -20, 10, -91, 72, 0, -144, -7, -44, -55, 0, -42, 28, -170, 56, 0, 32, 110, -78, -14, 0, -72, 16, 38, 2, 0, 48, 50, -4, -16, 0, 0, -16, -7, -28, 0, 48, -30, -18, -78, 0, -7, 6, -40, -104, 0, -12, 24, 36, -88, 0, 0, 112, 57, 4, 0, -60, 13, -8, -1, 0, 3, -24, -36, 42, 0, 52, 48, -20, 2, 0, 6, 36, -15, 56, 0, -48, 45, -16, 18, 0, -113, 8, 65, 36, 0, -44, -28, 32, -33, 0, -64, 28, -40, 0, 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, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, -1, 0, 0], [1, 0, 1, 0], [-1, 1, 1, 1], [0, 0, 0, 0], [1, -1, 0, -1], [0, 0, 1, 0], [3, 0, 0, 0], [0, 0, -2, 0], [0, 0, 0, 0], [3, -2, 3, 0], [-2, 0, 0, 1], [1, 0, 0, -2], [1, 0, 0, -1], [0, 0, 0, 0], [2, -1, 2, 0], [2, -2, -3, -2], [-2, 0, 0, 2], [2, -2, -1, -2], [0, 0, 0, 0], [-1, 0, 0, 0], [1, -1, 6, -1], [-3, 0, -3, 0], [3, 0, 3, 0], [0, 0, 0, 0], [-6, -1, -6, 0], [5, 0, 0, 0], [-1, -1, -1, 0], [-3, 4, -3, 0], [0, 0, 0, 0], [-4, 0, 0, 0], [1, -1, -3, -1], [2, -2, 3, -2], [-11, 0, 0, 5], [0, 0, 0, 0], [2, 2, 2, 0], [-1, 2, -1, 0], [-9, 0, 0, 3], [-1, 2, -1, 0], [0, 0, 0, 0], [-3, 0, -3, 0], [0, 1, 0, 0], [-4, 4, 1, 4], [4, 0, 0, -1], [0, 0, 0, 0], [-3, 3, 0, 3], [-4, 0, 0, 4], [1, -1, 2, -1], [6, 0, 6, 0], [0, 0, 0, 0], [5, 0, 0, -2], [-3, 3, 5, 3], [-2, 0, 0, -4], [0, -5, 0, 0], [0, 0, 0, 0], [0, 0, 3, 0], [3, 0, 0, -2], [1, -1, -12, -1], [6, -6, 3, -6], [0, 0, 0, 0], [0, 0, -1, 0], [0, 4, 0, 0], [2, 0, 2, 0], [-5, 0, 0, 6], [0, 0, 0, 0], [-5, 0, 0, -1], [-7, 0, -7, 0], [9, 7, 9, 0], [0, 0, -3, 0], [0, 0, 0, 0], [-6, 6, -9, 6], [0, 0, -6, 0], [6, 0, 0, 4], [1, -1, -6, -1], [0, 0, 0, 0], [7, 5, 7, 0], [-1, 0, 0, -2], [1, -1, -6, -1], [0, 0, 0, -4], [0, 0, 0, 0], [-1, 0, -1, 0], [-3, 3, 0, 3], [4, 0, 0, -4], [1, -1, -1, -1], [0, 0, 0, 0], [17, 0, 0, -5], [-4, 4, -3, 4], [9, -6, 9, 0], [-3, 4, -3, 0], [0, 0, 0, 0], [-2, 2, -1, 2], [6, 0, 0, -3], [-4, 0, -4, 0], [12, 4, 12, 0], [0, 0, 0, 0], [4, 0, 0, -1], [2, -2, 13, -2], [6, -6, 0, -6], [2, 0, 0, 4], [0, 0, 0, 0]]}