# Stored data for newform 104.2.e.a, downloaded from the LMFDB on 07 November 2025. {"Nk2": 416, "analytic_conductor": 0.830444181021316, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 104, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": 1, "char_values": [104, 2, [79, 53, 41], [2, 1, 1]], "cm_discs": [], "conrey_index": 77, "dim": 2, "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 4, "has_non_self_twist": 1, "hecke_cutters": [[3, [1, 0, 1]], [5, [-1, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 274911461480, "hecke_ring_generator_nbound": 2, "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, 104, 5, 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": "104.2.e.a", "level": 104, "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": [2, 13], "level_radical": 26, "minimal_twist": "104.2.e.a", "nf_label": "2.0.4.1", "prim_orbit_index": 5, "qexp_display": "q+(i-1)q^{2}-i q^{3}-2 i q^{4}+q^{5}+\\cdots", "related_objects": ["ModularForm/GL2/TotallyReal/2.2.104.1/holomorphic/2.2.104.1-1.1-a", "EllipticCurve/2.2.104.1/1.1/a"], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "104.2.e", "trace_display": [-2, 0, 2, 0], "trace_hash": 1451614229282413775, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.922", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.679", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "142.617", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.517", "prec": 17}, "traces": [0, 2, -2, 0, 0, 2, 2, 0, 4, 4, -2, 4, -4, -6, 6, 0, -8, 6, -4, 0, 0, -6, -4, -12, 4, -8, 2, 0, -12, 0, 2, 0, 8, 0, -6, 0, 0, 6, 0, 4, 4, 0, 6, 0, 0, 4, 12, 0, 0, -4, 8, 0, 8, 0, 10, 4, 12, 0, -12, 20, -4, 0, 0, 0, 0, -6, 4, -24, 0, 0, 6, 0, 8, 0, -6, 0, 0, 0, -10, 0, -8, 2, -20, -32, 0, 6, -18, 12, 8, 0, -4, 12, 0, 0, -14, 0, -8, 0, 4, 8, 0, 0, 6, 8, -20, -6, 12, 0, -20, 30, -4, 0, 0, -12, 0, -12, 24, -12, -20, 0, 4, -14, 20, 20, 0, -18, 12, 36, -16, 18, 2, 0, -8, 0, 24, 0, 12, 0, -12, 0, -12, 14, -10, -12, -16, 0, 12, 0, 0, -20, -8, 0, 0, 12, 12, 0, 12, 0, 0, -12, 8, 0, -2, -12, 40, 0, 32, 0, -12, 10, -6, 0, 36, 0, -12, 0, -16, 0, 8, 0, 0, 0, -30, -20, -24, 6, 0, 12, 28, -30, 0, -36, 16, 0, 36, 4, 0, 46, -8, 0, -16, 0, 0, 36, -12, 0, -8, -24, 24, 0, 6, 0, -24, 10, -24, 0, 20, 0, -30, -12, 0, -18, 6, 0, -24, -16, 12, -4, 0, -30, 12, -12, -24, 18, 4, 0, 0, 0, 18, 0, 0, 0, 14, 0, -40, -4, -20, 0, 0, 0, 18, 0, -24, -24, -36, 0, 32, 6, -18, 0, 8, 0, 30, -12, 8, 0, 0, -8, 0, 0, 10, 0, -24, 18, -4, -16, 24, 0, 18, 0, 12, 0, -14, 0, 20, 0, 4, 60, 16, -16, -12, -36, -24, -2, -4, 20, 12, 0, 20, 36, 16, 54, -30, 0, 0, 0, -12, 36, -24, 0, 0, 24, -4, 18, 36, 0, 0, -4, 12, 0, 0, 24, -36, 0, 0, 24, 12, 0, -40, 42, 4, 24, 0, 12, 16, -24, 24, -54, 14, 0, 0, 0, 0, 0, -36, 0, -48, 0, 0, -30, -24, 20, 16, 0, 20, 0, -16, -18, 18, 0, 8, -38, 0, 0, 36, 0, 20, 56, 48, 0, -6, -36, 0, 0, -12, 0, -28, -24, 30, -60, 0, 0, 36, 0, -16, 0, -48, 0, -72, 0, -10, -36, -8, -30, -46, 0, 0, 36, 0, 0, 32, 0, -24, 0, 0, 2, -36, 12, 12, 0, -20, 4, 0, 0, 24, -32, -8, -18, 0, 0, 0, -6, -10, 0, 24, -24, -10, -60, 48, 8, -18, 0, 0, 18, 0, 12, 0, 0, 12, -20, 8, -8, 6, 0, -12, 0, 42, 0, 48, 0, 16, 0, 0, 30, 4, 12, 0, 0, 30, 0, 0, 14, 12, 0, 0, 0, -18, 0, 16, 0, -14, -36, 40, 0, 0, 0, -36, 0, 38, 0, -8, -18, 0, 36, 0, 0, 32, 0, 40, 0, 4, 0, 0, 0, 0, 8, 0, 30, -32, 60, 0, -16, 0, 48, 24, 0, 24, -24, 0, -20, 6, -36, -32, 0, -6, 8, 0, 0, 18, 48, -20, -6, -24, 0, -60, 24, 12, 0, 0, 26, 12, 40, 0, -40, 8, 0, -48, -18, -12, -8, -20, -66, -30, 0, 24, 30, -6, 0, 8, 0, 16, 0, -24, 0, 36, 0, -36, 46, 0, -36, 0, 0, 40, 0, 0, -12, -8, 0, -20, 30, 0, 0, 16, 0, -60, 48, 0, 0, 16, 48, 24, 0, 36, 0, 24, -12, 2, -4, 8, 0, -20, 0, -24, 0, 20, 0, 0, 0, -12, -60, -16, 54, -54, -48, 60, -14, 0, -44, 0, 0, 20, -28, 0, -12, -36, 20, 24, 0, 8, -60, 0, 0, -24, -24, -16, 22, -18, 0, -72, 18, 12, 0, 0, 10, 4, 36, 0, 12, -24, 0, -16, -36, -24, 48, 72, 18, 0, 36, 4, 40, -8, 0, 0, 0, 30, 0, 0, 0, -42, 0, -8, -36, -24, 12, -64, 0, -12, 0, -32, -42, 24, 0, -24, 38, 54, 0, -48, 0, -12, -108, 12, 0, 0, 8, 0, 0, 30, 0, 0, 24, -12, 24, 96, 0, -54, 0, 24, 0, 30, 0, 48, 0, -50, 0, 0, 14, 32, 0, -40, 60, -10, 0, 16, 0, 18, -12, -36, -38, 8, 0, -16, 0, 38, 0, 0, 0, -14, 36, -12, -26, 12, 0, 0, -102, -56, 0, -48, -48, -40, 60, 0, 0, 36, 0, 0, -20, -8, -64, 0, 72, -18, 44, 0, 0, 60, 0, 0, 0, 60, 0, 0, 0, 36, 0, 0, 12, 2, -60, 0, 0, 12, 0, 96, 98, -36, 0, 72, -18, -12, 0, 12, 0, 36, 60, 16, 0, 30, 36, 0, 0, 0, 0, 16, 40, -36, -12, 0, 0, 0, 0, -32, 0, -20, 0, 48, 0, 0, 12, 0, -30, -2, 24, 0, 30, -12, -12, 0, 0, -12, 24, 40, -86, -4, 28, 16, 0, 60, -64, 0, 0, 32, -36, -32, -12, 18, 0, 0, 0, 18, 0, -12, -14, 6, -40, 20, 10, -28, 0, 0, 8, 24, -36, 0, 18, 60, 0, -48, -84, -20, 0, 36, 0, -10, 0, -40, 0, -18, 0, 0, 0, -12, 72, 60, 0, 0, 0, 0, 66, 20, 0, -16, -66, 8, 0, 24, 0, -18, -84, 12, 0, 8, 4, -84, 0, -20, 0, -48, -24, 28, 0, 0, 0, -40, 0, -24, 0, -30, 0, 0, 0, -30, 84, 0, -64, -24, -20, 0, -90, 30, 0, -24, 0, -14, -20, 0, -24, -48, 16, 48, 0, 0, 0, 0, 0, -24, 12, -40, 36, -72, 0, 28, 34, 36, 0, -80, -30, -36, -4, 0, 24, 0, 0, 36, -42, 24, -36, -76, 24, 58, 12, 16, 62, 6, 0, 0, 0, -36, 0, -28, 0, 36, 0, -64, -54, -24, -16, 0, 0, -12, 0, 0, 60, 30, 0, 40, 46, -36, 0, 0, 0, -8, 104, 0, 0, -30, 0, 64, 0, -60, 0, -36], "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], [1, 0], [-1, 1], [0, -1], [0, -2], [1, 0], [1, 1], [0, -3], [2, 2], [2, 0], [-1, 1], [2, 0], [-2, 0], [-3, 2], [3, 3], [0, -1], [-4, 0], [3, 0], [-2, 2], [0, 0], [0, -2], [-3, 0], [-2, 2], [-6, 0], [2, -2], [-4, 0], [1, -5], [0, -5], [-6, 0], [0, 6], [1, 1], [0, 0], [4, -4], [0, -2], [-3, 3], [0, -3], [0, -4], [3, 0], [0, 0], [2, 3], [2, 2], [0, 10], [3, -3], [0, 9], [0, -4], [2, 0], [6, -6], [0, 7], [0, 4], [-2, 0], [4, -4], [0, -3], [4, 6], [0, -6], [5, 5], [2, 0], [6, -6], [0, 0], [-6, -6], [10, 0], [-2, 0], [0, -10], [0, 0], [0, -6], [0, 8], [-3, 2], [2, 2], [-12, 0], [0, -6], [0, 6], [3, 3], [0, 5], [4, 4], [0, -6], [-3, 3], [0, 4], [0, 0], [0, -6], [-5, -1], [0, 0], [-4, 0], [1, 0], [-10, -10], [-16, 0], [0, 6], [3, 0], [-9, -9], [6, 0], [4, 4], [0, -4], [-2, 2], [6, 9], [0, 12], [0, 0], [-7, -7], [0, 0], [-4, -4], [0, -18], [2, -2], [4, 0], [0, 8]]}