# Stored data for newform 351.2.l.a, downloaded from the LMFDB on 18 June 2026. {"Nk2": 1404, "analytic_conductor": 2.8027491109469413, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 117, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 12, "char_orbit_label": "l", "char_order": 6, "char_parity": 1, "char_values": [351, 6, [326, 28], [4, 5]], "cm_discs": [], "conrey_index": 127, "dim": 2, "field_disc": -3, "field_disc_factorization": [[-1, 1], [3, 1]], "field_poly": [1, -1, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 6, "has_non_self_twist": 1, "hecke_cutters": [[2, [3, 0, 1]]], "hecke_orbit": 1, "hecke_orbit_code": 755947798879, "hecke_ring_generator_nbound": 5, "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, 117, 12, 1, 6, 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": "351.2.l.a", "level": 351, "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": [3, 13], "level_radical": 39, "minimal_twist": "117.2.l.a", "nf_label": "2.0.3.1", "prim_orbit_index": 12, "qexp_display": "q+(-1+2\\zeta_{6})q^{2}-q^{4}+(-1-\\zeta_{6})q^{5}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "1.2.3.c6", "self_twist_discs": [], "self_twist_type": 0, "space_label": "351.2.l", "trace_display": [0, 0, -3, 3], "trace_hash": 426038133154640609, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.942", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.508", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "98.084", "prec": 20}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.167", "prec": 17}, "traces": [0, 2, 0, 0, -2, -3, 0, 3, 0, 0, 3, 0, 0, -2, -3, 0, -10, 3, 0, -3, 3, 0, -12, -3, 0, -2, -12, 0, -3, 12, 0, 15, 0, 0, -9, -3, 0, -9, -3, 0, 3, 21, 0, 1, 0, 0, 9, -9, 0, -4, 6, 0, 2, -12, 0, 6, -3, 0, 0, 0, 0, 5, -15, 0, -2, 9, 0, 21, -3, 0, 9, 15, 0, 0, 9, 0, 3, -6, 0, 11, 15, 0, 21, -9, 0, 0, 3, 0, -12, -27, 0, -9, 3, 0, -9, 6, 0, 27, 12, 0, 2, 12, 0, 13, -12, 0, 0, 15, 0, 0, 18, 0, -15, -12, 0, 0, -12, 0, -12, 0, 0, -2, 15, 0, -15, 0, 0, 5, 0, 0, 15, 15, 0, -6, 21, 0, -9, 9, 0, -32, 3, 0, 15, -24, 0, -18, -24, 0, 9, 0, 0, 21, -3, 0, -18, -15, 0, -23, -33, 0, -9, 0, 0, 21, -21, 0, -9, -9, 0, -22, 18, 0, -1, -21, 0, 0, 0, 0, 27, 3, 0, -44, -15, 0, 9, 9, 0, -18, 9, 0, 0, 3, 0, -9, -27, 0, 4, -15, 0, -13, 6, 0, 0, 18, 0, -42, 39, 0, 10, -6, 0, -13, 12, 0, 45, -3, 0, 15, 0, 0, -6, -21, 0, 0, 9, 0, 0, 21, 0, 15, -18, 0, 0, 36, 0, 18, 0, 0, -18, 9, 0, -9, 0, 0, -5, 0, 0, -3, -15, 0, -42, 9, 0, 18, 15, 0, 38, 3, 0, -9, -9, 0, 45, -48, 0, 18, 0, 0, -21, 3, 0, 27, -15, 0, -9, 12, 0, -23, 0, 0, 9, 9, 0, 23, -15, 0, 12, 42, 0, 8, 18, 0, 0, 0, 0, 6, 9, 0, 0, 21, 0, 3, 21, 0, 15, -15, 0, 0, 6, 0, 45, 27, 0, -19, -69, 0, -11, -15, 0, 0, 3, 0, 18, -9, 0, 14, 21, 0, 21, -18, 0, 27, 9, 0, -9, -42, 0, 29, 24, 0, 0, -30, 0, 0, 3, 0, -63, 24, 0, 0, 12, 0, 36, 0, 0, -30, 27, 0, 9, 0, 0, -16, 0, 0, 9, 12, 0, 16, 15, 0, -27, -18, 0, -28, -18, 0, -9, -12, 0, -21, -6, 0, 9, 0, 0, 18, -9, 0, -27, 3, 0, 9, 12, 0, 15, 0, 0, -45, 39, 0, 10, -51, 0, -45, -12, 0, -18, 18, 0, 0, 0, 0, -13, -6, 0, 18, 36, 0, 18, 9, 0, 15, 39, 0, 0, 6, 0, 15, -15, 0, -3, -39, 0, 5, -45, 0, 0, 9, 0, 16, 18, 0, -9, 21, 0, 27, -12, 0, -3, -27, 0, 42, 12, 0, -21, 21, 0, 0, -15, 0, 0, -3, 0, -45, -60, 0, 0, 24, 0, 42, 0, 0, -12, 6, 0, 6, 0, 0, -9, 0, 0, 27, 9, 0, 2, -27, 0, -15, 15, 0, -24, -3, 0, 18, 21, 0, -75, 30, 0, -45, 0, 0, -27, 21, 0, -18, 18, 0, -5, -3, 0, -12, 0, 0, -9, -39, 0, -18, 27, 0, 15, -12, 0, 25, -15, 0, 0, 0, 0, 14, -18, 0, 6, 21, 0, -45, 21, 0, -9, 24, 0, 0, -27, 0, 27, 0, 0, -17, -9, 0, 12, -18, 0, 0, -69, 0, 32, 33, 0, 5, 15, 0, 9, -48, 0, 18, -69, 0, 15, 36, 0, 5, 24, 0, 0, -6, 0, 0, 24, 0, 18, -18, 0, 0, -24, 0, -48, 0, 0, -30, 18, 0, 45, 0, 0, 9, 0, 0, 9, 27, 0, 44, 3, 0, -21, 3, 0, 16, 9, 0, -15, -9, 0, -21, -84, 0, -18, 0, 0, 45, 15, 0, 81, -27, 0, 11, 57, 0, 23, 0, 0, -15, -33, 0, -15, -15, 0, 28, -72, 0, -21, 39, 0, 0, 0, 0, 9, -9, 0, -24, 6, 0, -21, -45, 0, -45, -105, 0, 0, 39, 0, -81, -27, 0, -9, 9, 0, -18, 9, 0, 0, 30, 0, -68, 87, 0, 22, -21, 0, 27, 18, 0, -90, 39, 0, -9, 66, 0, -5, 12, 0, 0, 21, 0, 0, 48, 0, 63, 96, 0, 0, 60, 0, 18, 0, 0, 24, 18, 0, -21, 0, 0, 27, 0, 0, 30, -3, 0, -36, -39, 0, 39, -48, 0, 44, -12, 0, -1, -15, 0, 36, 6, 0, -33, 0, 0, -27, 42, 0, -57, -9, 0, 18, -21, 0, 0, 0, 0, 18, 45, 0, 19, 45, 0, -72, -42, 0, -7, 21, 0, 0, 0, 0, 0, -3, 0, 12, -24, 0, 39, 18, 0, 9, -51, 0, 0, -27, 0, -9, -21, 0, 30, 27, 0, 20, 69, 0, 0, 15, 0, 66, -18, 0, 25, -45, 0, 13, -36, 0, -27, -18, 0, -51, -48, 0, -9, -75, 0, 0, 27, 0, 0, -18, 0, 54, -42, 0, 0, 24, 0, 42, 0, 0, 112, 39, 0, -18, 0, 0, 29, 0, 0, 2, 12, 0, 18, 6, 0, -27, 21, 0, 14, 15, 0, 13, 21, 0, -3, 60, 0, 18, 0, 0, -9, 15, 0, 45, 3, 0, 5, 3, 0, 39, 0, 0, 63, -15, 0, -15, -66, 0, 21, 0, 0, -9, -21, 0, 0, 0, 0, -30, -9, 0, 80, 21, 0, -63, -15, 0, 15, -81, 0, 0, 9, 0, -9, 21, 0, -27, 90, 0, -18, -126, 0, 0, 66, 0, 8, -21, 0, 9, 45, 0, -18, 0, 0, -15, 45, 0, -25, -18, 0, 3, 15, 0, 0, 45, 0, 0, -99, 0, 12, -36, 0, 0, 36, 0, -4, 0, 0, -18, -27, 0, -63, 0, 0, -6, 0, 0, -48, -6, 0, -18, 27, 0, -9, -9, 0, -84, 9, 0, 44, 45, 0, 9, 18, 0, -21, 0, 0, 81, -27, 0, -48, -15, 0, -25, 45, 0, 54, 0, 0, 9, -9, 0, 15, -54, 0, 3, -6, 0, 37, 45, 0, 0, 0, 0, -23, 45, 0, -42], "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, 2], [0, 0], [-1, 0], [-1, -1], [0, 0], [1, 1], [-1, 2], [0, 0], [3, -3], [-2, 4], [0, 0], [-3, 4], [-3, 3], [0, 0], [-5, 0], [0, 3], [0, 0], [-2, 1], [1, 1], [0, 0], [-6, 0], [0, -3], [0, 0], [0, -2], [-5, -2], [0, 0], [-1, -1], [6, 0], [0, 0], [5, 5], [3, -6], [0, 0], [-6, 3], [0, -3], [0, 0], [-3, -3], [0, -3], [0, 0], [3, -3], [14, -7], [0, 0], [1, -1], [2, -4], [0, 0], [6, -3], [-6, 3], [0, 0], [0, -4], [4, -2], [0, 0], [3, -4], [-6, 0], [0, 0], [6, -6], [-3, 3], [0, 0], [-6, 12], [-2, 4], [0, 0], [5, -5], [-15, 15], [0, 0], [-1, 0], [7, -5], [0, 0], [14, -7], [0, -3], [0, 0], [6, -3], [10, -5], [0, 0], [-4, 8], [9, -9], [0, 0], [2, -1], [-6, 6], [0, 0], [0, 11], [5, 5], [0, 0], [0, 21], [-6, 3], [0, 0], [3, -6], [1, 1], [0, 0], [-6, 0], [-9, -9], [0, 0], [-7, 5], [0, 3], [0, 0], [0, -9], [3, 0], [0, 0], [9, 9], [8, -4], [0, 0], [0, 2]]}