# Stored data for newform 322.2.e.a, downloaded from the LMFDB on 19 April 2024.
{"label": "322.2.e.a", "space_label": "322.2.e", "level": 322, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 274911461698, "dim": 8, "is_polredabs": true, "nf_label": "8.0.310217769.2", "trace_hash": 1994595114253745907, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, -5, 26, -1, 15, 7, 10, 3, 1]]], "qexp_display": "q+(-1+\\beta _{5})q^{2}+(\\beta _{1}+\\beta _{2}-\\beta _{5})q^{3}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 7, "char_orbit_label": "e", "char_is_real": false, "Nk2": 1288, "analytic_conductor": 2.571182945085228, "hecke_ring_index": 1, "level_radical": 322, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.004", "prec": 17}, "analytic_rank_proved": true, "char_values": [322, 3, [185, 281], [1, 3]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 7, 23], "conrey_indexes": [93, 277], "field_disc": 310217769, "field_disc_factorization": [[3, 4], [19, 2], [103, 2]], "field_poly": [1, 1, 5, -4, 15, -2, 4, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 17}, {"__RealLiteral__": 0, "data": "7.085", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "199.442", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "10202.917", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c3", "trace_display": [-4, -3, -7, -1], "traces": [0, 8, -4, -3, -4, -7, 6, -1, 8, 1, -7, -2, -3, 2, -1, 18, -4, -5, 1, -11, 14, 1, 4, 4, -3, -3, -1, 6, 2, 4, -9, -6, -4, -15, 10, -8, -2, 8, -11, -3, -7, 18, -2, 8, -2, -3, 4, -11, 6, -19, 6, 18, -1, -1, -3, 20, -1, 6, -2, -12, -9, -21, 12, -15, 8, 24, -15, 3, -5, -6, -8, 22, 1, 16, 8, -18, 22, -19, 6, 21, -7, 8, -9, 8, 1, 20, -4, 7, -2, -27, 6, -54, -8, 27, -11, -5, -3, 12, 14, 26, -3, -5, 18, -26, 2, 15, 2, 22, -3, -2, -10, -60, -1, -32, -3, 7, -2, 1, 24, -46, 18, 16, -21, 13, -6, 30, 18, 44, -4, 36, 24, -7, 30, -68, -6, 11, -5, 1, 3, -4, 16, 4, -11, -8, 1, 10, -32, -60, -16, 18, -18, 40, -11, -92, -1, 32, -3, 33, 21, 15, 14, 1, -16, -7, -9, -38, -4, 20, 1, 66, -10, -15, -4, 15, -14, -83, 4, -21, -27, 25, -3, 14, 39, 132, 4, 18, 27, 18, 22, -20, 10, -24, -3, 0, -6, -32, 5, -86, -13, -13, -3, -2, 10, -19, -36, -34, -26, -1, -1, -56, 12, 70, -1, 29, 22, 9, 6, -37, 4, 31, -10, 23, 30, 6, 2, 14, 16, -41, -3, 11, -14, -27, 4, -3, 1, -11, -12, 0, 23, 28, -9, -2, 16, 43, 42, 71, -26, -12, -6, -1, -15, 74, -3, -4, -22, 8, -4, 55, -72, -81, -48, 6, -7, 13, -15, -86, 94, 54, 3, 0, 11, -6, 10, 101, -2, -41, 3, -6, 2, -110, -8, -78, -2, -4, -11, 23, 16, 54, -2, -29, 10, -6, 16, 32, 0, 48, 8, 32, 18, 1, 36, 6, -80, -53, -11, -52, 46, -72, 20, 8, -16, -61, -3, 26, -66, 12, -42, -33, 15, 19, -7, -74, -2, -72, 8, 94, -7, -5, 18, 92, 76, 35, -4, 9, -10, -32, -2, 46, -33, 12, -10, 38, 30, 14, 8, 9, 15, 33, 7, -22, 73, 32, -2, 19, -21, -30, 54, 69, -50, 34, -3, -71, -7, -38, 15, -144, -66, -32, 4, 27, -36, 85, -54, 11, 18, -46, -11, 42, -32, 42, -5, -2, -24, -5, 6, 34, 0, 64, -6, -34, 16, -10, -19, -14, 43, 56, -13, -1, 26, -103, 6, -14, -2, 56, -5, -104, -13, -130, 18, 53, -34, -64, 52, 63, 2, 8, -1, -65, 28, 186, -27, -64, -35, 42, -1, -33, -58, 83, -44, 25, 9, 17, -3, -126, 41, -58, -2, 11, 31, 3, 20, 85, -46, 22, 30, -3, -3, 76, -1, -80, -7, 30, 16, 61, 82, -12, 6, 28, 11, 0, 7, 48, 15, -40, -2, 22, -3, 42, -2, -133, 22, 36, -12, 52, 0, -200, 23, -16, -14, 24, -9, 51, 4, 2, -32, 17, 43, -61, -21, -32, -46, -46, 13, 0, -12, -22, 12, 56, 2, 7, -15, -18, -37, 124, -15, 130, 2, 1, -22, 62, -16, 19, 8, -79, 55, -55, 36, 52, 63, -142, 24, -1, 6, -57, 14, 43, -26, -120, -15, -4, 43, 66, -26, -174, -27, 88, 3, 97, 0, -98, -22, 46, -6, 16, -5, 114, -43, -16, 1, -44, -41, -48, -6, 65, 12, 83, 2, -101, 55, -10, -8, -6, 39, -116, -2, 92, 8, -7, 22, -64, 23, 6, -8, 74, -45, -6, 1, 73, -29, 50, -20, -29, 12, 39, 16, -31, -16, 66, 60, -28, -24, 8, 8, 8, -64, 94, -36, -77, 1, -15, -18, -208, 9, -82, 40, 5, -53, -20, 22, 38, 104, -48, 46, 2, 36, 8, -19, -134, -4, -27, -16, 3, 122, -6, 6, -98, 26, -50, 33, 16, -21, 148, 21, -64, -33, -7, -30, 11, -38, 53, -7, 45, 37, 42, 1, -122, 36, 67, 8, -6, -188, 107, 14, -19, -5, 45, -9, -54, -79, 146, -38, -76, 35, 69, 8, 203, -18, 2, -10, -4, 16, 224, 1, 178, -23, 90, -33, 5, -24, -58, 20, 73, 38, 22, -15, 90, 47, -114, -4, -95, 9, -72, -30, -8, -66, -70, 7, -79, 11, -34, 10, -120, -16, -82, -2, -37, -38, -7, 42, 58, -30, -18, -27, -12, -138, -62, 25, -16, 34, -50, 6, -77, 142, -36, -7, 67, 19, -26, -54, -32, 72, -115, -66, -3, 64, 6, -8, -53, 27, 13, 18, 268, -74, -120, 27, 32, 11, -40, -36, 161, 92, 96, -11, -23, -21, -102, 52, -42, -21, 15, -5, 40, 4, 10, 48, 41, -5, 6, -3, -104, 43, -28, 0, 32, 64, -39, 12, -43, 68, -26, 16, 56, 5, 76, 14, -52, 7, -49, 43, 39, -112, -124, 26, -61, -1, 82, -13, 94, -10, 168, -3, -19, -14, 34, 4, 8, -112, -36, -5, -4, 52, -10, 32, -16, 65, -91, 18, -9, -106, -158, 68, -45, -64, 109, -26, 96, -9, 58, -1, 39, 8, -36, 2, 133, 130, 16, 28, -18, -93, 210, 15, -180, 32, 12, -35, -25, -84, -54, 2, -55, -33, -8, 29, -74, -58, 24, 22, 21, 25, 34, -18, -145, -34, -67, -3, 16, 63, 134, -4, 48, 29, -86, -2, -9, -22, 135, -62, 52, 3, -15, -10, 92, -92, 66, 23, -30, 22, 37, -60, -54, 6, 37, -3, 81, -38, -128, -1, -6, 40, -7, -7, 28, -60, -124, -32, -25, 61, 58, -41, 160, 102, 24, -3, 45, 28, -164, -22, 109, 0, -47, 7, 48, -24, -182, 12, -144, 20, 12, -2, -6, -44, 49, 6, -127, 42, 3, 1, -16, -25, 94, -11, -163, 36, 9, 24, -83, -104, -62, 0, -102, 100, -44, -46, 176, 8, -86, -14, 3, -48, -46, 18, -44, 51, 64, -2, 12, -1, 54, 16, 202, 17, -107, -86, 81, 122, 135, -21, 28, 16, 16, -25, 50, 23, -55, 13, 81, 0, 77, 24, 4, -22, 57, -6, -12, -49, 200, -1, 55, 7, -72, 30], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "322.2.e.a", "char_is_minimal": true, "conrey_index": 93, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 1, 0, 0], [0, 1, 1, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [-2, 0, 0, 0, -1, 2, -1, 0], [1, 0, 0, 0, 0, 0, 0, -1], [0, 0, 1, -1, 0, 0, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, -1, -1, -1, 0, 0, 0, 1], [0, 0, 0, 0, 1, -2, 0, 0], [0, 1, 2, 0, 0, -1, 0, 0], [-1, -1, -1, 0, 0, 1, 0, 1], [0, 1, 0, -1, 0, 0, -3, -2], [0, 2, 0, -1, -1, 0, -1, -1], [3, 1, 0, -1, 0, 0, 1, -2], [-1, 0, 0, 0, 0, 1, 0, 0], [0, -4, -2, 0, 1, -1, 0, 0], [0, 2, 1, 0, 0, 0, 0, 0], [-2, 2, 2, -4, 1, 2, 1, -2], [2, 0, 0, 0, 0, 0, 1, 0], [0, -1, 1, 1, 0, 0, -2, -2], [1, 1, 0, -1, 0, 0, 0, -2], [1, 0, 0, 0, 0, -1, 0, 0], [0, 1, 1, 0, 0, -1, 0, 0], [0, -1, 1, 0, 4, -2, 0, 0], [0, -2, -2, 1, 3, 0, 3, 2], [0, -2, 0, 2, 0, 0, -1, 2], [0, -2, -1, 2, 1, 0, 0, 1], [0, -1, 0, 1, 0, 0, -1, 1], [-3, -2, -2, 1, -1, 3, -1, 2], [0, -5, -4, 0, 2, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0, 0], [-4, 0, 0, -1, -1, 4, -1, 0], [1, 2, 0, -2, 0, 0, 1, 2], [-2, 2, -1, 0, -3, 3, -1, -1], [0, -1, 0, 1, 0, 0, 0, -1], [3, 5, 5, -4, -1, -3, -1, -5], [0, 2, -2, 0, -1, -2, 0, 0], [0, 3, -1, 0, -2, 0, 0, 0], [-2, 0, 0, 0, -1, 2, -1, 0], [2, -1, 0, 1, 0, 0, 3, 4], [0, -1, -2, -2, 2, 0, 2, 1], [0, 1, 0, -1, 0, 0, 0, 4], [-1, -2, -2, 1, 0, 1, 0, 2], [0, 2, 2, 0, -1, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [-3, -2, -2, 5, 1, 3, 1, 2], [1, 0, 0, 0, 0, 0, 0, -1], [-1, 5, 3, -1, 2, -2, 1, -3], [2, 2, 0, -2, 0, 0, 4, -1], [4, 1, 1, 5, -3, -4, -3, -1], [0, 1, 2, 0, -3, 0, 0, 0], [0, 1, -1, 0, -4, 1, 0, 0], [0, 2, 2, -2, 1, 0, 1, -2], [4, 3, 0, -3, 0, 0, 2, -4], [0, 0, 1, -1, 0, 0, 1, 0], [1, -3, 0, 3, 0, 0, -5, -6], [0, 1, 1, -1, 1, 0, 1, -1], [0, 3, 0, 0, 0, -3, 0, 0], [0, 1, 2, 0, 1, -3, 0, 0], [-7, -8, -8, 4, 1, 7, 1, 8], [1, 1, 0, -1, 0, 0, 2, 4], [-1, 1, 2, 3, -1, -2, 2, 2], [1, 0, 0, 0, 0, 0, 0, 0], [7, -1, -1, -3, 5, -7, 5, 1], [0, 1, 0, 0, 1, -4, 0, 0], [0, -3, 5, 0, -2, 0, 0, 0], [-1, 2, 2, 2, -1, 1, -1, -2], [-1, 0, 0, 0, 0, 0, 0, 1], [-1, -4, -1, 3, 1, -2, -2, 2], [2, -1, 0, 1, 0, 0, 3, 6], [0, -1, -1, -1, 0, 0, 0, 1], [0, -1, 0, 0, -4, 5, 0, 0], [0, -1, -5, 0, 1, 3, 0, 0], [-6, 0, 0, 5, -6, 6, -6, 0], [2, -4, 0, 4, 0, 0, -1, 2], [-3, 1, 3, 0, 0, 1, -3, -4], [0, -4, 0, 4, 0, 0, -2, 1], [5, -4, -4, 2, 3, -5, 3, 4], [0, 0, 0, 0, 1, -2, 0, 0], [0, -3, -1, 0, -3, 3, 0, 0], [-2, 4, 4, -1, -3, 2, -3, -4], [0, -7, 0, 7, 0, 0, -1, 3], [0, 2, 1, 1, -2, 0, 0, 1], [3, 2, 0, -2, 0, 0, 5, 3], [0, 4, 4, 1, 0, 0, 0, -4], [0, 2, 1, 0, -2, 2, 0, 0], [0, 1, 2, 0, 0, -1, 0, 0], [-6, -2, -2, -2, 5, 6, 5, 2], [1, 0, 0, 0, 0, 0, -1, -2], [-7, -8, -5, 2, -3, 0, -1, 4], [-1, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 7, -3, -6, -3, 0], [0, -3, 2, 0, -1, -3, 0, 0], [0, 3, -5, 0, -4, 1, 0, 0], [-1, -1, -1, 0, 0, 1, 0, 1], [1, -1, 0, 1, 0, 0, -3, -1], [3, -4, -3, 2, -1, -1, 1, 0], [3, -3, 0, 3, 0, 0, 0, 1], [-2, -1, -1, 2, -4, 2, -4, 1]]}