# Stored data for newform 430.2.k.a, downloaded from the LMFDB on 20 April 2024. {"label": "430.2.k.a", "space_label": "430.2.k", "level": 430, "weight": 2, "hecke_orbit": 1, "hecke_orbit_code": 687228322222, "dim": 12, "is_polredabs": true, "trace_hash": 758502460964497362, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [1, 15, 140, 181, 209, 196, 127, 42, 13, -15, 0, 1, 1]]], "qexp_display": "q+(-1+\\beta _{7}+\\beta _{8}-\\beta _{9}+\\beta _{10}-\\beta _{11})q^{2}+\\cdots", "char_order": 7, "char_parity": 1, "char_degree": 6, "char_conductor": 43, "char_orbit_label": "k", "char_is_real": false, "Nk2": 1720, "analytic_conductor": 3.4335672869150566, "hecke_ring_index": 1, "level_radical": 430, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [430, 7, [87, 261], [7, 5]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 5, 43], "conrey_indexes": [11, 21, 41, 121, 231, 391], "field_disc": 80248111013161, "field_disc_factorization": [[7, 10], [13, 2], [41, 2]], "field_poly": [1, 20, 115, -124, 270, -182, 141, -70, 44, -16, 6, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.217", "prec": 20}, {"__RealLiteral__": 0, "data": "0.034", "prec": 17}, {"__RealLiteral__": 0, "data": "370.339", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "21582.301", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c7", "trace_display": [-2, -1, -2, 4], "traces": [0, 12, -2, -1, -2, -2, -8, 4, -2, 7, -2, 3, -1, -4, -10, -1, -2, -5, 0, -2, -2, 22, -4, -16, -1, -2, -4, 8, 11, 2, 6, 27, -2, 6, 2, -3, 0, -18, -2, 5, -2, 14, -20, 14, -4, 0, -16, 2, 6, -12, 12, -5, -4, 2, -6, -4, -3, -19, 2, 4, 6, 16, -22, 13, -2, 10, -8, 9, 9, -15, -3, 27, 0, 28, 24, -1, -2, 26, 5, 10, 12, -12, 7, -31, 22, -12, -28, -6, -4, -38, 7, 8, 12, -2, -12, -2, 6, -15, -19, -6, -2, -17, -5, 10, 10, 1, 23, 34, 8, -55, 3, -48, -3, -29, 2, -16, 9, 7, -3, 35, -1, 31, 2, -66, 6, -2, -29, -24, 12, -5, -4, 6, -8, 23, -5, -20, -12, -12, -8, -17, 11, -65, -22, -1, 7, 9, 28, 47, -4, 86, -1, 19, -2, 8, 5, 6, 5, -61, 24, 35, -2, 25, -12, -31, -7, 20, 4, -58, 1, 18, 9, -74, 21, 18, 78, -10, 3, 31, -24, -26, -7, 76, 8, 33, -16, -11, -44, 28, -12, 32, -2, -35, -1, 31, 13, 5, 2, 8, -6, -22, -2, -16, 11, 10, 9, -7, 24, -14, -4, 26, -13, -20, -12, 48, 34, 7, -20, 59, 15, -70, 3, 18, 64, 25, 11, -7, 48, -37, -5, -14, -16, -12, 9, 3, -7, 2, 11, -68, -49, -21, -1, 7, 31, 46, 16, 23, 53, -4, 6, -16, -2, 14, 6, -18, 11, 16, -2, -98, 23, -36, 10, -133, 69, 11, 20, -26, -26, 98, -5, -34, 8, -86, 9, 9, -12, 3, 13, 44, 60, 79, -10, -49, 26, -13, -22, -5, -1, -12, -7, -21, 2, -34, -35, -45, 12, -24, -11, 45, -75, -4, -8, 36, 54, 26, -2, -19, -6, 2, -30, -75, -22, -20, 5, -85, 37, -29, -25, 79, 35, 25, -2, 4, 4, 53, -5, -4, 67, -16, -7, -37, -8, 131, -31, -53, -58, 9, -13, 76, -136, 27, 2, 18, 10, -58, 7, 20, 81, -115, -41, 52, 4, 16, 3, 111, 31, 27, -38, 34, -61, -66, -7, 14, -92, 16, -13, 21, -58, -110, -16, -80, -11, -1, 19, -10, -21, -1, 2, 11, -73, -6, 12, 64, -49, 85, -1, 5, 52, 128, -36, 80, -9, 37, 23, 56, -62, -4, -13, 2, 13, -62, -2, -89, -30, -16, 11, 23, -11, 29, 16, -26, 7, 100, -11, 17, -14, 11, 10, -51, -30, -56, -13, 141, -27, 158, -26, -5, -8, 75, 34, -16, 7, -132, 8, -21, -32, -34, 8, 12, 7, 169, 3, 39, -10, 48, -48, 11, 25, -18, -10, 5, 7, 40, -22, 9, 54, 15, -5, -114, 21, -63, 26, -45, 23, -59, 2, 26, -60, 96, 0, 26, 30, -37, -24, 13, 72, -2, -7, -57, 14, 116, -8, -15, 21, -20, -4, 13, -52, -28, -19, 74, 23, -48, -31, 54, 10, 15, -22, -35, 110, -22, -2, -53, 42, 184, -29, -17, -18, 9, 25, -32, -40, -84, -2, 60, -7, -46, 65, 58, 69, -131, -4, 63, -14, -108, -57, 1, 11, 42, -8, 86, -12, -13, -26, 0, -56, -1, 9, 1, -20, -75, -6, 100, -86, -114, 2, 15, -12, 51, 9, 53, 3, -26, 20, -102, -117, 43, -10, -85, 44, 28, 4, 15, -49, 18, 54, 6, 64, 13, 27, -23, 2, -127, 6, -155, -19, 26, -7, -99, -7, 7, 2, -45, -27, -62, 21, 0, -45, 80, 47, 59, 11, 73, -11, -46, -32, 42, -26, -109, 10, -28, -1, 116, -76, 130, 19, 17, 26, -85, 12, -204, 2, 18, -6, 48, -68, 11, 5, 109, -75, 31, 27, -6, 71, 5, -9, -2, 27, -8, 37, 34, 13, 90, -4, -123, 79, 25, -14, 25, -52, 234, -2, -1, 25, -163, -10, -5, -94, -2, 23, -38, -4, 158, 46, 8, 47, -57, 7, -77, 61, -8, -8, 109, 131, -31, 11, 23, 38, 37, 68, -49, 23, 23, -13, -50, 6, 8, 18, 40, 27, 43, -5, 16, 18, -140, -11, 44, 61, -34, 7, -24, 13, -120, -80, 24, 46, -66, -34, 40, 52, 9, -10, -8, -26, 58, 3, 54, -15, -94, -11, 99, -1, -38, 11, 6, 34, 6, 37, -99, 4, 60, 7, 24, 42, -130, 34, -26, -68, -17, 15, -77, -28, -127, 82, -205, -19, -58, 26, 100, 116, -41, -4, -3, 48, 26, 26, -75, -45, 136, -21, -71, -1, -43, 30, 101, 11, -16, 18, -12, -6, -64, -2, 99, -41, -68, -49, 8, -62, 22, -8, -17, 26, 180, 31, -212, -5, -22, 13, -215, -18, 22, -2, -70, -19, 34, 23, -61, -49, 94, 8, 102, -4, 42, 15, 18, 93, -21, 6, -97, 71, -18, -2, -16, 44, 14, 40, 4, 33, 31, -17, -49, -12, 166, -25, 37, -34, 67, -40, 53, 58, 19, 14, 106, -75, -112, -46, 6, 3, -33, 35, 192, 18, -248, -4, -67, -51, -23, -9, 83, 42, 48, 1, 182, -62, 45, -27, 32, 123, 17, -12, -135, -5, 52, 34, -32, -86, 38, -1, -9, 12, -62, 7, -98, 78, 97, -6, -10, -42, 250, 31, 11, -34, 18, 15, 131, -16, 11, 7, 127, -104, 38, 3, -121, -52, -135, 4, -4, 48, -74, 43, 9, 39, -27, -10, 94, 3, 37, 4, 26, 47, 64, 0, 30, -44, 154, 6, -92, -117, -119, 54, 94, -20, -292, 2, -32, 47, -58, -35, -17, -49, -112, 26, -63, -10, -23, -12, 24, 4, -31, 2, -117, 26, -95, 3, 65, -72, 28, 0, 30, -9, 198, -40, -179, -9, 28, 11, 46, -43, 92, -68, -63, -2, -48, 42, -80, -85, -35, 14, 8, -80, 98, -1, 161, -15, -62, -7, -60, 71, -37, 17, 21, -15, -91, -52, -80, -42, -9, 2, -114, 95, -145, 2, -62, -48, 114, 11, -34, -107, -57, -4, -7, 8, 112, 27, 5, 70, 6, -2, 52, 34, -2, -2], "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, 43, 5, 1, 7, 0]], "char_orbit_index": 11, "prim_orbit_index": 5, "minimal_twist": "430.2.k.a", "char_is_minimal": true, "conrey_index": 11, "id": null, "nf_label": 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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1], [0, 0, 0, 0, 1, 0, 0, 0, -1, 1, 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, -1, 0, 0, 0, 0, 0, 1, -1, 0], [0, 1, -1, 0, 1, 1, 0, -2, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, -1, -1, 0, 0, 1, 0, -1, 0, 1, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [-1, 1, -1, 0, 0, 1, 0, 0, 0, -1, 1, -1], [0, 0, 0, 0, 0, 1, 0, -1, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0], [0, 0, -1, -1, 1, 0, -1, 0, 0, 2, 0, 2], [0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0], [0, 2, -2, -1, 2, 1, -2, -2, -2, 2, 1, 2], [0, 0, -1, 0, -1, 0, -1, 0, 1, -1, 0, 0], [0, 0, -2, 0, 0, 0, 0, -1, -2, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [1, -2, 1, 2, -1, 0, 1, -1, 2, -2, 0, -2], [0, 0, -1, 0, 1, 0, -1, 0, -1, 1, 0, 1], [-3, 0, 0, 0, 0, 0, 0, 1, 0, -3, 3, -3], [0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1], [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, 2, -2, 0, 2, 0, -2, -1, -1, 1, 3, 1], [2, -1, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0], [3, 0, -3, -3, 0, 1, 0, -4, -3, 3, -4, 3], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1], [3, 0, 2, 2, -1, -2, 1, -1, -3, -1, -1, -1], [0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1], [2, -2, 1, 0, 0, -1, 0, 1, 0, 2, -2, 2], [-2, 0, 0, 1, -1, 0, 1, 0, 2, -2, 2, -2], [0, -1, 1, 2, -1, -1, 0, 0, 0, -1, 1, 0], [-3, 2, -2, -3, 1, 1, 0, 1, 1, -2, 2, 0], [1, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 1], [1, 0, 0, 0, 0, 1, -1, -1, 0, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [4, 0, -1, -1, -1, -2, 1, -2, -4, 3, -2, 3], [-3, 1, -1, 0, -1, -1, 0, 1, 1, -3, 3, 0], [5, 1, 1, -2, 3, -1, -2, -3, -4, 6, -3, 2], [1, -1, 1, 0, -1, -1, 0, 0, 0, 1, -1, 0], [0, 0, 1, 1, -1, -2, 1, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 2], [-3, 2, 2, 0, 2, -2, 2, 4, 4, 0, 3, -4], [1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1], [2, -3, 3, 1, -1, -1, 0, 0, 0, 4, -4, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, 1, -1, 0, 1, 0, 0, -5, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1], [0, -1, 0, -3, 0, 3, 1, 1, 0, -1, 0, 0], [1, -2, 2, 0, 0, -2, 0, 3, 0, 1, -1, 1], [-1, 0, 1, 1, -1, 0, 1, 0, 1, -1, 0, -1], [-2, 0, 0, 1, -1, 0, 1, 0, 2, -2, 2, -2], [-5, 0, 1, 1, -1, -1, 1, 4, 5, -4, 4, -4], [0, 0, -1, 0, 0, 3, -3, -1, 3, 0, 0, 1], [0, 1, -1, -3, 1, 3, -1, -1, 1, 1, 1, -1], [0, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1], [2, -1, 1, 1, 2, 0, 1, -2, -2, 2, 0, 2], [-4, 1, 1, 0, 1, -1, 1, 2, 3, 0, 4, -2], [-2, -1, 1, 3, 0, -1, 3, 1, 0, -2, 4, -4], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, -1, 0, -1, 1, -1], [-3, 4, -2, 0, 4, 1, -1, 1, 3, 0, 3, -1], [0, 0, 1, 0, -2, 0, 1, 0, 2, -2, 0, -3], [0, -2, 2, -1, -2, 1, 2, -1, 2, 1, -4, -2], [0, 1, -1, 0, 1, 0, -1, 0, -2, 0, 0, 2], [2, 0, 5, 0, 0, 0, 0, 4, 3, 0, -2, -4], [0, 0, 1, 1, -1, -2, 1, 1, 0, 0, 1, 0], [9, -4, 0, 0, 0, -4, -1, 0, -6, 5, -6, 9], [3, 0, -1, -1, 2, 3, -2, -1, -3, 2, -1, 2], [-1, 1, 0, 0, 0, 0, 0, 1, 0, -1, 1, -1], [0, -2, 2, 2, -2, -2, 2, 1, 1, -1, -1, -1], [4, 0, 0, -1, 0, 0, -1, 1, 0, 4, -2, 2], [0, -1, 0, 1, -1, -1, 1, 0, 1, -1, 1, 0], [0, 1, -1, -3, 0, 0, 0, 3, 3, -1, 1, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 2, -2, 0, -1, 0, -1, -2, -1, -1], [-1, 1, 1, 0, 1, 2, -2, 2, 4, 0, 1, -2], [-5, 2, 4, -2, -1, 0, 4, 5, 2, -2, 0, -6], [3, 0, 1, 1, 1, 0, -1, 0, -3, 2, 0, 2], [-3, 1, -1, 1, 1, 1, 0, 0, 0, -2, 2, 0], [-3, -2, 3, -1, -1, 0, 3, 2, 5, -1, -1, -2], [-6, -1, 1, 5, -4, -4, 0, 9, 9, -10, 10, 0], [-1, 0, 1, 1, -1, 0, 1, 0, 1, -1, 0, -1], [-6, -6, 5, 6, -5, 0, 5, 6, 3, -3, 0, -7], [0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, -1], [2, 0, 0, 0, 0, 0, -1, 0, -2, 0, -2, 2], [2, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0], [2, -1, 1, -1, 4, 4, 0, -4, -4, 6, -6, 0], [-1, 2, 0, -4, 4, 2, 0, 0, -3, -1, -3, -1], [-1, 2, 0, 0, 0, 0, 0, -1, 0, -1, 1, -1], [0, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1], [-7, 5, 0, 2, 0, 0, 2, 4, 0, -7, 4, -4], [-2, 0, 1, 1, -3, -1, 3, -2, 2, -2, -2, -2], [-1, 0, 0, 2, -2, 0, 1, 0, -1, -1, -1, -1], [-1, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, -1]]}