# Stored data for newform 2646.2.h.l, downloaded from the LMFDB on 25 April 2024. {"label": "2646.2.h.l", "space_label": "2646.2.h", "level": 2646, "weight": 2, "hecke_orbit": 12, "hecke_orbit_code": 49540076970969686, "dim": 4, "is_polredabs": true, "nf_label": "4.0.1089.1", "trace_hash": 1421585974018143267, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [-6, -3, 1]], [11, [-6, 3, 1]], [13, [4, -2, 1]]], "qexp_display": "q-\\beta _{1}q^{2}+(-1+\\beta _{1})q^{4}+(1-\\beta _{2})q^{5}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 63, "char_orbit_label": "h", "char_is_real": false, "Nk2": 10584, "analytic_conductor": 21.12841637483079, "hecke_ring_index": 3, "level_radical": 42, "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": "0.010", "prec": 17}, "analytic_rank_proved": true, "char_values": [2646, 3, [785, 1081], [1, 2]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 7], "conrey_indexes": [361, 667], "field_disc": 1089, "field_disc_factorization": [[3, 2], [11, 2]], "field_poly": [9, -3, -2, -1, 1], "hecke_ring_index_factorization": [[3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.989", "prec": 17}, {"__RealLiteral__": 0, "data": "0.057", "prec": 17}, {"__RealLiteral__": 0, "data": "60.794", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1556.357", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "1.2.3.c3", "trace_display": [-2, 0, 6, 0], "traces": [0, 4, -2, 0, -2, 6, 0, 0, 4, 0, -3, -6, 0, 4, 0, 0, -2, 3, 0, 10, -3, 0, 3, 18, 0, 22, 4, 0, 0, -6, 0, 4, -2, 0, 3, 0, 0, -4, -20, 0, 6, -15, 0, -1, 3, 0, -9, 0, 0, 0, -11, 0, -8, -6, 0, 24, 0, 0, 12, 3, 0, -11, -8, 0, 4, 6, 0, -13, -6, 0, 0, -6, 0, 7, 8, 0, 10, 0, 0, -7, -3, 0, -15, -12, 0, -12, 2, 0, -6, -18, 0, 0, -9, 0, 0, 15, 0, 1, 0, 0, -11, 18, 0, 40, 4, 0, -6, -9, 0, -28, -12, 0, 0, -3, 0, -6, -6, 0, -6, 0, 0, -2, -11, 0, 4, 102, 0, -22, -2, 0, 6, -18, 0, 0, 26, 0, 3, -54, 0, -8, 0, 0, 3, -6, 0, -42, 7, 0, -4, -36, 0, 2, 10, 0, 0, 6, 0, 1, -7, 0, -3, 0, 0, 2, 30, 0, 24, -12, 0, 18, -12, 0, -1, 12, 0, 0, 3, 0, 36, 18, 0, -38, 0, 0, 18, -6, 0, -21, 0, 0, -30, -21, 0, 14, -2, 0, 0, 24, 0, -20, 22, 0, -9, 0, 0, -6, -20, 0, 4, -15, 0, 32, 12, 0, 18, 48, 0, 0, -28, 0, -12, -6, 0, -8, 0, 0, -3, -72, 0, 46, 3, 0, -6, -12, 0, 0, 3, 0, 0, -9, 0, -38, 1, 0, 22, 0, 0, 40, 4, 0, -51, -36, 0, -60, 11, 0, -2, 30, 0, 0, -12, 0, 9, -42, 0, -42, 0, 0, -13, 9, 0, -2, 3, 0, 27, 66, 0, 20, -8, 0, 0, 27, 0, 37, 3, 0, -6, 0, 0, 13, 84, 0, -14, 15, 0, 54, -4, 0, 18, 18, 0, 0, -1, 0, -20, 33, 0, 52, 0, 0, -12, 18, 0, -23, -2, 0, 14, -12, 0, -24, 6, 0, 0, 30, 0, 22, -4, 0, -15, 0, 0, -10, -12, 0, -12, 30, 0, -1, -36, 0, 24, -6, 0, 0, -1, 0, 12, -3, 0, -44, 0, 0, 3, -42, 0, 90, -18, 0, 18, 15, 0, -12, 19, 0, 0, 60, 0, -20, -9, 0, 12, 0, 0, -40, -21, 0, 0, -24, 0, 2, 15, 0, -21, -108, 0, 0, -28, 0, 1, 48, 0, 30, 0, 0, -12, 39, 0, -44, -20, 0, -11, 24, 0, 16, -9, 0, 0, 6, 0, 7, -6, 0, -20, 0, 0, -84, -8, 0, 30, -15, 0, -34, 32, 0, -6, -33, 0, 0, -9, 0, -96, -36, 0, 46, 0, 0, 56, 45, 0, 16, 24, 0, 12, -63, 0, -60, 16, 0, 0, -132, 0, 39, 6, 0, 36, 0, 0, 2, -23, 0, 3, -33, 0, 29, 12, 0, 24, -3, 0, 0, 0, 0, 3, 51, 0, 55, 0, 0, -9, 108, 0, -16, 19, 0, 1, -48, 0, -19, -11, 0, 0, -45, 0, 48, -20, 0, -8, 0, 0, 38, -51, 0, 18, -60, 0, -6, 30, 0, 11, -24, 0, 0, 4, 0, -15, 60, 0, 0, 0, 0, 6, 21, 0, -53, 9, 0, 21, 12, 0, 22, -42, 0, 0, 30, 0, -30, -13, 0, 9, 0, 0, -22, 4, 0, -6, -42, 0, -19, 27, 0, -33, 30, 0, 0, -10, 0, 16, 36, 0, -4, 0, 0, -54, -6, 0, -21, -74, 0, -6, 15, 0, -7, 12, 0, 0, 0, 0, 37, -26, 0, -42, 0, 0, -24, 7, 0, 15, -6, 0, -20, -108, 0, 8, -18, 0, 0, 18, 0, 18, 48, 0, 31, 0, 0, -1, -102, 0, -20, 10, 0, 33, 0, 0, 38, -26, 0, 0, 9, 0, -44, 6, 0, -36, 0, 0, 208, -23, 0, 1, -12, 0, -46, -7, 0, -12, 66, 0, 0, 48, 0, -3, 24, 0, 1, 0, 0, -15, 12, 0, 45, 22, 0, 2, 84, 0, 6, -15, 0, 0, -30, 0, 37, -10, 0, -12, 0, 0, 6, 24, 0, -60, 66, 0, 23, -1, 0, 18, 0, 0, 0, -12, 0, 12, -15, 0, -48, 0, 0, 2, 12, 0, -29, -24, 0, 6, 87, 0, 39, 88, 0, 0, 84, 0, 20, -6, 0, 21, 0, 0, -88, -45, 0, -18, 18, 0, 24, -36, 0, -30, 6, 0, 0, -12, 0, 19, -132, 0, -38, 0, 0, 60, -102, 0, 130, 10, 0, -9, 69, 0, -1, -6, 0, 0, 30, 0, 12, 20, 0, 42, 0, 0, -34, 0, 0, 12, 102, 0, 116, -1, 0, 15, 96, 0, 0, 42, 0, 54, 12, 0, -20, 0, 0, 14, 51, 0, 22, 1, 0, -24, -150, 0, 108, 30, 0, 0, 51, 0, -8, -12, 0, 39, 0, 0, 22, 88, 0, 40, 45, 0, 0, -11, 0, -12, 39, 0, 0, -8, 0, 18, 15, 0, -134, 0, 0, -12, 102, 0, 5, -14, 0, 12, -42, 0, -10, 40, 0, 0, -48, 0, -62, 168, 0, 4, 0, 0, 48, -15, 0, -15, 12, 0, -26, 68, 0, -64, 27, 0, 0, -6, 0, -33, -18, 0, -53, 0, 0, -9, 24, 0, -170, 48, 0, -36, -9, 0, 18, -23, 0, 0, 60, 0, -52, -28, 0, -90, 0, 0, -28, 16, 0, -12, -12, 0, -58, -6, 0, -63, -12, 0, 0, 120, 0, -8, 0, 0, -6, 0, 0, 66, 12, 0, -24, 39, 0, -3, 42, 0, -70, 36, 0, 0, -81, 0, -48, 2, 0, -23, 0, 0, 77, -6, 0, 66, -6, 0, -22, 29, 0, -6, -54, 0, 0, -12, 0, 6, 18, 0, 16, 0, 0, 0, -21, 0, -84, -6, 0, -102, 51, 0, -14, -110, 0, 0, -78, 0, -81, 18, 0, -54, 0, 0, 54, 8, 0, 19, 21, 0, -79, -2, 0, 96, -9, 0, 0, -19, 0, -11, 63, 0, -6, 0, 0, -45, -180, 0, 36, -24, 0, -20, -54, 0, -28, 4, 0, 0, -30, 0, -14, -19, 0, 102, 0, 0, -90, 18, 0, 30, -60, 0, 104, 3, 0, 30, 6, 0, 0, -22, 0, 12, -198, 0, 13, 0, 0, -2, -33, 0, 14, -15, 0, -30, -78, 0, -40, 0, 0, 0, 66, 0, -80, 6, 0, 21, 0, 0, 60, 106, 0, -18, -42, 0, 23, 21, 0, -6, 48, 0, 0, -11, 0, 84, -42, 0, 100, 0, 0, -60, -51, 0, 79, 60, 0, 26, -12, 0, 143, -18, 0, 0, -48, 0, 0, 44, 0, -2, 0, 0, -31, 3, 0, -42, -21, 0, 116, 38, 0, -54, -75, 0, 0, -33, 0, 30, 39, 0, 24, 0, 0, -10, 24, 0, -60, -8, 0, 36, -12, 0, 2, 2, 0, 0, -15, 0, 202, 27, 0, 12, 0, 0, -136, -21, 0, 37, -60, 0, -42, 3, 0, 15, -138, 0, 0, 14, 0, -6, -30, 0, 8, 0, 0, 0, 36, 0, 37, 37, 0, 13, -72, 0, -110, -42, 0, 0, 51, 0, 15, -24, 0, 7, 0, 0, -43, -30, 0, 12, 0, 0, -3, -20, 0, 54, -81, 0, 0, -4, 0, 36, -9, 0, 24, 0, 0, -36, 15, 0, 69, -36, 0, -96, 42, 0, -40, -62, 0, 0, -156, 0, -54, 2, 0, 51, 0, 0, 74, 10, 0, 10, -51, 0, 6, -66, 0, 0, -18, 0, 0, 38, 0, -26, 0, 0, 64, 0, 0, 9, 60, 0, -98, 22, 0, 6, 39, 0, -12, 18, 0, 0, 96, 0, -2, -104, 0, 46, 0, 0, -54, 1, 0, 6, 132, 0, 4, 23, 0, -7, 108, 0, 0, 24, 0, -33, -60, 0, 65, 0, 0, -24, -3, 0, -2, -3, 0, -12, -18, 0, -120, 1, 0, 0, -63, 0, 28, -15, 0, 12, 0, 0, -76, -90, 0, -44, -6, 0, -82, 2, 0, -42, -3, 0, 0, -3, 0, 30, 18, 0, -30, 0, 0, 60, -66, 0, -35, -74, 0, 20, -132, 0, -55, 24, 0, 0, -30, 0, 2, -12, 0, -12, 0, 0, 40, 30, 0, 66, 60, 0, -3, -46, 0, 2, -15, 0, 0, 18, 0, 0, 96, 0, -36, 0, 0, -12, -90, 0, 0, -6, 0, -15, -6, 0, 66, 24, 0, 0, -54, 0, 12, -1, 0, -24, 0, 0, -28, -29, 0, 12, -168, 0, 70, -3, 0, 87, -36, 0, 0, -78, 0, -44, 132, 0, -8, 0, 0, -42, -99, 0, 57, 20, 0, 3, 204, 0, 96, 21, 0, 0, 105, 0, 56, -88, 0, -45, 0, 0, 38, 36, 0, -36, 27, 0, 26, 24, 0, 18, -30, 0, 0, 15, 0, -12, 69, 0, 60, 0, 0, 24, 69, 0, 112, -38, 0, 264, 24, 0, 38, 76, 0, 0, 0, 0, 25, -120, 0, 51, 0, 0, 39, -65, 0, 10, 6, 0, -67, 18, 0, -138, 165, 0, 0, -1, 0, -6, -63, 0, 7, 0, 0, 30, 192, 0, -68, -6, 0, 20, 0, 0, -6, -21, 0, 0, -33, 0, -70, 17, 0, 0, 0, 0, 114, 12, 0, -51, 36, 0, 12, -58, 0, -1, 60, 0, 0, -30, 0, -48, -222, 0, 88, 0, 0, -21, 111, 0, 88, 54, 0, -6, 78, 0, 168, -20, 0, 0, -108, 0, -44, 14, 0, 51, 0, 0, -34, -44, 0, -2, -99, 0, -72, -24, 0, 75, -18, 0, 0, -54, 0, -60, -84, 0, -8, 0, 0, -102, 54, 0, -2, 16, 0, 24, 60, 0, 44, -78, 0, 0, -66, 0, -18, -44, 0, -44, 0, 0, -2, -20, 0, 45, -36, 0, -28, 0, 0, 22, -21, 0, 0, -12, 0, 39, -39, 0, 58, 0, 0, -8, -24, 0, -120, -9, 0, 15, 45, 0, 8, 67, 0, 0, 102, 0, -62, 6, 0, -204, 0, 0, -126, 5, 0, 7, 30, 0, 120, -6, 0, -42, -24, 0, 0, 20, 0, -20, 102, 0, -22, 0, 0, 24, -114, 0, 79, -62, 0, -84, 96, 0, -28, 4, 0, 0, -87, 0, -32, 48, 0, -15, 0, 0, 77, 30, 0, -24, -18, 0, -47, -26, 0, -34, 48, 0, 0, 32, 0, -54, 90, 0, 34, 0, 0, 12, -114, 0, -17, 66, 0, 36, -18, 0, 24, 106, 0, 0, 144, 0, 108, 18, 0, -12, 0, 0, 30, 85, 0, 48, 27, 0, -49, 72, 0, 18, 48, 0, 0, 18, 0, -23, 6, 0, -54, 0, 0, 60, 0, 0, -56, 26, 0, -28, -66, 0, 20, 45, 0, 0, 30, 0, 46, 14, 0, -32, 0, 0, -40, -12, 0, 6, 114, 0, -96, 29, 0, -6, -132, 0, 0, 126, 0, 6, 264, 0, -41, 0, 0, -60, -54, 0, 16, -8, 0, 0, -48, 0, -244, -6, 0, 0, 96, 0, 105, 66, 0, 12, 0, 0, 119, 48, 0, -78, -18, 0, 16, -3, 0, -21, 36, 0, 0, 35, 0, -72, -81, 0, 6, 0, 0, 162, 96, 0, 187, 96, 0, -4, -6, 0, 14, 46, 0, 0, 168, 0, 84, -154, 0, 3, 0, 0, -5, -33, 0, -6, -60, 0, -63, 44, 0, -58, 42, 0, 0, -6, 0, -54, -27, 0, 103, 0, 0, -12, -60, 0, -80, -3, 0, 18, -39, 0, -7, -8, 0, 0, -102, 0, -44, 0, 0, 42, 0, 0, -168, -84, 0, 3, 174, 0, -44, 51, 0, 51, -96, 0, 0, 28, 0, 55, 12, 0, -18, 0, 0, 39, 48, 0, 12, -81, 0, -9, -72, 0, -228, -54, 0, 0, 45, 0, -12, 54, 0, 8, 0, 0, 0, -38, 0, -42, 99, 0, 20, -79, 0, 1, -36, 0, 0, -48, 0, 18, 60, 0, -192, 0, 0, 38, 105, 0, 106, 22, 0, -126, -54, 0, 100, 12, 0, 0, 24, 0, 2, 90, 0, 90, 0, 0, -60, -18, 0, -24, 27, 0, 110, 40, 0, 108, 60, 0, 0, -28, 0, 4, -66, 0, -8, 0, 0, -30, 156, 0, -206, 7, 0, -19, -48, 0, 11, -51], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 63, 7, 1, 3, 0]], "char_orbit_index": 8, "prim_orbit_index": 7, "minimal_twist": "126.2.f.d", "char_is_minimal": false, "conrey_index": 361, "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], [1, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [-1, 1, 0, 0], [1, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, 1], [-2, 0, -1, 0], [0, 0, 0, 0], [0, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, 0, 0], [0, 1, 0, 1], [0, 0, 0, 0], [5, -5, 0, 0], [-1, 2, 1, -1], [0, 0, 0, 0], [0, 1, 0, 1], [5, 0, 1, 0], [0, 0, 0, 0], [4, 0, -3, 0], [2, -2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 4, 2, -2], [0, 0, 0, 0], [2, -2, 0, 0], [-1, 1, 0, 0], [0, 0, 0, 0], [2, -1, 1, -1], [0, 0, 0, 0], [0, 0, 0, 0], [-2, 2, 0, 0], [-5, 0, 0, 0], [0, 0, 0, 0], [1, 0, -1, 0], [0, -7, 0, -1], [0, 0, 0, 0], [-2, -1, -3, 3], [2, -1, 1, -1], [0, 0, 0, 0], [0, -4, 0, -1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -7, 0, 3], [0, 0, 0, 0], [-2, 0, 0, 0], [0, -4, 0, 2], [0, 0, 0, 0], [6, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [2, 0, -2, 0], [0, -3, -3, 3], [0, 0, 0, 0], [0, -4, 0, -3], [-2, 0, 0, 0], [0, 0, 0, 0], [1, 0, 0, 0], [0, 4, 0, -2], [0, 0, 0, 0], [-8, 5, -3, 3], [-2, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-3, 0, -3, 0], [0, 0, 0, 0], [0, 5, 0, -3], [2, 0, 0, 0], [0, 0, 0, 0], [0, 5, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, 0, -3], [0, -2, 0, 1], [0, 0, 0, 0], [-8, 7, -1, 1], [-4, 8, 4, -4], [0, 0, 0, 0], [0, -6, 0, 0], [2, 0, 3, 0], [0, 0, 0, 0], [-2, 0, -1, 0], [-8, 10, 2, -2], [0, 0, 0, 0], [0, 0, 0, 0], [-5, 4, -1, 1], [0, 0, 0, 0], [0, 0, 0, 0], [5, -10, -5, 5], [0, 0, 0, 0], [2, 1, 3, -3], [0, 0, 0, 0], [0, 0, 0, 0], [-4, 7, 3, -3]]}