# Stored data for newform 637.2.q.h, downloaded from the LMFDB on 25 April 2024. {"label": "637.2.q.h", "space_label": "637.2.q", "level": 637, "weight": 2, "hecke_orbit": 8, "hecke_orbit_code": 31526296936776317, "dim": 12, "is_polredabs": true, "nf_label": "12.0.58891012706304.1", "trace_hash": 741236704755928466, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[2, [1, 12, 36, -144, 112, 72, -82, -36, 52, 0, -8, 0, 1]], [3, [16, 80, 300, 516, 709, 390, 287, 42, 96, 4, 11, 0, 1]]], "qexp_display": "q-\\beta _{8}q^{2}+(-\\beta _{4}-\\beta _{9})q^{3}+(1-\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 13, "char_orbit_label": "q", "char_is_real": false, "Nk2": 2548, "analytic_conductor": 5.086470608755561, "hecke_ring_index": 16, "level_radical": 91, "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": "0.177", "prec": 17}, "analytic_rank_proved": true, "char_values": [637, 6, [248, 197], [6, 5]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [7, 13], "conrey_indexes": [491, 589], "field_disc": 58891012706304, "field_disc_factorization": [[2, 12], [3, 6], [4441, 2]], "field_poly": [64, 0, -80, -16, 60, 4, -30, 2, 15, -2, -5, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "11.110", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "518.341", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "39844.318", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "1.2.3.c6", "trace_display": [0, 0, 0, 0], "traces": [0, 12, 0, 0, 4, 0, 18, 0, 0, -4, -12, 6, 4, -4, 0, 6, -8, 4, 0, 0, 12, 0, 6, -12, -12, -20, 42, -12, 0, 8, 8, 0, 36, 30, 0, 0, -10, -42, -4, -4, -92, -30, 0, 2, 0, 0, 12, 0, 2, 0, -18, 52, -2, -44, -12, 6, 0, 0, -12, -18, 0, -14, 4, 0, -52, 60, 52, -24, 8, -4, 0, -24, 60, 0, 6, -46, 18, 0, -10, -56, 72, 2, -14, 0, 0, -48, 0, 2, -14, 12, -24, 0, 24, -18, -4, -22, 0, -6, 0, 0, -48, -10, 42, 36, 8, 0, 60, 22, 6, 0, 30, -24, 0, 10, -32, -48, 36, 52, -8, 0, -18, -16, 0, 0, 66, 0, 0, 2, 72, 12, 86, -28, -24, 0, 30, 0, -36, 48, 0, -10, 0, 6, 16, -32, -136, -96, 10, 0, 0, -12, -66, 0, -44, 14, 0, 28, 24, -8, -48, 52, -8, 0, 90, 0, 0, -48, -40, 54, 0, -26, -32, 66, 66, -34, 0, 0, 42, 0, 34, -56, 162, 60, 0, 64, -108, -18, -70, 0, -18, 0, 0, 14, 52, 102, 108, 72, 0, -6, 4, 2, 0, 48, 108, 0, 24, 18, 24, 136, 86, -76, 0, 16, -36, 0, -78, 42, 0, 0, 58, 84, -128, 40, -216, 42, 0, 6, 0, 66, -18, 0, -28, 0, -72, 28, -52, -4, -150, 0, 0, 0, 48, -12, 0, -62, -70, 0, -120, 22, 20, -6, 38, -8, 0, -96, 36, 0, -20, -56, -48, 0, -136, -112, -54, 12, -70, 0, 0, -114, 0, 62, -22, 114, 28, 0, 72, -42, -20, 18, 0, -108, 0, 0, -6, 72, -36, 20, -34, 0, 102, 44, -4, 0, 6, -42, 0, 42, -30, 24, -24, 12, -24, 0, -134, -70, 0, 78, 60, 0, 0, 46, 150, 12, 88, -88, -96, 0, 36, 0, -6, 54, 0, -6, 0, -66, -20, 12, -88, -168, -26, 0, 0, 66, 90, 0, -24, -20, 0, -32, -58, 56, -138, 28, -6, 0, -42, 0, 0, -44, -40, 18, 0, -24, -112, -18, -26, -44, 0, 0, -78, 0, -60, -56, 54, 156, 0, 92, -96, 48, 28, 0, 210, 0, 0, 4, -26, -6, 156, 126, 0, 78, 62, 22, 0, 18, 18, 0, 14, 28, -72, -4, 202, -96, 0, 24, 26, 0, -6, 24, 0, 0, 70, 48, -28, 20, -280, 66, 0, -60, 0, -114, 222, 0, -34, 0, -60, -20, -170, -24, -30, 86, 0, 0, 102, -132, 0, -48, -48, 0, 184, 66, 288, -138, 52, -76, 0, -60, 18, 0, -48, 6, 30, 0, 32, -160, -24, -14, -86, 0, 0, 84, 0, 28, 4, 120, -176, 0, 116, 54, -68, 0, 0, -78, 0, 0, -20, 70, 90, 108, -42, 0, -90, -28, 134, 0, 24, 18, 0, -8, -82, -84, 260, 78, 160, 0, 74, -16, 0, 162, 234, 0, 0, 22, -120, -84, 78, -196, -60, 0, 50, 0, 60, 6, 0, 0, 0, 36, -32, -36, -220, 24, -70, 0, 0, -78, -48, 0, -26, 36, 0, -28, 160, -76, 18, -28, 172, 0, 54, 36, 0, -46, 28, -12, 0, -70, -32, -6, 28, 36, 0, 0, -84, 0, 52, 8, -12, 16, 0, 168, -78, -82, -84, 0, 204, 0, 0, -48, 40, 60, -36, 6, 0, 90, -6, -64, 0, 30, 0, 0, -24, -72, -24, -140, 78, -92, 0, -8, -28, 0, -84, 144, 0, 0, -38, 66, 140, -74, -156, 6, 0, 38, 0, -66, -6, 0, -14, 0, -54, 148, 92, -132, -54, 54, 0, 0, 186, 168, 0, 54, 22, 0, -140, 132, 120, -108, -34, -160, 0, -78, 174, 0, 64, -76, -54, 0, -106, -100, -36, -4, 6, 0, 0, -90, 0, -120, 8, -66, 76, 0, 32, 0, 84, 4, 0, -198, 0, 0, -42, -84, 102, 0, -120, 0, -84, 30, -26, 0, -66, -54, 0, 28, -74, 66, -12, 36, -156, 0, -42, -12, 0, 12, -126, 0, 0, -6, -24, 40, 142, 0, 6, 0, 32, 0, 42, 72, 0, 104, 0, 24, 264, 24, -32, -48, -22, 0, 0, -300, -114, 0, -60, 54, 0, 80, -4, 96, 66, -22, 44, 0, 12, 96, 0, -16, -128, 132, 0, 140, 116, 276, 72, 26, 0, 0, 60, 0, 10, -22, -54, -92, 0, -208, 66, 6, -36, 0, 84, 0, 0, -54, -30, -108, 60, 46, 0, 18, -38, 56, 0, 168, -18, 0, -50, 20, -204, -24, 82, -168, 0, -128, 102, 0, -138, 66, 0, 0, -132, -60, -20, -12, 52, 42, 0, -20, 0, -150, -126, 0, 14, 0, -66, -48, 68, 24, -144, 12, 0, 0, 6, -60, 0, -124, -72, 0, -204, 28, -168, -18, 130, -152, 0, -60, -240, 0, 48, -40, 90, 0, -108, -16, 78, -30, -2, 0, 0, 114, 0, 52, 58, 54, -64, 0, 84, 96, -14, 40, 0, -198, 0, 0, 52, 6, 138, -16, 128, 0, -30, -6, -8, 0, -48, 48, 0, 22, 22, -24, -44, 2, 164, 0, 68, -84, 0, 204, -96, 0, 0, 60, -270, 16, 36, 112, -270, 0, 36, 0, 6, -114, 0, 48, 0, 0, -148, 144, -32, -30, 32, 0, 0, -150, 198, 0, -50, 40, 0, 48, -10, -76, 168, -36, 96, 0, 312, 84, 0, 38, -22, 108, 0, 224, 32, -108, 82, 96, 0, 0, 54, 0, -2, 0, 126, 96, 0, -220, 0, -52, -190, 0, 132, 0, 0, 116, -64, -48, 96, 96, 0, 192, -10, -96, 0, 0, 198, 0, 100, -12, 144, 124, -156, 56, 0, 156, 112, 0, -174, -12, 0, 0, 46, 186, 32, -50, 228, 156, 0, -32, 0, -54, -18, 0, -162, 0, 102, 100, -264, 244, 234, 86, 0, 0, 48, -54, 0, 110, 34, 0, 24, -60, -308, -54, 88, -22, 0, -90, 60, 0, -56, 94, 36, 0, -136, 112, -12, 58, -94, 0, 0, 54, 0, -76, -64, -132, 0], "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, 13, 5, 1, 6, 0]], "char_orbit_index": 17, "prim_orbit_index": 5, "minimal_twist": "91.2.q.a", "char_is_minimal": true, "conrey_index": 491, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0], [1, 0, -1, -1, -1, 1, 1, 0, 1, 1, 0, -1], [0, 0, 0, 0, 0, -1, 0, 0, -2, 0, -1, -1], [1, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 1, 1, -1, -2, -1, -2, -2, 0, 0], [0, -1, -1, 0, -1, 0, 0, 2, 0, 1, -1, -1], [0, 0, 0, -2, -2, -1, 3, 0, -1, 2, -2, -1], [0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1], [1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0], [-1, 1, 1, 0, 0, 1, -1, -1, 1, -1, 2, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 2, 1, 0, -1, 0, 0, -2], [0, -2, 0, -1, -3, -1, 2, 1, 1, 3, -1, -1], [1, 0, -1, 1, 0, -1, 1, 0, -1, 1, -1, 0], [-1, 1, 2, 1, 1, 0, -2, -1, -1, -4, 1, 1], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1], [1, 2, -1, 1, 4, 1, -1, 0, 1, -1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, 0, -1, 0, 1, 0, 2, 2, 0, 0], [0, 2, 0, 1, -1, -1, 2, -1, 0, -1, 1, -1], [0, 0, -2, 0, -1, 2, 0, 2, 0, 1, 0, -2], [-2, 0, 3, 0, 2, -1, 0, 0, -1, 0, -1, 1], [4, -1, -1, 0, 0, 2, 0, 1, 3, 1, 2, -1], [-1, -1, 1, 0, 1, 0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -2, 0, -1, -1, -3, 0, 1, -3, 1, -1, -3], [3, 0, -1, -1, 0, 1, 3, 0, -5, 1, -2, -3], [-1, -2, 0, 1, 0, -1, -2, 2, 0, 0, 0, 0], [3, 1, -2, 3, 3, 3, -3, 0, 3, -2, 3, 0], [1, 0, -1, -2, -4, -2, -1, 0, -2, -1, -1, -1], [2, 1, -1, -1, -1, 0, 4, -1, 0, 2, -1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -2, 2, 1, 0, 4, 2, 0, 2], [-4, 0, 0, 2, 0, -1, -2, 3, -1, 0, -2, 1], [-1, 0, 3, -1, 1, -1, 0, 0, -2, 0, 0, 0], [-2, -1, -2, 0, 0, -1, -2, 2, 1, 1, 0, 2], [-8, -1, 5, 1, 1, -2, 0, -1, -4, 0, -3, 3], [-4, 0, 0, 2, 0, -3, -2, 1, 1, 0, -2, 3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 2, 0, 3, 0, -1, 0, -2, -2, 2, 2], [-1, 0, 1, 0, 1, -1, -2, 0, -4, -2, -1, -1], [1, 1, -1, 3, 2, 3, -1, 0, 3, -1, 4, -1], [0, -1, 3, -2, 2, -2, 0, 0, -2, 3, -1, -1], [3, -3, -1, 0, -1, -2, 6, 3, -2, 2, -2, -2], [-1, 1, 4, 0, 2, 0, -1, -2, 0, -4, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, -1, -1, 1, -1, 3, 5, 1, 1, -1], [4, -1, 0, -1, -1, 0, 0, -1, -1, 0, 1, -1], [-2, -1, 2, 2, 1, -3, -3, -1, -6, -3, 0, 0], [-3, 0, -2, 2, -2, 0, 0, 0, 0, 0, -2, 2], [0, 0, -4, 1, -2, 1, 0, 1, 2, 2, -1, -1], [0, -2, 0, -4, -4, -2, 1, 1, -4, 0, -4, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, -1, -1, 2, 1, 2, 1, -1, 2, 0, 0], [-1, 1, 0, -1, -3, -1, 1, 0, -1, 0, -1, 0], [-1, 0, 2, 0, 2, 0, 1, 0, 0, 2, -3, 3], [4, 1, -2, -1, 1, 0, 8, -1, -1, 4, -1, -1], [-2, -1, -4, -3, -2, 3, -2, 2, 3, 4, 1, -2], [0, 0, 0, 2, -3, 2, -2, 0, 4, -3, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, 0, 0, 4, -2, 0, 0, 0, -2, 0, -4, 4], [6, 0, -3, -1, -5, 0, 2, -1, 2, 3, -2, 0], [3, -1, 1, -2, -1, -2, 0, -1, -2, 0, 0, 0], [-2, 0, -2, -3, -1, 4, -1, 0, -1, 1, 3, -4], [0, 2, 0, -1, 3, 0, -1, -1, -3, -1, -1, 0], [0, -2, -6, -2, 0, 2, 0, 4, -2, 6, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, 0, -2, -2, -2, 2, 0, -2, 0, 0, -2], [4, 0, 0, 2, 7, 2, -4, 0, 2, 0, 4, -2], [-2, -1, -2, 1, 0, 0, -4, 1, 4, 4, 1, 1], [0, 0, 3, -1, -2, 1, 0, 0, 7, -3, 2, 1], [0, 4, 0, 1, 3, 1, 7, -2, 0, -1, 1, 1], [2, 0, -2, 0, -1, 0, 1, 1, 4, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, 3, 2, 0, 0, -1, -2, 5, -5, 3, 5], [-4, -1, -1, 1, 1, 1, 0, -1, 2, 0, 0, 0], [10, 0, -10, -3, -5, 6, 5, 1, 11, 5, 3, -6], [0, -2, 0, 0, -4, -1, 0, 1, 1, 0, 0, -1], [-4, 0, 1, 1, -2, -1, -4, 0, 9, -1, 2, 3], [1, 2, 2, 1, 4, 1, 2, -2, -2, -4, 2, 2], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, 1, -4, -1, -4, 4, 0, -4, 1, -3, -1], [3, -2, -1, -2, -3, 3, 6, 2, 6, 2, 1, 1], [1, 1, 4, -2, 0, 2, 1, -2, -2, -4, 0, -2], [0, -2, 0, -4, -6, -1, 4, 1, -2, 0, -4, -1], [0, 0, 8, -1, 4, -1, 0, -1, -6, -4, 1, 1], [-1, -1, 4, 2, 0, 1, 0, -1, -4, 0, -1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 1, -1, 1, 1, -1, 0, 1, 2, 0, -2, 2], [-4, 0, 6, -1, 3, -2, -2, -2, 2, -3, 1, 2], [0, 2, 0, 1, 4, 1, 0, -1, -2, -4, 1, 1], [-5, 1, 1, 2, 1, -2, -5, -2, 2, -1, 1, 3], [-1, 0, 0, 3, 0, 1, -2, 0, 8, 0, 4, 4], [-1, 0, 1, -2, -4, -2, 1, 0, -2, 1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3, -2, 0, -2, -3, -2, -6, 2, -5, 0, -4, -4], [-11, 1, 6, 3, 6, -3, -11, -2, -3, -6, 3, 6]]}