# Stored data for newform 975.2.n.o, downloaded from the LMFDB on 20 January 2026. {"Nk2": 3900, "analytic_conductor": 7.785414197074838, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 195, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 14, "char_orbit_label": "n", "char_order": 4, "char_parity": 1, "char_values": [975, 4, [326, 352, 301], [2, 2, 1]], "cm_discs": [], "conrey_index": 749, "dim": 8, "field_disc": 619810816, "field_disc_factorization": [[2, 12], [389, 2]], "field_poly": [1, 2, 2, -8, 14, -2, 0, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[2, [49, -84, 72, -18, 18, -24, 18, -6, 1]], [7, [2401, 392, 32, -910, 882, -384, 98, -14, 1]], [11, [25, 30, 18, -92, 134, -54, 8, 4, 1]], [37, [1444, 456, 72, -68, 68, 12, 2, -2, 1]]], "hecke_orbit": 15, "hecke_orbit_code": 63051288169939919, "hecke_ring_generator_nbound": 3, "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, 195, 14, 1, 4, 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": true, "label": "975.2.n.o", "level": 975, "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, 5, 13], "level_radical": 195, "minimal_twist": "975.2.o.l", "nf_label": "8.0.619810816.2", "prim_orbit_index": 14, "qexp_display": "q+(1-\\beta _{3}-\\beta _{4}+\\beta _{7})q^{2}+(\\beta _{1}-\\beta _{2}+\\cdots)q^{3}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "975.2.n", "trace_display": [6, 2, 0, 14], "trace_hash": 145593877062197732, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.275", "prec": 17}, {"__RealLiteral__": 0, "data": "0.118", "prec": 17}, {"__RealLiteral__": 0, "data": "206.154", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9312.619", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.252", "prec": 17}, "traces": [0, 8, 6, 2, 0, 0, -4, 14, -12, 4, 0, -4, 2, 14, 0, 0, -8, 0, 30, 2, 0, -8, 0, 0, 34, 0, 32, -10, -24, 0, 0, -12, -18, -18, -10, 0, 28, 2, 0, 20, 0, -38, -34, -4, -10, 0, 34, -22, 54, 0, 0, 26, -18, 28, -12, 0, -76, 6, 18, -14, 0, -8, 0, -10, 0, 0, 18, 0, -40, 0, 0, 10, 4, -10, 0, 0, 26, 0, 2, 56, 0, 8, -16, -38, 58, 0, 34, 34, 8, 28, 0, 8, 72, 22, -20, 0, 72, 4, -26, 28, 0, -12, -24, -92, -82, 0, -28, -12, 2, 6, 0, 6, -62, -12, -24, 0, 36, 54, 0, -42, 0, 0, -46, -6, 38, 0, 4, -44, 0, -16, 0, 0, 24, 0, 56, 0, -52, -16, -2, 0, 0, -28, 12, 38, -76, 0, 0, -8, 26, -24, 0, -54, 32, 16, -70, 0, 8, 0, 2, -42, 0, 78, 30, -22, -10, 0, 0, -10, 154, -4, 0, -50, 0, 0, -72, 0, -60, 60, 0, 72, 0, 0, 30, 18, 78, 0, 42, 44, 8, -104, 0, 0, 10, -18, 40, 0, -100, 90, -8, 0, 0, 14, -44, -10, 14, 0, -54, 4, -58, 0, 0, 80, 0, -46, -4, 0, -2, 0, 0, -66, 0, -46, -24, 38, 0, 0, -12, -16, -6, -40, 0, -74, 32, 0, 84, 0, 48, 56, 20, 6, 0, -46, 106, -78, 0, 0, -60, -22, 128, -56, 0, 36, -40, -2, 14, 0, 8, 0, -30, 0, 0, -8, -54, 12, 54, 0, 38, -40, 42, 0, 0, -30, 0, 22, -52, 0, -120, 16, 16, 4, 0, 56, 2, 12, 58, 0, -54, -120, -22, 0, 0, 24, -98, 0, 54, 0, 32, -6, -88, 4, 0, 10, -104, -2, 42, 0, -42, 18, -76, -40, 0, -84, 56, 0, 44, 0, 0, 22, -170, 72, 0, -44, 152, -10, 104, 0, 0, 6, 0, -120, 0, 26, 36, -50, -68, 0, 172, -12, 58, -8, 0, 0, -44, -24, -22, 0, -12, -104, -110, -26, 0, -36, 0, -2, 82, 0, -136, 76, 114, 78, 0, 0, 48, 68, -150, 0, -36, 0, 0, 2, 0, 156, -80, 0, -108, 0, 0, -34, -66, 12, 0, -12, 44, 46, -22, 0, 0, 72, 16, 68, 0, 108, -158, 28, 0, 0, -14, -8, 56, 28, 0, -14, -158, 6, 0, 0, 200, 0, 14, -18, 0, 128, 0, 0, 78, 0, -44, -8, -26, 0, 0, -52, 94, -54, -82, 0, -28, 46, 0, -52, 0, -2, 122, 84, 106, 0, 38, 4, -20, 0, 0, -20, -40, -12, -6, 0, 156, -68, 192, -48, 0, 100, 0, 12, 0, 0, -36, -66, -68, -38, 0, 92, 92, -64, 0, 0, 16, 0, 42, 116, 0, 14, 192, 78, 54, 0, -56, -84, -16, 96, 0, -22, 36, -42, 108, 0, -100, -64, 132, 10, 0, -76, -30, -128, 60, 0, 116, 20, 10, 26, 0, 58, 78, -12, -144, 0, 120, -34, 0, 14, 0, 0, 54, -42, 20, 0, -16, -8, 38, 70, 0, 0, -10, 0, -160, 0, -22, 36, 10, 0, 0, 34, 104, -50, 0, 0, 0, 4, 102, -6, 0, -86, -120, -26, 2, 0, 28, 0, -180, -84, 0, -42, -150, 58, -36, 0, 0, 2, -8, 28, 0, -82, 0, 0, 50, 0, 72, 78, 0, 184, 0, 0, -60, 20, 46, 0, 44, 8, 104, -90, 0, 0, -108, -54, -308, 0, 156, 44, 268, 0, 0, -6, 42, 92, -118, 0, -20, -40, 102, 0, 0, -108, 0, 100, -116, 0, 74, 0, 0, 16, 0, 40, -104, -68, 0, 0, -4, 4, 26, -6, 0, 88, -112, 0, 248, 0, -124, -60, -84, -10, 0, -34, 2, -64, 0, 0, -42, -40, -68, -50, 0, 88, -8, 98, 194, 0, 120, 0, -52, 0, 0, -18, 118, -96, 32, 0, -90, 78, -76, 0, 0, 10, 0, 36, 32, 0, -44, 32, -126, 154, 0, 4, 78, 148, 4, 0, -76, -64, 20, 112, 0, 102, 88, 12, 34, 0, -188, -148, -208, -58, 0, 58, -112, 16, -200, 0, -170, -154, 32, 92, 0, -128, 22, 0, -2, 0, 0, -88, -162, 110, 0, -52, -256, -82, 110, 0, 0, 84, 0, -32, 0, -158, 94, 126, 232, 0, -46, 124, -250, -92, 0, 0, 18, -40, -176, 0, -162, 156, -156, 76, 0, 50, 0, 80, -210, 0, 72, -26, -26, -48, 0, 0, 26, 204, 96, 0, 46, 0, 0, 42, 0, -178, 70, 0, 156, 0, 0, 8, -22, -20, 0, -2, 54, 0, -6, 0, 0, 28, -80, -80, 0, -68, 58, -22, 0, 0, 58, 48, -102, -100, 0, -40, -168, -134, 0, 0, 104, 0, -118, -34, 0, 136, 0, 0, -244, 0, -6, 58, -46, 0, 0, 6, 184, -48, -26, 0, 130, -36, 0, 148, 0, -90, 232, 160, 90, 0, 228, 44, 220, 0, 0, 104, 54, -68, 16, 0, 36, 130, 130, 66, 0, 0, 0, 8, 0, 0, -52, -2, -144, 144, 0, 4, -34, 36, 0, 0, -132, 0, 12, -108, 0, -24, -156, -140, 284, 0, -4, 0, 316, -106, 0, -58, 196, 92, -108, 0, 102, 28, 22, 16, 0, 36, -122, 108, -150, 0, -258, -184, -36, -126, 0, -76, 2, -80, -212, 0, 44, -68, 0, -24, 0, 0, -122, -122, -16, 0, -78, -60, 162, -76, 0, 0, -74, 0, -180, 0, 80, -2, 144, 8, 0, -70, 308, 118, 142, 0, 0, -16, -154, -88, 0, -12, 24, -16, -248, 0, -26, 0, 314, -102, 0, 2, 162, 144, 242, 0, 0, 128, 56, -66, 0, -106, 0, 0, -20, 0, -100, -134, 0, -132, 0, 0, 60, 4, -90, 0, -260, 4, -10, 50, 0, 0, -102, -24, 28, 0, 88, -12, -92, 0, 0, -6, -24, -48, -164, 0, 82, -66, 78, 0, 0, -112, 0, 122, -10, 0, -2, 0, 0, -42, 0], "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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, -1, -1, 0, 0, 1], [0, 1, -1, 0, 0, 1, 0, 0], [0, 0, 0, -2, -1, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 1, -2, 0, 0, 0, -1, -2], [2, 0, 1, -2, 1, 0, 1, 1], [-2, 1, -2, -2, 0, 2, 2, 0], [1, 1, 0, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 2], [0, -2, -1, 3, 0, -2, -3, -3], [2, 0, 0, 0, -1, -1, 1, 0], [0, 3, 0, -4, -1, 4, 3, 4], [0, 0, 0, 0, 0, 0, 0, 0], [-3, 3, -4, 0, 1, 4, 0, -4], [0, -1, 0, -3, 0, -1, 0, -1], [4, 2, 1, -2, -1, 0, 1, 1], [0, 0, 0, 0, 2, 0, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 1, -1, 1, 2, 2, -2, -2], [0, 1, 0, -3, 1, 0, 2, 0], [0, -1, 0, 5, 0, -1, -1, -1], [5, -4, 2, 4, 2, -5, -3, -2], [0, 0, 0, 0, 0, 0, 0, 0], [4, 0, 0, -3, -3, 2, 1, 2], [-2, 4, -1, -2, 2, 2, 2, -1], [-5, 5, -5, -5, 0, 8, 5, 0], [0, -2, 0, -1, 1, -3, -2, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 0, -2, 2, -1, 0, -2, -2], [-4, 0, -4, 4, -1, 0, -4, -7], [-2, 0, -1, -1, 1, -2, 0, -1], [-2, -2, 1, -2, 0, 3, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, 1, 0, -6, -3, 2, 3, 4], [0, 0, 0, 0, 2, 0, 0, -1], [0, 1, 0, 3, 1, 0, -1, 0], [1, 2, -3, 2, 1, 3, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-4, -1, 1, -4, 0, -3, -1, 0], [-4, -1, -1, 7, 2, -5, -5, -4], [1, -2, 1, 0, -1, -3, 0, 3], [-2, 2, -2, -2, 0, 3, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [6, -3, 2, 6, 0, -7, -2, 0], [-3, 4, 0, -3, 0, 1, 0, 0], [9, -1, 4, 3, -3, -4, -1, 5], [0, 4, 0, -5, 1, 3, 5, 3], [0, 0, 0, 0, 0, 0, 0, 0], [2, -1, 0, 0, 0, 1, -3, -4], [-3, 2, -1, -8, -3, 5, 3, 2], [4, -6, 5, 0, 5, -1, 0, 1], [-4, 7, -5, 3, 0, 6, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [-13, 4, -12, 0, 3, 7, 0, -7], [1, 0, 2, -1, 1, 1, 0, 2], [3, -6, 5, 3, 0, -3, -5, 0], [-3, 0, -4, 3, -3, 0, -4, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-1, -5, 0, 0, 5, 0, 0, 0], [0, -5, 0, 5, 1, -6, -6, -6], [1, 0, 4, -3, -3, -2, 0, 7], [0, -6, 0, 8, -2, -4, -7, -4], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 3, 3, 1, -2, -4], [2, -9, 3, 2, 0, -8, -3, 0], [-6, -1, -1, 0, 3, 2, 0, -2], [1, 0, 0, -2, -1, 1, 5, 5], [0, 0, 0, 0, 0, 0, 0, 0], [1, 3, 1, 1, 0, 1, -1, 0], [-1, 5, -3, -9, 0, 10, 5, 4], [0, 0, 5, 0, -2, 0, 5, 5], [0, 1, 0, 3, 1, 0, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [4, -1, 1, 4, 0, -3, -1, 0], [0, 2, 0, -1, -3, 5, 0, 5], [-1, 1, -7, 5, -2, 0, -5, -5], [5, 3, -3, 0, 1, 4, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 4, 4, 2, 0, 0, 0], [-3, -2, 5, 0, 4, 2, 0, -2], [-4, 0, 2, 4, 1, 0, 2, 3], [10, -8, 5, 13, 2, -13, -8, -2], [0, 0, 0, 0, 0, 0, 0, 0], [5, 0, 4, -5, 2, 0, 4, 3], [3, 1, 1, -5, -1, 4, 0, -1], [-2, 2, -3, 0, 4, 6, 0, -6], [5, 0, 2, -5, -4, 0, 2, 6], [0, 0, 0, 0, 0, 0, 0, 0], [3, -2, 1, -4, -1, -2, 6, 6], [13, -3, 9, 0, -5, -8, 0, 8], [4, 0, 1, -3, -3, -2, 2, 3], [-4, 4, -1, 0, -1, 3, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [11, 0, 3, -4, -8, -1, 4, 7], [2, -8, 2, 2, 0, -6, -2, 0], [-7, 13, -8, -7, 0, 15, 8, 0], [3, 0, 3, -3, 3, 0, 1, -2], [0, 0, 0, 0, 0, 0, 0, 0]]}