# Stored data for newform 961.2.c.i, downloaded from the LMFDB on 05 September 2025. {"Nk2": 3844, "analytic_conductor": 7.673623634245045, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 31, "char_degree": 2, "char_is_minimal": false, "char_is_real": false, "char_orbit_index": 3, "char_orbit_label": "c", "char_order": 3, "char_parity": 1, "char_values": [961, 3, [3], [2]], "cm_discs": [], "conrey_index": 439, "dim": 16, "field_disc": 4208972802978515625, "field_disc_factorization": [[3, 8], [5, 12], [1621, 2]], "field_poly": [1, 0, 44, 0, 410, 0, 956, 0, 979, 0, 511, 0, 140, 0, 19, 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, [-9, 27, 15, -63, 19, 23, -10, -2, 1]], [3, [961, -1488, 4474, -1104, 7147, -2133, 5998, -399, 2446, 129, 763, 108, 142, 24, 19, 3, 1]]], "hecke_orbit": 9, "hecke_orbit_code": 36028934491472833, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 81, "hecke_ring_index_factorization": [[3, 4]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 31, 3, 1, 3, 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": false, "label": "961.2.c.i", "level": 961, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": true, "level_is_square": true, "level_is_squarefree": false, "level_primes": [31], "level_radical": 31, "minimal_twist": "31.2.g.a", "prim_orbit_index": 3, "qexp_display": "q-\\beta _{5}q^{2}+(-1-\\beta _{6}-\\beta _{9}+\\beta _{10}-\\beta _{11}+\\cdots)q^{3}+\\cdots", "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "961.2.c", "trace_display": [4, -3, -3, 2], "trace_hash": 84421340713377148, "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "14.159", "prec": 20}, {"__RealLiteral__": 0, "data": "2.897", "prec": 17}, {"__RealLiteral__": 0, "data": "820.273", "prec": 24}, {"__RealLiteral__": 0, "data": "643.078", "prec": 24}, {"__RealLiteral__": 0, "data": "87699.789", "prec": 30}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.007", "prec": 17}, "traces": [0, 16, 4, -3, 16, -3, -11, 2, -18, -5, 13, -18, 0, -8, 9, 36, 8, -14, -23, 6, 7, 1, -4, 44, -30, -13, -9, 36, 5, 24, 22, 0, -42, 12, 7, -24, 1, 8, -7, 2, -11, 22, 6, 2, -4, 0, 36, -36, 1, 2, -27, -2, 1, -6, -14, -28, -30, 17, -10, 4, -80, 60, 0, -46, 18, -3, 20, 13, -30, -22, -78, 1, -3, -2, -8, -23, 33, -48, 0, -8, -24, 28, 19, -39, -8, -52, 16, 15, 17, 54, -8, 32, 64, 0, 44, -12, 12, 68, -10, -6, 47, 50, -32, -50, -48, 36, 33, -18, 42, 72, 1, 18, 26, -18, 50, 8, 86, 19, -14, -57, -80, 26, 14, -92, 0, -24, 12, -33, -80, -51, 21, -23, -22, 37, 54, 27, 20, -2, -54, 50, -60, 27, 39, -27, -10, 8, -30, -60, 88, 52, 24, 26, 21, -8, -120, 0, 128, 2, 36, -84, 31, -27, 61, 44, 30, -76, 64, -79, 24, 32, -144, 36, 16, 19, -28, -28, 6, 34, -86, -48, 46, -27, -150, -38, 38, 44, 0, -14, -82, -2, 74, -12, 128, -29, 198, 9, -7, 30, -37, -19, -36, -72, -72, 60, 6, 17, 40, -10, 91, 12, 66, 13, 45, -32, -53, 176, -186, 0, 74, -10, -4, 6, 106, 37, -63, 20, 9, 1, 23, 44, 62, 15, -208, 88, -42, 23, -36, 29, -42, -66, -42, 22, -15, 48, 52, 12, -152, -18, 0, -132, 34, -80, 32, -32, -30, 8, 12, 57, -35, 3, 6, -36, -54, 102, 86, 24, 45, 42, -51, 23, 52, 62, -12, -5, -32, 66, -65, -90, 50, 0, 30, -108, 68, -158, -34, -48, -12, -12, -3, 10, -5, -11, -8, -30, -46, -148, -49, -15, -12, -42, -20, 39, 48, -16, 38, -5, 106, -54, -72, 0, 0, 60, 6, 18, 24, 48, 31, -35, -174, -26, 41, 18, 6, 56, 70, 16, 30, -58, 20, 12, -80, 10, -104, -100, -40, 53, -47, -128, 89, 108, -50, 0, -88, -32, -13, 14, -17, -9, 56, -66, -36, 35, 44, 34, -2, 1, 148, -54, -10, -56, 67, 64, -5, -5, 98, 3, -64, 11, -48, 58, 36, 156, 0, 0, -120, -18, 56, 39, -33, 73, 74, 10, -31, -135, 64, 9, 39, 92, 56, -36, 15, -76, -9, 19, -51, 96, 20, -75, 5, 50, 41, -66, 30, 0, -26, 114, -3, 64, -58, -80, -21, -74, -125, -6, -87, -44, -51, -30, 112, 18, 57, -24, 46, 48, 30, -39, 36, 2, 4, 12, 108, -12, 118, -6, 0, 50, 240, 64, 6, -40, -63, 26, -60, -18, 5, 43, -6, -8, 38, -62, -24, 34, -180, -66, 60, -36, 51, -150, -135, -86, 48, 108, 51, -28, 192, 0, -84, 222, -65, 178, -62, 7, -22, 34, 60, 41, -39, 36, -132, 39, 76, 64, 104, 24, 74, 111, 43, 53, -116, 25, -55, -66, -84, 10, -18, 32, 0, 78, 76, -23, -104, -55, 61, 0, 24, 5, 4, 36, -82, -39, 33, 60, -78, -25, -30, -15, 86, 10, 36, 166, -63, 25, -31, 18, 71, -122, 184, 0, 6, -152, 63, -50, -17, 24, -32, -104, 38, 75, -91, -24, 4, -26, 122, -110, -4, -51, -54, -104, -54, -96, 18, -48, -85, 74, -60, -97, 80, 114, 0, -116, -12, 10, -82, 93, -58, -48, 70, -91, 52, -97, -85, 27, 6, -72, 78, -72, 99, -24, -12, -84, -43, -42, -39, 3, -96, -198, -4, -164, 132, 0, -192, 48, 94, 0, 17, 63, -28, -60, -6, 5, 15, 20, -45, 61, 228, 138, -3, -16, -108, -57, 63, -15, -24, 8, 132, 26, 126, 15, 250, -204, 0, 44, -64, -63, 116, 42, -75, 36, -40, 84, 24, 52, 102, 54, 52, 56, -198, -74, -34, 25, 10, 74, 22, 176, -15, -31, 50, 84, -75, -68, -72, 0, -34, -72, -178, -14, -9, 94, 48, -6, 11, -47, 103, -15, 112, -48, -206, -44, -96, 26, 104, -34, 15, 70, 72, 7, 5, 13, 468, 49, -10, -140, 0, 206, -150, 143, -210, 45, -149, -27, -82, -146, -15, 87, 153, -75, -118, -126, 152, 28, -10, 80, -33, -26, -23, 86, -24, -66, -120, -76, -11, -8, -284, 0, 24, 84, -52, 246, 33, -83, -30, 30, -30, 51, -123, 93, 69, -11, 6, -26, -30, 72, 56, 21, -96, 0, -118, 97, 109, 37, 4, 96, -84, 150, 0, -44, -90, 135, 14, -57, 34, 86, -258, -26, -129, -53, -17, 87, -11, 58, 38, -5, -72, 102, -91, -1, -27, 102, 11, 15, 75, -210, -174, 42, 4, 0, -108, -48, -194, 56, -24, 26, -62, 198, 151, -21, 90, -137, -3, 57, -72, -42, 50, 36, -34, -63, -76, 84, 84, 61, -24, 63, -120, -36, -118, -156, 0, 188, -172, -22, 58, 138, 66, 21, 72, -27, -6, 19, -51, 62, -65, -250, 34, -60, 135, -81, -57, 21, -86, -236, 74, 65, 97, -100, -70, -92, -26, 0, 62, -192, 39, -160, -11, 69, 25, 96, 110, 80, 87, -15, -183, 32, -160, 6, -39, -93, -107, 48, 18, -63, -212, -36, 34, -43, 30, 29, 292, -204, 0, 114, 136, 42, 0, -109, 72, 42, 338, 107, -60, -6, -39, -11, -4, -288, 54, 179, 45, -18, 95, 200, 143, -132, 115, -30, -36, -274, -6, 108, 34, 0, 98, 228, 15, 0, 15, 138, -180, -116, 44, -67, 90, -135, -89, -124, -56, 136, 111, 99, 16, 80, -29, 203, -98, 21, 78, -152, -178, -20, -214, -96, 0, 154, 200, 63, -352, 7, 30, 19, 360, -65, -124, 15, 27, 83, 12, -66, -66, 182, 176, -116, 63, 28, -3, 48, 18, 98, 45, -98, -10, 186, 104, 0, -168, -144, -85, 38, 9, 77, -87, 80, 96, 33, 186, 165, 145, -1, 190, -392, 42, -10, -142, -69, -115, -175, -58, 150, 96, 87, 54, 38, 184, -4, 0, -234, -24, 96, -140, -29, 93, 108, 232], "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, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0, 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, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0], [-1, 0, 1, 1, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [-1, 0, -1, 0, 1, 0, -1, 0, 1, -1, 1, -1, 0, 0, -1, 0], [-1, -1, 1, -1, 1, 0, 0, 0, 1, 0, 1, -2, -1, 0, 1, -1], [0, 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 2, 0, 0, 0, 0], [0, -1, 0, -1, 0, 1, 0, -1, 0, 1, -1, -1, -1, 1, 0, -1], [1, 0, -1, 0, 1, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0], [-3, 0, 3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [1, -2, 0, 2, 1, 0, 0, 0, 1, 0, -1, -1, -2, 0, 0, -1], [-3, 1, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, -1, 1], [-4, 1, 3, 0, 1, 0, 1, 0, 1, 1, 4, -3, 1, 0, -2, 1], [3, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 0, 0], [0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0], [-2, 0, 0, -1, 2, 0, 0, 0, 2, 0, 2, -2, 0, 0, 1, -1], [-3, 0, 3, 0, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0], [2, 1, 0, 1, -1, 0, 0, 0, -1, 0, -2, 3, 1, 0, 1, 1], [0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 3, 1, -1, -1, 0, 1], [0, -2, 1, -1, 0, 1, 0, -2, 0, -1, 1, -1, 1, 1, 1, -2], [-1, 0, 1, -2, 1, 2, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 0, 1, 0, 0], [0, 0, -4, 1, 1, 0, 2, 0, 1, 2, 0, 0, 0, 0, -3, 1], [-3, 0, 0, 0, -1, 0, 1, 0, -1, 1, 3, -3, 0, 0, 0, -1], [3, -2, 1, -2, 0, 2, 0, -2, 0, -1, -1, 2, -2, -2, 4, -2], [3, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, -2, 0, 0], [0, -2, 1, 0, 1, 0, -1, 0, 1, -1, 0, -2, -2, 0, 3, 0], [0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, -2, 0, -1, 0, 0], [0, -4, 0, 0, 0, 0, -1, -1, 2, 0, 0, -6, 0, 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, 1, -1, 0, 0, 0, 4, 0, -5, 0, 0], [2, -2, 0, 0, 0, 1, 2, -1, 1, 0, 0, 0, 0, 1, 0, 0], [-5, 0, 4, 2, 1, 0, 1, 0, 1, 1, 5, -5, 0, 0, -1, 0], [-1, 3, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, -2, 0, 0], [2, 1, 0, -2, -1, 2, 0, 1, 0, -1, 0, 3, 3, -3, 2, 1], [1, -1, 0, 0, -3, 0, 2, 0, -3, 2, -1, 0, -1, 0, 0, -1], [3, 1, -3, -1, -2, 0, 1, 0, -2, 1, -3, 4, 1, 0, 0, 1], [-2, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, -2, 0, 4, 0, 0], [-3, 2, 2, 0, 2, 0, 0, 2, 0, -3, 2, 1, 1, -1, -1, 2], [3, 0, -2, 0, 1, 0, 0, 0, 0, -2, 1, 1, 0, -1, 1, 0], [-2, -2, 0, -1, -1, 1, 0, -2, 0, 0, 1, -4, 3, 4, -2, -2], [-3, 1, 0, -1, -2, 0, -2, 0, -2, -2, 3, -2, 1, 0, -2, 2], [0, 1, 1, 0, -1, 0, 0, 1, 0, 0, 2, 2, -1, -2, 1, 1], [-2, 5, 2, 0, -1, 0, -2, 0, -1, -2, 2, 3, 5, 0, 2, 1], [1, 0, 0, 0, 0, -3, 0, 0, -2, 0, 0, 1, 0, 2, 0, 0], [-4, -2, 0, 0, 0, -1, -2, -2, 1, 0, 0, -4, 0, 2, 0, 0], [0, -1, 1, 1, -1, 0, -1, 0, -1, -1, 0, -1, -1, 0, 5, 0], [-4, 1, 2, -1, 0, 1, 0, 1, 0, 0, 6, -1, 1, 1, -2, 1], [-2, 2, -1, -1, 3, 0, 1, 0, 3, 1, 2, 0, 2, 0, 0, -1], [-1, -3, 1, -2, 0, 2, 0, -3, 0, 2, 0, -3, 1, 3, 0, -3], [-4, 2, -1, -1, -1, 1, 0, 2, 0, 3, 1, -3, 2, 3, -5, 2], [-5, 1, 0, 2, -1, -2, 0, 1, 0, 0, 1, -4, 0, 4, -5, 1], [1, 1, 0, 0, 0, -2, -1, 0, 1, 0, 0, 4, 0, -2, 0, 0], [-2, -1, -4, -2, -2, 0, -2, 0, -2, -2, 2, -3, -1, 0, -1, -1], [2, 0, -6, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, -2, 3], [3, 1, -4, 3, 0, -3, 0, 1, 0, 1, -3, 0, -3, 0, -1, 1], [1, 2, 0, 0, 0, -2, 1, -1, 2, 0, 0, 2, 0, -3, 0, 0], [2, -3, -1, 2, 1, 0, 2, 0, 1, 2, -2, -1, -3, 0, -2, 1], [-9, -3, 0, 0, 0, 0, -2, -3, 2, 0, 0, -10, 0, 3, 0, 0], [6, 0, 0, 0, 0, 0, 2, 2, -1, 0, 0, 4, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4, 1, 0, 0, 0, -1, -1, 1, -1, 0, 0, 1, 0, 2, 0, 0], [-2, -1, 0, 0, 0, 1, -5, 2, 1, 0, 0, -5, 0, 1, 0, 0], [2, -3, -2, -2, -1, 0, 1, 0, -1, 1, -2, -1, -3, 0, 0, -3], [0, -4, 0, 0, 0, 1, 2, -2, 0, 0, 0, -5, 0, 3, 0, 0], [4, 0, -3, 2, -3, -2, 0, 0, 0, -1, -3, 1, 1, -1, 1, 0], [-1, -2, -4, -1, 3, 0, 0, 0, 3, 0, 1, -3, -2, 0, -2, 1], [-1, -2, -3, 2, 1, 0, -2, 0, 1, -2, 1, -3, -2, 0, -2, 1], [-5, 3, 0, 0, 0, 0, -1, 4, 2, 0, 0, 1, 0, -3, 0, 0], [-1, 1, -1, 2, -2, -2, 0, 1, 0, 1, 0, -1, -1, 1, -2, 1], [4, 0, -1, -1, -3, 1, 0, 0, 0, -1, -2, 3, 0, -3, 3, 0], [-1, 5, 1, 0, 0, 0, 0, 5, 0, -2, 3, 5, 3, -5, 0, 5], [3, 4, -2, -3, 0, 0, 2, 0, 0, 2, -3, 7, 4, 0, 0, 0], [-4, -3, 5, 1, 2, -1, 0, -3, 0, 3, 0, -2, 0, 2, 1, -3], [2, -1, 3, -1, -3, 0, 1, 0, -3, 1, -2, 1, -1, 0, 2, -2], [1, 0, 0, 0, 0, 4, 0, -2, -2, 0, 0, 6, 0, 0, 0, 0], [1, 0, 0, 0, 0, -1, 2, -3, -2, 0, 0, 2, 0, 1, 0, 0], [-1, 1, -3, 0, -4, 0, 2, 0, -4, 2, 1, 0, 1, 0, -4, 4], [0, -2, 1, 0, 1, 0, 0, -2, 0, -2, -4, -1, -3, 1, 1, -2], [-2, -1, 4, -4, 0, 0, -2, 0, 0, -2, 2, -3, -1, 0, 3, -1], [-2, 1, -1, 3, 1, -3, 0, 1, 0, -1, 3, -2, 0, 2, -3, 1], [-6, 1, 9, 2, 1, -2, 0, 1, 0, -3, 5, 4, 3, -4, 3, 1], [4, -3, -2, 1, -3, -1, 0, -3, 0, 0, -7, -1, -1, 1, 2, -3], [-2, 3, 0, 0, 0, 2, 4, 3, 2, 0, 0, 0, 0, -5, 0, 0], [2, -2, 1, -2, 1, 0, -4, 0, 1, -4, -2, 0, -2, 0, 4, -1], [-4, 1, 5, -1, 1, 0, -3, 0, 1, -3, 4, -3, 1, 0, 3, -2], [1, 3, -2, 2, 1, -2, 0, 3, 0, 1, -1, 2, 3, -2, -1, 3], [3, -2, 0, 0, 0, 2, -3, -1, -2, 0, 0, 0, 0, 3, 0, 0], [2, 2, -2, -3, -3, 0, 0, 0, -3, 0, -2, 4, 2, 0, 2, -2], [6, 0, 0, 0, 0, 5, 2, -2, -3, 0, 0, 5, 0, -1, 0, 0], [3, 2, 0, 0, 0, -2, 2, 0, -4, 0, 0, 2, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -5, 0, 0, 0, 3, -2, -2, 1, 0, 0, -9, 0, 3, 0, 0], [1, -2, 0, 0, 0, -1, 2, 0, -4, 0, 0, 4, 0, -1, 0, 0], [-5, 6, 3, -4, 0, 0, 0, 0, 0, 0, 5, 1, 6, 0, -2, 4], [2, -1, 0, 0, 0, -5, -2, 1, -1, 0, 0, -1, 0, 0, 0, 0], [1, -2, 4, -2, 4, 2, 0, -2, 0, -2, 3, 3, -3, -3, 5, -2], [0, 4, 0, 2, -1, 0, -2, 0, -1, -2, 0, 4, 4, 0, 1, 2], [3, -2, 6, 4, 1, 0, -1, 0, 1, -1, -3, 1, -2, 0, 3, -1]]}