# Stored data for newform 1274.2.g.m, downloaded from the LMFDB on 13 September 2025.
{"Nk2": 5096, "analytic_conductor": 10.172941217511122, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 13, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 3, "char_parity": 1, "char_values": [1274, 3, [885, 197], [3, 2]], "cm_discs": [], "conrey_index": 295, "dim": 6, "field_disc": -4740147, "field_disc_factorization": [[-1, 1], [3, 3], [419, 2]], "field_poly": [3, 0, 25, 0, 10, 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": [[3, [81, 72, 73, 10, 9, 1, 1]], [5, [-9, -15, 0, 1]], [11, [225, 45, 69, 18, 19, 4, 1]]], "hecke_orbit": 13, "hecke_orbit_code": 54043607878862074, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 3, "hecke_ring_index_factorization": [[3, 1]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 13, 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": "1274.2.g.m", "level": 1274, "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": [2, 7, 13], "level_radical": 182, "minimal_twist": "182.2.e.c", "nf_label": "6.0.4740147.1", "prim_orbit_index": 3, "qexp_display": "q+\\beta _{1}q^{2}+(\\beta _{2}+\\beta _{4})q^{3}+(-1+\\beta _{1}+\\cdots)q^{4}+\\cdots", "related_objects": [], "relative_dim": 3, "rm_discs": [], "sato_tate_group": "1.2.3.c3", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1274.2.g", "trace_display": [3, -1, 0, 0], "trace_hash": 278401402870754358, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "6.088", "prec": 17}, {"__RealLiteral__": 0, "data": "1.810", "prec": 17}, {"__RealLiteral__": 0, "data": "148.203", "prec": 24}, {"__RealLiteral__": 0, "data": "157.843", "prec": 24}, {"__RealLiteral__": 0, "data": "6273.656", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.006", "prec": 17}, "traces": [0, 6, 3, -1, -3, 0, 1, 0, -6, -8, 0, -4, 2, 4, 0, -9, -3, -1, -16, -3, 0, 0, 4, 4, 1, 30, 2, -16, 0, -1, 9, 26, 3, -18, -2, 0, -8, -2, -6, -2, 0, 3, 0, -7, 8, -21, -4, 26, -1, 0, 15, -48, -2, -26, -8, -9, 0, 2, 1, 9, 18, 11, 13, 0, 6, 12, -36, -6, -1, 0, 0, -15, 8, 44, 2, -55, -3, 0, -25, -2, 0, 1, -3, 28, 0, -12, -14, 15, 4, 17, -42, 0, -8, 20, 13, 0, -2, -27, 0, 6, -15, 15, -24, 34, -4, 0, -13, 11, 8, -22, 9, 25, 0, 32, 1, -51, 2, 8, 18, 0, 9, 11, 22, 33, -13, 54, 0, 11, 3, -44, 51, 38, -18, 0, 6, 78, 1, 0, 0, 26, 0, -12, -30, -4, 16, -42, 22, 0, 4, -31, 55, -16, 3, -39, 0, 24, -23, 20, -1, 21, 0, 0, -1, 7, -6, -30, 14, 11, 0, -12, -24, -8, -7, -12, 30, 0, -4, -6, -17, -7, -21, -52, 0, -10, -4, 39, -20, -46, -13, 0, 0, -11, -1, 28, -54, -108, 0, 15, 3, -25, -30, -29, -15, 0, 24, -33, 17, 78, -2, 8, 0, 10, 13, -108, -11, -12, 16, 0, -11, 17, 18, -13, 50, 4, 0, -17, 64, -15, -1, 80, 51, 0, 1, -12, -47, -42, 9, 76, 0, -72, -9, -38, 22, -7, 11, 0, 66, -2, -26, -6, 27, -1, 0, 4, -11, 54, -3, -11, -22, 0, 39, 120, 19, 9, 18, -18, 0, 30, 12, 22, 39, 6, 2, 0, 0, -70, 0, 45, 52, -71, 0, 16, 12, 7, -15, 18, -23, 0, 8, -10, 42, -82, -22, -24, 0, 0, 2, -15, -62, -98, 110, 0, -8, -54, 6, 51, 39, 66, 0, 20, 12, 68, 2, -62, 10, 0, 1, 52, -21, 14, 0, 78, 0, -1, -2, -53, 14, 28, -3, 0, -60, 11, -14, -16, -11, -90, 0, -40, 12, 66, -12, 7, 8, 0, 7, -90, -24, -25, 15, 6, 0, -23, -8, -36, -3, 57, -34, 0, 7, 40, 21, 54, -26, 44, 0, 24, -5, 27, 4, 114, -39, 0, -40, 4, -23, -54, -26, -100, 0, 30, 0, 55, -22, 30, 1, 0, -28, -55, -27, 34, -72, 94, 0, 63, -15, -132, -3, -11, -50, 0, -15, 16, -58, 78, -30, 9, 0, 23, 48, 49, 33, -54, -17, 0, 39, 102, 2, -166, 4, 45, 0, 118, -10, -6, 26, 68, -54, 0, -22, 27, -24, 75, 8, 24, 0, -87, 11, -8, -17, -25, 9, 0, -62, -54, 25, -12, -4, 90, 0, 39, -34, 36, 32, -23, -30, 0, -2, -9, 40, 15, 102, 36, 0, -10, -1, -63, -6, -102, -55, 0, -21, -79, -9, -30, -76, -15, 0, 27, -36, 20, -18, 51, -76, 0, 11, 27, -14, -2, -11, -56, 0, -25, 33, 146, -4, 174, -13, 0, 6, 64, -27, 87, -2, -16, 0, -57, 8, 23, -22, -9, 27, 0, -6, 8, 11, -78, 22, -25, 0, -156, -12, 4, 60, 45, -19, 0, -9, -65, 36, -37, -9, 24, 0, -96, 60, 15, 6, -42, 44, 0, -39, -130, -6, 83, 1, 24, 0, 142, 0, 79, 70, 2, 0, 0, 90, 72, 26, -60, -142, -17, 0, -18, 8, -16, 24, -99, -7, 0, 15, -57, 9, -26, -19, 174, 0, 16, -8, -48, 10, -11, 84, 0, -41, 34, -44, 102, -48, -72, 0, -13, 0, -54, -2, -64, 15, 0, -31, 14, -55, 60, 55, 0, 0, 158, 8, -39, -108, -16, 3, 0, 102, -19, 78, -50, 33, -57, 0, -72, -20, -38, -12, -63, 34, 0, 25, 150, -31, -18, -10, 26, 0, 10, 2, 52, 26, 78, -42, 0, 28, -42, 0, -96, 156, -83, 0, 90, 1, -45, -1, -24, 14, 0, 7, 18, -28, -276, 3, -95, 0, 13, -30, -10, 22, -105, -28, 0, -8, -98, -22, 77, 90, -32, 0, -19, -20, 74, 24, 18, 33, 0, 12, -90, -7, -6, 16, 90, 0, -16, 14, 7, -180, -41, -12, 0, -50, 15, -15, 192, -6, -39, 0, -114, 47, 4, -4, 3, 36, 0, 3, -9, 114, -7, -17, -31, 0, -159, 14, -15, 20, -30, 42, 0, -54, 74, 26, 41, 22, -54, 0, -128, 12, -63, 5, 120, -27, 0, 8, -35, 57, 27, -78, -23, 0, -9, -20, -69, 8, -87, 23, 0, 54, -11, -13, 162, -26, 78, 0, -28, -30, 54, 0, -12, 110, 0, -11, 54, 60, 6, 2, -24, 0, 99, -56, 34, 55, -16, 27, 0, 17, -6, 36, -78, 47, -24, 0, 132, -63, 42, -30, 108, -66, 0, -6, -45, -22, 57, -25, -24, 0, 32, 15, -18, -16, -5, -29, 0, 57, -66, -15, -96, -9, 20, 0, 2, 46, 39, 24, -7, 98, 0, 66, 21, -27, 56, -34, -117, 0, -168, -39, -50, 51, 124, 4, 0, -83, 45, -4, -94, -45, 8, 0, -28, 59, 96, -20, -81, -12, 0, 13, 128, 136, 55, 54, -42, 0, -21, -11, -52, -36, 96, -12, 0, -75, 72, -8, -6, 48, 98, 0, 77, -174, -157, 22, -95, -4, 0, -34, 19, 25, -66, -9, -27, 0, 2, -49, -54, -27, -33, -25, 0, 12, 18, -8, -13, 45, 54, 0, 117, 78, -77, -17, -20, 72, 0, -32, -30, 23, 9, -15, -84, 0, -94, -1, -20, 9, -270, -40, 0, 30, 28, 51, -34, 72, -126, 0, 67, -5, -32, -2, 91, 63, 0, 6, -78, -51, 78, -8, -136, 0, 86, 21, 12, 79, -102, -18, 0, -15, 58, -152, 90, -30, -78, 0, -48, 54, -45, 36, 96, -20, 0, -9, 48, 66, 60, -38, 165, 0, 30, -11, 24, 54, 117, -7, 0, -4, -191, -22, -31, -28, 47, 0, -7, 25, 4, -33, -57, 73, 0, -2, 78, 87, -15, 13, 244, 0, 51, 12, -59, 32, 70, -54, 0, 174, 3, -1, -198, -32, 13, 0, 20, 57, 31, 4, 186, -131, 0, -11, 30, 9, -28, -27, -29, 0, -90, -3, 111, 16, 84, 22, 0, -39, 66, 44, -34, 25, 54, 0, 52, -78, 110, -51, 114, 2, 0, -60, 18, -45, -148, -38, 58, 0, -87, -18, 2, -130, -24, 18, 0, -74, -144, 9, -126, -24, 27, 0, -138, -3, -28, 30, -23, -15, 0, -6, 26, -84, 38, 22, 24, 0, 67, -78, 67, -65, 18, -12, 0, -83, 16, -1, 16, 12, -178, 0, -114, 71, -90, 0, 0, -79, 0, 140, 59, 1, -96, 0, -48, 0, -9, 45, 35, 144, -39, -26, 0, 60, 66, -71, 54, -70, 292, 0, 9, 18, 230, -8, -177, -32, 0, 12, -68, -198, 165, -14, 3, 0, 27, 30, 10, 57, 76, -9, 0, -13, -112, 4, 204, 87, -21, 0, 54, -16, 15, -16, 63, -24, 0, 20, -37, -22, 11, 42, 31, 0, 60, 41, -6, -34, -162, -22, 0, 33, 30, -24, -36, 72, 176, 0, 89, -26, 18, 0, 86, -108, 0, -4, 135, -32, 24, 30, -129, 0, 164, 31, 10, 7, 180, 43, 0, 30, 39, -55, 30, 0, 27, 0, 12, 79, -66, 16, 4, -78, 0, -54, -50, -32, 138, -3, 252, 0, -16, 51, -54, -41, 150, 39, 0, 50, 8, -33, -60, -114, -11, 0, 63, -144, 39, -40, -75, -19, 0, -24, -68, 63, 2, -34, -144, 0, 150, 23, -144, 75, 10, 31, 0, 18, 57, -20, -30, 13, -39, 0, -95, 20, -44, 1, -141, 104, 0, -26, -96, -78, -84, -21, 12, 0, 60, 14, 16, 42, -112, 0, 0, -192, 51, 78, 156, -166, -45, 0, -66, 45, 78, 2, 84, 45, 0, 1, -19, -12, 92, 67, 34, 0, -57, -7, 6, -18, -88, -56, 0, -138, 0, 6, -45, -190, -69, 0, 116, 26, 73, 30, -192, 10, 0, 11, -230, -12, -150, -14, -78, 0, -66, 8, -91, -196, 27, -11, 0, 154, 35, 180, -117, -16, -85, 0, 39, 19, -36, 20, -15, 37, 0, 12, 30, 9, 0, -33, 24, 0, 8, 24, 53, -45, 53, -14, 0, -12, -56, 8, 45, 180, -53, 0, 98, 16, -81, 7, 48, -10, 0, -90, 104, 41, -114, 12, -117, 0, -22, -25, 103, 30, -37, -30, 0, 96, -30, -12, 66, 39, -102, 0, -15, -57, -172, 70, -6, 2, 0, 4, -44, -3, -53, 72, -17, 0, 93, 6, 46, -18, -54, 57, 0, -14, -11, 17, 110, 31, 27, 0, -66, -111, 18, 7, 48, 15, 0, -20, 45, -60, -9, 21, 44, 0, -49, -108, 105, 37, 32, 52, 0, -41, 284, -22, 50, -27, 54, 0, 40, -64, 63, -12, 4, 63, 0, 10, -3, 60, 32, -54, 164, 0, 115, 4, 3, -70, 45, -57, 0, -27, 54, -39, 20, 2, 166, 0, -93, 9, 14, 20, -54, -138, 0, 4, 13, -174, 111, 46, 61, 0, -153, 108, 1, 11, 18, 13, 0, 81, -54, 74, 234, 39, -9, 0, 110, 28, -69, -60, 3, 27, 0, 0, -68, -24, 40, 55, 59, 0, -180, 11, -218, -54, -28, 30, 0, 12, -126, 1, -11, 24, -2, 0, -145, 198, -138, -28, 27, 68, 0, 110, -29, -8, -57, 54, 141, 0, 72, -17, -120, -3, -32, 108, 0, -39, -39, -47, -132, 24, -59, 0, 38, 66, 81, -126, 72, 84, 0, -15, -14, 216, 12, 66, -354, 0, 33, -3, 276, 63, 260, -11, 0, -57, 34, 25, -24, -48, -129, 0, -40, 64, 138, 30, 19, -9, 0, -32, 63, 5, 30, 29, 5, 0, -150, -21, 254, -33, -12, 15, 0, 96, 51, -18, 60, 10, 46, 0, 96, 4, -57, 23, 10, 78, 0, -24, -150, 7, 9, 49, -180, 0, 152, 33, -98, -21, -64, 27, 0, 112, 23, -17, -82, -234, 112, 0, 15, -84, -93, -78, -119, 50, 0, -51, -15, 62, 12, 2, -204, 0, -2, 83, 90, -45, -15, -8, 0, -47, -111, -90, -151, 16, -19, 0, -42, -56, 48, -59, 24, -96, 0, -10, 354, -90, -34, -6, -68, 0, 204, -13, -11, 256, -107, 68, 0, 110, 26, 108, -75, -21, -69, 0, -41, 21, -6, 11, -101, -26, 0, -63, -132, 48, 9, 12, -46, 0, -31, -150, -81, 36, -89, -16, 0, -12, -46, 24, 72, 196, 24, 0, -520, -77, -22, -87, 134, -113, 0, 11, -81, 95, -26, 4, 87, 0, -18, -17, -25, 38, -33, 50, 0, -33, -50, -18, 12, 27, 180, 0, -21, 1, -40, 13, -206, -27, 0, 27, -84, 33, 102, -50, 21, 0, -24, 24, -117, 36, -92, -4, 0, -26, 139, -45, -92, -54, -17, 0, -70, -36, 168, 39, -138, 77, 0, 17, -71, -40, 23, 36, 0, 0, -72, -64, -101, -15, 13, 46, 0, -9, 90, 15, 55, -42, 260, 0, -76, -47, -97, 1, 74, 20, 0, 18, 39, -135, 10, -80, 39, 0, 27, 15, 98, 56, 190, -51, 0, 34, -27, 36, -168, -81, -294, 0, 52, -67, -78, 5, -57, -64, 0, -1, 32, 182, 11, 126, 142, 0, 0, 12, 21, 78, 214, 51, 0, 39, 12, 47, -82, -68, -106, 0, 86, -86, -130, 42, -3, 6, 0, 158, 117, -204, 93, -9, 27, 0, 96, 15, 88, -58, 0, -76, 0, 63, 92, -15, -5, 78, -132, 0, 189, -96, -22, 27, -82, -90, 0, 72, 66, 48, 156, -40, 156, 0, -30, 9, -1, 24, -90, 15, 0, 30, 78, 38, 50, -165, -39, 0, 25, 15, 12, -22, 83, 48, 0, 27, -120, 234, -128, 7, 18, 0, 54, -2, -90, -106, 62, -11, 0, 31, -330, 28, -17, 94, -198, 0, -17, -14, -23, 50, 219, 2, 0, -66, -49, 57, -142, -73, -130, 0, -464, 2, 222, 39, 23, -87, 0, 15, 29, 26, -168, 122, 50, 0, -18, 102, 109, 6, 41, -118, 0, -32, 390, -70, -37, -27], "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], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 1, 0], [-1, 1, 0, 0, 0, 0], [0, 0, -1, -1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0], [-3, 3, 0, 0, 0, -1], [0, 0, -1, -1, -1, -1], [0, -1, 1, 0, 1, 0], [0, 0, -1, 0, 0, 0], [1, 0, 1, 0, 1, 1], [0, 0, 0, 0, 0, 0], [0, -3, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0], [-1, 1, 0, 0, 1, -1], [-3, 0, 0, 1, 0, 0], [-1, 1, 0, 0, 0, 0], [0, 0, 0, 0, -1, -1], [0, 0, 0, 0, 0, 0], [1, -1, 0, 0, 1, 0], [0, 1, 1, 2, 1, 2], [0, 0, -1, 0, -1, 0], [4, 0, -3, 0, 0, 0], [0, 1, 0, -1, 1, 0], [-3, 0, -2, -1, 0, 0], [0, 0, 0, 0, 0, 0], [0, -1, 0, 2, 0, 2], [3, -3, 0, 0, 2, 2], [5, 0, 1, -1, 0, 0], [1, -1, 0, 0, 0, 0], [-6, 6, 0, 0, -1, -1], [-1, 0, -1, 1, 0, 0], [0, 0, 0, 0, 0, 0], [0, -3, 0, 1, 0, 1], [0, -1, -2, -1, -2, -1], [-1, 0, 0, 0, 0, 0], [-3, 6, 3, 1, 1, -1], [0, 0, 1, 1, 0, 0], [0, 0, -1, 2, -1, 2], [0, 0, 0, 0, 0, 0], [-3, 3, 0, 0, 1, -1], [1, 0, -1, 0, 0, 0], [-6, 6, 0, 0, -4, -1], [-1, 1, 0, 0, 1, 2], [4, 0, 0, 1, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0], [0, 4, -3, 0, -3, 0], [-9, 0, -3, 0, 0, 0], [-1, 1, -1, -1, 0, -1], [-4, 0, 1, 0, 0, 0], [0, -3, -2, -1, -2, -1], [0, -3, 3, 3, 3, 3], [0, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [1, -1, 0, 0, 0, 2], [3, -3, 0, 0, 0, 0], [3, 0, -2, -2, 0, 0], [4, -4, 0, 0, 1, 2], [0, 5, 1, -1, 1, -1], [0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [6, -9, 1, 1, 3, 0], [-6, 0, 1, 1, 0, 0], [0, -2, 3, 3, 3, 3], [0, -1, -1, 1, -1, 1], [0, 0, 0, 0, -3, -3], [0, 0, 0, 0, 0, 0], [-6, 6, 0, 0, 4, 1], [3, -3, 0, 0, 0, 1], [8, 0, 1, -1, 0, 0], [1, -1, 0, 0, -2, -1], [0, -18, 4, 3, 4, 3], [0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [-6, 3, 2, 2, 3, 1], [1, 0, 5, 1, 0, 0], [0, 0, 1, 1, 1, 1], [0, 0, -1, 0, -1, 0], [0, 0, 0, 0, -1, 2], [5, 0, -1, -2, 0, 0], [0, 0, 0, 0, 0, 0], [-3, 3, 0, 0, 0, 3], [-3, 0, -1, 1, 0, 0], [6, -6, 0, 0, -5, -2], [0, 1, -1, 0, -1, 0], [0, 5, -1, 1, -1, 1], [-6, 0, 4, 1, 0, 0], [0, 0, 0, 0, 0, 0], [-1, 0, -1, -2, 0, 0], [0, 9, 7, 0, 7, 0], [0, 4, 0, 1, 0, 1], [0, 0, 0, 0, -1, -1], [0, 0, 1, 0, 0, 0], [-10, 10, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0], [0, 0, -5, -2, 0, 0], [-4, 4, 0, 0, -3, 0]]}