# Stored data for newform 2736.3.o.c, downloaded from the LMFDB on 24 April 2024.
{"label": "2736.3.o.c", "space_label": "2736.3.o", "level": 2736, "weight": 3, "hecke_orbit": 3, "hecke_orbit_code": 9008161377749680, "dim": 2, "is_polredabs": true, "nf_label": "2.2.57.1", "trace_hash": 1382702908083093144, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [6, 9, 1]], [7, [-122, 5, 1]]], "qexp_display": "q+(-4-\\beta )q^{5}+(-4+3\\beta )q^{7}+(-4+\\cdots)q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "o", "char_is_real": true, "Nk2": 24624, "analytic_conductor": 74.55060032897723, "hecke_ring_index": 1, "level_radical": 114, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.514", "prec": 17}, "analytic_rank_proved": true, "char_values": [2736, 2, [1711, 2053, 1217, 1009], [2, 2, 2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 19], "conrey_indexes": [721], "field_disc": 57, "field_disc_factorization": [[3, 1], [19, 1]], "field_poly": [-14, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.882", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.402", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "195.489", "prec": 24}], "related_objects": [], "self_twist_discs": [-19], "cm_discs": [-19], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "2.2.1.d2", "trace_display": [0, 0, -9, -5], "traces": [0, 2, 0, 0, 0, -9, 0, -5, 0, 0, 0, -3, 0, 0, 0, 0, 0, 15, 0, 38, 0, 0, 0, -60, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, -63, 0, 0, 0, 0, 0, 0, 0, -85, 0, 0, 0, -75, 0, 171, 0, 0, 0, 0, 0, -129, 0, 0, 0, 0, 0, -103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 435, 0, 0, 0, 0, 0, 180, 0, -267, 0, 0, 0, 0, 0, 0, 0, 0, 0, -171, 0, 0, 0, 0, 0, 204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 270, 0, 0, 0, 561, 0, 475, 0, 0, 0, -117, 0, 0, 0, 0, 0, 213, 0, -95, 0, 0, 0, 255, 0, -197, 0, 0, 0, 0, 0, 0, 0, 0, 0, -177, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 150, 0, -500, 0, 0, 0, 0, 0, 338, 0, 0, 0, 0, 0, 722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 975, 0, 0, 0, 93, 0, 0, 0, 0, 0, -180, 0, 227, 0, 0, 0, 0, 0, 0, 0, 0, 0, -57, 0, 0, 0, 0, 0, 297, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, -465, 0, -33, 0, 0, 0, 453, 0, 0, 0, 0, 0, -342, 0, 0, 0, 0, 0, -27, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 405, 0, 0, 0, 0, 0, 0, 0, 284, 0, 0, 0, 1254, 0, -535, 0, 0, 0, 0, 0, 395, 0, 0, 0, 0, 0, 931, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 469, 0, 0, 0, 891, 0, 0, 0, 0, 0, -603, 0, -1180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 285, 0, 0, 0, 0, 0, 1299, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1465, 0, 0, 0, -675, 0, -527, 0, 0, 0, 1020, 0, 0, 0, 0, 0, -243, 0, 722, 0, 0, 0, -1053, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1473, 0, 0, 0, -153, 0, -450, 0, 0, 0, 0, 0, 745, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -810, 0, 0, 0, 1524, 0, 0, 0, 0, 0, 1938, 0, -1025, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1140, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 625, 0, 0, 0, 447, 0, 755, 0, 0, 0, -915, 0, 0, 0, 0, 0, 555, 0, 361, 0, 0, 0, -1884, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1836, 0, 0, 0, 0, 0, 0, 0, 523, 0, 0, 0, 1860, 0, -918, 0, 0, 0, 0, 0, 2759, 0, 0, 0, 0, 0, 1965, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 742, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2394, 0, 457, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1095, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -916, 0, 0, 0, -570, 0, 1145, 0, 0, 0, -450, 0, 0, 0, 0, 0, 1125, 0, 0, 0, 0, 0, 60, 0, -2667, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1710, 0, 0, 0, 0, 0, 0, 0, -295, 0, 0, 0, -1065, 0, 1324, 0, 0, 0, 0, 0, 764, 0, 0, 0, 0, 0, -1037, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1115, 0, 0, 0, 1005, 0, 0, 0, 0, 0, 375, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1197, 0, 0, 0, 0, 0, -1983, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1803, 0, 0, 0, 0, 0, -157, 0, 0, 0, 2169, 0, 0, 0, 0, 0, -2196, 0, 0, 0, 0, 0, -510, 0, -2636, 0, 0, 0, 0, 0, 0, 0, 0, 0, -963, 0, 0, 0, 0, 0, 0, 0, -85, 0, 0, 0, -39, 0, -2540, 0, 0, 0, 0, 0, 547, 0, 0, 0, 0, 0, -771, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 785, 0, 0, 0, 1503, 0, 0, 0, 0, 0, 0, 0, -1063, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2031, 0, 0, 0, 4665, 0, 1890, 0, 0, 0, -1593, 0, 0, 0, 0, 0, 2250, 0, -1615, 0, 0, 0, 1167, 0, -1565, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1710, 0, 0, 0, 0, 0, 0, 0, 1682, 0, 0, 0, -1521, 0, -2470, 0, 0, 0, 0, 0, -2060, 0, 0, 0, 0, 0, -1493, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1845, 0, 0, 0, 0, 0, -537, 0, 835, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -270, 0, 0, 0, -3525, 0, -3524, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1284, 0, 3249, 0, 0, 0, -5157, 0, -335, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3660, 0, 0, 0, 0, 0, 0, 0, -2841, 0, 0, 0, 1329, 0, 1922, 0, 0, 0, 0, 0, 3580, 0, 0, 0, 0, 0, -3355, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 810, 0, 0, 0, 2550, 0, 0, 0, 0, 0, -3159, 0, -1975, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1185, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3324, 0, 1700, 0, 0, 0, -3765, 0, 0, 0, 0, 0, 5145, 0, -2451, 0, 0, 0, 1623, 0, -404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2103, 0, 0, 0, 0, 0, 0, 0, 2137, 0, 0, 0, 0, 0, -38, 0, 0, 0, 0, 0, 2250, 0, 0, 0, 0, 0, 635, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, -1275, 0, 0, 0, 0, 0, -993, 0, -306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5130, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1250, 0, 0, 0, -3069, 0, 0, 0, 0, 0, 804, 0, 0, 0, 0, 0, 0, 0, -1957, 0, 0, 0, -1395, 0, 1893, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2622, 0, 0, 0, 0, 0, 0, 0, -845, 0, 0, 0, -2700, 0, 0, 0, 0, 0, 0, 0, -1041, 0, 0, 0, 0, 0, 1873, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -620, 0, 0, 0, 4860, 0, 0, 0, 0, 0, 765, 0, -2223, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6771, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3399, 0, 0, 0, 1236, 0, 0, 0, 0, 0, 3870, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 255, 0, -1717, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1647, 0, 0, 0, 0, 0, 0, 0, -4540, 0, 0, 0, -4596, 0, 2435, 0, 0, 0, 0, 0, -129, 0, 0, 0, 0, 0, -4017, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3940, 0, 0, 0, -2487, 0, 0, 0, 0, 0, 7035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1278, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2738, 0, 0, 0, -2745, 0, -3387, 0, 0, 0, 450, 0, 0, 0, 0, 0, 1467, 0, 475, 0, 0, 0, 0, 0, 5845, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3090, 0, 0, 0, 0, 0, 0, 0, 1350, 0, 0, 0, 873, 0, 0, 0, 0, 0, 0, 0, 1915, 0, 0, 0, 0, 0, 2633, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5307, 0, 0, 0, -7182, 0, 0, 0, 0, 0, -2427, 0, 305, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8265, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2525, 0, 0, 0, -2955, 0, 1297, 0, 0, 0, 2055, 0, 0, 0, 0, 0, 2196, 0, 0, 0, 0, 0, 1737, 0, 2895, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4826, 0, 0, 0, -6117, 0, -1213, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3711, 0, 0, 0, 93, 0, 0, 0, 0, 0, 5310, 0, 835, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3420, 0, 0, 0, 0, 0, 2325, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5780, 0, 0, 0, 2727, 0, 8935, 0, 0, 0, -1020, 0, 0, 0, 0, 0, -2265, 0, -5073, 0, 0, 0, 6324, 0, 1033, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1761, 0, 0, 0, 0, 0, 0, 0, 8103, 0, 0, 0, 0, 0, -1713, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 937, 0, 0, 0, -4125, 0, 0, 0, 0, 0, -750, 0, 3362, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1095, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2403, 0, 1530, 0, 0, 0, -3417, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 255, 0, 1983, 0, 0, 0, 0, 0, 0, 0, 0, 0, -621, 0, 0, 0, 0, 0, 0, 0, 1985, 0, 0, 0, -9765, 0, 3043, 0, 0, 0, 0, 0, -4590, 0, 0, 0, 0, 0, -13050, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6980, 0, 0, 0, 3285, 0, 0, 0, 0, 0, 750, 0, 5511, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3249, 0, 0, 0, 0, 0, -3603, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8702, 0, 0, 0, 0, 0, 124, 0, 0, 0, 450, 0, 0, 0, 0, 0, 5571, 0, 0, 0, 0, 0, 3165, 0, 171, 0, 0, 0, 0, 0, 0, 0, 0, 0, -507, 0, 0, 0, 0, 0, 0, 0, 2195, 0, 0, 0, 3117, 0, -2815, 0, 0, 0, 0, 0, -1733, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -710, 0, 0, 0, 7596, 0, 0, 0, 0, 0, -1515, 0, -5400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3876, 0, 0, 0, 0, 0, -228, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4159, 0, 0, 0, 0, 0, -4299, 0, 0, 0, 7404, 0, 0, 0, 0, 0, 8010, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1545, 0, 0, 0, 0, 0, 0, 0, -8939, 0, 0, 0, -1557, 0, -2885, 0, 0, 0, 0, 0, -775, 0, 0, 0, 0, 0, -277, 0], "weight_parity": -1, "has_non_self_twist": 0, "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, 19, 2, -1, 2, -19]], "char_orbit_index": 15, "prim_orbit_index": 2, "minimal_twist": "76.3.c.b", "char_is_minimal": false, "conrey_index": 721, "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], [1, 0], [0, 0], [0, 0], [0, 0], [-4, -1], [0, 0], [-4, 3], [0, 0], [0, 0], [0, 0], [-4, 5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [4, 7], [0, 0], [19, 0], [0, 0], [0, 0], [0, 0], [-30, 0], [0, 0], [5, 9], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-26, -11], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-44, 3], [0, 0], [0, 0], [0, 0], [-44, 13], [0, 0], [93, -15], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-54, -21], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-44, -15], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-4, 33], [0, 0], [0, 0], [0, 0], [226, -17], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [90, 0], [0, 0], [-114, -39], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-76, -19], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}