# Stored data for newform 1900.3.e.a, downloaded from the LMFDB on 19 April 2024. {"label": "1900.3.e.a", "space_label": "1900.3.e", "level": 1900, "weight": 3, "hecke_orbit": 1, "hecke_orbit_code": 274928240492, "dim": 2, "is_polredabs": true, "nf_label": "2.2.57.1", "trace_hash": 2065757211324132308, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [0, 1]], [7, [-122, 5, 1]]], "qexp_display": "q+(-1-3\\beta )q^{7}+9q^{9}+(1-5\\beta )q^{11}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 19, "char_orbit_label": "e", "char_is_real": true, "Nk2": 17100, "analytic_conductor": 51.77125022845641, "hecke_ring_index": 1, "level_radical": 190, "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": "0.515", "prec": 17}, "analytic_rank_proved": true, "char_values": [1900, 2, [951, 77, 401], [2, 2, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 2, "level_primes": [2, 5, 19], "conrey_indexes": [1101], "field_disc": 57, "field_disc_factorization": [[3, 1], [19, 1]], "field_poly": [-14, -1, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.011", "prec": 17}, {"__RealLiteral__": 0, "data": "1.879", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "16.392", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "195.456", "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, 0, -5], "traces": [0, 2, 0, 0, 0, 0, 0, -5, 0, 18, 0, -3, 0, 0, 0, 0, 0, 15, 0, -38, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -85, 0, 0, 0, 75, 0, 171, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -103, 0, -45, 0, 0, 0, 0, 0, 0, 0, 0, 0, -25, 0, 0, 0, 435, 0, 0, 0, 162, 0, -180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 0, -204, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 561, 0, 475, 0, 0, 0, 0, 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, 135, 0, 0, 0, -20, 0, 0, 0, -150, 0, -500, 0, 0, 0, 0, 0, 338, 0, -342, 0, 0, 0, 0, 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, 540, 0, 57, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, -465, 0, 0, 0, 0, 0, 453, 0, 0, 0, 0, 0, 0, 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, 0, 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, 0, 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, 0, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -765, 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, 0, 0, 0, 0, 1524, 0, 0, 0, 675, 0, 0, 0, -1025, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1140, 0, 0, 0, 1539, 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, 0, 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, 0, 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, -927, 0, 0, 0, 0, 0, 0, 0, 1095, 0, 0, 0, 0, 0, 0, 0, 0, 0, -405, 0, 0, 0, 916, 0, 0, 0, 0, 0, -1145, 0, 0, 0, 450, 0, 0, 0, 0, 0, -1125, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 295, 0, 0, 0, -1065, 0, -1324, 0, 0, 0, 0, 0, 0, 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, 0, 0, -225, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1983, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 157, 0, 3915, 0, 0, 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, 1458, 0, -39, 0, 2540, 0, 0, 0, 0, 0, -547, 0, 0, 0, 0, 0, 0, 0, -1620, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2031, 0, 0, 0, -4665, 0, 0, 0, 0, 0, 1593, 0, 0, 0, 0, 0, 0, 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, 0, 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, 0, 0, 0, 0, 0, 0, 537, 0, 835, 0, 0, 0, 0, 0, 0, 0, -243, 0, -1425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1836, 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, 0, 0, 335, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3660, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, -2550, 0, 0, 0, 0, 0, 0, 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, 0, 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, 5049, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2250, 0, 0, 0, 0, 0, 635, 0, 4275, 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, 0, 0, 0, 0, 0, 0, 804, 0, 0, 0, 0, 0, 0, 0, 1957, 0, 0, 0, 1395, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1917, 0, 0, 0, -845, 0, 0, 0, 2700, 0, 0, 0, 0, 0, 0, 0, 0, 0, 855, 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, 0, 0, 0, 0, 0, 0, 0, 0, 2295, 0, 0, 0, 0, 0, 0, 0, -6771, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1773, 0, 0, 0, 0, 0, 0, 0, 1236, 0, 0, 0, 0, 0, 0, 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, 0, 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, 1593, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2738, 0, 0, 0, -2745, 0, 0, 0, 1215, 0, 450, 0, 0, 0, 0, 0, 0, 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, -180, 0, 0, 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, 0, 0, 0, 0, -1350, 0, -2427, 0, -305, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8265, 0, 0, 0, -4500, 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, 0, 0, 2895, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3042, 0, 0, 0, 0, 0, 0, 0, 6117, 0, 1213, 0, 0, 0, 0, 0, 0, 0, -3078, 0, 0, 0, 6140, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 93, 0, 0, 0, 0, 0, 0, 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, 0, 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, 0, 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, 8775, 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, 0, 0, -1530, 0, 837, 0, 3417, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 255, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1985, 0, 0, 0, -9765, 0, -3043, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13050, 0, -1620, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6980, 0, 0, 0, -3285, 0, 0, 0, -2043, 0, 750, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3603, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -124, 0, 0, 0, 0, 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, 4860, 0, 0, 0, 2195, 0, 0, 0, 3117, 0, 2815, 0, 0, 0, 0, 0, 1733, 0, 513, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4159, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7404, 0, 0, 0, 0, 0, 0, 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, 0, 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": 5, "prim_orbit_index": 2, "minimal_twist": "76.3.c.b", "char_is_minimal": true, "conrey_index": 1101, "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], [0, 0], [0, 0], [-1, -3], [0, 0], [9, 0], [0, 0], [1, -5], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [11, -7], [0, 0], [-19, 0], [0, 0], [0, 0], [0, 0], [30, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-41, -3], [0, 0], [0, 0], [0, 0], [31, 13], [0, 0], [78, 15], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-59, 15], [0, 0], [-9, -27], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [-29, 33], [0, 0], [0, 0], [0, 0], [209, 17], [0, 0], [0, 0], [0, 0], [81, 0], [0, 0], [-90, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [9, -45], [0, 0]]}