# Stored data for newform 1900.3.e.c, downloaded from the LMFDB on 13 August 2026.
{"Nk2": 17100, "analytic_conductor": 51.77125022845641, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 19, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 2, "char_parity": -1, "char_values": [1900, 2, [951, 77, 401], [2, 2, 1]], "cm_discs": [], "conrey_index": 1101, "dim": 4, "field_disc": 112896, "field_disc_factorization": [[2, 8], [3, 2], [7, 2]], "field_poly": [25, 0, 4, 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, [14, 0, 1]], [7, [-96, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007474182981484, "hecke_ring_generator_nbound": 19, "hecke_ring_index": 32, "hecke_ring_index_factorization": [[2, 5]], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0], [1, 1, 95, 4, -1, 2, 0], [1, 1, 19, 2, -1, 2, 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": "1900.3.e.c", "level": 1900, "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, 5, 19], "level_radical": 190, "minimal_twist": "380.3.g.a", "nf_label": "4.0.112896.2", "prim_orbit_index": 2, "qexp_display": "q-\\beta _{1}q^{3}+\\beta _{2}q^{7}-5q^{9}+4q^{11}-3\\beta _{1}q^{13}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "2.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1900.3.e", "trace_display": [0, 0, 0, 0], "trace_hash": 153791553676137485, "trace_moments": [0, {"__RealLiteral__": 0, "data": "3.530", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "103.792", "prec": 20}, 0, {"__RealLiteral__": 0, "data": "3816.522", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.761", "prec": 10}, "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -20, 0, 16, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 188, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -404, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 0, 0, 768, 0, -420, 0, 0, 0, 0, 0, 0, 0, 0, 0, 104, 0, 0, 0, 0, 0, 0, 0, -592, 0, 0, 0, 0, 0, 0, 0, 0, 0, -208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 840, 0, 384, 0, 0, 0, 0, 0, 0, 0, 172, 0, -100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 632, 0, 0, 0, 0, 0, 0, 0, -1208, 0, 168, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 944, 0, 0, 0, 0, 0, 0, 0, 0, 0, -584, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 380, 0, 1848, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 1176, 0, -2000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1512, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 0, 0, -168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -920, 0, -672, 0, 0, 0, 0, 0, 0, 0, -2416, 0, -1244, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3528, 0, 0, 0, 0, 0, 0, 0, -488, 0, 768, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1432, 0, 0, 0, 0, 0, 0, 0, 0, 0, -672, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2000, 0, 1512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 920, 0, 0, 0, 0, 0, 0, 0, 2480, 0, 504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 768, 0, 0, 0, 0, 0, 0, 0, -4200, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1732, 0, 0, 0, 0, 0, 0, 0, 0, 0, 752, 0, -2480, 0, 0, 0, 0, 0, 0, 0, -2000, 0, -2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1328, 0, 0, 0, 0, 0, 0, 0, -3192, 0, 1152, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2704, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 496, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3192, 0, 1600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4200, 0, 0, 0, 0, 0, 0, 0, 2520, 0, -2288, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3280, 0, 0, 0, 0, 0, 0, 0, -1112, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 1192, 0, -840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3152, 0, 0, 0, 0, 0, 0, 0, 2192, 0, -2184, 0, 0, 0, 0, 0, 0, 0, -2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -768, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5272, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2012, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2984, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 504, 0, 0, 0, 0, 0, 0, 0, 7560, 0, -4112, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1616, 0, 0, 0, 0, 0, 0, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, -80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4600, 0, 1512, 0, 0, 0, 0, 0, 0, 0, -5816, 0, 940, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4200, 0, 0, 0, 0, 0, 0, 0, -9984, 0, -1532, 0, 0, 0, 0, 0, 0, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1840, 0, 5288, 0, 0, 0, 0, 0, 0, 0, 0, 0, -368, 0, 0, 0, 0, 0, 0, 0, 6320, 0, -3840, 0, 0, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, 2100, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4608, 0, 0, 0, 0, 0, 0, 0, 0, 0, -488, 0, 64, 0, 0, 0, 0, 0, 0, 0, -1848, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -384, 0, 0, 0, 0, 0, 0, 0, -168, 0, -8584, 0, 0, 0, 0, 0, 0, 0, 2000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -520, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2016, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10752, 0, 1536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2960, 0, 0, 0, 0, 0, 0, 0, 2864, 0, 5544, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5376, 0, 0, 0, 0, 0, 0, 0, 6992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5128, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2856, 0, -176, 0, 0, 0, 0, 0, 0, 0, 3072, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3616, 0, 0, 0, 0, 0, 0, 0, 3528, 0, 1040, 0, 0, 0, 0, 0, 0, 0, 2688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 940, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -344, 0, 3360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 416, 0, 0, 0, 0, 0, 0, 0, -1920, 0, 3992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168, 0, 0, 0, 0, 0, 0, 0, -504, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10752, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7600, 0, -5376, 0, 0, 0, 0, 0, 0, 0, 4784, 0, -8064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -860, 0, 0, 0, 0, 0, 0, 0, -2368, 0, -2392, 0, 0, 0, 0, 0, 0, 0, -2020, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2248, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3800, 0, -3880, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8448, 0, 0, 0, 0, 0, 0, 0, -832, 0, 13944, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10584, 0, 0, 0, 0, 0, 0, 0, 16128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 768, 0, 1348, 0, 0, 0, 0, 0, 0, 0, 4872, 0, 10752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10752, 0, 0, 0, 0, 0, 0, 0, -3160, 0, 6640, 0, 0, 0, 0, 0, 0, 0, 8064, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3360, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3760, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1536, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6040, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 672, 0, -10544, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14616, 0, 0, 0, 0, 0, 0, 0, -10752, 0, -6416, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 0, 0, 0, 0, 0, 0, 11420, 0, 0, 0, 0, 0, 0, 0, 0, 0, 688, 0, 0, 0, 0, 0, 0, 0, 0, 0, -21504, 0, -5840, 0, 0, 0, 0, 0, 0, 0, -6920, 0, -400, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8920, 0, 0, 0, 0, 0, 0, 0, 1152, 0, -7896, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6144, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5008, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7560, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18816, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13744, 0], "weight": 3, "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], [1, 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, 1, 0], [0, 0, 0, 0], [-5, 0, 0, 0], [0, 0, 0, 0], [4, 0, 0, 0], [0, 0, 0, 0], [0, -3, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [5, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, -4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 9, 0, 0], [0, 0, 0, 0], [-42, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 2], [0, 0, 0, 0], [0, 0, 7, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [47, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [0, 15, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -5, 7, 0], [0, 0, 0, 0], [0, 0, 0, -4], [0, 0, 0, 0], [100, 0, 0, 0], [0, 0, 0, 0], [0, 0, -5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 3, 0, 0], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 0, -2], [0, 0, 0, 0], [0, 0, 2, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [0, 0, 0, 6], [0, 0, 0, 0], [-101, 0, 0, 0], [0, 0, 0, 0], [0, 0, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 14, 0], [0, 0, 0, 0], [0, 0, 0, -8], [0, 0, 0, 0], [0, 0, 0, -6], [0, 0, 0, 0], [0, 0, -14, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 33, 0, 0], [0, 0, 0, 0], [-20, 0, 0, 0], [0, 0, 0, 0]]}