# Stored data for newform 75.10.e.b, downloaded from the LMFDB on 15 September 2026.
{"Nk2": 7500, "analytic_conductor": 38.62768771229049, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 15, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 5, "char_orbit_label": "e", "char_order": 4, "char_parity": 1, "char_values": [75, 4, [26, 52], [2, 1]], "cm_discs": [-3], "conrey_index": 32, "dim": 4, "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 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, [0, 1]], [7, [9973140848784, 0, 0, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503874673049675, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 729, "hecke_ring_index_factorization": [[3, 6]], "hecke_ring_index_proved": true, "inner_twist_count": 8, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, -3], [1, 2, 5, 3, -1, 4, 0], [1, 1, 15, 4, -1, 2, 0], [1, 1, 5, 2, 1, 2, 0], [1, 2, 15, 5, 1, 4, 0]], "is_cm": true, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "75.10.e.b", "level": 75, "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": [3, 5], "level_radical": 15, "minimal_twist": "75.10.e.b", "nf_label": "4.0.2304.2", "prim_orbit_index": 5, "qexp_display": "q-3\\beta _{3}q^{3}+2^{9}\\beta _{2}q^{4}-38\\beta _{1}q^{7}-3^{9}\\beta _{2}q^{9}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "9.2.1.d4", "self_twist_discs": [-3], "self_twist_type": 1, "space_label": "75.10.e", "trace_display": [0, 0, 0, 0], "trace_hash": 1838802037290225022, "trace_moments": [{"__RealLiteral__": 0, "data": "0.015", "prec": 7}, {"__RealLiteral__": 0, "data": "3.516", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "166.881", "prec": 20}, 0, {"__RealLiteral__": 0, "data": "8927.121", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.880", "prec": 10}, "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1048576, 0, 0, 0, 0, -997272, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6764912, 0, 0, 0, 0, 40310784, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -471612232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2000273408, 0, 0, 0, 0, -1549681956, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1198056096, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -9443326032, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9431790764, 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, 50855256208, 0, 0, 0, 0, -48426688512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -76897229472, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80660740888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76176545792, 0, 0, 0, 0, -174021811992, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197927557568, 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, -367197777352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 274877906944, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -191788517872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 659144094048, 0, 0, 0, 0, 0, 0, 0, 0, 0, 296134601616, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1263067799552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -427790115712, 0, 0, 0, 0, 261428871168, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1861684589808, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2524989514548, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3031399877688, 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, -4788745272872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4587888775168, 0, 0, 0, 0, -2928482325828, 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, -4982297113872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11344582339776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1773381091328, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2731416313536, 0, 0, 0, 0, -11970072317952, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3562298429752, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7497123135488, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1404211281472, 0, 0, 0, 0, -10567230160896, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24304461971608, 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, -5677052776912, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1686614330016, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36613788612632, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36458580416512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -47027246027552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48556569333168, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16233196701744, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92379205005696, 0, 0, 0, 0, 0, 0, 0, 0, 0, -67607233199792, 0, 0, 0, 0, -10050204045312, 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, -40468756815872, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7935922535968, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23330334747888, 0, 0, 0, 0, 0, 0, 0, 0, 0, -58028583903476, 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, 209058203473056, 0, 0, 0, 0, -110406722568192, 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, 147090161512448, 0, 0, 0, 0, -75198385490472, 0, 0, 0, 0, 0, 0, 0, 0, 0, -145315092907936, 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, -94317480050748, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 123630316945408, 0, 0, 0, 0, -176373856956312, 0, 0, 0, 0, 0, 0, 0, 0, 0, 152910822041648, 0, 0, 0, 0, 0, 0, 0, 0, 0], "weight": 10, "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, 0, 0, -3], [0, 0, 512, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -38, 0, 0], [0, 0, 0, 0], [0, 0, -19683, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1536, 0, 0], [0, 0, 0, 3604], [0, 0, 0, 0], [0, 0, 0, 0], [-262144, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -976696, 0], [0, 0, 0, 0], [-249318, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -59049, 0, 0], [0, 0, 0, -19456], [0, 0, 0, 0], [0, 0, 0, 0], [-1691228, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [10077696, 0, 0, 0], [0, -359828, 0, 0], [0, 0, 0, 0], [0, 0, 23645844, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 890834], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 786432], [0, 0, -37195579, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1845248, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2930088, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [-117903058, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 747954], [0, 0, -134217728, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -6630918, 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, 8216664], [0, 0, 0, 0], [0, 0, 0, 0], [500068352, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 616732324, 0], [0, 0, 0, 0], [-387420489, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, -127650816, 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], [299514024, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 5073684], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 25115992, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]}