# Stored data for newform 75.9.f.d, downloaded from the LMFDB on 19 April 2024.
{"label": "75.9.f.d", "space_label": "75.9.f", "level": 75, "weight": 9, "hecke_orbit": 4, "hecke_orbit_code": 13511142630490187, "dim": 12, "is_polredabs": true, "trace_hash": 1280787324830675307, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [60170924888064, 0, 0, 0, 161889694848, 0, 0, 0, 959337, 0, 0, 0, 1]]], "qexp_display": "q-\\beta _{2}q^{2}+\\beta _{9}q^{3}+(193\\beta _{1}-\\beta _{5})q^{4}+\\cdots", "char_order": 4, "char_parity": -1, "char_degree": 2, "char_conductor": 5, "char_orbit_label": "f", "char_is_real": false, "Nk2": 6075, "analytic_conductor": 30.553395754584542, "hecke_ring_index": 247949112960000, "level_radical": 15, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.754", "prec": 17}, "analytic_rank_proved": true, "char_values": [75, 4, [26, 52], [4, 1]], "hecke_ring_generator_nbound": 4, "inner_twist_count": 4, "level_primes": [3, 5], "conrey_indexes": [7, 43], "field_disc": 79904751658856183915782078464, "field_disc_factorization": [[2, 24], [3, 6], [13, 4], [3889, 4]], "field_poly": [846810000, 558720000, 184320000, -223046400, 128589064, -2072064, 18432, -24384, 27713, -192, 0, 0, 1], "hecke_ring_index_factorization": [[2, 10], [3, 18], [5, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.138", "prec": 17}, {"__RealLiteral__": 0, "data": "11.444", "prec": 20}, {"__RealLiteral__": 0, "data": "18.131", "prec": 20}, {"__RealLiteral__": 0, "data": "1269.018", "prec": 27}, {"__RealLiteral__": 0, "data": "3887.614", "prec": 27}, {"__RealLiteral__": 0, "data": "195279.505", "prec": 34}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 6, "sato_tate_group": "8.2.3.c4", "trace_display": [0, 0, 0, 0], "traces": [0, 12, 0, 0, 0, 0, 2268, 0, 0, 0, 0, -88920, 0, 0, 0, 0, -485796, 0, 0, 0, 0, 79704, 0, 0, 0, 0, -4055976, 0, 0, 0, 0, 5658696, 0, 0, 0, 0, 5065092, 0, 0, 0, 0, 1798056, 0, 0, 0, 0, -10882464, 0, 0, 0, 0, 4329936, 0, 0, 0, 0, 7268040, 0, 0, 0, 0, 33649848, 0, 0, 0, 0, -141361848, 0, 0, 0, 0, 335506464, 0, 0, 0, 0, -395386536, 0, 0, 0, 0, -57395628, 0, 0, 0, 0, 489958560, 0, 0, 0, 0, -216875664, 0, 0, 0, 0, -710311356, 0, 0, 0, 0, 421470000, 0, 0, 0, 0, -388395984, 0, 0, 0, 0, -547195176, 0, 0, 0, 0, 3485809728, 0, 0, 0, 0, -506727516, 0, 0, 0, 0, -709690248, 0, 0, 0, 0, 1709889768, 0, 0, 0, 0, -3902656656, 0, 0, 0, 0, -3075061968, 0, 0, 0, 0, 8821657296, 0, 0, 0, 0, -3296453496, 0, 0, 0, 0, -8399015064, 0, 0, 0, 0, 4380037056, 0, 0, 0, 0, -6348823152, 0, 0, 0, 0, -127703304, 0, 0, 0, 0, 14993193672, 0, 0, 0, 0, -6813648504, 0, 0, 0, 0, -4162505112, 0, 0, 0, 0, 15556588560, 0, 0, 0, 0, 8610216060, 0, 0, 0, 0, -3070559664, 0, 0, 0, 0, -7177167000, 0, 0, 0, 0, 3324243096, 0, 0, 0, 0, 3699537948, 0, 0, 0, 0, -17568246240, 0, 0, 0, 0, -15980793552, 0, 0, 0, 0, 6269131728, 0, 0, 0, 0, -42908424264, 0, 0, 0, 0, 28312079400, 0, 0, 0, 0, 24145465608, 0, 0, 0, 0, -1729398456, 0, 0, 0, 0, 4539722820, 0, 0, 0, 0, -6360285888, 0, 0, 0, 0, -19715793840, 0, 0, 0, 0, -11563911720, 0, 0, 0, 0, 47001920544, 0, 0, 0, 0, -39161764008, 0, 0, 0, 0, 153177667920, 0, 0, 0, 0, 17585023536, 0, 0, 0, 0, -94882456440, 0, 0, 0, 0, -41754930624, 0, 0, 0, 0, 35188899984, 0, 0, 0, 0, -31451767920, 0, 0, 0, 0, -33041229000, 0, 0, 0, 0, 26942125392, 0, 0, 0, 0, -185310330048, 0, 0, 0, 0, 80282162184, 0, 0, 0, 0, 67707072504, 0, 0, 0, 0, 5661034992, 0, 0, 0, 0, 105662500368, 0, 0, 0, 0, 25275333960, 0, 0, 0, 0, -198908659656, 0, 0, 0, 0, -69591024804, 0, 0, 0, 0, 75297959640, 0, 0, 0, 0, 114792124896, 0, 0, 0, 0, 83000357136, 0, 0, 0, 0, -62839393704, 0, 0, 0, 0, 19520375328, 0, 0, 0, 0, 24080989056, 0, 0, 0, 0, -96261364872, 0, 0, 0, 0, 185392205208, 0, 0, 0, 0, -266208405120, 0, 0, 0, 0, -215460644112, 0, 0, 0, 0, 451714110696, 0, 0, 0, 0, 1080599112, 0, 0, 0, 0, -11884286304, 0, 0, 0, 0, 160368736176, 0, 0, 0, 0, -435044904936, 0, 0, 0, 0, -75063429972, 0, 0, 0, 0, 330869336904, 0, 0, 0, 0, -228984450768, 0, 0, 0, 0, -372967734168, 0, 0, 0, 0, 628706535984, 0, 0, 0, 0, 269669977200, 0, 0, 0, 0, -334677179592, 0, 0, 0, 0, 310248493344, 0, 0, 0, 0, -564344213904, 0, 0, 0, 0, -10847773692, 0, 0, 0, 0, 273882953448, 0, 0, 0, 0, 289738930536, 0, 0, 0, 0, -116177439456, 0, 0, 0, 0, -533721071808, 0, 0, 0, 0, -789468993504, 0, 0, 0, 0, -28951719840, 0, 0, 0, 0, 375793317576, 0, 0, 0, 0, 326914892352, 0, 0, 0, 0, 14593920984, 0, 0, 0, 0, 512080097904, 0, 0, 0, 0, 318912805176, 0, 0, 0, 0, 461519600688, 0, 0, 0, 0, 41970400128, 0, 0, 0, 0, -529583457624, 0, 0, 0, 0, -427643413920, 0, 0, 0, 0, -313692669936, 0, 0, 0, 0, 342725730120, 0, 0, 0, 0, 78855635484, 0, 0, 0, 0, 475240549536, 0, 0, 0, 0, 1261298493312, 0, 0, 0, 0, -279790342560, 0, 0, 0, 0, -2057232857328, 0, 0, 0, 0, 129474075960, 0, 0, 0, 0, 1110736394352, 0, 0, 0, 0, 555806787552, 0, 0, 0, 0, -613690868880, 0, 0, 0, 0, -50887955808, 0, 0, 0, 0, -3016876448448, 0, 0, 0, 0, 407045766744, 0, 0, 0, 0, 1045842333264, 0, 0, 0, 0, 777248671896, 0, 0, 0, 0, -1487982240672, 0, 0, 0, 0, 636121321488, 0, 0, 0, 0, -2436515631864, 0, 0, 0, 0, 358928965704, 0, 0, 0, 0, 504995393592, 0, 0, 0, 0, -992521917936, 0, 0, 0, 0, 6089527539204, 0, 0, 0, 0, 421765171344, 0, 0, 0, 0, -2282797904400, 0, 0, 0, 0, -816998014440, 0, 0, 0, 0, 1879419340224, 0, 0, 0, 0, -1881606718512, 0, 0, 0, 0, 2802262629744, 0, 0, 0, 0, 242788230360, 0, 0, 0, 0, -1325276888760, 0, 0, 0, 0, 463072568976, 0, 0, 0, 0, 2040368607252, 0, 0, 0, 0, 1616694357888, 0, 0, 0, 0, -1701235221984, 0, 0, 0, 0, -1541878432848, 0, 0, 0, 0, -2430538080120, 0, 0, 0, 0, -2970813864600, 0, 0, 0, 0, 174997144008, 0, 0, 0, 0, 867462282072, 0, 0, 0, 0, 1003060357872, 0, 0, 0, 0, -172893350448, 0, 0, 0, 0, 2910636725904, 0, 0, 0, 0, -1877669605440, 0, 0, 0, 0, -2307078401400, 0, 0, 0, 0, 160143876576, 0, 0, 0, 0, -3899145033768, 0, 0, 0, 0, -444242318184, 0, 0, 0, 0, 1281864596112, 0, 0, 0, 0, 3920644444584, 0, 0, 0, 0, -3293374753008, 0, 0, 0, 0, -320914925568, 0, 0, 0, 0, 85983515280, 0, 0, 0, 0, -1648928259000, 0, 0, 0, 0, 11312760024144, 0, 0, 0, 0, -4645378502772, 0, 0, 0, 0, -263177456400, 0, 0, 0, 0, 4757893730496, 0, 0, 0, 0, 85378901616, 0, 0, 0, 0, -2735242093872, 0, 0, 0, 0, 5141617070832, 0, 0, 0, 0, 635057690400, 0, 0, 0, 0, 138947761584, 0, 0, 0, 0, 5774000915592, 0, 0, 0, 0, -9443412029136, 0, 0, 0, 0, 425301603480, 0, 0, 0, 0, 342073622520, 0, 0, 0, 0, 518891543616, 0, 0, 0, 0, -4104084025944, 0, 0, 0, 0, -3432534741216, 0, 0, 0, 0, -1638386921784, 0, 0, 0, 0, 209647604592, 0, 0, 0, 0, -3676668814440, 0, 0, 0, 0, 3731637226248, 0, 0, 0, 0, -5715085178664, 0, 0, 0, 0, 6808156747776, 0, 0, 0, 0, 537341812416, 0, 0, 0, 0, 2390666182272, 0, 0, 0, 0, -395710650576, 0, 0, 0, 0, -2777486568540, 0, 0, 0, 0, -3290106330432, 0, 0, 0, 0, 78181309656, 0, 0, 0, 0, -7792025017896, 0, 0, 0, 0, 2123620757496, 0, 0, 0, 0, 13255554790656, 0, 0, 0, 0, -360391561416, 0, 0, 0, 0, -704011192848, 0, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 1, "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, 2, 5, 3, -1, 4, 0], [1, 1, 5, 2, 1, 2, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "75.9.f.d", "char_is_minimal": true, "conrey_index": 7, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 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, 0, 0, 1, 0, 0], [0, 193, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [189, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 64, 0, 0, 0, 8, 0, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -179, 0, -47, 7, 0], [0, -2187, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-7410, 0, 0, 16, -10, 0, 0, 0, 0, 0, 0, 0], [0, 0, -351, 0, 0, 0, 155, 0, -27, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -584, 0, -374, 56, 0], [0, -27042, 0, 0, 0, 26, 0, 0, 0, 0, 0, -22], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-40483, 0, 0, 75, -96, 0, 0, 0, 0, 0, 0, 0], [0, 0, -3024, 0, 0, 0, -106, 0, -34, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2187, 0, 0, 0, 0], [0, -4866, 0, 0, 0, -248, 0, 0, 0, 0, 0, -132], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6642, 0, 0, -72, -90, 0, 0, 0, 0, 0, 0, 0], [0, 0, 10482, 0, 0, 0, -4392, 0, 312, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2528, 0, 958, -518, 0], [0, 140967, 0, 0, 0, -655, 0, 0, 0, 0, 0, -88], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-337998, 0, 0, 1798, -766, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -2187, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 18710, 0, -4738, -254, 0], [0, -242352, 0, 0, 0, 2256, 0, 0, 0, 0, 0, -660], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [471558, 0, 0, -760, -696, 0, 0, 0, 0, 0, 0, 0], [0, 0, 5129, 0, 0, 0, -26437, 0, 653, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -23976, 0, -5292, 162, 0], [0, 1340836, 0, 0, 0, -3428, 0, 0, 0, 0, 0, -132], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [422091, 0, 0, -2187, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -53288, 0, 0, 0, -26422, 0, -3404, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -44590, 0, -59704, 4376, 0], [0, 963090, 0, 0, 0, -4392, 0, 0, 0, 0, 0, 144], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [149838, 0, 0, 3568, 3188, 0, 0, 0, 0, 0, 0, 0], [0, 0, -31266, 0, 0, 0, -29376, 0, 1296, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 115808, 0, -59128, -80, 0], [0, -3667938, 0, 0, 0, 15458, 0, 0, 0, 0, 0, 4016], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-906872, 0, 0, -6200, 4584, 0, 0, 0, 0, 0, 0, 0], [0, 0, -27680, 0, 0, 0, -120638, 0, -3782, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -202581, 0, -23137, -567, 0], [0, -2860213, 0, 0, 0, 576, 0, 0, 0, 0, 0, 2808], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [360828, 0, 0, -5336, 2582, 0, 0, 0, 0, 0, 0, 0], [0, 0, 562330, 0, 0, 0, -267586, 0, 13570, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -64720, 0, -24352, -14236, 0], [0, -413343, 0, 0, 0, 2187, 0, 0, 0, 0, 0, 2187], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [605670, 0, 0, -11126, 2672, 0, 0, 0, 0, 0, 0, 0], [0, 0, -329400, 0, 0, 0, -34222, 0, -3132, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 841104, 0, -134208, -2592, 0], [0, 556086, 0, 0, 0, -28000, 0, 0, 0, 0, 0, -4594], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2804154, 0, 0, -4448, 6384, 0, 0, 0, 0, 0, 0, 0], [0, 0, -711158, 0, 0, 0, -217624, 0, 8600, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -139968, 0, 17496, -4374, 0], [0, 3004711, 0, 0, 0, 22161, 0, 0, 0, 0, 0, 6432], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11780154, 0, 0, 31698, -6426, 0, 0, 0, 0, 0, 0, 0], [0, 0, 735072, 0, 0, 0, -57936, 0, -15708, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1385708, 0, -236300, 17932, 0], [0, -1939032, 0, 0, 0, 32696, 0, 0, 0, 0, 0, -9262], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [27958872, 0, 0, -20464, -11852, 0, 0, 0, 0, 0, 0, 0], [0, 0, -391473, 0, 0, 0, 102789, 0, -15309, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1674384, 0, -70932, 35760, 0], [0, 19242318, 0, 0, 0, -77926, 0, 0, 0, 0, 0, 2594], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-32948878, 0, 0, 106446, -56544, 0, 0, 0, 0, 0, 0, 0], [0, 0, -78768, 0, 0, 0, 230436, 0, -5760, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -2037474, 0, -154008, 27864, 0], [0, 9251190, 0, 0, 0, 9608, 0, 0, 0, 0, 0, -60624], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-4782969, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 968658, 0, 0, 0, 992736, 0, -38784, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1432704, 0, 607040, 5660, 0], [0, 6668082, 0, 0, 0, 35982, 0, 0, 0, 0, 0, 15408], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [40829880, 0, 0, -57880, -58568, 0, 0, 0, 0, 0, 0, 0], [0, 0, -419904, 0, 0, 0, -256284, 0, 78732, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 4404102, 0, 1063998, -108654, 0], [0, -16927386, 0, 0, 0, -149584, 0, 0, 0, 0, 0, -62404], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-18072972, 0, 0, -67104, 39852, 0, 0, 0, 0, 0, 0, 0], [0, 0, -873976, 0, 0, 0, 1714728, 0, -2472, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1011096, 0, 547774, -39312, 0], [0, -10028100, 0, 0, 0, 36228, 0, 0, 0, 0, 0, 94164], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-59192613, 0, 0, 49533, 3360, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1284592, 0, 0, 0, 815264, 0, 120412, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 2774965, 0, 1049184, -60192, 0], [0, 16205670, 0, 0, 0, -34992, 0, 0, 0, 0, 0, -21870], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}