# Stored data for newform 45.5.g.d, downloaded from the LMFDB on 27 April 2025.
{"Nk2": 1125, "analytic_conductor": 4.651648338772994, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 7, "char_orbit_label": "g", "char_order": 4, "char_parity": -1, "char_values": [45, 4, [11, 37], [4, 3]], "cm_discs": [], "conrey_index": 28, "dim": 4, "field_disc": 6400, "field_disc_factorization": [[2, 8], [5, 2]], "field_poly": [25, 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, [25, 0, 0, 0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13511211282858029, "hecke_ring_generator_nbound": 4, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0], [1, 1, 5, 3, -1, 4, 0], [1, 1, 15, 5, 1, 4, 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": true, "label": "45.5.g.d", "level": 45, "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": "45.5.g.d", "nf_label": "4.0.6400.3", "prim_orbit_index": 3, "qexp_display": "q+\\beta _{1}q^{2}-11\\beta _{2}q^{4}+(2\\beta _{1}-11\\beta _{3})q^{5}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "4.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "45.5.g", "trace_display": [0, 0, 0, -20], "trace_hash": 1602795094460182913, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.849", "prec": 17}, {"__RealLiteral__": 0, "data": "0.740", "prec": 17}, {"__RealLiteral__": 0, "data": "89.864", "prec": 20}, {"__RealLiteral__": 0, "data": "81.180", "prec": 20}, {"__RealLiteral__": 0, "data": "2918.745", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.628", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 0, -20, 0, 0, 220, 0, 0, -440, 0, 0, -164, 0, 0, 0, 0, 0, 1100, 0, 0, 880, 0, 0, -220, 0, 0, -4768, 0, 0, 0, 0, 0, 7240, 0, 0, 1080, 0, 0, -5240, 0, 0, -6760, 0, 0, 0, 0, 0, 4840, 0, 0, 14300, 0, 0, -6300, 0, 0, -5512, 0, 0, 0, 0, 0, 7480, 0, 0, -900, 0, 0, -15620, 0, 0, -8712, 0, 0, 0, 0, 0, 9800, 0, 0, -440, 0, 0, 29700, 0, 0, 4400, 0, 0, 0, 0, 0, -28820, 0, 0, -25740, 0, 0, 12340, 0, 0, 20480, 0, 0, 0, 0, 0, 820, 0, 0, -13520, 0, 0, 6300, 0, 0, 62436, 0, 0, 0, 0, 0, -78980, 0, 0, -28600, 0, 0, -3960, 0, 0, -1080, 0, 0, 0, 0, 0, -43600, 0, 0, 56700, 0, 0, 79640, 0, 0, 125672, 0, 0, 0, 0, 0, -44000, 0, 0, -104060, 0, 0, -57200, 0, 0, -60280, 0, 0, 0, 0, 0, 57640, 0, 0, -16100, 0, 0, 72000, 0, 0, 5192, 0, 0, 0, 0, 0, -2200, 0, 0, 7920, 0, 0, -34100, 0, 0, -103444, 0, 0, 0, 0, 0, 109100, 0, 0, 127400, 0, 0, 18040, 0, 0, -119752, 0, 0, 0, 0, 0, 23840, 0, 0, -108900, 0, 0, -178940, 0, 0, 109880, 0, 0, 0, 0, 0, 170100, 0, 0, 311080, 0, 0, -200, 0, 0, -250672, 0, 0, 0, 0, 0, 87120, 0, 0, 71800, 0, 0, -371800, 0, 0, -226556, 0, 0, 0, 0, 0, -72100, 0, 0, 40960, 0, 0, 82280, 0, 0, 212408, 0, 0, 0, 0, 0, 265480, 0, 0, -35100, 0, 0, 217000, 0, 0, -242000, 0, 0, 0, 0, 0, 171820, 0, 0, -56700, 0, 0, -29700, 0, 0, 52400, 0, 0, 0, 0, 0, -352040, 0, 0, -262240, 0, 0, 21220, 0, 0, -26928, 0, 0, 0, 0, 0, 33800, 0, 0, 160600, 0, 0, 264600, 0, 0, 117608, 0, 0, 0, 0, 0, 56980, 0, 0, -880, 0, 0, -95040, 0, 0, 248600, 0, 0, 0, 0, 0, -520300, 0, 0, -566800, 0, 0, -89100, 0, 0, 364468, 0, 0, 0, 0, 0, -511940, 0, 0, 325800, 0, 0, 470800, 0, 0, 763560, 0, 0, 0, 0, 0, -25000, 0, 0, -121000, 0, 0, -317020, 0, 0, 13520, 0, 0, 0, 0, 0, -389840, 0, 0, -36080, 0, 0, 524480, 0, 0, 63000, 0, 0, 0, 0, 0, -135740, 0, 0, -120560, 0, 0, 217800, 0, 0, -389848, 0, 0, 0, 0, 0, 27560, 0, 0, -340600, 0, 0, -365180, 0, 0, -78408, 0, 0, 0, 0, 0, 4400, 0, 0, -648000, 0, 0, -34180, 0, 0, 1078000, 0, 0, 0, 0, 0, 682540, 0, 0, 817960, 0, 0, 969940, 0, 0, -387400, 0, 0, 0, 0, 0, -170100, 0, 0, -463320, 0, 0, -554400, 0, 0, -1592800, 0, 0, 0, 0, 0, 186700, 0, 0, 94040, 0, 0, 12600, 0, 0, 195488, 0, 0, 0, 0, 0, -289300, 0, 0, 1418300, 0, 0, -868780, 0, 0, 156200, 0, 0, 0, 0, 0, 1555400, 0, 0, 534600, 0, 0, -861080, 0, 0, -19960, 0, 0, 0, 0, 0, 43560, 0, 0, -879560, 0, 0, -306900, 0, 0, -1414072, 0, 0, 0, 0, 0, 210760, 0, 0, 885500, 0, 0, -12240, 0, 0, -151272, 0, 0, 0, 0, 0, 407000, 0, 0, 219760, 0, 0, -1177200, 0, 0, -930472, 0, 0, 0, 0, 0, 907060, 0, 0, 900900, 0, 0, 1126400, 0, 0, 1021760, 0, 0, 0, 0, 0, -296840, 0, 0, 1800, 0, 0, 743600, 0, 0, -607288, 0, 0, 0, 0, 0, -263780, 0, 0, -303160, 0, 0, -817520, 0, 0, -297000, 0, 0, 0, 0, 0, 281600, 0, 0, -1175300, 0, 0, -484000, 0, 0, -1024912, 0, 0, 0, 0, 0, 1034440, 0, 0, -234360, 0, 0, 1245520, 0, 0, -7920, 0, 0, 0, 0, 0, 629200, 0, 0, -937300, 0, 0, 141400, 0, 0, 2035352, 0, 0, 0, 0, 0, -2129400, 0, 0, 336600, 0, 0, -265700, 0, 0, 191884, 0, 0, 0, 0, 0, -1311200, 0, 0, 794200, 0, 0, 214840, 0, 0, 2037272, 0, 0, 0, 0, 0, -19600, 0, 0, 80300, 0, 0, 1433520, 0, 0, -1358440, 0, 0, 0, 0, 0, -1944000, 0, 0, -484000, 0, 0, 214200, 0, 0, -123400, 0, 0, 0, 0, 0, -1414820, 0, 0, -1015300, 0, 0, -182600, 0, 0, 3197480, 0, 0, 0, 0, 0, -102400, 0, 0, 267300, 0, 0, -24200, 0, 0, 3690272, 0, 0, 0, 0, 0, 136120, 0, 0, -1176120, 0, 0, -35640, 0, 0, 990440, 0, 0, 0, 0, 0, 375100, 0, 0, -1048960, 0, 0, -758700, 0, 0, -4796000, 0, 0, 0, 0, 0, -3087800, 0, 0, 24480, 0, 0, 606320, 0, 0, -1844568, 0, 0, 0, 0, 0, 281600, 0, 0, 439400, 0, 0, 2945700, 0, 0, 5078312, 0, 0, 0, 0, 0, 1037520, 0, 0, -970200, 0, 0, 1197460, 0, 0, -63000, 0, 0, 0, 0, 0, 751960, 0, 0, -137720, 0, 0, 1197900, 0, 0, -1139876, 0, 0, 0, 0, 0, -312180, 0, 0, -23400, 0, 0, -2780480, 0, 0, -2158920, 0, 0, 0, 0, 0, 1412600, 0, 0, 497200, 0, 0, 262240, 0, 0, -1645600, 0, 0, 0, 0, 0, -83600, 0, 0, -586300, 0, 0, -1664960, 0, 0, 1662320, 0, 0, 0, 0, 0, 1968340, 0, 0, 801900, 0, 0, -1009800, 0, 0, -40960, 0, 0, 0, 0, 0, 864160, 0, 0, 242000, 0, 0, -3315400, 0, 0, -2265912, 0, 0, 0, 0, 0, -58300, 0, 0, 5828200, 0, 0, 2979900, 0, 0, -1861992, 0, 0, 0, 0, 0, 2689060, 0, 0, 622160, 0, 0, -3312400, 0, 0, -2882000, 0, 0, 0, 0, 0, 5400, 0, 0, -325000, 0, 0, -2613600, 0, 0, 1989372, 0, 0, 0, 0, 0, -1689380, 0, 0, -1296900, 0, 0, -68760, 0, 0, 225992, 0, 0, 0, 0, 0, 1384100, 0, 0, 5682160, 0, 0, 958320, 0, 0, -2211832, 0, 0, 0, 0, 0, 3320440, 0, 0, -3237300], "weight": 5, "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, 1, 0, 0], [0, 0, 0, 0], [0, 0, -11, 0], [0, 2, 0, -11], [0, 0, 0, 0], [-5, 0, -5, 0], [0, 0, 0, -27], [0, 0, 0, 0], [55, 0, 10, 0], [0, 55, 0, -55], [0, 0, 0, 0], [-110, 0, 110, 0], [0, -5, 0, -5], [0, 0, 0, 0], [-41, 0, 0, 0], [0, -2, 0, 0], [0, 0, 0, 0], [0, 0, -198, 0], [0, -121, 0, -22], [0, 0, 0, 0], [275, 0, 275, 0], [0, 0, 0, 338], [0, 0, 0, 0], [220, 0, -585, 0], [0, -110, 0, 110], [0, 0, 0, 0], [-55, 0, 55, 0], [0, 315, 0, 315], [0, 0, 0, 0], [-1192, 0, 0, 0], [0, -473, 0, 0], [0, 0, 0, 0], [0, 0, -10, 0], [0, -65, 0, 45], [0, 0, 0, 0], [1810, 0, 1810, 0], [0, 0, 0, -198], [0, 0, 0, 0], [270, 0, -1485, 0], [0, 490, 0, -490], [0, 0, 0, 0], [-1310, 0, 1310, 0], [0, -605, 0, -605], [0, 0, 0, 0], [-1690, 0, 0, 0], [0, 1414, 0, 0], [0, 0, 0, 0], [0, 0, -2351, 0], [0, 220, 0, -585], [0, 0, 0, 0], [1210, 0, 1210, 0], [0, 0, 0, -1024], [0, 0, 0, 0], [3575, 0, -2475, 0], [0, -135, 0, 135], [0, 0, 0, 0], [-1575, 0, 1575, 0], [0, -315, 0, -315], [0, 0, 0, 0], [-1378, 0, 0, 0], [0, -1192, 0, 0], [0, 0, 0, 0], [0, 0, -1709, 0], [0, 990, 0, 1430], [0, 0, 0, 0], [1870, 0, 1870, 0], [0, 0, 0, 22], [0, 0, 0, 0], [-225, 0, -325, 0], [0, -2180, 0, 2180], [0, 0, 0, 0], [-3905, 0, 3905, 0], [0, 1810, 0, 1810], [0, 0, 0, 0], [-2178, 0, 0, 0], [0, -550, 0, 0], [0, 0, 0, 0], [0, 0, -612, 0], [0, -82, 0, 451], [0, 0, 0, 0], [2450, 0, 2450, 0], [0, 0, 0, 3014], [0, 0, 0, 0], [-110, 0, -20, 0], [0, -1310, 0, 1310], [0, 0, 0, 0], [7425, 0, -7425, 0], [0, -3600, 0, -3600], [0, 0, 0, 0], [1100, 0, 0, 0], [0, 3718, 0, 0], [0, 0, 0, 0], [0, 0, 7070, 0], [0, -2178, 0, -396], [0, 0, 0, 0], [-7205, 0, -7205, 0], [0, 0, 0, -2351], [0, 0, 0, 0], [-6435, 0, -2420, 0]]}