# Stored data for newform 450.7.d.a, downloaded from the LMFDB on 25 April 2024.
{"label": "450.7.d.a", "space_label": "450.7.d", "level": 450, "weight": 7, "hecke_orbit": 1, "hecke_orbit_code": 206275871170, "dim": 2, "is_polredabs": true, "nf_label": "2.0.8.1", "trace_hash": 1350520567320344619, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [-484, 1]]], "qexp_display": "q-4\\beta q^{2}-2^{5}q^{4}+22^{2}q^{7}+2^{7}\\beta q^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "d", "char_is_real": true, "Nk2": 22050, "analytic_conductor": 103.52433762893295, "hecke_ring_index": 1, "level_radical": 30, "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": "0.509", "prec": 17}, "analytic_rank_proved": true, "char_values": [450, 2, [101, 127], [1, 2]], "hecke_ring_generator_nbound": 17, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [251], "field_disc": -8, "field_disc_factorization": [[-1, 1], [2, 3]], "field_poly": [2, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.946", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "15.385", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "151.624", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "6.2.3.c2", "trace_display": [0, 0, 0, 968], "traces": [0, 2, 0, 0, -64, 0, 0, 968, 0, 0, 0, 0, 0, -6736, 0, 0, 2048, 0, 0, 11488, 0, 0, 15168, 0, 0, 0, 0, 0, -30976, 0, 0, -79592, 0, 0, -144, 0, 0, -105052, 0, 0, 0, 0, 0, -7600, 0, 0, 38208, 0, 0, 233214, 0, 0, 215552, 0, 0, 0, 0, 0, 332112, 0, 0, 26500, 0, 0, -65536, 0, 0, -337936, 0, 0, 0, 0, 0, -472288, 0, 0, -367616, 0, 0, -70232, 0, 0, -419088, 0, 0, 0, 0, 0, -485376, 0, 0, -3260224, 0, 0, -868800, 0, 0, 642848, 0, 0, 0, 0, 0, -3986824, 0, 0, -2701008, 0, 0, 388912, 0, 0, 991232, 0, 0, 0, 0, 0, -2826624, 0, 0, -51694, 0, 0, 2546944, 0, 0, -6114424, 0, 0, 0, 0, 0, 5560192, 0, 0, 4608, 0, 0, -2184656, 0, 0, -6012864, 0, 0, 0, 0, 0, 3361664, 0, 0, -8157416, 0, 0, 7341312, 0, 0, -12311356, 0, 0, 0, 0, 0, -1601392, 0, 0, 124224, 0, 0, 13033230, 0, 0, 243200, 0, 0, 0, 0, 0, -1463184, 0, 0, -20762384, 0, 0, -1222656, 0, 0, 34128, 0, 0, 0, 0, 0, 7863908, 0, 0, -7462848, 0, 0, -1131800, 0, 0, 7566384, 0, 0, 0, 0, 0, -6897664, 0, 0, -27033008, 0, 0, 2949120, 0, 0, -38522528, 0, 0, 0, 0, 0, 10709672, 0, 0, 9298704, 0, 0, 8692816, 0, 0, -10627584, 0, 0, 0, 0, 0, -69696, 0, 0, -6241856, 0, 0, -848000, 0, 0, -38691584, 0, 0, 0, 0, 0, -9055296, 0, 0, 2097152, 0, 0, -50845168, 0, 0, 34776960, 0, 0, 0, 0, 0, 10813952, 0, 0, 59279800, 0, 0, 50732016, 0, 0, -26442544, 0, 0, 0, 0, 0, 13486496, 0, 0, -51085824, 0, 0, 48274814, 0, 0, 15113216, 0, 0, 0, 0, 0, -25126320, 0, 0, -3678400, 0, 0, 11763712, 0, 0, 10461200, 0, 0, 0, 0, 0, -44955652, 0, 0, 2247424, 0, 0, -78710544, 0, 0, 18492672, 0, 0, 0, 0, 0, 13410816, 0, 0, -11522768, 0, 0, -54358656, 0, 0, 80210336, 0, 0, 0, 0, 0, -1008656, 0, 0, 40389072, 0, 0, -84127676, 0, 0, 15532032, 0, 0, 0, 0, 0, -84139776, 0, 0, -28104690, 0, 0, 104327168, 0, 0, 53170952, 0, 0, 0, 0, 0, -35765860, 0, 0, 27801600, 0, 0, 144195520, 0, 0, 147010944, 0, 0, 0, 0, 0, -20571136, 0, 0, 85968, 0, 0, -60864048, 0, 0, -31382212, 0, 0, 0, 0, 0, 268065856, 0, 0, 160742208, 0, 0, -231023264, 0, 0, 127578368, 0, 0, 0, 0, 0, 87124992, 0, 0, 278477680, 0, 0, 86432256, 0, 0, 12826000, 0, 0, 0, 0, 0, 80126276, 0, 0, -12445184, 0, 0, -277183688, 0, 0, 484992, 0, 0, 0, 0, 0, -31719424, 0, 0, 99323856, 0, 0, 153938112, 0, 0, -71332960, 0, 0, 0, 0, 0, -229956232, 0, 0, 228913776, 0, 0, -163561024, 0, 0, 90451968, 0, 0, 0, 0, 0, -230739456, 0, 0, 353815136, 0, 0, 1654208, 0, 0, 150337688, 0, 0, 0, 0, 0, 747252, 0, 0, -81502208, 0, 0, 183091648, 0, 0, 57645504, 0, 0, 0, 0, 0, 195661568, 0, 0, -228587392, 0, 0, -163340304, 0, 0, 205905600, 0, 0, 0, 0, 0, 75538112, 0, 0, -353629056, 0, 0, 273261602, 0, 0, -177926144, 0, 0, 0, 0, 0, 2843568, 0, 0, 50959984, 0, 0, -147456, 0, 0, -410431792, 0, 0, 0, 0, 0, -33992288, 0, 0, 69908992, 0, 0, 25596800, 0, 0, -69280656, 0, 0, 0, 0, 0, 192411648, 0, 0, 483003616, 0, 0, -202838592, 0, 0, 98795804, 0, 0, 0, 0, 0, 640138896, 0, 0, 113407536, 0, 0, -457176448, 0, 0, -107573248, 0, 0, 0, 0, 0, -128684544, 0, 0, -862180484, 0, 0, 261037312, 0, 0, -33398104, 0, 0, 0, 0, 0, 384641564, 0, 0, -234921984, 0, 0, 509746432, 0, 0, 353238144, 0, 0, 0, 0, 0, 393963392, 0, 0, 184720360, 0, 0, 312497232, 0, 0, -785464752, 0, 0, 0, 0, 0, -751892656, 0, 0, -827136, 0, 0, 669909888, 0, 0, 51244544, 0, 0, 0, 0, 0, -420499200, 0, 0, -945089636, 0, 0, -3975168, 0, 0, -198270864, 0, 0, 0, 0, 0, -1097666500, 0, 0, -417063360, 0, 0, 311138432, 0, 0, -603625728, 0, 0, 0, 0, 0, -7782400, 0, 0, -745624400, 0, 0, -767213376, 0, 0, -942948, 0, 0, 0, 0, 0, -603418688, 0, 0, 199093776, 0, 0, -493020464, 0, 0, 46821888, 0, 0, 0, 0, 0, -158301504, 0, 0, -1929622816, 0, 0, 664396288, 0, 0, -782741704, 0, 0, 0, 0, 0, -69815632, 0, 0, 39124992, 0, 0, -605998688, 0, 0, -1307287872, 0, 0, 0, 0, 0, -1092096, 0, 0, -164654024, 0, 0, -1118553216, 0, 0, 1207157360, 0, 0, 0, 0, 0, 188233408, 0, 0, -98276352, 0, 0, 1631591140, 0, 0, -251645056, 0, 0, 0, 0, 0, -559362480, 0, 0, 1425048768, 0, 0, 238811136, 0, 0, 804924320, 0, 0, 0, 0, 0, -89252000, 0, 0, 36217600, 0, 0, -1954800, 0, 0, -536851056, 0, 0, 0, 0, 0, -242124288, 0, 0, 451042240, 0, 0, -796714368, 0, 0, -43654400, 0, 0, 0, 0, 0, 1414671656, 0, 0, -1368086016, 0, 0, 1007652784, 0, 0, 220725248, 0, 0, 0, 0, 0, 1659643584, 0, 0, -533765554, 0, 0, 865056256, 0, 0, -25019896, 0, 0, 0, 0, 0, 37597028, 0, 0, -94371840, 0, 0, 1103863216, 0, 0, -1135801152, 0, 0, 0, 0, 0, 1232720896, 0, 0, 1138168448, 0, 0, 219466752, 0, 0, 1170774140, 0, 0, 0, 0, 0, -440169808, 0, 0, 1260829248, 0, 0, -2959381216, 0, 0, -342709504, 0, 0, 0, 0, 0, -691455888, 0, 0, -6077268, 0, 0, -297558528, 0, 0, -1463228464, 0, 0, 0, 0, 0, -29441088, 0, 0, -278170112, 0, 0, -431973320, 0, 0, 1719488208, 0, 0, 0, 0, 0, 340082688, 0, 0, 1339581216, 0, 0, -997535808, 0, 0, 1484896676, 0, 0, 0, 0, 0, 250195536, 0, 0, -57638400, 0, 0, 1590665984, 0, 0, 2230272, 0, 0, 0, 0, 0, -1011884352, 0, 0, 1392435870, 0, 0, 199739392, 0, 0, 2188219640, 0, 0, 0, 0, 0, -1057373504, 0, 0, 27136000, 0, 0, 346774608, 0, 0, 510047232, 0, 0, 0, 0, 0, 1238130688, 0, 0, 1019204536, 0, 0, -2910226176, 0, 0, 1981560092, 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, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 2, "minimal_twist": "18.7.b.a", "char_is_minimal": true, "conrey_index": 251, "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, -4], [0, 0], [-32, 0], [0, 0], [0, 0], [484, 0], [0, 128], [0, 0], [0, 0], [0, 948], [0, 0], [-3368, 0], [0, -1936], [0, 0], [1024, 0], [0, -9], [0, 0], [5744, 0], [0, 0], [0, 0], [7584, 0], [0, 2388], [0, 0], [0, 0], [0, 13472], [0, 0], [-15488, 0], [0, 20757], [0, 0], [-39796, 0], [0, -4096], [0, 0], [-72, 0], [0, 0], [0, 0], [-52526, 0], [0, -22976], [0, 0], [0, 0], [0, -26193], [0, 0], [-3800, 0], [0, -30336], [0, 0], [19104, 0], [0, -54300], [0, 0], [116607, 0], [0, 0], [0, 0], [107776, 0], [0, -168813], [0, 0], [0, 0], [0, 61952], [0, 0], [166056, 0], [0, -176664], [0, 0], [13250, 0], [0, 159184], [0, 0], [-32768, 0], [0, 0], [0, 0], [-168968, 0], [0, 288], [0, 0], [0, 0], [0, -375804], [0, 0], [-236144, 0], [0, 210104], [0, 0], [-183808, 0], [0, 458832], [0, 0], [-35116, 0], [0, 0], [0, 0], [-209544, 0], [0, 7764], [0, 0], [0, 0], [0, 15200], [0, 0], [-242688, 0], [0, -91449], [0, 0], [-1630112, 0], [0, -76416], [0, 0], [-434400, 0], [0, 0], [0, 0], [321424, 0], [0, -466428], [0, 0], [0, 0]]}