# Stored data for newform 40.6.k.a, downloaded from the LMFDB on 24 April 2024.
{"label": "40.6.k.a", "space_label": "40.6.k", "level": 40, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 687295430696, "dim": 56, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 40, "char_orbit_label": "k", "char_is_real": false, "Nk2": 1440, "analytic_conductor": 6.415352792519226, "level_radical": 10, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [40, 4, [31, 21, 17], [2, 2, 3]], "inner_twist_count": 4, "level_primes": [2, 5], "conrey_indexes": [3, 27], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 28, "sato_tate_group": "5.2.3.c4", "trace_display": [-2, -4, 0, 0], "traces": [56, -2, -4, 0, 0, 176, 0, 244, 0, -570, -8, -308, 0, 0, 0, 456, -408, 3370, 0, 1360, 0, -3148, 0, 0, -3120, -5084, 968, -10020, 0, 21100, 0, 7968, -976, 0, -4780, 23132, 0, -49524, 0, -58980, -8, 42060, 1308, 0, 0, 42416, 0, 93776, 0, -94010, 20872, -67180, 0, 0, 0, -43384, 968, 86100, 0, 118180, 0, 6240, 0, 0, 17680, -41128, 89252, -158164, 0, 116980, 0, 1180, -25184, 0, -127740, 41592, 0, -161440, 0, -167360, -67792, 23412, -126444, 0, 0, -192704, 0, 100176, 0, -82330, 329432, 226020, 0, 0, 0, 358176, 212576, 65834, 0, -138680, 0, 421728, 0, 0, -3200, 372516, -786188, 227184, 0, -36940, 0, -696960, -305184, 0, 509500, -751400, 0, 370068, 0, 277240, 234248, -1064840, 757504, 0, 0, -1200784, 0, -336016, 0, 191280, -1196488, 1404008, 0, 0, 0, 1468376, -216408, 55460, 0, -35220, 0, 1316360, 0, 0, 400600, 1595076, 1422372, -511860, 0, 405800, 0, -1637608, 71600, 0, -930600, -2214600, 0, -574600, 0, -997440, 25432, -2613338, -1520084, 0, 0, -2641624, 0, 1896800, 0, -1283020, 2001664, 2653756, 0, 0, 0, 1635792, -829816, 2072976, 0, 2945540, 0, 3139720, 0, 0, 281880, 4354200, -2048632, -2577940, 0, 2941140, 0, -4561248, 756376, 0, 2995280, -4333428, 0, -4517580, 0, -3273620, -275128, -3692600, 2216680, 0, 0, -3467984, 0, 4974120, 0, -6600100, -5092408, 4082060, 0, 0, 0, 7890272, -472600, 6290980, 0, 6108600, 0, 7294160, 0, 0, -1840240, 5228476, 5857836, -9174856, 0, 7996380, 0, -6923000, 198648, 0, -4243300, -5996488, 0, -8298920, 0, -10480640, 2393992, -8162410, -5481700, 0, 0, -12015128, 0, 7165880, 0, -9329530, 5559592, 14660700, 0, 0, 0, 10482656, -506384, 11507492, 0, 8655380, 0, 11966316, 0, 0, -2394360, 14809232, -5483472, -8852804, 0, 11300800, 0, -14248008, -105560, 0, 4871720, -20509200, 0, -9522724, 0, -10161600, 1516712, -22577260, 8011316, 0, 0, -19014568, 0, 14519360, 0, -9000660, -2902248, 19204652, 0, 0, 0, 23550216, 4814352, 9796060, 0, 14343980, 0, 24334480, 0, 0, 1016760, 29709948, 710052, -13311800, 0, 10840320, 0, -33768440, -4738512, 0, -9549180, -26268400, 0, -16732520, 0, -13005360, -1280728, -29653700, -1447056, 0, 0, -32201824, 0, 12958176, 0, -18509760, -2662408, 32276492, 0, 0, 0, 41934000, 2163672, 13485154, 0, 16630860, 0, 45675900, 0, 0, 8581080, 35346316, 3209052, -21401800, 0, 17646960, 0, -38195808, -2596952, 0, 3785720, -39415408, 0, -17874164, 0, -23484060, -8128952, -42592400, 3972860, 0, 0, -53934200, 0, 19098160, 0, -18216780, 11275432, 56475600, 0, 0, 0, 49152616, -8001760, 31959000, 0, 20090680, 0, 46863800, 0, 0, 474240, 47539476, -15351020, -22775292, 0, 36761320, 0, -54761652, 15001632, 0, 1400880, -69719936, 0, -30198520, 0, -29598440, -3679408, -66274372, -5853480, 0, 0, -55860800, 0, 41118264, 0, -32059340, -22637128, 54413780, 0, 0, 0, 53638016, 4061528, 38717064, 0, 54610440, 0, 56283092, 0, 0, -18192560, 78364200, 22053160, -41517044, 0, 47091500, 0, -77643472, -1852304, 0, 13923560, -50395600, 0, -59852776, 0, -48724720, 16160248, -61094260, 8750436, 0, 0, -61837384, 0, 58643840, 0, -67891150, 24354704, 60219652, 0, 0, 0, 83919472, 5634912, 52767660, 0, 51193660, 0, 92420000, 0, 0, 6821720, 58802596, -29605844, -72676300, 0, 49893380, 0, -65988904, -22363248, 0, -12817280, -93078200, 0, -58989360, 0, -73942400, -1971568, -70981868, -23003920, 0, 0, -89300352, 0, 57796120, 0, -63366090, -27094888, 97336568, 0, 0, 0, 78941600, -16781880, 77780764, 0, 63023360, 0, 75790332, 0, 0, 29371920, 90483832, 54792572, -64089700, 0, 73779680, 0, -77088032, 15888976, 0, 8410220, -89283648, 0, -55575000, 0, -68313520, -18454208, -112785100, 10100836, 0, 0, -95091384, 0, 82104944, 0, -58663800, 62931664, 95134760, 0, 0, 0, 58581976, -19005352, 64422100, 0, 83306960, 0, 83835480, 0, 0, -17181960, 127565800, -57070708, -54315404, 0, 59330700, 0, -114465840, 36544880, 0, -28277800, -95133208, 0, -79645000, 0, -53126080, 24261024, -94457484, -28422372, 0, 0, -64774024, 0, 52706520, 0, -85783080, -82015688, 106141760, 0, 0, 0, 159878832, 20799952, 46602850, 0, 51413880, 0, 123043864, 0, 0, -49420000, 80866316, 70434652, -74771884, 0, 46057660, 0, -89511000, -37660504, 0, 40562560, -127980800, 0, -52329920, 0, -61469520, 23609192, -103440820, 54609620, 0, 0, -147505600, 0, 31396416, 0, -46724360, 73397832, 137115620, 0, 0, 0, 82138032, 48641736, 67293780, 0, 14265560, 0, 105946040, 0, 0, 22352440, 136918396, -94349408, -33226620, 0, 53768740, 0, -110354640, -63155296, 0, -71528540, -86790600, 0, -15322840, 0, -26757840, -21965688, -133625972, -62710732, 0, 0, -112857528, 0, 43552636, 0, -11269220, -72287200, 94224972, 0, 0, 0, 107057392, -16686920, 23667700, 0, 47954760, 0, 95939612, 0, 0, 76837480, 80789116, 57895240, -23136340, 0, 35340460, 0, -125267200, 44500048, 0, 135018600, -134072428, 0, -46332136, 0, -29965080, -58194648, -85162040, 122083116, 0, 0, -57738168, 0, 36466288, 0, -42741740, 69527592, 80864940, 0, 0, 0, 133533200, -44495032, 11406140, 0, 45958380, 0, 87549320, 0, 0, -45564400, 78651996, -63156880, -41447928, 0, 19391080, 0, -54055728, 103428360, 0, -151819560, -9213208, 0, -39902040, 0, -33388440, 18458232, -49469470, -190408656, 0, 0, -110971552, 0, 37443960, 0, -21948760, -48504248, 19466320, 0, 0, 0, -58499584, 12088688, 38905460, 0, 18434780, 0, 20302160, 0, 0, -75289240, 56031516, 71617580, -29115856, 0, 40807220, 0, -61357520, -19026096, 0, 185200520, -27098000, 0, -18599884, 0, -35029560, 21711792, 14637980, 201446320, 0, 0, 31404216, 0, 29095776, 0, -8686520, 108950952, -27879228, 0, 0, 0, 79373896, 54792680, 23436260, 0, 54075280, 0, 26222880, 0, 0, 73470720, -98865448, -45608524, 17271900, 0, 47413320, 0, 46127040, -128876200, 0, -287920640, 425200, 0, -16638440, 0, 6909120, -58664336, 52404132, -259480216, 0, 0, 35492000, 0, 56341200, 0, -25909890, -91368088, -39772120, 0, 0, 0, -150119328, -52541816, -30371384, 0, -11127880, 0, -84229472, 0, 0, 122003840, -31068768, 84105052, -17799540, 0, -11501260, 0, 87720880, 18764096, 0, 296415340, 122017504, 0, -32275484, 0, 17157280, -54989944, 62024640, 371254032, 0, 0, 123549016, 0, -56620760, 0, 5662840, 45451432, -139426720, 0, 0, 0, -89273224, -75074888, -2822520, 0, -43237420, 0, -170975640, 0, 0, -56345040, -150068924, -149144260, 10863600, 0, -31611320, 0, 146734800, 155016680, 0, -390056180, 122164072, 0, 34178520, 0, 12813360, 100378712, 231338570, -331343924, 0, 0, 237647976, 0, -68336200, 0, 84402720, -116938664, -116245260, 0, 0, 0, -85305184, 103407480, -17550624, 0, -96830180, 0, -160853712, 0, 0, -200946080, -182562200, 144105156, 126434828, 0, -84848760, 0, 232595168, -67955776, 0, 505471960, 273696600, 0, 159963256, 0, 129980360, 142546472, 170548520, 426989960, 0, 0, 28088016, 0, -158313600, 0, 146026680, 123816224, -177070284, 0, 0, 0, -390318984, 84228632, -211800660, 0, -115775620, 0, -293550920, 0, 0, -6661520, -195853448, -165679084, 126898160, 0, -232348980, 0, 271888440, -170959104, 0, -410307160, 229541200, 0, 206211640, 0, 206351840, -69715144, 116258220, -628178780, 0, 0, 448033800, 0, -251727180, 0, 168565020, -272017208, -313768900, 0, 0, 0, -81639200, -44976768, -224510476, 0, -313024700, 0, -243159684, 0, 0, 140821200, -347153800, 279757680, 186431880, 0, -292474780, 0, 252130560, 57705344, 0, 532484880, 233470672, 0, 332621668, 0, 190355460], "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, 5, 3, -1, 4, 0], [1, 1, 8, 4, -1, 2, 0], [1, 1, 40, 11, 1, 4, 0]], "char_orbit_index": 11, "prim_orbit_index": 11, "minimal_twist": "40.6.k.a", "char_is_minimal": true, "conrey_index": 3, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}