# Stored data for newform 2740.1.bs.b, downloaded from the LMFDB on 25 May 2024.
{"Nk2": 2740, "analytic_conductor": 1.3674381346144266, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 2740, "char_degree": 32, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 45, "char_orbit_label": "bs", "char_order": 68, "char_parity": -1, "char_values": [2740, 68, [1371, 1097, 1921], [34, 34, 23]], "cm_discs": [-4], "conrey_index": 19, "dim": 32, "field_disc": 35190667333271321019306672876612934335729762304, "field_disc_factorization": [[2, 32], [17, 30]], "field_poly": [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], "field_poly_is_cyclotomic": true, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 68, "has_non_self_twist": 1, "hecke_cutters": [[13, [1, 16, 247, 2210, 13196, 55314, 166823, 364650, 573426, 633472, 469038, 213588, 51574, 6362, 797, -510, 256, 0, -128, 128, -64, 0, 32, -32, 16, 0, -8, 8, -4, 0, 2, -2, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4506623301126836, "hecke_ring_generator_nbound": 9, "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, 4, 2, -1, 2, -4], [1, 1, 685, 19, 1, 68, 0], [1, 1, 2740, 45, -1, 68, 0]], "is_cm": true, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": true, "is_twist_minimal": true, "label": "2740.1.bs.b", "level": 2740, "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": [2, 5, 137], "level_radical": 1370, "minimal_twist": "2740.1.bs.a", "nf_label": "32.0.35190667333271321019306672876612934335729762304.1", "prim_orbit_index": 45, "projective_field": [106151244410004309632881879123713314336538624, 309050737835326984404380783639706530444476416, 649858841350760913312996298293931530220732416, 955926178960153102865727337369359197675716608, 1130510496703613907338141741391259374823931904, 1086404674025447095607723599696614820348428288, 839907362387097683804412947615914165715075072, 520236249475102011361785347981488145265852416, 242903436231945951373347520157993742693826560, 77822624562946346736598959042644922626736128, 16514499510796248844663370164757333654110208, 2651598678262786931008334041461699114958848, -16133053153412948203522664130877435150336, -504621211058116765149068512962188851019776, -297326223611398635625427536622055279296512, -96874762372506238788482715190850972745728, -28503202422105324157871083869261357875200, -9362598884717065721178640712471486709760, -1966579349717454042486299269121362608128, 35804037620210827527301327334656618496, 97110583951656231170761790751796216832, 19120536701523323978529511709703473152, 8385577340742520863200565994601967616, 3873401349271344839953743880113550336, 773316654572683990867848417372718336, 99875646641359547840776578291888640, 61138672364955468121716675031338496, 32566435851466159821415099395189760, 9516090834837111517021741968649600, 2308806383261669656850131760689408, 596945971279885362414207873942528, 94972289877023952382689357559680, -2011833517493509468299743226080, -3949777943936859513322062414720, -1460669071044058918458632484480, -481607682454536648308003179472, -99473376906706756860154551180, -13635333958941189316999477272, -1613802793722461517500384880, 35133550346305915637192900, 91707705638515372473439137, 26797350173161638020280114, 6261297302399523909644774, 1330954948492453774375926, 242999805673467934508919, 41670286232225878301900, 6997343361702310468748, 1145918972482293622568, 183341390021947631777, 28253420429539775582, 4240737712898504474, 601839009660515810, 77964655975302503, 9433971771867632, 1055810311290232, 106625732799076, 9774611456747, 829024039438, 71002987066, 5806137146, 478936237, 42973468, 3562924, 264432, 9523, 802, 6, -2, 1], "projective_image": "D68", "projective_image_type": "Dn", "qexp_display": "q-\\zeta_{68}^{20}q^{2}-\\zeta_{68}^{6}q^{4}+\\zeta_{68}^{2}q^{5}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "self_twist_discs": [-4], "self_twist_type": 1, "space_label": "2740.1.bs", "trace_display": [2, 0, 2, 0], "trace_hash": 1898781845831300662, "trace_moments": [{"__RealLiteral__": 0, "data": "0.076", "prec": 17}, {"__RealLiteral__": 0, "data": "30.541", "prec": 20}, {"__RealLiteral__": 0, "data": "96.163", "prec": 20}, {"__RealLiteral__": 0, "data": "29373.588", "prec": 30}, {"__RealLiteral__": 0, "data": "100473.432", "prec": 34}, {"__RealLiteral__": 0, "data": "30234321.494", "prec": 40}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.674", "prec": 17}, "traces": [0, 32, 2, 0, -2, 2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, -32, -2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, -34, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 32, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, -2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, -32, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 32, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 2, 2, 0, 0, -4, 0, 0, 2, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 34, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 32, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 32, 0, 32, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, -30, 0, 0, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 34, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34, 0, 0, -2, 0, -2, 0, -2, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 2, 30, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, -34, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -32, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 2, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 34, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, -30, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, -2, 0, 0, 32, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, -34, -2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 32, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2, 0, 0, -2, 2, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 2, 0, -2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 34, 2, 0, 0, 0, -4, 0, 0, 0, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -4, -2, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 34, 0, 0, -2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, -32, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2], "weight": 1, "weight_parity": -1, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "sato_tate_group": null, "atkin_lehner_eigenvals": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[], [[1, 0]], [[-1, 20]], [], [[-1, 6]], [[1, 2]], [], [], [[1, 26]], [[-1, 21]], [[-1, 22]], [], [], [[1, 5], [1, 10]], [], [], [[1, 12]], [[-1, 17], [1, 33]], [[-1, 7]], [], [[-1, 8]], [], [], [], [], [[1, 4]], [[-1, 25], [-1, 30]], [], [], [[1, 13], [-1, 28]], [], [], [[-1, 32]], [], [[-1, 3], [1, 19]], [], [[1, 27]], [[-1, 3], [1, 31]], [], [], [[1, 28]], [[-1, 24], [-1, 27]], [], [], [], [[-1, 23]], [], [], [], [[1, 32]], [[-1, 24]], [], [[-1, 11], [-1, 16]], [[-1, 15], [1, 16]], [], [], [], [], [[-1, 14], [-1, 33]], [], [], [[1, 1], [1, 25]], [], [], [[-1, 18]], [[1, 7], [1, 12]], [], [], [[1, 5], [1, 23]], [], [], [], [[1, 13]], [[-1, 14], [1, 22]], [[1, 17], [1, 23]], [], [], [], [], [], [[1, 14]], [[-1, 8]], [[-1, 10], [-1, 13]], [], [], [[-1, 1], [-1, 19]], [], [], [], [[-1, 16], [-1, 29]], [[-1, 9]], [], [], [], [], [], [], [[1, 6], [-1, 23]], [[1, 18]], [], [[-1, 10]]]}