# Stored data for newform 7.15.b.a, downloaded from the LMFDB on 06 May 2024.
{"label": "7.15.b.a", "space_label": "7.15.b", "level": 7, "weight": 15, "hecke_orbit": 1, "hecke_orbit_code": 68971134983, "dim": 1, "is_polredabs": true, "nf_label": "1.1.1.1", "trace_hash": 2273795105243140432, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [87, 1]]], "qexp_display": "q-87q^{2}-8815q^{4}-7^{7}q^{7}+2192313q^{8}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 7, "char_orbit_label": "b", "char_is_real": true, "Nk2": 1575, "analytic_conductor": 8.703027770633419, "hecke_ring_index": 1, "level_radical": 7, "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": 1, "is_self_dual": true, "is_self_twist": true, "is_cm": true, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.505", "prec": 17}, "analytic_rank_proved": true, "char_values": [7, 2, [3], [1]], "hecke_ring_generator_nbound": 1, "inner_twist_count": 2, "level_primes": [7], "conrey_indexes": [6], "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.973", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "2.884", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.532", "prec": 17}], "related_objects": [], "self_twist_discs": [-7], "cm_discs": [-7], "rm_discs": [], "relative_dim": 1, "sato_tate_group": "14.2.1.d2", "trace_display": [-87, 0, 0, -823543], "traces": [0, 1, -87, 0, -8815, 0, 0, -823543, 2192313, 4782969, 0, 36437514, 0, 0, 71648241, 0, -46306271, 0, -416118303, 0, 0, 0, -3170063718, -2188914318, 0, 6103515625, 0, 0, 7259531545, 29824366266, 0, 0, -31890210615, 0, 0, 0, -42161871735, -112367216342, 0, 0, 0, 0, 0, 484972531402, -321196685910, 0, 190435545666, 0, 0, 678223072849, -531005859375, 0, 0, 907194972426, 0, 0, -1805464024959, 0, -2594719865142, 0, 0, 0, 0, -3938980639167, 3533130267569, 0, 0, 11528240589818, 0, 0, 0, -4338861915246, 10485765117297, 0, 9775947821754, 0, 0, -30007859592102, 0, -37193960502814, 0, 22876792454961, 0, 0, 0, 0, -42192610231974, 0, 79882435629882, 0, 0, 0, 19295279713170, 0, 0, 0, 0, 0, -59005407337863, 174279499899066, -53802490234375, 0, 0, 0, 0, 0, -78925962601062, -284939730575286, 0, 146695473474586, 0, 0, 38135205338153, -117245990452638, 0, 0, -262901788634790, 0, 0, 0, 0, 947942592916955, 0, 0, 0, 0, 342691315607529, -58713088218622, 215106877437657, 0, 0, 0, 0, 0, -1002956931314166, 0, 0, -1801859786402766, 0, 0, 0, 0, 377480986626402, 0, -221481458698599, 0, 0, 0, 990517012054730, 3260813988662346, 0, -3560728212669326, 0, 0, 2610683784512874, 0, 0, 0, 3235874563744818, 0, 0, 1802665064188674, -1990280943581607, -6111094245934534, 0, 0, 0, 0, 0, 3937376385699289, 0, 0, -4275032864308630, 0, 0, -5026507568359375, -1687285397850294, 0, 0, 5952149230451418, 0, 0, 0, 0, -4798785315237534, 0, 0, 0, 0, 0, 0, 10495941696602562, 0, 18036094842549442, 0, 0, -5978536387163935, 14826506976087018, -15162316491218742, 0, 13380816650390625, 0, 0, -24561648067800438, 0, 0, 0, -10469509326650142, 0, 0, 0, -35327366222637158, -7996923681935190, 0, 24789756560049882, 0, 0, 0, -12762506192288982, 0, 0, 0, 0, 0, 26262959720508945, 29192926025390625, 10200401169379506, 0, 0, 0, 0, 0, 65384345881713258, -19920798226367118, 0, 0, 0, 0, 0, -21122967173018142, 0, 0, -82471005583775085, 0, 0, 0, 0, 0, 0, 0, 0, 0, 34722114334257105, -79758596106925452, 5108038675020114, 0, -76601104640926655, 0, 0, 92539234447939706, 0, 142649019294923754, 0, -115232187713719278, 0, 0, 0, 0, -101621440799245670, 0, 0, 0, 0, 0, 156761801417040642, 222396936035156250, 0, 106711340337333194, 0, 0, 0, -273934124620836846, 0, 0, 38247067782893490, 0, 0, 0, -152529888775015935, 168377826559400929, 0, 0, 0, 0, 0, 0, -246344109160379046, 0, -283690817013624102, 0, 0, -399395733428397286, 309783354502231362, 0, 0, 0, 0, 0, 264519282304379130, 0, 0, 0, 0, 0, 0, 0, 327864761832305410, -301503090685328262, 0, 1086725763358502724, 0, 0, -156831860584414638, 0, -201658925490481215, 0, 531665199396304458, 0, 0, 0, 0, -396135563896703606, 0, -537448912380079398, 0, 0, 0, -671550380453155166, -342551745555838143, 0, 0, 0, 0, -558545864083284007, 1063211585235512826, 0, 0, -78421954027845462, 0, 0, 437306158447265625, 0, -1161999995747011110, 0, 0, 0, 0, 0, -517836983049273366, 1516532438242606866, 0, 799006685782884121, 0, 0, 0, 0, 0, 0, 101360459605088178, 0, 0, -747114069176625318, 0, 1182938216005388042, 0, 0, 0, 0, 0, 719866312141328746, 0, 0, -913146927604422894, 0, 0, 0, -1569140251301801454, 2319608583547292538, 0, -2127872942102924694, 0, 0, 1486877259506809737, 0, -1289906106919570566, 0, -1536273791610266790, 0, 0, 0, -282631048583984375, 194922054995264034, 0, 0, 0, 0, 2136863381898638106, -4094382018602653788, 0, 0, 0, 0, 0, 0, 910847311418562354, 0, 0, 0, 0, 0, 0, 4611050309294145194, 3073480861369432746, 0, 1988855331584161338, 0, 0, 0, 2511743725021146090, 0, 0, -5357278524325976478, 0, 0, 0, 0, -1293120598678475590, 0, 0, 0, 0, 3243919932521508681, 0, -5338644130249256214, 0, 0, 0, 0, -2909684699944576967, -5808418746812210814, -2539784564208984375, 0, 1033523405840003970, 0, 0, 0, 0, 3245318796640436338, 0, 0, 0, 0, 0, 4974675421369776866, -1381055186716654086, 0, 1733109445693939266, 0, 0, -9494001840060485174, 0, 0, 0, 17671193402575814628, 0, 0, 0, 4339085430069412794, 1837698144052578354, 0, 0, 0, 0, 0, -8356113956562958325, 0, 0, 2517352146610178578, 0, 0, 0, -1439575868938499766, 0, 0, 0, 0, 0, 3573239358267436578, 0, -13121120082620667302, 0, 0, 0, 0, -8635478461994123271, 0, 6938997861302514324, 0, 517555872647152930, 0, 0, 0, 3139985023822046697, 0, 0, 0, 0, 0, -8050913396970754422, 0, 0, 0, -12410464678658366598, 0, 0, 0, 10025200331093577186, 0, 0, -6801490432993344685, 0, 0, 0, 0, 0, 0, 25273511712185669034, 0, 0, 24712762712058457386, 0, -12505695810333641926, 0, 0, 0, 0, 0, 3947265523897373498, 15883394017140382290, 0, -19348533435058593750, 0, 0, 30630825814368950002, -9283886609347987878, 0, 0, -33257440859585714022, 0, 0, 0, 0, 23832268842012805602, 0, 0, 0, 0, -18840022288735946823, -9512143381998703998, -35156030403706810734, 0, -15328089473791979926, 0, 0, 0, -13360072741699218750, 16898852542744232361, 0, -14648870910667880823, 0, 0, 0, 0, 33055929508501988964, 0, 0, 0, 0, 0, 0, 0, 0, 5203306771448280682, 0, 0, 0, -28744075310058579990, 0, 0, 47162119731508975026, 0, 0, 34747428808270563882, 55139217365641209642, 31387819194680108690, 0, 0, 0, 0, 0, 0, 0, 0, -61759989321450453718, 0, 0, -65786620685939911926, -9697455725184580302, 0, 0, 0, 0, 0, 0, 0, 37252902984619140625, 0, 0, 0, 0, 0, 13846192223014659314, -81540803131805668782, 0, 26230768889623558794, 0, 0, 0, -94545141412189736988, -20752642035902245374, 0, 86256072187199900994, 0, 0, -15890492540823161310, 0, 0, 0, 50153089497312914793, 0, 0, 0, 53869295777912917210, -98783677649653620774, 0, 0, 0, 0, 0, 29278601507175987738, 0, 0, 34463794059013213722, 0, 0, 0, 46758055377066907626, -65282982344923596588, 0, 0, 0, 0, 0, 87727524901301319106, 58424883099424499442, 0, -34707972839939232535, 0, 0, 0, 0, 0, 0, 20865911833250397642, 0, 0, 48593490175245708609, 0, -22457269466657021942, 0, 0, 0, 0, -143526662185376510838, 6822710000422555194, 0, 0, 0, 0, 0, 44308664215087890625, -143631518158477147398, 0, 0, 128738483588369183466, 0, 0, 0, 0, 1783684075054002538, 0, -177897560072183774766, 0, 0, 0, 0, -52468195466429249670, 0, -131938322127106797342, 0, 0, 0, -69513581663110918527, 0, 0, 182033485510253906250, 0, 0, 0, 109418989131512359209, 0, 0, 0, 0, 0, 0, 69804938619209085570, 420060427886861632452, 0, -128749298387207675974, 0, 0, 64998924018366402666, -128009618911243640814, 0, 0, -102915624792468759654, 0, 0, 234660120537162758298, 0, 193550281284085791202, 0, 0, 0, 0, 0, -258708745482249032822, -62628369156295600902, 0, 0, 0, 0, -120810030311680978198, -92521726055551584030, 0, 0, 0, 0, 0, 0, 0, -158988176037073331230, 0, -201805946768614450806, 0, 0, 0, 185124945962954448378, 0, 0, -158097341780842938444, 0, 0, -31405981409798536079, 0, 0, 0, -130695658994207063670, 0, 0, 96557114715336856434, 382075213262221079658, 0, 0, 0, 0, 0, 0, 0, -194642398773193359375, 0, -16958218784587970958, 0, 0, 0, 0, 0, 0, 310593287622183266226, 0, 0, 216510927717660860970, 0, 356211235618430879556, 0, 0, 0, 0, 0, 0, -362073309528936108918, 0, 212761166050006254962, 0, 0, 0, -493048180337573749782, 92288724714421001730, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 591934590492719319275, -401161376908590631878, 0, 311410733252546547770, 0, 0, -780671486798607871565, -42008816242995883446, 0, 0, 245962208724807384756, 0, 0, 0, 0, -624677075556696976518, 0, 0, 0, 0, 0, 466083231616359953586, 238729884516024874242, 0, 0, 0, 0, 0, -1355255456536732164396, 0, 0, 321602393539490057418, 0, 0, 0, 0, -52978605722981788006, 0, 0, 0, 0, -282221034129371255247, 800849508791385887962, 0, 0, 464462039331685290618, 0, 0, 48352752810828617746, 0, 833573445352735806954, 0, 0, 0, 0, -177149763165640358751, 0, 505332430972662340818, 0, -257335642913818359375, 0, 0, 0, -257039909067194171694, 0, 0, 336122735206875919114, 0, 0, 0, 851259939424123439394, 0, 0, -282342735307717961406, 0, 0, 0, 0, -1079681478109663231694, 0, 0, 0, 0, 0, -685835060681152343750, -432796761659170587342, 0, -951105321681641113590, 0, 0, 0, 175601836365426145170, 0, 0, 0, 0, 0, 825978160085262210138, 0, 0, 0, 0, 0, 0, 0, -1537393826024095872636, 107633554858930282074, 0, 0, 0, 0, 0, 264624196995864840402, -377500432416038913078, 0, 186198955630154921730, 0, 0, 1483909014073493119938, 0, 756943935220796320321, 0, -1362857898209945104134, 0, 0, 0, 1482257413579708569554, 2078186869705548366915, 0, 0, 0, 0, 0, -219009636755085536286, 0, 0, -932746191026703165342, 0, 0, 0, 701639902069267125834, 125243100597649479642, 0, 0, 0, 0, 0, 0, -1061563317822542413836, 0, -1297171500902229618686, 0, 0, -310871824169266982286, 0, 0, 0, 1141537447187998055274, 0, 0], "weight_parity": -1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, -7]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "7.15.b.a", "char_is_minimal": true, "conrey_index": 6, "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], [1], [-87], [0], [-8815], [0], [0], [-823543], [2192313], [4782969], [0], [36437514], [0], [0], [71648241], [0], [-46306271], [0], [-416118303], [0], [0], [0], [-3170063718], [-2188914318], [0], [6103515625], [0], [0], [7259531545], [29824366266], [0], [0], [-31890210615], [0], [0], [0], [-42161871735], [-112367216342], [0], [0], [0], [0], [0], [484972531402], [-321196685910], [0], [190435545666], [0], [0], [678223072849], [-531005859375], [0], [0], [907194972426], [0], [0], [-1805464024959], [0], [-2594719865142], [0], [0], [0], [0], [-3938980639167], [3533130267569], [0], [0], [11528240589818], [0], [0], [0], [-4338861915246], [10485765117297], [0], [9775947821754], [0], [0], [-30007859592102], [0], [-37193960502814], [0], [22876792454961], [0], [0], [0], [0], [-42192610231974], [0], [79882435629882], [0], [0], [0], [19295279713170], [0], [0], [0], [0], [0], [-59005407337863], [174279499899066], [-53802490234375]]}