# Stored data for newform 820.2.j.c, downloaded from the LMFDB on 21 September 2025.
{"Nk2": 3280, "analytic_conductor": 6.547732965744991, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 820, "char_degree": 2, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 10, "char_orbit_label": "j", "char_order": 4, "char_parity": 1, "char_values": [820, 4, [411, 657, 621], [2, 3, 1]], "cm_discs": [], "conrey_index": 483, "dim": 240, "has_non_self_twist": 1, "hecke_cutters": [[3, [4009174312681472, 0, 2038116419490021376, 0, 322324592457911959552, 0, 24243719749768664317952, 0, 1036856408375854846427136, 0, 27895507628633618078990336, 0, 506753311886600842649473024, 0, 6558594976665834151092338688, 0, 63084712008940411888632737792, 0, 466450947778939377964769394688, 0, 2724662698899919571361770771456, 0, 12856733199274892652008330573824, 0, 49918008869799073896285237388288, 0, 161942817203060455475681309497344, 0, 444687750015853610821433930254336, 0, 1044952992233260159809997350221824, 0, 2121053368730030350199265362599680, 0, 3748987799872932607634267877861888, 0, 5810377926653242590718921763469056, 0, 7944120129790929606429849658868736, 0, 9632204058584429078206405420166912, 0, 10405071886367255451591349761462272, 0, 10054463484046976053704858194028736, 0, 8721845516440369326342355996192640, 0, 6813148836396414544205156773682560, 0, 4805809821373884306652268245081984, 0, 3068361489940984840346239649158784, 0, 1776958093977991231395426203827072, 0, 935120253106633351286606122450320, 0, 447873460816172635193852713692896, 0, 195485944089870680964722901053968, 0, 77844082775071509806524462599872, 0, 28305464350282466274699281107120, 0, 9404692608901380198130064119808, 0, 2856640888522482130535658626656, 0, 793456314791305941012387901312, 0, 201547808261222591215636977912, 0, 46812499751864547284592846936, 0, 9938513486524211986661036584, 0, 1927547542246508728763012096, 0, 341236333087442784270943932, 0, 55080720220035876716050776, 0, 8095423015063320642410032, 0, 1081522617715466767584152, 0, 131065643798609505601049, 0, 14372004067354279109464, 0, 1421758086428296388336, 0, 126434708444219069032, 0, 10064401187242767740, 0, 713457116392438968, 0, 44763057062905152, 0, 2466980532741464, 0, 118318963206630, 0, 4880807675344, 0, 170579892728, 0, 4950926968, 0, 116091792, 0, 2112528, 0, 27984, 0, 240, 0, 1]], [13, [3159021950599168000, -411759697221019238400, 10776532289059728916480, -16362586165041654923264, -492849182026957191118848, 1803881133865810719932416, 3380032092353485572145152, -22842457848281506974793728, 11190204729392434832146432, 84745052003517040517971968, -101532684853103457389641728, -145682258448507713159757824, 270591861748160987751350272, 123392905965360927670272000, -397512670336443736762777600, -25604319076146331591294976, 377736255851900323884032000, -55167522443257656952430592, -250935737109710133729374208, 70077630229484759770263552, 122223884768656070246825984, -45651464913713424883990528, -45123340024521435579108352, 20108481351689584276491264, 12950384005910065885858816, -6520203827147165394741248, -2949230523013620688615808, 1622440836099535458222848, 542293450499220423958400, -317608909482070919449664, -81735505946415153670656, 49714632908727949191488, 10229452288294804192592, -6290252446697177058112, -1074144063436299535568, 647889165675615219520, 95301257336839997568, -54538578414481931184, -7165302370211164696, 3756864770914380200, 455824026163971804, -211488671150742476, -24392399492119862, 9690056679731496, 1087578035730553, -358775055378124, -39889053371176, 10615751425524, 1184148952306, -246924768436, -27871223314, 4406222252, 505953635, -58105752, -6807980, 532548, 63754, -3024, -370, 8, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007817763586868, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 4, 2, -1, 2, 0], [1, 1, 205, 9, -1, 4, 0], [1, 1, 820, 10, 1, 4, 0]], "is_cm": false, "is_largest": true, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "820.2.j.c", "level": 820, "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, 41], "level_radical": 410, "minimal_twist": "820.2.j.c", "prim_orbit_index": 10, "related_objects": [], "relative_dim": 120, "rm_discs": [], "sato_tate_group": "1.2.3.c4", "self_twist_discs": [], "self_twist_type": 0, "space_label": "820.2.j", "trace_display": [0, 0, 0, 0], "traces": [240, 0, 0, 0, 0, -4, 0, 12, -240, -20, 0, 0, -32, -8, 0, 8, 32, -12, 0, 16, 0, -28, 0, 12, -16, 0, 0, -8, 0, -10, 0, 0, 24, -20, 0, 0, -8, 16, 0, -4, -16, 84, 0, 0, -80, 0, 0, 8, 224, -12, 0, 0, -32, 48, 0, 24, -8, 0, 0, 6, 0, 0, 0, 0, -8, -8, 0, 0, 16, 10, 0, -96, -72, 112, 0, 20, -56, 4, 0, 60, 48, -56, 0, -32, -32, -8, 0, 0, -64, 76, 0, 20, -16, 48, 0, 24, -48, -12, 0, -32, -16, 28, 0, -36, 32, 4, 0, 0, -32, 94, 0, 0, -8, 104, 0, -16, -96, 64, 0, -6, 0, -76, 0, 0, 48, -4, 0, -84, 64, 0, 0, -108, -40, -80, 0, 16, 32, 0, 0, -94, -32, 64, 0, -8, -40, 80, 0, 76, -48, 68, 0, 0, -96, 0, 0, 0, 0, 0, 0, -4, -80, 136, 0, 44, -136, 0, 0, 28, 96, -76, 0, 72, 32, 0, 0, 64, 0, 0, 0, 44, 32, -12, 0, -40, 32, 128, 0, 0, 0, -42, 0, 0, -96, -60, 0, 0, 0, 196, 0, 44, -16, 0, 0, 0, -16, -280, 0, -40, 0, -16, 0, 0, -8, 160, 0, -100, 0, -276, 0, -82, 96, -328, 0, 40, 160, 0, 0, 76, 16, 80, 0, -124, 32, -112, 0, 120, -120, -172, 0, 154, 0, -204, 0, -40, 16, 36, 0, -64, 32, 36, 0, -228, 160, -80, 0, -200, 0, -252, 0, 56, -128, -20, 0, 0, 80, 0, 0, 0, 0, 104, 0, -160, 0, -84, 0, 56, 120, -88, 0, 118, 64, 136, 0, 4, 56, 72, 0, -40, 48, -124, 0, -40, 0, 80, 0, 0, -80, 276, 0, -188, -32, 28, 0, -36, 32, -156, 0, 60, 16, 100, 0, -12, 0, -12, 0, -104, 0, 56, 0, -248, 48, 44, 0, 0, -80, 0, 0, -124, 0, -8, 0, 80, -8, 40, 0, 0, 216, 312, 0, -328, 80, -40, 0, 0, 40, -96, 0, 140, 144, 52, 0, 148, 104, 224, 0, 120, 0, 332, 0, 92, 0, 0, 0, -88, -32, -48, 0, -28, 128, 32, 0, 0, 256, -224, 0, -124, -144, -264, 0, 346, 0, 0, 0, 124, -8, 304, 0, 0, 0, -120, 0, 140, 0, 0, 0, -80, 0, 168, 0, -88, 0, -124, 0, 32, 176, 152, 0, 24, 0, -80, 0, -12, -112, 0, 0, 28, 0, 76, 0, 556, -96, 0, 0, 120, -8, -64, 0, 144, -48, -180, 0, 520, 48, 20, 0, -12, -160, 76, 0, 178, 128, -128, 0, 204, -88, 0, 0, 28, -80, -96, 0, -388, -8, -112, 0, 0, 208, -312, 0, 264, -32, 0, 0, -124, 16, -28, 0, 0, 0, 34, 0, -88, 0, 0, 0, 80, 224, 0, 0, 242, 32, 388, 0, -408, -256, -104, 0, -96, 176, -260, 0, 316, 240, -192, 0, 112, 136, 0, 0, -444, 0, -88, 0, -228, 40, -24, 0, 132, 48, 264, 0, -240, 176, 124, 0, -60, -8, 0, 0, -80, -64, 0, 0, 40, 0, -56, 0, 24, 0, -4, 0, 60, -160, 0, 0, -76, -8, 124, 0, -32, 0, 196, 0, 292, -72, 164, 0, 0, 0, 304, 0, -576, -56, 240, 0, -496, -240, -340, 0, -114, 128, 0, 0, 0, -32, 0, 0, 0, -320, -124, 0, -388, -248, -312, 0, 0, 0, -36, 0, 312, -144, -332, 0, 0, -304, -300, 0, 0, 32, 76, 0, -68, 0, 376, 0, -200, -8, 0, 0, 520, -144, 0, 0, 124, -56, 0, 0, -404, -176, -264, 0, 0, 104, 0, 0, 440, 192, 244, 0, 36, -64, 0, 0, -232, -400, 76, 0, 448, -176, 254, 0, 920, -8, -100, 0, 0, -240, -280, 0, -344, 160, 96, 0, 92, -432, -440, 0, 612, 64, -176, 0, 192, -96, 48, 0, -76, 200, 32, 0, -332, 0, 236, 0, 136, -184, 104, 0, 416, 64, 114, 0, -12, 0, 0, 0, 0, 152, 0, 0, -16, -16, 112, 0, 72, -184, -220, 0, 172, -480, -96, 0, -140, -120, 88, 0, -112, -224, -4, 0, 156, -16, 52, 0, -120, 128, 0, 0, -920, 64, 202, 0, -8, 176, -212, 0, 184, 344, 28, 0, -448, -32, 132, 0, 12, 264, 200, 0, -120, 144, 204, 0, 132, -160, 0, 0, 0, 376, 288, 0, -4, 336, -24, 0, 32, -136, 0, 0, -608, -48, 622, 0, 284, 0, 0, 0, 176, 528, -232, 0, -342, -16, -108, 0, -180, 344, -144, 0, -744, 0, 172, 0, 0, 0, 48, 0, -52, 128, -20, 0, 164, 0, 0, 0, -8, -88, 248, 0, 424, 0, -450, 0, 0, 0, -288, 0, -356, -16, 0, 0, 180, -336, -364, 0, 0, -296, 144, 0, -220, 416, 4, 0, 256, -160, -24, 0, -40, 0, 76, 0, -60, 48, -48, 0, 0, -136, -356, 0, -152, -288, -504, 0, 0, -80, -244, 0, 144, -192, -144, 0, 416, 0, -260, 0, -196, 112, -292, 0, 244, 336, -24, 0, 220, -96, -424, 0, 0, 184, -36, 0, -140, -128, 484, 0, 224, 488, 0, 0, 476, 32, -472, 0, 0, -64, 308, 0, -204, -128, 0, 0, 234, 0, 300, 0, 0, -72, -8, 0, 0, -224, -284, 0, -408, 312, 704, 0, 116, 272, 292, 0, 560, 400, -300, 0, 120, 120, 40, 0, 0, -272, 340, 0, 36, -144, 380, 0, -184, -80, -260, 0, -296, 240, 272, 0, -84, 184, 196, 0, 0, 240, 232, 0, 0, -8, 224, 0, 336, -240, -64, 0, 66, 0, -144, 0, 0, -96, 172, 0, -336, -400, -60, 0, -472, 136, -760, 0, -44, -144, 0, 0, -822, -80, 568, 0, 224, 64, 824, 0, 376, -272, 156, 0, 0, 80, 0, 0, 0, 0, 0, 0, -20, -80, 428, 0, 460, 328, 0, 0, 364, 32, -714, 0, 640, -88, 0, 0, 300, 0, 0, 0, -296], "weight": 2, "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}