# Stored data for newform 510.2.z.c, downloaded from the LMFDB on 13 November 2024. {"Nk2": 2040, "analytic_conductor": 4.0723705030853, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 255, "char_degree": 4, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 26, "char_orbit_label": "z", "char_order": 8, "char_parity": 1, "char_values": [510, 8, [341, 307, 241], [4, 6, 7]], "cm_discs": [], "conrey_index": 53, "dim": 68, "has_non_self_twist": 1, "hecke_cutters": [[7, [903201718586703872, -9433346431830458368, 96984558578139529216, -451859852305877434368, 2033808248956696199168, -3747591807043660939264, 8277520785193833463808, 530833743230561419264, 11031020605353714810880, -14134406283448211406848, -26215842091840238682112, -46533802233335921180672, 285302297210048630505472, -466360919290434573238272, 542064501005960110702592, -555051343899784053194752, 483215928032538820362240, -302693198121433241747456, 81047556632550305546240, 46370595466533717671936, -41261119472419128139776, 2077813869448911355904, 10660052251100277334016, -5982379870275201646592, 1883067205451469830144, -1411359190574597328896, 822140472917999699968, 377615007605288488960, -385555588223120868352, -485314394840125440, 89400243268176754688, -30652643854800183296, -6482515843563373568, 4566230674190962688, 2812023278408752128, -50639635258894336, -613441004473246208, -27212468825438208, 97518850840164864, -21150217866694656, -8610602362486400, 4866403094460160, 3063916769931392, -54389413741824, -541962341990208, -111795155755264, 52662976793472, 16865193023744, -148702218560, -1256483039232, -166282258880, 51480304384, 5874455648, -3122349440, 1084808736, 283685440, 6548520, -27576816, -4273960, 1135664, 267636, -15152, 2952, 704, 18, -92, -14, 4, 1]], [11, [163799766245580946276352, -10594220592301645246758912, 269880870869189873413128192, -3297395270617606472203239424, 23225982017833635124290256896, -105828030694781115292132048896, 345700514130894978426580500480, -872984044370376195690293362688, 1799219235981873189499141357568, -3148621186027945816898123333632, 4800494254752892790001618649088, -6439369570991088658866344296448, 7588102423198303026593923072000, -7845695848567954970946694021120, 7167611798281030345478079774720, -5855267032529868897604448813056, 4310467509083904754488256233472, -2860952031123819799413916696576, 1709961728093445044265688236032, -921726825552718877626101399552, 448401650703546836455887208448, -195869923484090543751863205888, 76111386234175759023111405568, -26129748230952140221620682752, 7954091040240865494145990656, -2201384400171959984818290688, 591227666543578847727157248, -175702175711210127535243264, 65706595849098752076955648, -28243752745393221071568896, 11396169553457612399525888, -3923774902860097594015744, 1135657145983244744962048, -276967298979009639399424, 58068690145023701295104, -10991768518521351901184, 2499810967636520695808, -994266429069619472384, 438598436163285228544, -156084745894354713600, 44416883160832985216, -9670916027477072640, 1836131560141372032, -261105156278861568, 33287673465624640, -7945192450715136, 4140229140546560, -1577662438341120, 481138021701216, -84698044064576, 17478066943584, -1567116072128, 305746394032, -16083869568, 14146531520, -5475465664, 1705866520, -272896400, 54846904, -3620752, 1083660, -6944, 16672, -5504, 1650, -284, 50, -4, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9008917275214334, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 255, 22, 1, 8, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "510.2.z.c", "level": 510, "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": true, "level_primes": [2, 3, 5, 17], "level_radical": 510, "minimal_twist": "510.2.w.c", "prim_orbit_index": 22, "related_objects": [], "relative_dim": 17, "rm_discs": [], "sato_tate_group": "1.2.3.c8", "self_twist_discs": [], "self_twist_type": 0, "space_label": "510.2.z", "trace_display": [0, -4, -8, -4], "traces": [68, 0, -4, -68, -8, 4, -4, 0, 0, 0, 4, 4, -4, -8, 20, 68, 8, 4, -4, 8, -32, 8, 4, -4, -8, 4, -4, 4, -16, 16, 8, 0, 12, -12, 36, 0, 4, 4, 0, 0, -44, -12, 24, -4, 56, 8, 12, -4, 44, 20, -60, 4, -16, -4, 32, 8, 16, -4, -20, -20, -24, -4, -32, -68, -16, -24, 4, -8, 104, -8, -24, -4, -64, 24, -4, 4, 24, 0, 8, -8, -92, -32, 24, 32, -16, 0, -36, -8, 0, 24, -100, -4, -60, -12, 0, 4, -8, -44, 0, 8, 0, -4, 20, -4, -28, 0, 8, 4, 24, 20, 92, -4, 64, 40, 84, 16, -4, 20, -96, -16, -84, -20, 36, -8, -56, 44, 0, 0, 32, -16, 28, -12, -76, -4, -48, 12, 132, 4, 20, -36, -40, 28, 68, 0, 48, -60, 52, -4, 0, 84, 4, -4, -68, 0, -56, 0, 28, 4, -136, 0, -84, -16, -32, 44, 20, 0, 12, 12, 0, 24, 92, -24, 52, 40, 80, 4, 64, -16, -44, -56, 40, -36, -8, -8, -112, -24, -48, -12, -84, -8, 144, 4, -24, 52, 12, -44, 52, -84, -24, -20, -96, -32, -36, 60, 64, 20, 8, -4, 84, 80, -36, 16, -52, -12, -24, 4, -60, 20, -232, -32, 60, -24, 0, -8, 84, -12, -128, -16, -68, 64, 292, 4, 40, 52, 64, 20, 56, 44, -192, 20, 116, -84, 156, 24, -12, 48, 0, 4, -96, -48, 64, 32, 0, 16, -32, 68, 0, -16, -24, 16, 84, 40, 0, 24, -72, -108, 184, -4, -48, 28, 80, 8, -12, 132, 104, -104, 68, 16, -244, 8, -52, -48, 112, 24, 92, 4, 0, 4, -4, 108, 24, 64, -92, -16, -24, -24, -80, 32, 60, 4, 136, 4, 32, -4, 4, -64, 28, -24, -8, -4, 56, 0, -40, 28, -136, -8, 12, -8, -48, 8, -16, -84, -92, 92, -124, -44, 16, 32, 300, -24, -20, -24, -200, -24, 48, -32, -48, -36, 28, 16, 0, -44, -68, 0, -76, 24, -8, 36, -84, 20, 200, 8, -148, 112, -16, 0, -124, 44, -4, -24, 0, -36, 16, 100, 12, 156, 44, 4, 120, -12, 136, 60, 20, -76, -144, 12, 4, 0, -28, 0, 160, 0, 0, -4, -92, 12, 144, 8, 132, -84, -136, 44, -56, 24, -164, 0, 124, -28, 108, -8, -180, -72, 212, 0, 0, 36, 28, 4, 0, 100, -128, -20, -124, -140, -24, 4, -112, -12, 140, 28, 0, 24, 44, 0, 20, -64, 240, -8, 44, -32, -160, -4, 160, -60, -24, -24, -28, 44, -112, -20, -340, -196, -20, -92, 8, 128, -64, 4, 172, -136, -332, -64, -304, -60, -132, -40, 0, -68, 276, -84, -4, -68, 52, -16, 232, -148, -72, 4, -28, 0, -64, -20, 32, -68, -20, 96, -248, 0, 80, 16, -36, 48, 40, 84, 116, 164, -20, 20, 252, 32, -4, -36, 284, -136, 148, 8, -140, 88, 36, 56, -60, 0, 156, -44, 0, 96, 100, 0, -136, -100, -288, 0, 160, 152, -32, -32, -84, 0, 140, 16, -364, 8, 220, -28, 228, 64, 268, 12, 116, 104, -396, 76, 36, -216, -148, 4, -64, 76, 168, 48, 96, 0, 16, -12, 276, -4, 72, -132, 132, 4, -316, -4, -144, -40, 84, -20, 68, -64, 48, 36, -80, -52, 152, 40, -200, -28, 4, -28, 76, -124, -172, -68, -224, -112, -208, 0, -124, -144, 444, -48, 72, -20, -200, 60, -8, -92, -40, -52, 4, -24, -200, 4, 16, 60, -48, 0, -356, -52, 0, -84, -12, 64, -44, -4, -64, 296, -236, 4, 200, 8, 0, 68, 36, -28, -76, 0, -32, 72, 116, 56, 284, 44, 376, 0, 100, 28, 100, -28, -328, -36, 20, -4, 180, -128, -408, 136, 0, 0, 244, 0, 44, -52, 168, 84, -216, -28, 68, 16, 220, 36, -32, 32, 60, -60, -92, -44, 228, 100, 0, -20, 20, 20, -24, 0, -92, -52, 84, -12, -464, 32, 52, -12, 152, 76, 52, 0, 84, -8, 0, -24, 60, -56, 56, -92, 224, 132, 80, 24, -240, -112, 76, -52, -64, -84, -220, -40, 64, -84, -136, -80, 808, -88, -268, -4, -28, -148, -120, -64, -192, -92, -212, 16, -44, 40, 116, 44, -96, -4, 32, 56, 164, 20, 0, -40, 76, 116, -292, 36, -264, 64, 328, 8, 0, -8, 188, 8, -372, 172, -28, 112, 456, 168, 180, 24, 288, 20, 128, 48, -720, 12, 136, 12, 432, 188, 16, 84, 0, 240, -172, 8, 296, 120, 0, -144, 112, 32, 0, -4, -152, -92, -112, 24, 0, 136, -132, -52, 364, 132, -4, -12, 368, 12, 128, 44, 280, -228, 48, -52, -384, 272, -284, 84, 188, -104, 48, 24, 0, 148, -28, 20, 56, 232, -124, 96, 128, -228, 156, 32, -28, -16, 100, 36, 80, 28, 224, -60, 136, 32, -252, -64, 328, 128, -188, -20, -352, -92, -24, -8, -200, -296, -12, 4, -308, 236, -240, -84, 112, -136, 240, -80, 36, 96, -336, 36, -224, -108, -312, -16, 172, -8, 0, 52, -364, 0, -264, 12, -48, 76, -68, 24, 572, 180, -244, -4, -168, 0, -188, 60, -156, 12, 0, -20, 260, 84, 16, 232, 52, 156, -16, 32, 300, 28, -148, -60, -404, 20, -84, 24, 128, -104, 404, 0, 0, 64, -112, 8, 172, 96, 292, -84, -208, 332, 192, 12, -52, -336, -8, 128, -72, 172, -432, 16, 8, 0, -144, 68, 108, 4, 0, -64, -160, 4, -140, -292, -80, -52, -148, -4, 244, -36, 0, -40, -188, 0, 68, -52, 432, 84, -204, -64, 264, -128, -120, -20, 184, -136, -56, -56, -180, -260, -176, -44, 36, -88, -176, 192, 92, -212, 300, -20, -36, 44, -532, -116, -72, -400, -184, 84, 504, -120, 4, -156, -68, -24, 392, -24, -480, -136, -136, 12, -300, 4, 28, -48, 140, 64, -476, 0, -328, 120, 0, -4, 128, 140, 312, 96, -76, 184, 216, 48], "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}