# Stored data for newform 32.7.d.b, downloaded from the LMFDB on 19 April 2024.
{"label": "32.7.d.b", "space_label": "32.7.d", "level": 32, "weight": 7, "hecke_orbit": 2, "hecke_orbit_code": 4503805903241248, "dim": 4, "is_polredabs": true, "nf_label": "4.0.3803625.2", "trace_hash": 640570880051321504, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[3, [-276, -24, 1]]], "qexp_display": "q+(12-\\beta _{1})q^{3}-\\beta _{2}q^{5}+(\\beta _{2}-\\beta _{3})q^{7}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "d", "char_is_real": true, "Nk2": 1568, "analytic_conductor": 7.361730675835232, "hecke_ring_index": 8192, "level_radical": 2, "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": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "analytic_rank_proved": true, "char_values": [32, 2, [31, 5], [1, 1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [15], "field_disc": 3803625, "field_disc_factorization": [[3, 3], [5, 3], [7, 2], [23, 1]], "field_poly": [256, -16, 6, -1, 1], "hecke_ring_index_factorization": [[2, 13]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.026", "prec": 17}, {"__RealLiteral__": 0, "data": "3.585", "prec": 17}, {"__RealLiteral__": 0, "data": "0.635", "prec": 17}, {"__RealLiteral__": 0, "data": "66.154", "prec": 20}, {"__RealLiteral__": 0, "data": "29.093", "prec": 20}, {"__RealLiteral__": 0, "data": "1744.626", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "6.2.3.c2", "trace_display": [0, 48, 0, 0], "traces": [0, 4, 0, 48, 0, 0, 0, 0, 0, -660, 0, -976, 0, 0, 0, 0, 0, 4168, 0, 1456, 0, 0, 0, 0, 0, -23900, 0, -2592, 0, 0, 0, 0, 0, 84048, 0, 49920, 0, 0, 0, 0, 0, -117944, 0, -197456, 0, 0, 0, 0, 0, 2116, 0, 386016, 0, 0, 0, 0, 0, 126672, 0, -542032, 0, 0, 0, 0, 0, -205440, 0, 790192, 0, 0, 0, 0, 0, 443912, 0, -1765200, 0, 0, 0, 0, 0, -568044, 0, 3465008, 0, 0, 0, 0, 0, 761224, 0, -3398400, 0, 0, 0, 0, 0, -926776, 0, 2459280, 0, 0, 0, 0, 0, -744960, 0, -5798608, 0, 0, 0, 0, 0, 2547592, 0, 8044800, 0, 0, 0, 0, 0, -1389780, 0, -3270048, 0, 0, 0, 0, 0, 1193808, 0, 2209712, 0, 0, 0, 0, 0, -5191352, 0, -8419664, 0, 0, 0, 0, 0, 3457920, 0, 9594672, 0, 0, 0, 0, 0, 7376280, 0, -230400, 0, 0, 0, 0, 0, -2449920, 0, -6606032, 0, 0, 0, 0, 0, -9318044, 0, 2380560, 0, 0, 0, 0, 0, -7053744, 0, -5972944, 0, 0, 0, 0, 0, 15841920, 0, 18135008, 0, 0, 0, 0, 0, -4666168, 0, -23566080, 0, 0, 0, 0, 0, -542256, 0, 26138880, 0, 0, 0, 0, 0, 5869136, 0, -22605776, 0, 0, 0, 0, 0, 26511360, 0, 19667424, 0, 0, 0, 0, 0, -31538100, 0, -31048144, 0, 0, 0, 0, 0, -51619064, 0, 44689920, 0, 0, 0, 0, 0, 43146056, 0, -47625840, 0, 0, 0, 0, 0, 46769616, 0, 50900144, 0, 0, 0, 0, 0, 1968904, 0, -33772800, 0, 0, 0, 0, 0, -88936320, 0, 29173728, 0, 0, 0, 0, 0, 26365440, 0, -78437200, 0, 0, 0, 0, 0, 51317128, 0, 5731888, 0, 0, 0, 0, 0, -25007220, 0, 60607968, 0, 0, 0, 0, 0, -57398112, 0, 36714240, 0, 0, 0, 0, 0, 61042560, 0, 4902832, 0, 0, 0, 0, 0, 114303176, 0, -40492800, 0, 0, 0, 0, 0, -99378096, 0, 23357152, 0, 0, 0, 0, 0, -151557120, 0, -90377936, 0, 0, 0, 0, 0, 34512008, 0, 29872224, 0, 0, 0, 0, 0, 245184000, 0, -100848208, 0, 0, 0, 0, 0, -58723064, 0, 197917440, 0, 0, 0, 0, 0, -180555540, 0, -63408240, 0, 0, 0, 0, 0, -25052520, 0, 76005120, 0, 0, 0, 0, 0, 233316480, 0, -154811984, 0, 0, 0, 0, 0, -88788480, 0, 118098960, 0, 0, 0, 0, 0, -237631536, 0, -116513280, 0, 0, 0, 0, 0, 153401416, 0, 210478080, 0, 0, 0, 0, 0, 240985544, 0, -283975584, 0, 0, 0, 0, 0, -83763888, 0, 152962736, 0, 0, 0, 0, 0, -320583800, 0, -179470080, 0, 0, 0, 0, 0, 308215112, 0, 241347840, 0, 0, 0, 0, 0, 229313580, 0, 187554608, 0, 0, 0, 0, 0, -154272056, 0, -76940704, 0, 0, 0, 0, 0, -509714872, 0, -206316864, 0, 0, 0, 0, 0, 125184000, 0, -153185104, 0, 0, 0, 0, 0, 251286224, 0, -104795600, 0, 0, 0, 0, 0, -159288960, 0, 51778560, 0, 0, 0, 0, 0, -93893424, 0, 331044272, 0, 0, 0, 0, 0, 212298240, 0, 133830448, 0, 0, 0, 0, 0, 438456960, 0, 277647792, 0, 0, 0, 0, 0, -67118688, 0, -775645440, 0, 0, 0, 0, 0, -398180024, 0, -118188752, 0, 0, 0, 0, 0, -167907644, 0, 76250640, 0, 0, 0, 0, 0, 326177232, 0, 544932656, 0, 0, 0, 0, 0, -364437120, 0, -142418768, 0, 0, 0, 0, 0, -172723200, 0, 338077440, 0, 0, 0, 0, 0, 235418016, 0, -723078736, 0, 0, 0, 0, 0, 682559944, 0, 582064432, 0, 0, 0, 0, 0, -67034872, 0, -610031136, 0, 0, 0, 0, 0, -472521600, 0, 849642032, 0, 0, 0, 0, 0, -139232888, 0, -216783360, 0, 0, 0, 0, 0, 334140296, 0, -370971120, 0, 0, 0, 0, 0, -195279360, 0, -899627520, 0, 0, 0, 0, 0, -1010936, 0, 252820528, 0, 0, 0, 0, 0, 93794500, 0, 78641472, 0, 0, 0, 0, 0, -786960432, 0, 1268674560, 0, 0, 0, 0, 0, 550650568, 0, 129295024, 0, 0, 0, 0, 0, 100942288, 0, -213012480, 0, 0, 0, 0, 0, 270926040, 0, -862020304, 0, 0, 0, 0, 0, -69189120, 0, -462654720, 0, 0, 0, 0, 0, 114460616, 0, 911397600, 0, 0, 0, 0, 0, 39386832, 0, 613562288, 0, 0, 0, 0, 0, -14513280, 0, 317564464, 0, 0, 0, 0, 0, -493841648, 0, -905606688, 0, 0, 0, 0, 0, 672291840, 0, -749241600, 0, 0, 0, 0, 0, -110438400, 0, -1152618240, 0, 0, 0, 0, 0, -683036160, 0, 732376032, 0, 0, 0, 0, 0, -166190724, 0, 506906848, 0, 0, 0, 0, 0, -764206768, 0, 2211988528, 0, 0, 0, 0, 0, 1787057280, 0, -447177840, 0, 0, 0, 0, 0, 961627728, 0, -760139520, 0, 0, 0, 0, 0, -1128031544, 0, -1716806400, 0, 0, 0, 0, 0, -221914936, 0, 1576269408, 0, 0, 0, 0, 0, 333550080, 0, -163488416, 0, 0, 0, 0, 0, -1827392640, 0, 865358896, 0, 0, 0, 0, 0, -1008462720, 0, -2465936640, 0, 0, 0, 0, 0, 355335000, 0, 709092832, 0, 0, 0, 0, 0, 3301876552, 0, -2035613648, 0, 0, 0, 0, 0, 159739216, 0, 2172245760, 0, 0, 0, 0, 0, -1152682800, 0, 986714672, 0, 0, 0, 0, 0, 1916060872, 0, 2186530560, 0, 0, 0, 0, 0, 440145124, 0, -787827744, 0, 0, 0, 0, 0, -2830747824, 0, -1351960320, 0, 0, 0, 0, 0, -1470625592, 0, -1658594384, 0, 0, 0, 0, 0, 10008960, 0, 400137360, 0, 0, 0, 0, 0, 1874420760, 0, 1664448000, 0, 0, 0, 0, 0, 191131528, 0, 1328917168, 0, 0, 0, 0, 0, -2336808960, 0, -2295233424, 0, 0, 0, 0, 0, 2130516480, 0, -1678986240, 0, 0, 0, 0, 0, 790945920, 0, -846365264, 0, 0, 0, 0, 0, -549659312, 0, 1056011520, 0, 0, 0, 0, 0, -2871998256, 0, 3083808000, 0, 0, 0, 0, 0, 902911432, 0, 622773424, 0, 0, 0, 0, 0, 3695366408, 0, -795884448, 0, 0, 0, 0, 0, 782115840, 0, -3817962064, 0, 0, 0, 0, 0, -3717914168, 0, 409528320, 0, 0, 0, 0, 0, 1966705924, 0, 241695120, 0, 0, 0, 0, 0, 516376224, 0, 3119179184, 0, 0, 0, 0, 0, -2575084472, 0, 956486624, 0, 0, 0, 0, 0, -2503182720, 0, 1391216640, 0, 0, 0, 0, 0, -699679152, 0, -6089544960, 0, 0, 0, 0, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "8.7.d.b", "char_is_minimal": false, "conrey_index": 15, "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, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [12, -1, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [0, 0, 1, -1], [0, 0, 0, 0], [-165, -24, 0, 0], [0, 0, 0, 0], [-244, -57, 0, 0], [0, 0, 0, 0], [0, 0, 1, -8], [0, 0, 0, 0], [0, 0, -27, -5], [0, 0, 0, 0], [1042, -200, 0, 0], [0, 0, 0, 0], [364, -65, 0, 0], [0, 0, 0, 0], [0, 0, -12, 8], [0, 0, 0, 0], [0, 0, 91, 5], [0, 0, 0, 0], [-5975, 880, 0, 0], [0, 0, 0, 0], [-648, 606, 0, 0], [0, 0, 0, 0], [0, 0, 13, 64], [0, 0, 0, 0], [0, 0, -28, 60], [0, 0, 0, 0], [21012, -440, 0, 0], [0, 0, 0, 0], [12480, 800, 0, 0], [0, 0, 0, 0], [0, 0, 207, -56], [0, 0, 0, 0], [0, 0, -285, 29], [0, 0, 0, 0], [-29486, 1104, 0, 0], [0, 0, 0, 0], [-49364, -2121, 0, 0], [0, 0, 0, 0], [0, 0, -195, -120], [0, 0, 0, 0], [0, 0, 638, -286], [0, 0, 0, 0], [529, -5696, 0, 0], [0, 0, 0, 0], [96504, -3442, 0, 0], [0, 0, 0, 0], [0, 0, -1053, 56], [0, 0, 0, 0], [0, 0, -611, -285], [0, 0, 0, 0], [31668, -1144, 0, 0], [0, 0, 0, 0], [-135508, 327, 0, 0], [0, 0, 0, 0], [0, 0, 845, -328], [0, 0, 0, 0], [0, 0, -741, 645], [0, 0, 0, 0], [-51360, 12560, 0, 0], [0, 0, 0, 0], [197548, 5967, 0, 0], [0, 0, 0, 0], [0, 0, 2652, 440], [0, 0, 0, 0], [0, 0, 1977, 743], [0, 0, 0, 0], [110978, -8536, 0, 0], [0, 0, 0, 0], [-441300, 16535, 0, 0], [0, 0, 0, 0], [0, 0, -1612, 1384], [0, 0, 0, 0], [0, 0, -1118, -546], [0, 0, 0, 0], [-142011, 25416, 0, 0], [0, 0, 0, 0], [866252, -3089, 0, 0], [0, 0, 0, 0], [0, 0, -4042, -1000], [0, 0, 0, 0], [0, 0, 2847, -127], [0, 0, 0, 0], [190306, -11928, 0, 0], [0, 0, 0, 0], [-849600, -39968, 0, 0], [0, 0, 0, 0], [0, 0, 1584, -320], [0, 0, 0, 0], [0, 0, -1339, -325], [0, 0, 0, 0], [-231694, -42696, 0, 0], [0, 0, 0, 0], [614820, 15261, 0, 0], [0, 0, 0, 0]]}