# Stored data for newform 192.7.e.e, downloaded from the LMFDB on 28 March 2024. {"label": "192.7.e.e", "space_label": "192.7.e", "level": 192, "weight": 7, "hecke_orbit": 5, "hecke_orbit_code": 18014673504829632, "dim": 2, "is_polredabs": true, "nf_label": "2.0.20.1", "trace_hash": 973122316792313084, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [25920, 0, 1]], [7, [-242, 1]]], "qexp_display": "q+(3+\\beta )q^{3}+6\\beta q^{5}+242q^{7}+(-711+\\cdots)q^{9}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 3, "char_orbit_label": "e", "char_is_real": true, "Nk2": 9408, "analytic_conductor": 44.17038405501139, "hecke_ring_index": 12, "level_radical": 6, "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": "0.508", "prec": 17}, "analytic_rank_proved": true, "char_values": [192, 2, [127, 133, 65], [2, 2, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [65], "field_disc": -20, "field_disc_factorization": [[-1, 1], [2, 2], [5, 1]], "field_poly": [5, 0, 1], "hecke_ring_index_factorization": [[2, 2], [3, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.897", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "14.913", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "146.612", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "6.2.3.c2", "trace_display": [0, 6, 0, 484], "traces": [0, 2, 0, 6, 0, 0, 0, 484, 0, -1422, 0, 0, 0, -5236, 0, -8640, 0, 0, 0, -11572, 0, 1452, 0, 0, 0, -20590, 0, -12906, 0, 0, 0, -40892, 0, 95040, 0, 0, 0, 93548, 0, -15708, 0, 0, 0, -137236, 0, -51840, 0, 0, 0, -118170, 0, 380160, 0, 0, 0, 570240, 0, -34716, 0, 0, 0, -49588, 0, -344124, 0, 0, 0, 168716, 0, -501120, 0, 0, 0, -227612, 0, -61770, 0, 0, 0, -319484, 0, 959202, 0, 0, 0, 2280960, 0, 665280, 0, 0, 0, -1267112, 0, -122676, 0, 0, 0, 1799044, 0, 570240, 0, 0, 0, -3194012, 0, -2090880, 0, 0, 0, -4436212, 0, 280644, 0, 0, 0, -3006720, 0, 3722796, 0, 0, 0, -2729518, 0, 190080, 0, 0, 0, 1418692, 0, -411708, 0, 0, 0, -2800424, 0, 5987520, 0, 0, 0, 10148204, 0, -1140480, 0, 0, 0, 3991680, 0, -354510, 0, 0, 0, -7862492, 0, 2280960, 0, 0, 0, 7223756, 0, 9218880, 0, 0, 0, -7527796, 0, 1710720, 0, 0, 0, 4054230, 0, 8227692, 0, 0, 0, -4982780, 0, -8026560, 0, 0, 0, -7711828, 0, -148764, 0, 0, 0, -25090560, 0, -3123252, 0, 0, 0, -9063164, 0, 22619520, 0, 0, 0, -5835548, 0, 506148, 0, 0, 0, 1140480, 0, -3006720, 0, 0, 0, -22415668, 0, -17400960, 0, 0, 0, -9895864, 0, -682836, 0, 0, 0, -29746364, 0, 14639490, 0, 0, 0, 17922668, 0, 22999680, 0, 0, 0, -6842880, 0, -958452, 0, 0, 0, -20043452, 0, 15163686, 0, 0, 0, 30295496, 0, 27656640, 0, 0, 0, 33073920, 0, 6842880, 0, 0, 0, 22638616, 0, 3991680, 0, 0, 0, 55313280, 0, 67409280, 0, 0, 0, -19150076, 0, -3801336, 0, 0, 0, -65733844, 0, 29074212, 0, 0, 0, -78608596, 0, 49991040, 0, 0, 0, -52087102, 0, 5397132, 0, 0, 0, -48159360, 0, -65862720, 0, 0, 0, -33211112, 0, 64342080, 0, 0, 0, -18102964, 0, -9582036, 0, 0, 0, 21702436, 0, -12545280, 0, 0, 0, -43908480, 0, 11499840, 0, 0, 0, 53904620, 0, -13308636, 0, 0, 0, 113719916, 0, -66512628, 0, 0, 0, 90114244, 0, -107930880, 0, 0, 0, -85539256, 0, -9020160, 0, 0, 0, 28221644, 0, 33787908, 0, 0, 0, -104405760, 0, 91998720, 0, 0, 0, -27136170, 0, -8188554, 0, 0, 0, -10792316, 0, 1140480, 0, 0, 0, 42430124, 0, -46051200, 0, 0, 0, 13805228, 0, 4256076, 0, 0, 0, 137998080, 0, 97574796, 0, 0, 0, 132295680, 0, -42672960, 0, 0, 0, -187870324, 0, -8401272, 0, 0, 0, 107055256, 0, 73716480, 0, 0, 0, -226872668, 0, 78779520, 0, 0, 0, 165939840, 0, 30444612, 0, 0, 0, -131667604, 0, -6842880, 0, 0, 0, -12000296, 0, -248814720, 0, 0, 0, -183446204, 0, 11975040, 0, 0, 0, 34128292, 0, 84018870, 0, 0, 0, 404455680, 0, -178580160, 0, 0, 0, -12545280, 0, -23587476, 0, 0, 0, 99610852, 0, -263450880, 0, 0, 0, -8318972, 0, 176653440, 0, 0, 0, 40829272, 0, 21671268, 0, 0, 0, 119133740, 0, 55313280, 0, 0, 0, -244908664, 0, -121271040, 0, 0, 0, 291473764, 0, -22583388, 0, 0, 0, -175633920, 0, -405440640, 0, 0, 0, 188411468, 0, 25660800, 0, 0, 0, 386052480, 0, 12162690, 0, 0, 0, -55082104, 0, 74674116, 0, 0, 0, 75271680, 0, -268868160, 0, 0, 0, -332882836, 0, -14948340, 0, 0, 0, 121682018, 0, -48159360, 0, 0, 0, 68999040, 0, -515557440, 0, 0, 0, 165256652, 0, -23135484, 0, 0, 0, 88470668, 0, 35257068, 0, 0, 0, -77315128, 0, -404127360, 0, 0, 0, 359283848, 0, -75271680, 0, 0, 0, -647585280, 0, 232126884, 0, 0, 0, 689513132, 0, -73128960, 0, 0, 0, -293383676, 0, -27189492, 0, 0, 0, -608446080, 0, 135717120, 0, 0, 0, 236601112, 0, 326652480, 0, 0, 0, 551992320, 0, -17506644, 0, 0, 0, 756280228, 0, -119957076, 0, 0, 0, 542238532, 0, 160997760, 0, 0, 0, 179116652, 0, 3421440, 0, 0, 0, 602986988, 0, 347276160, 0, 0, 0, -598025950, 0, -549901440, 0, 0, 0, 357983908, 0, -67247004, 0, 0, 0, 309369060, 0, -104405760, 0, 0, 0, -840520948, 0, 592859520, 0, 0, 0, 529752960, 0, -29687592, 0, 0, 0, -256037760, 0, 161832132, 0, 0, 0, -981166804, 0, -995258880, 0, 0, 0, 231517440, 0, -89239092, 0, 0, 0, 156192388, 0, 132867270, 0, 0, 0, 435368648, 0, -146836800, 0, 0, 0, 472677120, 0, 53768004, 0, 0, 0, 11192396, 0, 137998080, 0, 0, 0, -50181120, 0, 570430080, 0, 0, 0, -541268728, 0, -20528640, 0, 0, 0, -424527892, 0, 227153124, 0, 0, 0, -1492888320, 0, -1283040000, 0, 0, 0, -772950904, 0, -60130356, 0, 0, 0, -919081436, 0, -608276142, 0, 0, 0, 15262412, 0, 510494400, 0, 0, 0, 324440204, 0, 90886488, 0, 0, 0, -1071480960, 0, 165939840, 0, 0, 0, 94408324, 0, 1385570880, 0, 0, 0, 1301008556, 0, 99221760, 0, 0, 0, -1073563304, 0, -1621762560, 0, 0, 0, 483345412, 0, 748154880, 0, 0, 0, 420983140, 0, 67915848, 0, 0, 0, 1148463360, 0, -461039040, 0, 0, 0, 653153996, 0, 1544019840, 0, 0, 0, 129821384, 0, 165939840, 0, 0, 0, 301086720, 0, 404455680, 0, 0, 0, -727626240, 0, 1094385600, 0, 0, 0, 430001132, 0, -57450228, 0, 0, 0, 794047496, 0, 900916632, 0, 0, 0, 991922596, 0, -978436800, 0, 0, 0, -1006948276, 0, -197201532, 0, 0, 0, 153964800, 0, 263876076, 0, 0, 0, 882287282, 0, 1274106240, 0, 0, 0, -660543356, 0, -235825788, 0, 0, 0, 5491244, 0, 299946240, 0, 0, 0, -2080861396, 0, 45999360, 0, 0, 0, -1613208960, 0, -156261306, 0, 0, 0, -441698488, 0, -1279120284, 0, 0, 0, 635634956, 0, 1245879360, 0, 0, 0, -1555933876, 0, -144478080, 0, 0, 0, 343323464, 0, -810881280, 0, 0, 0, -3093344640, 0, 1311932160, 0, 0, 0, -2433784320, 0, -99633336, 0, 0, 0, 1505492588, 0, 386052480, 0, 0, 0, -1825338240, 0, 214220160, 0, 0, 0, -2166681308, 0, -54308892, 0, 0, 0, -963076660, 0, 2270942532, 0, 0, 0, 683731620, 0, 116519040, 0, 0, 0, 2254285924, 0, 65107308, 0, 0, 0, 66147840, 0, 1448979840, 0, 0, 0, 595888216, 0, 1712698560, 0, 0, 0, -438773760, 0, -131725440, 0, 0, 0, -938929530, 0, 68999040, 0, 0, 0, -3551023388, 0, -2199605760, 0, 0, 0, 2455865368, 0, 161713860, 0, 0, 0, -4449012480, 0, 3154146732, 0, 0, 0, 1959914880, 0, -275996160, 0, 0, 0, 2692087108, 0, 341159748, 0, 0, 0, -525936532, 0, -603665244, 0], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 3, 2, -1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "12.7.c.a", "char_is_minimal": false, "conrey_index": 65, "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], [1, 0], [0, 0], [3, 1], [0, 0], [0, 6], [0, 0], [242, 0], [0, 0], [-711, 6], [0, 0], [0, -66], [0, 0], [-2618, 0], [0, 0], [-4320, 18], [0, 0], [0, -264], [0, 0], [-5786, 0], [0, 0], [726, 242], [0, 0], [0, 348], [0, 0], [-10295, 0], [0, 0], [-6453, -693], [0, 0], [0, -462], [0, 0], [-20446, 0], [0, 0], [47520, -198], [0, 0], [0, 1452], [0, 0], [46774, 0], [0, 0], [-7854, -2618], [0, 0], [0, -132], [0, 0], [-68618, 0], [0, 0], [-25920, -4266], [0, 0], [0, 792], [0, 0], [-59085, 0], [0, 0], [190080, -792], [0, 0], [0, -6402], [0, 0], [285120, 0], [0, 0], [-17358, -5786], [0, 0], [0, 5574], [0, 0], [-24794, 0], [0, 0], [-172062, 1452], [0, 0], [0, -15708], [0, 0], [84358, 0], [0, 0], [-250560, 1044], [0, 0], [0, 12084], [0, 0], [-113806, 0], [0, 0], [-30885, -10295], [0, 0], [0, -15972], [0, 0], [-159742, 0], [0, 0], [479601, -8532], [0, 0], [0, -19206], [0, 0], [1140480, 0], [0, 0], [332640, -1386], [0, 0], [0, -46812], [0, 0], [-633556, 0], [0, 0], [-61338, -20446], [0, 0], [0, -34716], [0, 0], [899522, 0], [0, 0], [285120, 46926], [0, 0]]}