# Stored data for newform 90.6.c.b, downloaded from the LMFDB on 25 April 2024.
{"label": "90.6.c.b", "space_label": "90.6.c", "level": 90, "weight": 6, "hecke_orbit": 2, "hecke_orbit_code": 4503737166987354, "dim": 2, "is_polredabs": true, "nf_label": "2.0.4.1", "trace_hash": 2278625975192009354, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[7, [16, 0, 1]]], "qexp_display": "q+2iq^{2}-2^{4}q^{4}+(55+5i)q^{5}+2iq^{7}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 5, "char_orbit_label": "c", "char_is_real": true, "Nk2": 3240, "analytic_conductor": 14.434543783168257, "hecke_ring_index": 2, "level_radical": 30, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 4, "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": [90, 2, [11, 37], [2, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2, 3, 5], "conrey_indexes": [19], "field_disc": -4, "field_disc_factorization": [[-1, 1], [2, 2]], "field_poly": [1, 0, 1], "hecke_ring_index_factorization": [[2, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.005", "prec": 17}, {"__RealLiteral__": 0, "data": "1.870", "prec": 17}, {"__RealLiteral__": 0, "data": "0.019", "prec": 17}, {"__RealLiteral__": 0, "data": "14.365", "prec": 20}, {"__RealLiteral__": 0, "data": "0.684", "prec": 17}, {"__RealLiteral__": 0, "data": "140.418", "prec": 24}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "5.2.3.c2", "trace_display": [0, 0, 110, 0], "traces": [0, 2, 0, 0, -32, 110, 0, 0, 0, 0, -80, 1000, 0, 0, -32, 0, 512, 0, 0, 2688, -1760, 0, 0, 0, 0, 5850, 2304, 0, 0, -5292, 0, -11224, 0, 0, -12128, -80, 0, 0, 0, 0, 1280, 37972, 0, 0, -16000, 0, -32800, 0, 0, 33582, -8800, 0, 0, 0, 0, 55000, 512, 0, 0, -56600, 0, 36580, 0, 0, -8192, 5760, 0, 0, 0, 0, -1760, 57600, 0, 0, -58304, 0, -43008, 0, 0, -120456, 28160, 0, 0, 0, 0, -30320, 19232, 0, 0, 45356, 0, 2304, 0, 0, -71200, 147840, 0, 0, 0, 0, -93600, -335836, 0, 0, -36864, 0, 318432, 0, 0, 107620, -40000, 0, 0, 0, 0, -82000, 84672, 0, 0, -12128, 0, 177898, 0, 0, 179584, 299750, 0, 0, 0, 0, 126720, -339000, 0, 0, 527648, 0, 194048, 0, 0, -384032, 1280, 0, 0, 0, 0, -291060, 246464, 0, 0, 471388, 0, -742984, 0, 0, -16000, -617320, 0, 0, 0, 0, -20480, -32800, 0, 0, -607552, 0, -19744, 0, 0, 576698, -667040, 0, 0, 0, 0, -8800, 256000, 0, 0, -219032, 0, -106292, 0, 0, 524800, -145760, 0, 0, 0, 0, -107520, -464112, 0, 0, -295744, 0, -537312, 0, 0, 430584, 140800, 0, 0, 0, 0, 2088460, 1234912, 0, 0, 1344000, 0, -2060160, 0, 0, -1094304, 48080, 0, 0, 0, 0, -880000, 873216, 0, 0, -8192, 0, 661536, 0, 0, 1445420, -1804000, 0, 0, 0, 0, -178000, 905600, 0, 0, 649808, 0, 1830524, 0, 0, -585280, 1847010, 0, 0, 0, 0, -718000, -2734152, 0, 0, -1694240, 0, 131072, 0, 0, -58304, -92160, 0, 0, 0, 0, 796080, -43008, 0, 0, -2744532, 0, 917288, 0, 0, -2016288, 2925000, 0, 0, 0, 0, 28160, -331596, 0, 0, -921600, 0, 1152000, 0, 0, -1756798, 211680, 0, 0, 0, 0, -3113000, 932864, 0, 0, 2361600, 0, 19232, 0, 0, 688128, 2011900, 0, 0, 0, 0, 448960, -3433200, 0, 0, 2119616, 0, 1927296, 0, 0, -2646000, -450560, 0, 0, 0, 0, 633600, 3224992, 0, 0, -71200, 0, 887984, 0, 0, 2095200, 1319120, 0, 0, 0, 0, 485120, -5612000, 0, 0, -307712, 0, 2609824, 0, 0, 597820, -93600, 0, 0, 0, 0, 3168000, -725696, 0, 0, -4681488, 0, -1339526, 0, 0, -36864, 616160, 0, 0, 0, 0, -3206720, 318432, 0, 0, -6064000, 0, 1139200, 0, 0, -2024272, -2365440, 0, 0, 0, 0, -40000, 8245376, 0, 0, 2849948, 0, -12431200, 0, 0, 4182368, -6625080, 0, 0, 0, 0, 1497600, 5690012, 0, 0, 5373376, 0, 84672, 0, 0, 3781388, -1518880, 0, 0, 0, 0, -49360, 589824, 0, 0, 9218600, 0, -12083020, 0, 0, -5094912, -3335200, 0, 0, 0, 0, 1057760, 7600, 0, 0, 179584, 0, -1721920, 0, 0, 7177464, 640000, 0, 0, 0, 0, 2494580, -3648160, 0, 0, -1659612, 0, 18986000, 0, 0, 3474016, 126720, 0, 0, 0, 0, 1312000, 283860, 0, 0, -1354752, 0, -4522784, 0, 0, 527648, -3916000, 0, 0, 0, 0, 7862400, 194048, 0, 0, -2654368, 0, 4197888, 0, 0, -2846368, -739360, 0, 0, 0, 0, -1343280, 12246312, 0, 0, 3096576, 0, -2873344, 0, 0, 15809808, -4796000, 0, 0, 0, 0, -18470980, -16400000, 0, 0, 1563828, 0, 246464, 0, 0, -7143456, 3087280, 0, 0, 0, 0, -2027520, -11653876, 0, 0, 5424000, 0, -14932000, 0, 0, -20747314, 17513760, 0, 0, 0, 0, -2735760, -8442368, 0, 0, 16791000, 0, 9521180, 0, 0, -3104768, 5919100, 0, 0, 0, 0, -4400000, -7112448, 0, 0, -7883264, 0, 6144512, 0, 0, -1384704, -20480, 0, 0, 0, 0, 1653840, 13317664, 0, 0, -28801804, 0, 9495440, 0, 0, -607552, -9020000, 0, 0, 0, 0, 4656960, -19744, 0, 0, -3943424, 0, 20408352, 0, 0, -15085056, 2264000, 0, 0, 0, 0, -667040, -7542208, 0, 0, 12551952, 0, 15439756, 0, 0, 11887744, 9784390, 0, 0, 0, 0, -1463200, 5126400, 0, 0, 5888160, 0, 256000, 0, 0, 14803232, 9877120, 0, 0, 0, 0, 14691250, -22708096, 0, 0, -22097216, 0, 320104, 0, 0, 10208416, -4235600, 0, 0, 0, 0, 327680, 33913060, 0, 0, 524800, 0, -16300032, 0, 0, -28300000, 6739200, 0, 0, 0, 0, -18645000, 9720832, 0, 0, 1596376, 0, -30809612, 0, 0, 315904, -107520, 0, 0, 0, 0, 29020640, 18290000, 0, 0, 21706048, 0, -9227168, 0, 0, -295744, 10672640, 0, 0, 0, 0, -5040720, -1075136, 0, 0, -22927104, 0, -10900672, 0, 0, 10484064, -21121760, 0, 0, 0, 0, 140800, 8879212, 0, 0, -4096000, 0, 5903968, 0, 0, -9118356, -2304000, 0, 0, 0, 0, 2880000, 3504512, 0, 0, -41326000, 0, 1234912, 0, 0, 1700672, -15479100, 0, 0, 0, 0, 13555520, 7288928, 0, 0, 1018336, 0, -8396800, 0, 0, 10582384, 2332160, 0, 0, 0, 0, 25926340, -32309568, 0, 0, -1094304, 0, -17593880, 0, 0, -6096384, -40864120, 0, 0, 0, 0, 1720320, 25259244, 0, 0, 7425792, 0, -19008800, 0, 0, 46437156, -880000, 0, 0, 0, 0, -32830200, 4731904, 0, 0, 51034368, 0, 28800000, 0, 0, 8596992, 5299040, 0, 0, 0, 0, 4818240, 661536, 0, 0, 13547584, 0, -6889344, 0, 0, -26984800, -2252800, 0, 0, 0, 0, -1804000, -12930048, 0, 0, 4463052, 0, 44972432, 0, 0, -29152000, 8062480, 0, 0, 0, 0, -33415360, 33184124, 0, 0, -19758592, 0, 905600, 0, 0, 1018884, -1085920, 0, 0, 0, 0, 5238000, -21504000, 0, 0, 80121808, 0, -27019666, 0, 0, 32962560, 31718390, 0, 0, 0, 0, -35474400, -59761600, 0, 0, -585280, 0, 17508864, 0, 0, 43484048, -769280, 0, 0, 0, 0, 6524560, -2005888, 0, 0, -60228000, 0, -37990656, 0, 0, -44083200, -718000, 0, 0, 0, 0, 14080000, -52148412, 0, 0, -13971456, 0, -11318304, 0, 0, -1694240, -1814240, 0, 0, 0, 0, -12046760, 131072, 0, 0, 29698704, 0, 120685728, 0, 0, -10584576, -5846060, 0, 0, 0, 0, -92160, -92796384, 0, 0, 37455808, 0, -23126720, 0, 0, -45571848, 28864000, 0, 0, 0, 0, -16033600, -5819808, 0, 0, 54070308, 0, 45134208, 0, 0, 35811168, -15160000, 0, 0, 0, 0, 2848000, 73578484, 0, 0, -14489600, 0, 9616000, 0, 0, -17745408, -11827200, 0, 0, 0, 0, -25526160, -10396928, 0, 0, -2016288, 0, 5730786, 0, 0, -29288384, 20613440, 0, 0, 0, 0, -16265920, 81103032, 0, 0, -32931744, 0, 9364480, 0, 0, 22678000, -29552160, 0, 0, 0, 0, 10455920, 32090688, 0, 0, 19712800, 0, -111145192, 0, 0, -921600, 23682120, 0, 0, 0, 0, 11488000], "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, 5, 2, 1, 2, 0]], "char_orbit_index": 3, "prim_orbit_index": 2, "minimal_twist": "30.6.c.a", "char_is_minimal": true, "conrey_index": 19, "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, 2], [0, 0], [-16, 0], [55, 5], [0, 0], [0, 2], [0, -32], [0, 0], [-40, 110], [500, 0], [0, 0], [0, -144], [-16, 0], [0, 0], [256, 0], [0, 758], [0, 0], [1344, 0], [-880, -80], [0, 0], [0, 1000], [0, 2050], [0, 0], [2925, 550], [1152, 0], [0, 0], [0, -32], [-2646, 0], [0, 0], [-5612, 0], [0, 512], [0, 0], [-6064, 0], [-40, 110], [0, 0], [0, 3644], [0, 2688], [0, 0], [640, -1760], [18986, 0], [0, 0], [0, -1202], [-8000, 0], [0, 0], [-16400, 0], [0, 4450], [0, 0], [16791, 0], [-4400, 5850], [0, 0], [0, 2304], [0, -19902], [0, 0], [27500, 2500], [256, 0], [0, 0], [0, -5292], [-28300, 0], [0, 0], [18290, 0], [0, -11224], [0, 0], [-4096, 0], [2880, -7920], [0, 0], [0, -32978], [0, -12128], [0, 0], [-880, -80], [28800, 0], [0, 0], [0, -15404], [-29152, 0], [0, 0], [-21504, 0], [0, 1000], [0, 0], [-60228, 0], [14080, 1280], [0, 0], [0, 37972], [0, 1234], [0, 0], [-15160, 41690], [9616, 0], [0, 0], [0, -16000], [22678, 0], [0, 0], [1152, 0], [0, -32800], [0, 0], [-35600, 0], [73920, 6720], [0, 0], [0, 18484], [0, 33582], [0, 0], [-46800, -8800]]}