# Stored data for newform 49.6.a.c, downloaded from the LMFDB on 09 December 2025.
{"Nk2": 1764, "analytic_conductor": 7.858807170836051, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[7, -1]], "atkin_lehner_string": "-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [49, 1, [3], [1]], "cm_discs": [], "conrey_index": 1, "dim": 2, "field_disc": 156, "field_disc_factorization": [[2, 2], [3, 1], [13, 1]], "field_poly": [-39, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": -1, "has_non_self_twist": 1, "hecke_cutters": [[2, [2, 1]], [3, [-624, 0, 1]]], "hecke_orbit": 3, "hecke_orbit_code": 9007199355404337, "hecke_ring_generator_nbound": 3, "hecke_ring_index": 4, "hecke_ring_index_factorization": [[2, 2]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": true, "label": "49.6.a.c", "level": 49, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": true, "level_is_square": true, "level_is_squarefree": false, "level_primes": [7], "level_radical": 7, "minimal_twist": "49.6.a.c", "nf_label": "2.2.156.1", "prim_orbit_index": 1, "qexp_display": "q-2q^{2}+\\beta q^{3}-28q^{4}+3\\beta q^{5}-2\\beta q^{6}+\\cdots", "related_objects": [], "relative_dim": 2, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "49.6.a", "trace_display": [-4, 0, 0, 0], "trace_hash": 1632942861717787175, "trace_moments": [{"__RealLiteral__": 0, "data": "0.069", "prec": 17}, {"__RealLiteral__": 0, "data": "1.921", "prec": 17}, {"__RealLiteral__": 0, "data": "0.279", "prec": 17}, {"__RealLiteral__": 0, "data": "15.045", "prec": 20}, {"__RealLiteral__": 0, "data": "1.665", "prec": 17}, {"__RealLiteral__": 0, "data": "148.779", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "traces": [0, 2, -4, 0, -56, 0, 0, 0, 240, 762, 0, -568, 0, 0, 0, 3744, 1312, 0, -1524, 0, 0, 0, 1136, 2992, 0, 4982, 0, 0, 0, -8732, -7488, 0, -10304, 0, 0, 0, -21336, -25260, 0, 26208, 0, 0, 0, -2712, 15904, 0, -5984, 0, 0, 0, -9964, -7488, 0, 28300, 0, 0, 0, 108576, 17464, 0, -104832, 0, 0, 0, -21376, 78624, 0, -7288, 0, 0, 0, 71264, 91440, 0, 50520, 0, 0, 0, -52416, -109232, 0, -12942, 0, 0, 0, -22464, 5424, 0, -68160, 0, 0, 0, -83776, -321984, 0, 325728, 0, 0, 0, -216408, -139496, 0, 14976, 0, 0, 0, -56600, 436376, 0, -192060, 0, 0, 0, -274844, -217152, 0, 244496, 0, 0, 0, 449280, -160790, 0, -471744, 0, 0, 0, 340736, 372480, 0, -157248, 0, 0, 0, 14576, 516672, 0, -151124, 0, 0, 0, 501696, -142528, 0, 499872, 0, 0, 0, 707280, 722060, 0, 64560, 0, 0, 0, -965952, -733824, 0, 218464, 0, 0, 0, 25884, -122728, 0, -1063296, 0, 0, 0, -192218, 44928, 0, 75936, 0, 0, 0, -372608, -1868256, 0, 1221128, 0, 0, 0, -1778400, 359040, 0, 643968, 0, 0, 0, -651456, 682384, 0, -1232316, 0, 0, 0, 462956, 432816, 0, 597840, 0, 0, 0, 209664, -1415232, 0, 1139952, 0, 0, 0, 1553640, -792400, 0, -872752, 0, 0, 0, 384120, 2036736, 0, -157248, 0, 0, 0, 1898142, 549688, 0, -3040128, 0, 0, 0, -1047840, 95084, 0, 1505088, 0, 0, 0, 2177984, 2456064, 0, 321580, 0, 0, 0, 943488, 2280096, 0, -26208, 0, 0, 0, -849728, -681472, 0, -60928, 0, 0, 0, -2201472, -3326892, 0, -2234240, 0, 0, 0, -1018368, 204064, 0, -1033344, 0, 0, 0, 302248, -1414888, 0, 3792844, 0, 0, 0, 2638220, -1003392, 0, -1995392, 0, 0, 0, -3925824, -2794786, 0, 9172800, 0, 0, 0, -5604768, -3031200, 0, -1444120, 0, 0, 0, -129120, 3792672, 0, -5335200, 0, 0, 0, -546624, 1931904, 0, 3144960, 0, 0, 0, 3058496, -3199844, 0, 2479888, 0, 0, 0, -651456, 362376, 0, 245456, 0, 0, 0, 2126592, -223416, 0, -9624060, 0, 0, 0, 3186012, 384436, 0, 628992, 0, 0, 0, -325440, 5601024, 0, -6673528, 0, 0, 0, 3616704, 2926336, 0, 3736512, 0, 0, 0, -2442256, 1841584, 0, 4493914, 0, 0, 0, 6110208, 3556800, 0, 1962752, 0, 0, 0, 9015552, 6275468, 0, -2373696, 0, 0, 0, -3663768, -9120384, 0, -1364768, 0, 0, 0, 2464632, -1033272, 0, -1096684, 0, 0, 0, -17398368, -925912, 0, 6059424, 0, 0, 0, 3268192, -8328548, 0, -6761664, 0, 0, 0, 7173840, -898560, 0, 2830464, 0, 0, 0, -2279904, -78624, 0, 4848480, 0, 0, 0, -5599828, -3107280, 0, 3396000, 0, 0, 0, -12218528, -7443072, 0, 1908640, 0, 0, 0, -16346304, 5377680, 0, -4073472, 0, 0, 0, 314496, 7496408, 0, -3055104, 0, 0, 0, 198916, -3796284, 0, 7695632, 0, 0, 0, 13029120, -323628, 0, -1033344, 0, 0, 0, 7187632, -5728192, 0, -190168, 0, 0, 0, -3010176, -6638112, 0, 770208, 0, 0, 0, 10782300, -4355968, 0, -19289088, 0, 0, 0, 4502120, 27518400, 0, 4342512, 0, 0, 0, 6091096, 13208832, 0, -4560192, 0, 0, 0, 52416, -15984504, 0, 19027008, 0, 0, 0, 11378016, 1699456, 0, -9540608, 0, 0, 0, -11797504, 14983488, 0, -1639872, 0, 0, 0, 25844832, 9434880, 0, 6653784, 0, 0, 0, 4468480, 1931904, 0, -8396654, 0, 0, 0, -9906624, 2036736, 0, -874560, 0, 0, 0, -14466816, -6950948, 0, -21674016, 0, 0, 0, -15715304, 4231472, 0, 2829776, 0, 0, 0, -7585688, -47286720, 0, 18130748, 0, 0, 0, 2126592, -5276440, 0, -14047488, 0, 0, 0, 8551680, 21111884, 0, 15991688, 0, 0, 0, 7453072, -8144256, 0, 5589572, 0, 0, 0, -18345600, -8037200, 0, 29955744, 0, 0, 0, -28012608, 11209536, 0, -16570560, 0, 0, 0, -20217680, -20240064, 0, 10172224, 0, 0, 0, -2776728, -1807680, 0, -7585344, 0, 0, 0, 10670400, 10535616, 0, 7202516, 0, 0, 0, 14458028, 1093248, 0, 27046656, 0, 0, 0, 17192448, -22689838, 0, -30835584, 0, 0, 0, 11967008, -13107840, 0, 6399688, 0, 0, 0, -4959776, 27151584, 0, -15480004, 0, 0, 0, -5076864, 1302912, 0, -1553040, 0, 0, 0, 3436384, 26833348, 0, -52195104, 0, 0, 0, 27714712, 29772288, 0, 446832, 0, 0, 0, 19248120, -13063072, 0, 4088448, 0, 0, 0, -10649796, -6372024, 0, 5382104, 0, 0, 0, -2695680, 37653408, 0, 36453976, 0, 0, 0, 1314144, -1779072, 0, -11202048, 0, 0, 0, 13347056, 14545440, 0, 2830464, 0, 0, 0, 628324, -7233408, 0, 6070784, 0, 0, 0, 52311168, 49657044, 0, -41617392, 0, 0, 0, -22329216, -34191584, 0, -3683168, 0, 0, 0, -8987828, -67414464, 0, -21751412, 0, 0, 0, -46781334, -12220416, 0, 49795200, 0, 0, 0, -15414784, 2069792, 0, 28836184, 0, 0, 0, 11150416, -38638080, 0, -12550936, 0, 0, 0, 4747392, 1017600, 0, 31475808, 0, 0, 0, 22093236, 7327536, 0, 39087360, 0, 0, 0, -19106752, -8558784, 0, -39233376, 0, 0, 0, -96625152, 34504848, 0, 2066544, 0, 0, 0, 2193368, -41041728, 0, -20238976, 0, 0, 0, -19914336, 34796736, 0, -12962768, 0, 0, 0, -25968960, -37346400, 0, 52977600, 0, 0, 0, -3010176, -25667264, 0, 16657096, 0, 0, 0, 13523328, 75969504, 0, -49029100, 0, 0, 0, 50978304, -14347680, 0, -4912128, 0, 0, 0, 39626496, -50919796, 0, 11904640, 0, 0, 0, -15717992, -31918656, 0, 157248, 0, 0, 0, -9696960, 57081024, 0, -44433792, 0, 0, 0, -2898386, 11199656, 0, -43501920, 0, 0, 0, 18564800, 23920416, 0, -37788960, 0, 0, 0, 124102368, 52365120, 0, 14886144, 0, 0, 0, -3817280, 8198032, 0, 77534496, 0, 0, 0, 31021888, 32692608, 0, -23047200, 0, 0, 0, -57028608, 1575556, 0, 75033504, 0, 0, 0, 24798120, 4402944, 0, -14992816, 0, 0, 0, 6110208, 3675528, 0, 43647552, 0, 0, 0, 39207168, -397832, 0, -53147976, 0, 0, 0, -32981280, -65022048, 0, -79308552, 0, 0, 0, 59827520, 71225856, 0, 647256, 0, 0, 0, 2066688, 39799392, 0, -59780448, 0, 0, 0, -62922660, -14375264, 0, 44987264, 0, 0, 0, -2662352, -65684736, 0, 6379776, 0, 0, 0, -132530112, -42142464, 0, 13276224, 0, 0, 0, -1540416, -96855784, 0, 42771456, 0, 0, 0, 45356084, -21564600, 0, -60983552, 0, 0, 0, -40015872, 25813570, 0, 166259256, 0, 0, 0, -7208624, -19294800, 0, -55036800, 0, 0, 0, -8685024, 65284128, 0, -36391972, 0, 0, 0, -73174860, -12182192, 0, -56609280, 0, 0, 0, -63842688, -4057152, 0, 105084048, 0, 0, 0, -60720192, 733824, 0, 31969008, 0, 0], "weight": 6, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0], [1, 0], [-2, 0], [0, 1], [-28, 0], [0, 3], [0, -2], [0, 0], [120, 0], [381, 0], [0, -6], [-284, 0], [0, -28], [0, 21], [0, 0], [1872, 0], [656, 0], [0, -6], [-762, 0], [0, 87], [0, -84], [0, 0], [568, 0], [1496, 0], [0, 120], [2491, 0], [0, -42], [0, 138], [0, 0], [-4366, 0], [-3744, 0], [0, -258], [-5152, 0], [0, -284], [0, 12], [0, 0], [-10668, 0], [-12630, 0], [0, -174], [13104, 0], [0, 360], [0, -378], [0, 0], [-1356, 0], [7952, 0], [0, 1143], [-2992, 0], [0, 402], [0, 656], [0, 0], [-4982, 0], [-3744, 0], [0, -588], [14150, 0], [0, -276], [0, -852], [0, 0], [54288, 0], [8732, 0], [0, -1497], [-52416, 0], [0, -1425], [0, 516], [0, 0], [-10688, 0], [39312, 0], [0, 568], [-3644, 0], [0, 168], [0, 1496], [0, 0], [35632, 0], [45720, 0], [0, 1632], [25260, 0], [0, 2491], [0, -2436], [0, 0], [-26208, 0], [-54616, 0], [0, 1968], [-6471, 0], [0, 756], [0, -21], [0, 0], [-11232, 0], [2712, 0], [0, -4366], [-34080, 0], [0, -816], [0, -2286], [0, 0], [-41888, 0], [-160992, 0], [0, -804], [162864, 0], [0, -5152], [0, 7350], [0, 0], [-108204, 0], [-69748, 0]]}