# Stored data for newform 108.6.e.a, downloaded from the LMFDB on 19 April 2024. {"label": "108.6.e.a", "space_label": "108.6.e", "level": 108, "weight": 6, "hecke_orbit": 1, "hecke_orbit_code": 274978570348, "dim": 10, "is_polredabs": true, "trace_hash": 1993954327338792822, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [], "qexp_display": "q+(4-4\\beta _{1}+\\beta _{7})q^{5}+(6\\beta _{1}+\\beta _{2}+\\beta _{7}+\\cdots)q^{7}+\\cdots", "char_order": 3, "char_parity": 1, "char_degree": 2, "char_conductor": 9, "char_orbit_label": "e", "char_is_real": false, "Nk2": 3888, "analytic_conductor": 17.321452539801907, "hecke_ring_index": 11019960576, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [108, 3, [55, 29], [3, 1]], "hecke_ring_generator_nbound": 19, "inner_twist_count": 2, "level_primes": [2, 3], "conrey_indexes": [37, 73], "field_disc": -71384460604942959017883, "field_disc_factorization": [[-1, 1], [3, 5], [17, 2], [1008207173, 2]], "field_poly": [442368, 0, 498609, 0, 124623, 0, 8800, 0, 175, 0, 1], "hecke_ring_index_factorization": [[2, 8], [3, 16]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.642", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "392.455", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "29602.755", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "5.2.3.c3", "trace_display": [0, 0, 21, 29], "traces": [0, 10, 0, 0, 0, 21, 0, 29, 0, 0, 0, -177, 0, -181, 0, 0, 0, -2280, 0, -832, 0, 0, 0, -399, 0, -4778, 0, 0, 0, 6033, 0, 2759, 0, 0, 0, -37146, 0, -15172, 0, 0, 0, 18435, 0, 1469, 0, 0, 0, 25155, 0, -4056, 0, 0, 0, -116844, 0, 14778, 0, 0, 0, 90537, 0, 1403, 0, 0, 0, 148407, 0, 13907, 0, 0, 0, -229368, 0, 15200, 0, 0, 0, 211983, 0, 29993, 0, 0, 0, 228951, 0, -49662, 0, 0, 0, -598332, 0, 124930, 0, 0, 0, 394764, 0, 40541, 0, 0, 0, 398337, 0, 13403, 0, 0, 0, -648240, 0, -38644, 0, 0, 0, 401697, 0, -8271, 0, 0, 0, 311394, 0, 18538, 0, 0, 0, -1353990, 0, -254320, 0, 0, 0, 169005, 0, -229904, 0, 0, 0, 596523, 0, 148127, 0, 0, 0, -217938, 0, -437850, 0, 0, 0, 191805, 0, -75295, 0, 0, 0, -400161, 0, -57397, 0, 0, 0, -573378, 0, 737192, 0, 0, 0, -263187, 0, 200958, 0, 0, 0, 87525, 0, -78268, 0, 0, 0, 1728840, 0, -569500, 0, 0, 0, -239286, 0, -33030, 0, 0, 0, -1717653, 0, -500083, 0, 0, 0, 1911372, 0, 951800, 0, 0, 0, -2193771, 0, 33705, 0, 0, 0, -347214, 0, 566063, 0, 0, 0, 6802926, 0, 678514, 0, 0, 0, -525894, 0, 829685, 0, 0, 0, -2920185, 0, 790799, 0, 0, 0, 2239176, 0, -1637766, 0, 0, 0, -4029615, 0, -247975, 0, 0, 0, -1470222, 0, -1874660, 0, 0, 0, 7388688, 0, 1356714, 0, 0, 0, -22581, 0, -227534, 0, 0, 0, -4714041, 0, 627678, 0, 0, 0, -1725180, 0, 670544, 0, 0, 0, -4689168, 0, 1366931, 0, 0, 0, 378093, 0, 1027931, 0, 0, 0, 8595726, 0, -3124430, 0, 0, 0, 969369, 0, -3532419, 0, 0, 0, -2462037, 0, -1059155, 0, 0, 0, -5707398, 0, -2746960, 0, 0, 0, -4950951, 0, -1196575, 0, 0, 0, 2988249, 0, 1908963, 0, 0, 0, 4303848, 0, 7002896, 0, 0, 0, 4699035, 0, 3132437, 0, 0, 0, -2458569, 0, 241277, 0, 0, 0, -14407986, 0, -8795246, 0, 0, 0, 121725, 0, -3581881, 0, 0, 0, 8076063, 0, -6168132, 0, 0, 0, 1064016, 0, 4922070, 0, 0, 0, 12154542, 0, 1828961, 0, 0, 0, 791718, 0, 4938155, 0, 0, 0, -15898782, 0, 10102376, 0, 0, 0, -1022163, 0, 8848755, 0, 0, 0, 11341221, 0, 4654026, 0, 0, 0, -2006274, 0, -16047844, 0, 0, 0, 15250107, 0, -4652459, 0, 0, 0, 2111262, 0, -10277311, 0, 0, 0, -26194866, 0, 9499410, 0, 0, 0, 3303081, 0, -4190245, 0, 0, 0, 18622158, 0, 4057771, 0, 0, 0, -4772352, 0, 13435400, 0, 0, 0, 14176056, 0, 9444665, 0, 0, 0, 1214235, 0, 7222194, 0, 0, 0, -22712040, 0, -24177654, 0, 0, 0, -2493753, 0, -9216331, 0, 0, 0, 9345657, 0, -13726657, 0, 0, 0, -720384, 0, 5397226, 0, 0, 0, 7629909, 0, -3446212, 0, 0, 0, -5818689, 0, 7713934, 0, 0, 0, -32654190, 0, 29263568, 0, 0, 0, 2847129, 0, 15884118, 0, 0, 0, 10870788, 0, 7449071, 0, 0, 0, 22378104, 0, -42625746, 0, 0, 0, 4765881, 0, -21490418, 0, 0, 0, -8815989, 0, -21105711, 0, 0, 0, -20036784, 0, 1721312, 0, 0, 0, -16427778, 0, 131968, 0, 0, 0, -1613937, 0, 16512804, 0, 0, 0, 16872012, 0, 34507172, 0, 0, 0, -8890518, 0, 23006753, 0, 0, 0, -18502284, 0, 10153465, 0, 0, 0, 1077036, 0, -60728246, 0, 0, 0, -10168515, 0, -31128003, 0, 0, 0, 430143, 0, -22539253, 0, 0, 0, 57601176, 0, 12456656, 0, 0, 0, -7526457, 0, 820026, 0, 0, 0, -6612861, 0, 18862540, 0, 0, 0, 52622340, 0, 67911948, 0, 0, 0, -21608643, 0, 35376113, 0, 0, 0, -23544402, 0, 13532315, 0, 0, 0, 11719710, 0, -66827044, 0, 0, 0, -18651633, 0, -22876975, 0, 0, 0, -38119974, 0, -51233555, 0, 0, 0, 48313128, 0, 33246272, 0, 0, 0, -8133168, 0, -954894, 0, 0, 0, -23137377, 0, 18626819, 0, 0, 0, 56400624, 0, 49539078, 0, 0, 0, -22917639, 0, 47528109, 0, 0, 0, -3064125, 0, 30918395, 0, 0, 0, 53431464, 0, -83403954, 0, 0, 0, -17227083, 0, -37102837, 0, 0, 0, -5725047, 0, -55848809, 0, 0, 0, 9547056, 0, 30145806, 0, 0, 0, -13736694, 0, -14619679, 0, 0, 0, -26965893, 0, 31989240, 0, 0, 0, 24524652, 0, 84664144, 0, 0, 0, 3211545, 0, 49869887, 0, 0, 0, -15357525, 0, 37240281, 0, 0, 0, 32734368, 0, -116369894, 0, 0, 0, -25060128, 0, -53944855, 0, 0, 0, 29020926, 0, -67094437, 0, 0, 0, 15087210, 0, 16750136, 0, 0, 0, -15127659, 0, -20180943, 0, 0, 0, -18408432, 0, 41982179, 0, 0, 0, -100328898, 0, 98336492, 0, 0, 0, 5535405, 0, 62936194, 0, 0, 0, 19796871, 0, 20123999, 0, 0, 0, 6058764, 0, -193843528, 0, 0, 0, 47189976, 0, -60129900, 0, 0, 0, -23300805, 0, -76772653, 0, 0, 0, -77667354, 0, 44073166, 0, 0, 0, 4595553, 0, 4518126, 0, 0, 0, 55811310, 0, 63067041, 0, 0, 0, -1375176, 0, 123116960, 0, 0, 0, 29524596, 0, 92406250, 0, 0, 0, 4020585, 0, 32999687, 0, 0, 0, -162075144, 0, -136835644, 0, 0, 0, -10717362, 0, -91626363, 0, 0, 0, 47040147, 0, -73462970, 0, 0, 0, -13457592, 0, 18656084, 0, 0, 0, 102160506, 0, -27182593, 0, 0, 0, 35126325, 0, 28313987, 0, 0, 0, -18036912, 0, 158567598, 0, 0, 0, 24134343, 0, 70717765, 0, 0, 0, 113043099, 0, 31811783, 0, 0, 0, -79425420, 0, -190459264, 0, 0, 0, 37512273, 0, -70293848, 0, 0, 0, -17835408, 0, -104311980, 0, 0, 0, -213640014, 0, 56223576, 0, 0, 0, 10682538, 0, 9408605, 0, 0, 0, 43290351, 0, 76829121, 0, 0, 0, 10205286, 0, 168088016, 0, 0, 0, 88299156, 0, 125812640, 0, 0, 0, 6353829, 0, 57711660, 0, 0, 0, -32433804, 0, -184181524, 0, 0, 0, 54844413, 0, -74861667, 0, 0, 0, 140760855, 0, -125464994, 0, 0, 0, 101601432, 0, 79262730, 0, 0, 0, 20779449, 0, -25728720, 0, 0, 0, -13817577, 0, 39291239, 0, 0, 0, -307731312, 0, 123524626, 0, 0, 0, 3845319, 0, 102031182, 0, 0, 0, -36282585, 0, 58727826, 0, 0, 0, 52755294, 0, -209741680, 0, 0, 0, 108054348, 0, -66653449, 0, 0, 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, 9, 3, 1, 3, 0]], "char_orbit_index": 5, "prim_orbit_index": 3, "minimal_twist": "36.6.e.a", "char_is_minimal": false, "conrey_index": 37, "id": null, "nf_label": 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, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [4, -4, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 1, 0, 0, 0, 0, 1, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -36, -1, 0, 0, 0, 0, -1, -3, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-34, 34, 0, -1, 0, -1, 1, -8, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-229, 0, 2, 0, -3, 3, -5, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-86, 0, -17, 0, -7, 1, -2, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-78, 78, 0, -15, 0, -6, -5, -4, 6, -5], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, -955, 33, 14, -14, 0, 0, 33, -12, 22], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1198, 2, -15, 15, 0, 0, 2, 27, 15], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [562, -562, 0, -7, 0, 12, 25, 6, -12, 25], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-3726, 0, -7, 0, -30, -21, -40, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1512, 0, 23, 0, -49, -13, -23, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3693, -3693, 0, -45, 0, 51, -19, -23, -51, -19], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 256, -162, 21, -21, 0, 0, -162, 54, 24], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 5026, 33, 18, -18, 0, 0, 33, -87, 38], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-817, 817, 0, -35, 0, -53, -1, 62, 53, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11704, 0, -53, 0, 15, 27, -15, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1542, 0, 264, 0, 41, 66, 49, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [18076, -18076, 0, 75, 0, -138, 50, 182, 138, 50], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 304, 120, -49, 49, 0, 0, 120, -87, -23], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 29692, -140, -45, 45, 0, 0, -140, 87, -119], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2692, -2692, 0, 138, 0, 75, -57, 195, -75, -57], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-22780, 0, 347, 0, 81, 129, 259, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1331, 0, -690, 0, 133, -141, -61, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [42430, -42430, 0, 132, 0, 24, -52, -403, -24, -52], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6134, 122, -91, 91, 0, 0, 122, -112, -323], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 45886, -21, 240, -240, 0, 0, -21, 129, -130], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-9780, 9780, 0, -91, 0, 165, -197, -1065, -165, -197], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-59962, 0, -529, 0, 225, -375, 55, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [12562, 0, 84, 0, 357, -24, 309, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [79024, -79024, 0, 390, 0, 438, 386, 26, -438, 386], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 8219, 749, -281, 281, 0, 0, 749, 605, -43], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}