# Stored data for newform 108.4.h.a, downloaded from the LMFDB on 24 April 2024. {"label": "108.4.h.a", "space_label": "108.4.h", "level": 108, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 481103446124, "dim": 8, "is_polredabs": true, "nf_label": "8.0.553553856144.1", "trace_hash": 1776812368976174210, "analytic_rank": 0, "is_twist_minimal": false, "hecke_cutters": [[5, [4900, 2310, 433, 33, 1]]], "qexp_display": "q+\\beta _{7}q^{2}+(2\\beta _{2}-2\\beta _{3}-2\\beta _{4}+\\beta _{6}+\\cdots)q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 36, "char_orbit_label": "h", "char_is_real": false, "Nk2": 1728, "analytic_conductor": 6.372206280619986, "hecke_ring_index": 1, "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": "0.589", "prec": 17}, "analytic_rank_proved": true, "char_values": [108, 6, [55, 29], [3, 1]], "hecke_ring_generator_nbound": 11, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [35, 71], "field_disc": 553553856144, "field_disc_factorization": [[2, 4], [3, 6], [83, 4]], "field_poly": [4096, 0, 704, 0, 96, 0, 11, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.079", "prec": 17}, {"__RealLiteral__": 0, "data": "7.716", "prec": 17}, {"__RealLiteral__": 0, "data": "13.700", "prec": 20}, {"__RealLiteral__": 0, "data": "439.870", "prec": 24}, {"__RealLiteral__": 0, "data": "1740.095", "prec": 27}, {"__RealLiteral__": 0, "data": "40181.185", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c6", "trace_display": [3, 0, -66, 0], "traces": [0, 8, 3, 0, 11, -66, 0, 0, 0, 0, -116, 0, 0, 214, 42, 0, 71, 0, 0, 0, -306, 0, 207, 0, 0, -54, 0, 0, 540, 498, 0, 0, -327, 0, 469, 0, 0, -1256, -1035, 0, -602, 1272, 0, 0, 0, 0, -912, 0, 0, -154, 1329, 0, -464, 0, 0, 0, 1314, 0, -830, 0, 0, 262, 0, 0, -550, -3282, 0, 0, 843, 0, -480, 0, 0, 3940, -222, 0, 105, -330, 0, 0, 0, 0, 4786, 0, 0, -472, -1209, 0, -1425, 0, 0, 0, 1308, 0, 1356, 0, 0, -572, 0, 0, 2442, 3894, 0, 0, -6384, 0, -3152, 0, 0, -5840, -2046, 0, 2730, -6078, 0, 0, 0, 0, -2958, 0, 0, 1172, 9036, 0, 3864, 0, 0, 0, 7059, 0, -2356, 0, 0, 6360, 0, 0, -6578, -636, 0, 0, -5700, 0, 1758, 0, 0, -1660, -9105, 0, -1478, 3894, 0, 0, 0, 0, -3900, 0, 0, 3538, 10194, 0, 1342, 0, 0, 0, 9723, 0, -2268, 0, 0, -2910, 0, 0, -1458, -1554, 0, 0, -5007, 0, 1672, 0, 0, -4064, 1500, 0, -4164, 9864, 0, 0, 0, 0, 10140, 0, 0, -6920, -11883, 0, -4183, 0, 0, 0, -2949, 0, 6742, 0, 0, -11146, 0, 0, 10336, 18270, 0, 0, -10104, 0, 6015, 0, 0, 10980, -23604, 0, 2214, -18324, 0, 0, 0, 0, -6608, 0, 0, 9262, 5532, 0, -5810, 0, 0, 0, 6123, 0, -2250, 0, 0, -4004, 0, 0, 19120, -6672, 0, 0, -3240, 0, -184, 0, 0, 17268, -2124, 0, -1201, 10068, 0, 0, 0, 0, -3672, 0, 0, -7924, 34650, 0, -3537, 0, 0, 0, 22809, 0, 4987, 0, 0, 14458, 0, 0, -22920, -38202, 0, 0, -4086, 0, -12444, 0, 0, -2004, 9960, 0, -5165, -8130, 0, 0, 0, 0, -16064, 0, 0, -10410, 7476, 0, 19965, 0, 0, 0, -6510, 0, -2316, 0, 0, 2524, 0, 0, -23172, 15222, 0, 0, -318, 0, 9420, 0, 0, -11256, -28386, 0, 10327, 37902, 0, 0, 0, 0, 4404, 0, 0, -3320, 11139, 0, -4678, 0, 0, 0, -16695, 0, -4082, 0, 0, 4138, 0, 0, 22026, -18300, 0, 0, 3120, 0, -10752, 0, 0, -55828, 22380, 0, 13200, -11340, 0, 0, 0, 0, 15224, 0, 0, -9602, -32397, 0, 2112, 0, 0, 0, 18810, 0, 9798, 0, 0, 5550, 0, 0, -26054, 45150, 0, 0, 9111, 0, 9760, 0, 0, 49336, 24066, 0, 16023, -11460, 0, 0, 0, 0, -7968, 0, 0, 55552, -55794, 0, 12180, 0, 0, 0, -18864, 0, -6015, 0, 0, -32174, 0, 0, -176, -39414, 0, 0, -3303, 0, 6774, 0, 0, 75556, 14700, 0, -29444, -55620, 0, 0, 0, 0, 54416, 0, 0, -1396, -11532, 0, -21390, 0, 0, 0, -22068, 0, -14541, 0, 0, 5452, 0, 0, 2544, 52710, 0, 0, 40338, 0, -22835, 0, 0, -35796, -1956, 0, -11625, 20064, 0, 0, 0, 0, 9120, 0, 0, -34096, 23391, 0, -17914, 0, 0, 0, -1176, 0, -25406, 0, 0, -36520, 0, 0, 4656, 19980, 0, 0, 12252, 0, 6291, 0, 0, -65908, -17304, 0, -8532, 6294, 0, 0, 0, 0, -54062, 0, 0, -32922, -5100, 0, 30464, 0, 0, 0, -44088, 0, 36666, 0, 0, 27086, 0, 0, 94740, 55602, 0, 0, -20799, 0, 24988, 0, 0, 1744, 43380, 0, -13619, 91008, 0, 0, 0, 0, -35718, 0, 0, 25710, -54768, 0, -6237, 0, 0, 0, -68700, 0, 17632, 0, 0, 36998, 0, 0, 34020, -59244, 0, 0, 67488, 0, 16902, 0, 0, -34700, 75318, 0, 8300, -71106, 0, 0, 0, 0, -45980, 0, 0, 10020, 16062, 0, -13886, 0, 0, 0, -16308, 0, -26388, 0, 0, 35644, 0, 0, -81168, -48720, 0, 0, 39555, 0, -56836, 0, 0, 8824, 45135, 0, -1350, -49836, 0, 0, 0, 0, 10212, 0, 0, 24892, -82269, 0, -16328, 0, 0, 0, 87570, 0, 58876, 0, 0, 17452, 0, 0, -63788, -143160, 0, 0, 36888, 0, 32415, 0, 0, 57888, 70728, 0, 51294, 45678, 0, 0, 0, 0, 88920, 0, 0, 53422, -38766, 0, -5736, 0, 0, 0, -71646, 0, -7782, 0, 0, -61646, 0, 0, 10638, 31794, 0, 0, 19782, 0, -37092, 0, 0, -13588, 11616, 0, -29283, 1092, 0, 0, 0, 0, -20670, 0, 0, -24058, -56532, 0, 10050, 0, 0, 0, -88965, 0, -55205, 0, 0, 41842, 0, 0, -22304, 38382, 0, 0, -4176, 0, -2814, 0, 0, 13500, -123648, 0, 18316, -69720, 0, 0, 0, 0, 69860, 0, 0, -53822, 99366, 0, -4788, 0, 0, 0, 42564, 0, 19560, 0, 0, -3406, 0, 0, 143646, 105732, 0, 0, 47328, 0, 48140, 0, 0, -79376, -58923, 0, 79650, 250566, 0, 0, 0, 0, 75780, 0, 0, -58082, 38400, 0, 57625, 0, 0, 0, -5277, 0, -57146, 0, 0, -32808, 0, 0, -106810, -71574, 0, 0, -5520, 0, -39384, 0, 0, -7324, 30702, 0, -123174, -143886, 0, 0, 0, 0, -88730, 0, 0, 40410, -79572, 0, -32198, 0, 0, 0, 4980, 0, -35238, 0, 0, -77430, 0, 0, -156172, 168690, 0, 0, -29700, 0, 21150, 0, 0, 92488, 1068, 0, -19568, 130626, 0, 0, 0, 0, -8856, 0, 0, -32982, 109458, 0, 44034, 0, 0, 0, -95592, 0, 29613, 0, 0, -31418, 0, 0, 137754, -83562, 0, 0, 37302, 0, -47334, 0, 0, 31868, 128307, 0, 25680, -195774, 0, 0, 0, 0, -45240, 0, 0, -1754, -81984, 0, 25422, 0, 0, 0, 44976, 0, 2409, 0, 0, 43668, 0, 0, 63168, -52020, 0, 0, -114546, 0, 33163, 0, 0, 144464, -2649, 0, -57476, -14280, 0, 0, 0, 0, -41400, 0, 0, 56166, 8073, 0, -40286, 0, 0, 0, 70200, 0, 37372, 0, 0, 13956, 0, 0, -48140, 7734, 0, 0, -90165, 0, -19593, 0, 0, -73688, -82770, 0, 83184, -115302, 0, 0, 0, 0, -426, 0, 0, 126560, 34515, 0, 24150, 0, 0, 0, 101460, 0, 65118, 0, 0, -26818, 0, 0, 30766, 191370, 0, 0, -19590, 0, 77018, 0, 0, -163740, -100098, 0, 92584, 48792, 0, 0, 0, 0, 112086, 0, 0, -67480, 107070, 0, -26160, 0, 0, 0, 165864, 0, 41100, 0, 0, 53554, 0, 0, 128408], "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, 4, 2, -1, 2, 0], [1, 1, 9, 4, -1, 6, 0], [1, 1, 36, 8, 1, 6, 0]], "char_orbit_index": 8, "prim_orbit_index": 8, "minimal_twist": "36.4.h.a", "char_is_minimal": false, "conrey_index": 35, "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, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 2, -2, -2, 0, 1, 0], [-10, 1, 0, 1, -5, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -3, 0, -5, 0, -7, 3, -2], [-10, -6, 2, -2, -20, -2, 5, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-10, 2, -2, 2, 0, -2, 4, -6], [0, -1, 2, -10, 0, 1, 1, -9], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 1, -55, 0, -1, -2], [4, -8, -10, -18, 2, -20, 2, -10], [0, 0, 0, 0, 0, 0, 0, 0], [26, -2, 0, -8, 26, -14, 24, 5], [-30, -13, 0, 0, -60, 0, -13, -13], [0, 0, 0, 0, 0, 0, 0, 0], [0, 5, 30, 40, 0, 30, -5, 35], [-20, 12, -24, 16, 20, -12, -12, -18], [0, 0, 0, 0, 0, 0, 0, 0], [0, -4, -16, 20, -60, 0, -7, 2], [0, 21, 5, 26, 0, 10, -21, 5], [0, 0, 0, 0, 0, 0, 0, 0], [-30, -22, 0, -11, -30, 0, -22, -11], [10, -2, -2, 2, 20, 2, 54, 56], [0, 0, 0, 0, 0, 0, 0, 0], [60, 4, -44, -36, 0, -44, -14, -30], [53, 0, 0, 23, -53, 0, 0, -23], [0, 0, 0, 0, 0, 0, 0, 0], [0, -7, 43, -36, 0, 0, 7, -29], [-60, 20, -38, -18, -30, -76, -31, -38], [0, 0, 0, 0, 0, 0, 0, 0], [130, -26, 0, 0, 130, 26, 60, 43], [0, 70, -55, 55, 0, 55, -70, -15], [0, 0, 0, 0, 0, 0, 0, 0], [-160, -2, 0, -4, 0, 0, -2, 2], [-90, -70, 140, -20, 90, 70, 70, 65], [0, 0, 0, 0, 0, 0, 0, 0], [0, 48, -60, 12, 140, 0, -62, -64], [162, -50, 0, -50, 81, 0, -50, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 51, 0, 52, 0, 53, -51, 1], [110, 50, -14, 14, 220, 14, 37, 51], [0, 0, 0, 0, 0, 0, 0, 0], [-126, -42, 62, -22, 0, 62, 26, 36], [0, -87, 174, -77, 0, 87, 87, 10], [0, 0, 0, 0, 0, 0, 0, 0], [0, 37, 0, -37, 94, 0, 37, 74], [220, -44, 22, -22, 110, 44, 41, 22], [0, 0, 0, 0, 0, 0, 0, 0], [-80, 120, 0, 8, -80, -104, -24, -64], [10, 74, 0, 0, 20, 0, 74, 74], [0, 0, 0, 0, 0, 0, 0, 0], [0, 26, 17, 69, 0, 17, -26, 43], [84, 60, -120, -56, -84, -60, -60, -14], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, -46, 46, 230, 0, 30, 106], [0, 70, 3, 73, 0, 6, -70, 3], [0, 0, 0, 0, 0, 0, 0, 0], [-41, -142, 0, -71, -41, 0, -142, -71], [-130, -158, 14, -14, -260, -14, 50, 36], [0, 0, 0, 0, 0, 0, 0, 0], [-98, -62, -90, -214, 0, -90, 23, -113], [-255, 0, 0, 37, 255, 0, 0, -37], [0, 0, 0, 0, 0, 0, 0, 0], [0, 76, -101, 25, 0, 0, -76, -51], [140, 172, -34, 138, 70, -68, -173, -34], [0, 0, 0, 0, 0, 0, 0, 0], [-90, 190, 0, 220, -90, 250, -110, 70], [0, -106, 26, -26, 0, -26, 106, 80], [0, 0, 0, 0, 0, 0, 0, 0], [620, 85, 0, 170, 0, 0, 85, -85], [20, -4, 8, -8, -20, 4, 4, -158], [0, 0, 0, 0, 0, 0, 0, 0], [0, -280, 270, 10, -150, 0, 115, -40], [-10, 45, 0, 45, -5, 0, 45, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -341, 0, -207, 0, -73, 341, 134], [-20, 116, -124, 124, -40, 124, -262, -138], [0, 0, 0, 0, 0, 0, 0, 0], [500, -100, 100, -100, 0, 100, -31, 131], [0, 161, -322, 131, 0, -161, -161, -30], [0, 0, 0, 0, 0, 0, 0, 0], [0, 48, 0, -48, 190, 0, 48, 96], [-200, 4, 104, 108, -100, 208, -1, 104], [0, 0, 0, 0, 0, 0, 0, 0], [-390, 158, 0, 56, -390, -46, -248, -147], [-102, -46, 0, 0, -204, 0, -46, -46], [0, 0, 0, 0, 0, 0, 0, 0], [0, 100, -325, -125, 0, -325, -100, -225], [160, -72, 144, 104, -160, 72, 72, -28], [0, 0, 0, 0, 0, 0, 0, 0], [0, -348, 194, 154, -462, 0, 184, 174], [0, -200, -290, -490, 0, -580, 200, -290], [0, 0, 0, 0, 0, 0, 0, 0], [-5, 184, 0, 92, -5, 0, 184, 92], [-370, 74, 74, -74, -740, -74, -57, -131], [0, 0, 0, 0, 0, 0, 0, 0], [270, 82, 6, 170, 0, 6, -129, 135]]}