# Stored data for newform 108.4.l.a, downloaded from the LMFDB on 19 April 2024. {"label": "108.4.l.a", "space_label": "108.4.l", "level": 108, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 755981353068, "dim": 312, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "char_order": 18, "char_parity": 1, "char_degree": 6, "char_conductor": 108, "char_orbit_label": "l", "char_is_real": false, "Nk2": 1728, "analytic_conductor": 6.372206280619986, "level_radical": 6, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [108, 18, [55, 29], [9, 13]], "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [11, 23, 47, 59, 83, 95], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 52, "sato_tate_group": "3.2.3.c18", "trace_display": [-6, 0, -12, 0], "traces": [312, -6, 0, -6, -12, -6, 0, -9, -12, -3, 0, -123, -12, 69, 0, -6, -18, 351, 0, 225, -12, -6, 0, -300, -12, 0, 0, -12, -96, -207, 0, -696, 858, -30, 0, -1056, -6, -900, 0, -381, 138, 2574, 0, 2655, -672, -3, 0, -435, -12, -2829, 0, 1371, 0, -4458, 0, -2925, 660, 885, 0, 966, -12, 1872, 0, -3, -708, 3093, 0, 2211, -1572, -1011, 0, -4524, -6, -5883, 0, -198, -996, -2976, 0, 0, 444, -12, 0, 6324, -762, 8322, 0, 1530, 4212, -1104, 0, -3255, 7404, 2019, 0, 582, -66, 2898, 0, -3, -9372, 4185, 0, 2859, -7122, -4683, 0, 2733, -24, 4938, 0, -3921, -5556, 5208, 0, 5346, -2460, -3, 0, 1644, -1362, 5220, 0, 4449, 21474, 615, 0, -1581, 8268, 3744, 0, 5772, -2070, 0, 0, -3084, -7890, -732, 0, 2688, -9876, 11844, 0, -5949, -6, -8457, 0, 2076, -8148, -15234, 0, -11511, -8520, -3, 0, -9924, -12, -5421, 0, -20040, 0, -6627, 0, -5919, 10680, -17772, 0, -14061, -12, -20034, 0, -3, 6564, -25671, 0, -15015, 18672, 9960, 0, -2886, -6, 870, 0, 20160, 16830, 20841, 0, 0, -7428, -6012, 0, -21621, 5226, -12054, 0, 9477, -13734, 17709, 0, 27381, -16632, -2085, 0, 33411, -3792, 23616, 0, -3, 6534, 22449, 0, 28722, 15198, -15390, 0, 14886, -24, 11748, 0, -14037, 126, 35130, 0, 38601, -336, -3, 0, 35256, -1200, 34467, 0, 2049, -9846, 11733, 0, -7791, -12876, 4857, 0, 294, 7818, 0, 0, -12, 8898, 4308, 0, 13797, 11748, -4023, 0, -27609, -6, -39429, 0, 6258, 29886, -37296, 0, -58005, 47256, -3, 0, -62415, 1488, -56259, 0, 24024, 0, -47595, 0, -57246, -17010, 22404, 0, -57453, -12, -62064, 0, 3069, -44268, -38265, 0, -32292, -67470, -8184, 0, -21354, 17334, -31557, 0, -50871, -14052, -8526, 0, 0, 35472, -12, 0, 33303, 13164, 56031, 0, -20502, 6822, 23601, 0, 44682, 10140, 21999, 0, 57720, -38352, 73386, 0, -14421, 14988, 80637, 0, 103281, -74190, 56793, 0, 88725, -24, 103617, 0, 52998, -70872, 112641, 0, 58725, -1542, -11505, 0, 62544, -25392, 45330, 0, -5565, -2466, 52227, 0, 58302, 24408, -54033, 0, 43677, 23532, 0, 0, -12, 66300, -71475, 0, -86052, -16554, -47070, 0, -67161, 17322, -35724, 0, 4170, -61470, -76611, 0, -113661, -29046, 5997, 0, -108885, -12, -140739, 0, 38655, 0, -187584, 0, -184842, 24750, 35337, 0, -111693, 12090, -87849, 0, -3, 92292, -94980, 0, -79773, -14598, 35745, 0, -90732, -6, -78471, 0, 24477, -88086, -44808, 0, 0, 12, -12, 0, 77874, 6738, 101832, 0, -41181, 28818, 98850, 0, 124938, 59616, -45234, 0, 146355, -34680, 82854, 0, 1533, 90600, 189237, 0, 177228, 15246, -53247, 0, 218514, -24, 213591, 0, -48477, 28782, 130170, 0, 172611, 94548, 14736, 0, 129540, -27654, 150549, 0, 66114, 53982, 107256, 0, 119205, 14880, 79752, 0, 16395, 19698, 0, 0, 17808, -58800, -41883, 0, -57267, -31044, 26997, 0, -144057, -6, -186942, 0, -36729, 21684, -148695, 0, -204201, 36384, -34752, 0, -275355, 13170, -260982, 0, -117729, 0, -255861, 0, -231765, -20064, -106329, 0, -220230, -29490, -240156, 0, -30378, -13158, -229143, 0, -229407, 76416, 4797, 0, -170217, -6, -86226, 0, 44730, 67188, -43551, 0, 0, -46386, 35304, 0, 15261, 3552, 73740, 0, 81375, -42570, 220464, 0, 198615, -141126, 58962, 0, 277656, 30876, 298476, 0, 20574, -72684, 302472, 0, 314424, 38274, -72453, 0, 391893, -24, 356607, 0, -84810, 12240, 331860, 0, 352161, -118464, 2997, 0, 254712, 25692, 258351, 0, -92184, -167778, 191058, 0, 130299, -104088, -39777, 0, 5010, -12000, 0, 0, 3060, -168630, -57927, 0, -143184, 27960, 87504, 0, -194124, -6, -257502, 0, 124659, 16572, -411147, 0, -427500, -47664, -3, 0, -426081, -41166, -442146, 0, 81429, 0, -386526, 0, -362241, -8046, 624, 0, -544392, -54552, -442800, 0, -3, 9132, -314160, 0, -262206, 114060, -90315, 0, -128652, -6, -48537, 0, -58890, 197880, -192, 0, 0, 146112, 474, 0, 90681, 19542, 108189, 0, 18354, 43902, 323040, 0, 293112, 98616, 33420, 0, 451890, 75258, 535491, 0, -3, -35718, 459570, 0, 491118, -48288, 127170, 0, 426345, -69684, 568113, 0, 111159, 51780, 500619, 0, 489141, -57108, -3, 0, 523437, 66948, 288951, 0, 25830, 98190, 167919, 0, 133860, 151776, 1767, 0, 102003, -444, 0, 0, 26718, 265200, -158499, 0, -197316, 116460, -65994, 0, -212022, -6, -455826, 0, -113352, 8148, -633090, 0, -532395, 16872, -3, 0, -586290, -94398, -552279, 0, 48744, 0, -571137, 0, -629784, 114282, 192720, 0, -570153, -50664, -660753, 0, -3075, 70404, -564153, 0, -486963, -71076, 118521, 0, -264522, -6, -269844, 0, 52863, -272634, -101721, 0, 0, -239670, 5988, 0, 171519, 17916, 197070, 0, -104469, -297378, 300861, 0, 518304, -106410, -166035, 0, 527778, 116088, 767502, 0, -29481, -65124, 775296, 0, 735486, -249516, -71973, 0, 792537, -24, 724770, 0, 68274, -179868, 804483, 0, 704556, -18738, -58485, 0, 631278, 103128, 671856, 0, 57099, -113166, 379533, 0, 239991, -188946, 18030, 0, 99615, 15534, 0, 0, -12, -98952, -195921, 0, -314985, -65004, -94890, 0, -542520, -6, -518289, 0, -115731, 68856, -752859, 0, -832383, 233094, 81321, 0, -843255, 13470, -855453, 0, -127632, 0, -1076106, 0, -981906, -239700, -123636, 0, -807006, 75744, -740124, 0, 75489, -242448, -594165, 0, -565488, -56028, -106629, 0, -502458, -6, -428268, 0, -81948, 92304, -40569, 0, 0, 252516, -12, 0, 264546, -64272, 327060, 0, 24618, 487638, 551463, 0, 669255, 117498, 65883, 0, 755196, -162660, 908955, 0, -74601, 130224, 1010133, 0, 1185585, 463278, 16200, 0, 1089642, -24, 975639, 0, -135627, 460128, 966921, 0, 733230, 253332, -41157, 0, 722550, -147108, 617001, 0, -150492, 350892, 509340, 0, 330816, 321168, -67290, 0, 109848, -40410, 0, 0, -12, 79218, -235782, 0, -445899, 231312, 130056, 0, -760134, 29472, -663186, 0, 208815, -37734, -701898, 0, -703134, -408204, -58731, 0, -972168, 231054, -1192374, 0, 2316, 0, -1277985, 0, -1423683, -55584, -67965, 0, -1069458, 350994, -856566, 0, -74604, 336, -875310, 0, -772869, 156972, -3087, 0, -616623, 11820, -521439, 0, 63651, -139188, -249954, 0, 0, -258654, 69324, 0, 357141, -187710, 541917, 0, 135297, -113238, 773487, 0, 788592, -250740, 129621, 0, 1035204, -185988, 897921, 0, 123522, -531312, 1369356, 0, 1385850, -99384, 55854, 0, 1223874, -209328, 1253097, 0, 105672, -76596, 1059249, 0, 1312461, -666876, 116232, 0, 835314, -171186, 814659, 0, 132723, -359118, 729771, 0, 591591, -450972, 155862, 0, 250014, -138684, 0, 0, 31260], "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, 27, 6, -1, 18, 0], [1, 1, 108, 12, 1, 18, 0]], "char_orbit_index": 12, "prim_orbit_index": 12, "minimal_twist": "108.4.l.a", "char_is_minimal": true, "conrey_index": 11, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "qexp_display": null, "fricke_eigenval": null, "atkin_lehner_string": null, "hecke_ring_index": null, "projective_image": null, "projective_image_type": null, "field_poly_is_cyclotomic": null, "field_poly_root_of_unity": null, "artin_degree": null, "artin_image": null, "field_poly_is_real_cyclotomic": null, "artin_field_label": null, "projective_field_label": null, "hecke_ring_index_proved": null, "trace_zratio": null, "hecke_ring_generator_nbound": null, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "hecke_ring_index_factorization": null, "trace_moments": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null}