# Stored data for newform 336.2.s.d, downloaded from the LMFDB on 24 April 2024. {"label": "336.2.s.d", "space_label": "336.2.s", "level": 336, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13512035866247504, "dim": 48, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [40960000, 0, 0, 0, 1024916914176, 0, 0, 0, 216312723169280, 0, 0, 0, 1266871673606144, 0, 0, 0, 492296913989888, 0, 0, 0, 67930945379840, 0, 0, 0, 4177756384768, 0, 0, 0, 136749727616, 0, 0, 0, 2599544544, 0, 0, 0, 29529376, 0, 0, 0, 196224, 0, 0, 0, 696, 0, 0, 0, 1]]], "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 48, "char_orbit_label": "s", "char_is_real": false, "Nk2": 1344, "analytic_conductor": 2.6829735079150208, "level_radical": 42, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [336, 4, [127, 85, 113, 241], [2, 1, 2, 4]], "inner_twist_count": 4, "level_primes": [2, 3, 7], "conrey_indexes": [155, 323], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 24, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, 0, 48], "traces": [48, 0, 0, 0, 0, 6, 48, 0, 0, -16, 0, 6, 0, 0, 0, -28, 0, -20, 8, 0, 0, -8, 0, -38, 0, 0, -12, 0, 0, -24, 0, 0, 0, 12, 0, -4, 16, 0, -24, 60, 0, 6, -48, 0, 20, 52, 0, 62, 48, 0, 0, 12, 0, 14, -32, 0, 0, -100, 0, -16, 8, 0, 0, -60, 0, -96, -16, 0, -28, -16, 0, -80, 0, 0, -12, 4, 0, -56, 0, 0, 0, 4, 0, 6, -48, 0, 56, 116, 0, 68, 0, 0, -64, 48, 0, 62, 0, 0, 32, -28, 0, 104, 0, 0, 0, -60, 0, -6, -80, 0, 0, -28, 0, -128, 8, 0, 20, -100, 0, -124, 0, 0, -32, 40, 0, -20, 0, 0, 24, 184, 0, 56, 8, 0, -72, 96, 0, 56, -24, 0, 40, 100, 0, 152, 48, 0, 0, -52, 0, 86, -112, 0, 0, -8, 0, -12, 64, 0, 0, -156, 0, -76, -16, 0, -72, 20, 0, -38, 0, 0, 84, 108, 0, -56, 0, 0, -96, 124, 0, 96, -72, 0, 0, 136, 0, 160, 32, 0, -12, 128, 0, 122, -128, 0, 84, 0, 0, 132, 32, 0, 0, -232, 0, -96, -32, 0, 0, -20, 0, -24, 32, 0, 96, -104, 0, -114, 0, 0, -8, -96, 0, 36, 0, 0, 128, 112, 0, 72, 32, 0, 0, 92, 0, 204, -128, 0, 64, 12, 0, 228, 64, 0, -100, -212, 0, -36, -48, 0, 0, -104, 0, -4, 80, 0, 0, -268, 0, -100, 16, 0, -112, -116, 0, -28, 0, 0, -56, 44, 0, -124, 0, 0, -24, 168, 0, -24, -112, 0, 104, 60, 0, 164, 32, 0, -156, -96, 0, 68, -176, 0, 48, -40, 0, 6, 0, 0, 0, -12, 0, -82, -48, 0, 0, -268, 0, -164, 160, 0, 16, -32, 0, -232, 0, 0, 20, 136, 0, -116, 0, 0, 128, 52, 0, 8, 200, 0, 96, 128, 0, 172, 160, 0, 32, -32, 0, 62, 224, 0, -4, 24, 0, 8, 48, 0, 0, -368, 0, -192, 56, 0, 0, -212, 0, -192, -112, 0, 0, 136, 0, -248, 0, 0, 216, 12, 0, -76, 0, 0, -200, 24, 0, 116, -48, 0, 152, 0, 0, 14, -16, 0, -36, 84, 0, 118, -32, 0, -24, -296, 0, -192, 128, 0, 0, -260, 0, -28, -168, 0, 0, -128, 0, -192, -64, 0, 248, -100, 0, -264, 0, 0, -104, -8, 0, 32, 0, 0, 192, 256, 0, -16, 64, 0, -104, 188, 0, 184, 8, 0, 168, 104, 0, -62, 80, 0, -104, 148, 0, 176, 32, 0, 0, -56, 0, -84, 48, 0, 0, -60, 0, -256, -112, 0, -132, 60, 0, -32, 0, 0, -64, 440, 0, -96, 0, 0, -248, 296, 0, 204, -16, 0, -8, 236, 0, 132, 160, 0, -152, 332, 0, 368, -336, 0, -28, -108, 0, 66, 128, 0, 0, -16, 0, -92, -80, 0, 0, 8, 0, -132, 112, 0, 40, 244, 0, -80, 0, 0, 4, -24, 0, 8, 0, 0, 128, 116, 0, 120, 48, 0, -120, 408, 0, 236, 8, 0, -12, -156, 0, 280, 112, 0, -68, 4, 0, 200, -64, 0, 0, -168, 0, -164, 368, 0, 0, 144, 0, -56, 80, 0, -44, -536, 0, -92, 0, 0, 80, 12, 0, 136, 0, 0, -304, 296, 0, 32, 8, 0, 0, -32, 0, 244, 16, 0, -56, 4, 0, 272, -224, 0, 52, -8, 0, 40, -192, 0, 0, -24, 0, 6, 48, 0, 0, -348, 0, -188, -48, 0, 128, -144, 0, 102, 0, 0, -96, 320, 0, -164, 0, 0, 56, 264, 0, 120, 272, 0, -200, 116, 0, 132, -256, 0, 172, 248, 0, 32, 336, 0, -160, -236, 0, 68, 48, 0, 0, -372, 0, -12, 0, 0, 0, -308, 0, -80, -216, 0, -152, -72, 0, -408, 0, 0, -64, 44, 0, -224, 0, 0, -208, 48, 0, 124, -208, 0, -8, 228, 0, 256, 96, 0, -184, -416, 0, 62, -160, 0, 32, -180, 0, 20, 0, 0, 0, -112, 0, -292, -240, 0, 0, -372, 0, -316, 32, 0, 32, -192, 0, -328, 0, 0, -96, -28, 0, -284, 0, 0, 392, 244, 0, 204, 192, 0, -128, -96, 0, 104, 80, 0, 140, 92, 0, 124, 0, 0, 232, 204, 0, -318, -288, 0, 0, -176, 0, 12, 184, 0, 0, -48, 0, -44, -112, 0, -276, -60, 0, -372, 0, 0, 148, 464, 0, 100, 0, 0, -128, 104, 0, -6, -176, 0, 16, 376, 0, 196, -80, 0, -72, 272, 0, -118, -448, 0, -56, -80, 0, 228, 64, 0, 0, -172, 0, -96, -128, 0, 0, -28, 0, -396, -232, 0, 264, 152, 0, -88, 0, 0, -168, -176, 0, -128, 0, 0, 272, 208, 0, 140, 8, 0, 24, 508, 0, 56, -256, 0, 392, 200, 0, 456, 192, 0, 20, -496, 0, 268, -80, 0, 0, -100, 0, -16, 40, 0, 0, -132, 0, -192, 272, 0, -144, -180, 0, -124, 0, 0, -120, -268, 0, 120, 0, 0, -352, 532, 0, 212, -448, 0, -296, 468, 0, 292, 176, 0, -32, -252, 0, 354, -192, 0, 120, 40, 0, 312, 256, 0, 0, -24, 0, 32, -240, 0, 0, 16, 0, -20, 96, 0, 148, -8, 0, -164, 0, 0, 240, 512, 0, 212, 0, 0, 304, 96, 0, -156, 304, 0, 24, 56, 0, 312, 320, 0, 188, 184, 0, 416, 528, 0, 204, 284, 0, -64, -64, 0, 0, -88, 0, 56, 272, 0, 0, -492, 0, -240, 8, 0, -144, -284, 0, 124, 0, 0, 112, -296, 0, -400, 0, 0, -72, 40, 0, 92, 48, 0, 224, 96, 0, 300, -112, 0, -144, -16, 0, 100, -304, 0, 40, -496, 0, 56, -256, 0, 0, -488, 0, -14, -24, 0, 0, -196, 0, 8, -16, 0, 368, -816, 0, -372, 0, 0, 40, -80, 0, -352, 0, 0, 168, 100, 0, -192, 104, 0, 200, -32], "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, 3, 2, -1, 2, 0], [1, 1, 16, 6, -1, 4, 0], [1, 1, 48, 11, 1, 4, 0]], "char_orbit_index": 19, "prim_orbit_index": 11, "minimal_twist": "336.2.s.d", "char_is_minimal": true, "conrey_index": 155, "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}