# Stored data for newform 784.2.x.p, downloaded from the LMFDB on 27 April 2024.
{"label": "784.2.x.p", "space_label": "784.2.x", "level": 784, "weight": 2, "hecke_orbit": 16, "hecke_orbit_code": 67555574992077584, "dim": 96, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [4294967296, 0, 0, 0, -32311038967808, 0, 0, 0, 240532834278703104, 0, 0, 0, -19096564361003532288, 0, 0, 0, 1373137317150878334976, 0, 0, 0, -10114973896195002335232, 0, 0, 0, 59502764111697222303744, 0, 0, 0, -78460929427749666291712, 0, 0, 0, 72004952424752735125504, 0, 0, 0, -31949050074833315954688, 0, 0, 0, 9831047739401653125120, 0, 0, 0, -1823413996320809680896, 0, 0, 0, 241458515147210006528, 0, 0, 0, -22758390154016522240, 0, 0, 0, 1627396910840127488, 0, 0, 0, -88448475147563008, 0, 0, 0, 3747155880329984, 0, 0, 0, -122067528105984, 0, 0, 0, 3083985715200, 0, 0, 0, -58586222592, 0, 0, 0, 849400992, 0, 0, 0, -8966400, 0, 0, 0, 69072, 0, 0, 0, -336, 0, 0, 0, 1]], [5, [60336661037197280935936, 0, 0, 0, -751198847848347384938496, 0, 0, 0, 6009447160366829444005888, 0, 0, 0, -27836113651082923379523584, 0, 0, 0, 92560209871836212382138368, 0, 0, 0, -214307052860740945829691392, 0, 0, 0, 370730570978095952534962176, 0, 0, 0, -451216726118344511929188352, 0, 0, 0, 402066795035085285202395136, 0, 0, 0, -230617296993716713008136192, 0, 0, 0, 92511098480941416888598528, 0, 0, 0, -19349397154483816932835328, 0, 0, 0, 2798689268917314753372160, 0, 0, 0, -177299015397965436387328, 0, 0, 0, 7643664485211123138560, 0, 0, 0, -216645259463118340096, 0, 0, 0, 4515884835488973568, 0, 0, 0, -66735808233768960, 0, 0, 0, 736377886682112, 0, 0, 0, -5731077684224, 0, 0, 0, 33435938208, 0, 0, 0, -139298048, 0, 0, 0, 426416, 0, 0, 0, -832, 0, 0, 0, 1]]], "char_order": 12, "char_parity": 1, "char_degree": 4, "char_conductor": 112, "char_orbit_label": "x", "char_is_real": false, "Nk2": 3136, "analytic_conductor": 6.260271518468382, "level_radical": 14, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [784, 12, [687, 197, 689], [12, 3, 8]], "inner_twist_count": 8, "level_primes": [2, 7], "conrey_indexes": [165, 373, 557, 765], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 24, "sato_tate_group": "1.2.3.c12", "trace_display": [0, 0, 0, 0], "traces": [96, 0, 0, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 64, -36, 0, -20, 0, 0, 0, -56, 0, 0, 0, 0, 0, 0, -32, -96, 0, -40, 0, 0, 0, 80, 16, 0, 0, 0, 0, 0, 16, -4, 0, -64, 0, 0, 0, -56, 0, 0, -16, 0, 0, 0, 0, 20, 0, -8, 0, 0, 0, 88, 0, 0, -40, 0, 0, 0, 0, 196, 0, 28, 0, 0, 0, 112, -80, 0, 48, 0, 0, 0, 0, 108, 0, 100, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, -80, 48, 0, 192, 0, 0, 0, 88, -8, 0, -80, 0, 0, 0, -64, -72, 0, 100, 0, 0, 0, -208, 0, 0, -80, 0, 0, 0, -320, -168, 0, -32, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, -192, -216, 0, -200, 0, 0, 0, -72, -16, 0, 0, 0, 0, 0, -160, -144, 0, -64, 0, 0, 0, 80, 40, 0, 0, 0, 0, 0, 0, 176, 0, -52, 0, 0, 0, -40, -64, 0, 56, 0, 0, 0, 0, 168, 0, 8, 0, 0, 0, 160, 208, 0, 0, 0, 0, 0, -32, 364, 0, 148, 0, 0, 0, 96, 128, 0, -144, 0, 0, 0, 176, 164, 0, 132, 0, 0, 0, -360, 128, 0, 0, 0, 0, 0, 96, -64, 0, 64, 0, 0, 0, -136, 0, 0, 32, 0, 0, 0, 704, -408, 0, -244, 0, 0, 0, -160, 0, 0, 0, 0, 0, 0, 128, -280, 0, -132, 0, 0, 0, -416, -80, 0, 0, 0, 0, 0, 416, -212, 0, -368, 0, 0, 0, -16, -136, 0, 80, 0, 0, 0, 0, 232, 0, -152, 0, 0, 0, -8, -48, 0, 16, 0, 0, 0, 0, 348, 0, 60, 0, 0, 0, 144, -160, 0, -160, 0, 0, 0, 0, 384, 0, 416, 0, 0, 0, -48, 16, 0, 80, 0, 0, 0, -384, 172, 0, 92, 0, 0, 0, -224, -216, 0, 304, 0, 0, 0, 0, -236, 0, 56, 0, 0, 0, 24, 0, 0, 104, 0, 0, 0, -960, -436, 0, -8, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 320, -528, 0, -144, 0, 0, 0, 240, 80, 0, 0, 0, 0, 0, -272, -248, 0, -352, 0, 0, 0, 272, 280, 0, 16, 0, 0, 0, 0, 84, 0, -60, 0, 0, 0, 384, 0, 0, -16, 0, 0, 0, 0, 536, 0, 400, 0, 0, 0, 240, 160, 0, 0, 0, 0, 0, 160, 372, 0, 220, 0, 0, 0, 568, -256, 0, -224, 0, 0, 0, 736, 84, 0, 408, 0, 0, 0, 80, 24, 0, 0, 0, 0, 0, -256, -312, 0, 264, 0, 0, 0, -112, 0, 0, -48, 0, 0, 0, 736, -356, 0, 80, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, -160, -272, 0, -472, 0, 0, 0, 0, 160, 0, 0, 0, 0, 0, 592, 0, 0, -104, 0, 0, 0, 48, -232, 0, -224, 0, 0, 0, 0, 136, 0, -112, 0, 0, 0, 432, 0, 0, 48, 0, 0, 0, 0, 544, 0, 156, 0, 0, 0, 144, -288, 0, -80, 0, 0, 0, -192, 408, 0, 212, 0, 0, 0, -32, -80, 0, -32, 0, 0, 0, -816, 336, 0, 308, 0, 0, 0, -184, -368, 0, -336, 0, 0, 0, 640, -192, 0, -120, 0, 0, 0, -208, 0, 0, 56, 0, 0, 0, -1120, -424, 0, -224, 0, 0, 0, -672, 0, 0, 0, 0, 0, 0, -512, -448, 0, -388, 0, 0, 0, -56, -32, 0, 0, 0, 0, 0, -944, -88, 0, -400, 0, 0, 0, -160, 160, 0, -80, 0, 0, 0, 0, 88, 0, -480, 0, 0, 0, 160, 208, 0, -160, 0, 0, 0, 0, 192, 0, -116, 0, 0, 0, -160, 416, 0, 0, 0, 0, 0, -320, 392, 0, 88, 0, 0, 0, -424, 208, 0, 64, 0, 0, 0, 688, 304, 0, 276, 0, 0, 0, 904, 384, 0, 0, 0, 0, 0, -256, -144, 0, -144, 0, 0, 0, 80, 0, 0, 24, 0, 0, 0, 1088, -220, 0, 144, 0, 0, 0, -568, 0, 0, 0, 0, 0, 0, -96, -656, 0, -20, 0, 0, 0, -32, -112, 0, 0, 0, 0, 0, 1056, 76, 0, -104, 0, 0, 0, 424, -336, 0, 336, 0, 0, 0, 0, 144, 0, 88, 0, 0, 0, 144, 128, 0, 200, 0, 0, 0, 0, 296, 0, 292, 0, 0, 0, -32, -352, 0, 384, 0, 0, 0, 352, 300, 0, 408, 0, 0, 0, 176, 160, 0, 128, 0, 0, 0, -960, -96, 0, 108, 0, 0, 0, -248, -112, 0, 448, 0, 0, 0, 0, 232, 0, 388, 0, 0, 0, -872, 0, 0, 224, 0, 0, 0, -640, -348, 0, -144, 0, 0, 0, -448, 0, 0, 0, 0, 0, 0, 832, -168, 0, -80, 0, 0, 0, -48, -144, 0, 0, 0, 0, 0, -944, -296, 0, -112, 0, 0, 0, -640, 256, 0, 160, 0, 0, 0, 0, 100, 0, 236, 0, 0, 0, -600, 0, 0, -160, 0, 0, 0, 0, 356, 0, -48, 0, 0, 0, 384, 560, 0, 0, 0, 0, 0, 192, 144, 0, 148, 0, 0, 0, -528, -208, 0, 0, 0, 0, 0, 816, -48, 0, 180, 0, 0, 0, -960, 504, 0, 0, 0, 0, 0, 256, 0, 0, 204, 0, 0, 0, 0, 0, 0, -360, 0, 0, 0, 1344, -400, 0, -384, 0, 0, 0, 288, 0, 0, 0, 0, 0, 0, -160, 8, 0, -340, 0, 0, 0, -16, 192, 0, 0, 0, 0, 0, 1248, -336, 0, -296, 0, 0, 0, -592, -152, 0, -352, 0, 0, 0, 0, 180, 0, -392, 0, 0, 0, 144, -48, 0, 136, 0, 0, 0, 0, 52, 0, -320, 0, 0, 0, 0, -576, 0, 0, 0, 0, 0, -672, 428, 0, -24, 0, 0, 0, 160, -96, 0, 208, 0, 0, 0, -1312, -176, 0, -84, 0, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0], [1, 1, 7, 3, 1, 3, 0], [1, 1, 7, 4, -1, 6, 0], [1, 1, 16, 5, 1, 4, 0], [1, 1, 112, 12, -1, 4, 0], [1, 1, 112, 23, 1, 12, 0], [1, 1, 112, 24, -1, 12, 0]], "char_orbit_index": 24, "prim_orbit_index": 23, "minimal_twist": "784.2.m.l", "char_is_minimal": false, "conrey_index": 165, "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}