# Stored data for newform 731.2.f.d, downloaded from the LMFDB on 19 April 2024.
{"label": "731.2.f.d", "space_label": "731.2.f", "level": 731, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511142513050331, "dim": 68, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [82944, 0, 17547264, 0, 1201742848, 0, 39514983936, 0, 743150564736, 0, 8838495767616, 0, 70935802502976, 0, 402311206696720, 0, 1670463963102868, 0, 5225522485698308, 0, 12611547001952581, 0, 23955674530640238, 0, 36418015549223537, 0, 44934736513701590, 0, 45529266031816026, 0, 38252442781880952, 0, 26862726596918643, 0, 15869305471910530, 0, 7926378994959872, 0, 3359974450517128, 0, 1211841233307228, 0, 372378897614112, 0, 97498675433559, 0, 21724958167708, 0, 4108657370290, 0, 656617113580, 0, 88100687958, 0, 9833880918, 0, 901598591, 0, 66694494, 0, 3879979, 0, 170816, 0, 5347, 0, 106, 0, 1]], [3, [1150566400, 49642598400, 1070945395200, 13427297661440, 107674425597184, 548992525074048, 1813147348297088, 3680560193943936, 4837658315377232, 6337289377846688, 17822476565197024, 35786569564183664, 40619863930886396, 21385115542800608, 44128885719256616, 88538404659688020, 98557870299650141, 33582922072063176, 48613513726287864, 97249203457453092, 108703363735685207, 28674726933199786, 27815918184690824, 55213601511536494, 62899091903559781, 14154287368543398, 8665148848308802, 16971571021062712, 20174570995581354, 4088888277697052, 1483450768450536, 2860522268497456, 3719093883665318, 677557518156082, 147825467773864, 279868101871320, 419423521141336, 66714599566110, 8941614268472, 16547891995350, 30349147026091, 4031461507462, 334801197044, 601726792512, 1448436567688, 151861639250, 7781287176, 13459503066, 46034221524, 3569149794, 110950840, 182514028, 967457818, 51683828, 936024, 1441748, 13130712, 444532, 4258, 6008, 109664, 2070, 8, 10, 509, 4, 0, 0, 1]]], "char_order": 4, "char_parity": 1, "char_degree": 2, "char_conductor": 17, "char_orbit_label": "f", "char_is_real": false, "Nk2": 2924, "analytic_conductor": 5.837064387755596, "level_radical": 731, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [731, 4, [173, 562], [3, 4]], "inner_twist_count": 2, "level_primes": [17, 43], "conrey_indexes": [259, 302], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 34, "sato_tate_group": "1.2.3.c4", "trace_display": [0, 0, -4, 0], "traces": [68, 0, 0, -76, -4, 4, 0, 0, 0, 2, -6, -10, -24, -22, 0, 84, -2, 28, 0, 10, -36, 8, 14, -62, 0, 0, -12, -58, 2, 160, -26, 0, 44, 16, 56, 0, -6, -56, -24, 70, 6, 0, 0, 14, 10, 2, -68, -58, 0, 40, 16, 4, 0, 26, -16, 50, 18, -94, 0, 0, 22, -48, 16, 60, -22, 0, 24, 20, 8, 0, -14, -84, 34, 26, -102, 0, 0, 40, 4, -30, -92, -76, 0, 108, 8, 8, 0, 16, -72, 132, 12, -174, 0, 0, 50, 10, -16, -28, -86, 0, 152, -30, -4, 0, 52, -84, 22, 188, -78, 0, 0, 98, -36, -80, 112, -132, 0, 84, -34, -356, 0, 40, -8, 74, 28, -10, 0, 0, 0, -156, -10, 136, -64, 0, 112, -80, 44, 0, -12, -232, 78, 114, -64, 0, 0, 56, 56, -40, -8, -142, 0, 272, -78, -12, 0, 162, -108, 40, 90, -226, 0, 0, 32, -80, -34, 360, -46, 0, 108, -206, -252, 0, 54, -72, 134, 80, -48, 0, 0, 88, 72, -126, 16, -230, 0, 288, 6, 228, 0, 4, -80, 140, 14, -100, 0, 0, 74, -92, -26, 140, -192, 0, 160, -96, -144, 0, 82, -16, 34, 384, -148, 0, 0, -46, 4, -192, 56, -284, 0, 100, -50, -76, 0, 130, 36, 114, 48, -140, 0, 0, 120, -10, -72, 440, -172, 0, 228, -72, -120, 0, -46, -48, 94, 212, -140, 0, 0, 110, 200, -92, -124, -560, 0, 136, -108, -108, 0, 4, 4, 8, 12, -66, 0, 0, 38, -58, -166, 212, -92, 0, 96, -132, -232, 0, -12, 64, 116, 58, -182, 0, 0, 104, 74, -248, 180, -176, 0, 272, -4, 112, 0, -84, -312, 118, 86, 118, 0, 0, 72, 124, 0, 76, -52, 0, 288, -232, -176, 0, 4, 224, 72, 168, -122, 0, 0, 84, 10, -154, 96, -366, 0, 184, -120, -96, 0, 148, 76, 76, -116, -424, 0, 0, 166, 90, -56, 84, 72, 0, 32, -298, 112, 0, -102, -24, 158, -18, 64, 0, 0, 190, 348, -172, -284, -394, 0, 604, -172, -72, 0, -146, 228, 92, -38, -282, 0, 0, 118, 176, 2, 212, -168, 0, 100, -314, -212, 0, -96, 128, 118, 226, -216, 0, 0, 54, 336, -354, -80, -176, 0, 148, -136, 328, 0, -82, 72, 374, -100, 32, 0, 0, -16, 164, -94, 136, -22, 0, 264, -230, -80, 0, -108, -72, 120, 114, -262, 0, 0, 74, 54, -222, 20, -198, 0, 264, -124, -280, 0, 188, 408, 2, 12, -652, 0, 0, 244, -86, -36, 240, -56, 0, 616, -426, -108, 0, -276, -84, 198, 42, -102, 0, 0, 250, 148, -40, -216, -120, 0, 844, -56, -332, 0, -274, 108, 222, -238, -54, 0, 0, -18, -72, -154, 276, -6, 0, 148, -250, 208, 0, -76, 504, 90, 10, -310, 0, 0, 256, 134, -188, 52, -348, 0, 188, -48, 256, 0, -228, 4, -70, 22, 134, 0, 0, 108, -354, -168, -28, 54, 0, 192, -628, -560, 0, -158, 272, 308, 10, -192, 0, 0, 416, 106, -470, 172, -234, 0, 332, -106, -76, 0, 186, -24, -274, -114, -328, 0, 0, -20, -92, -208, 940, 14, 0, 136, -24, 204, 0, -30, -224, 134, 204, -26, 0, 0, 164, 332, -174, -324, -262, 0, 916, -16, 344, 0, -230, 128, -38, -200, -250, 0, 0, 328, -184, -52, 652, 266, 0, 88, -546, -196, 0, 10, 136, 196, 4, -132, 0, 0, 412, 8, -624, -264, -174, 0, 672, -60, -24, 0, -10, 12, -200, -72, 22, 0, 0, -288, -102, 52, -224, -124, 0, 404, -262, 56, 0, 40, -52, 52, 78, -260, 0, 0, 168, -34, -518, 164, -624, 0, 324, 198, 384, 0, 50, 220, -62, -186, -334, 0, 0, 98, 380, -186, 600, -10, 0, 36, -228, 48, 0, -316, -176, 690, 164, 124, 0, 0, 284, 322, -242, -196, -378, 0, 380, 158, -552, 0, -98, 212, -24, -106, -344, 0, 0, 32, -288, -436, -8, 12, 0, -84, 6, -228, 0, -96, 304, 26, -260, -174, 0, 0, 676, 138, -566, -412, -372, 0, 796, -78, 336, 0, -298, -160, -294, -160, -30, 0, 0, 228, -190, 2, 84, -18, 0, 300, -284, -504, 0, -328, 220, 318, 126, -88, 0, 0, -34, 86, 140, -140, -90, 0, 144, -14, 548, 0, 320, 220, -46, -140, -412, 0, 0, 222, -246, -264, -152, -102, 0, 112, -138, 28, 0, 214, -544, 158, 58, -76, 0, 0, -150, 204, -56, -24, 148, 0, 612, 140, 252, 0, -160, 536, -22, -150, -148, 0, 0, 106, 266, -28, 672, 210, 0, -120, 108, -364, 0, 162, 60, 86, -88, -294, 0, 0, 234, 338, -564, -36, -22, 0, -40, 168, -48, 0, -284, -48, -66, 158, 396, 0, 0, -226, -578, -192, -8, 260, 0, 656, -154, 12, 0, -318, 184, 232, -414, -280, 0, 0, 134, 12, -640, -84, -162, 0, -124, 84, -44, 0, 476, -152, -372, 98, -1058, 0, 0, 84, 216, -146, 336, -16, 0, 172, -206, -436, 0, -278, -24, 662, 236, 80, 0, 0, -10, 242, 336, -464, -226, 0, 784, -162, 24, 0, -32, -112, 386, -8, -366, 0, 0, -314, 18, -24, 216, -130, 0, 132, -442, -72, 0, 72, -292, 172, 292, -162, 0, 0, 138, 198, -532, -80, -180, 0, 476, -46, 104, 0, -60, 156, -390, -38, 166, 0, 0, -74, -46, 176, 116, -14, 0, 480, -370, 80, 0, -214, -144, 200, -290, -106, 0, 0, 554, -58, 544, 228, -18, 0, 88, -150, -220, 0, 490, 260, 314, 278, 104, 0, 0, -582, -8, -378, 412, -86, 0, -228, -226, -112, 0, -42, 308, 86, 132, 134, 0, 0, -26, 482, 244, -568, -478, 0, 436, 222, -392, 0, -62, 476, -216, 176, -332, 0, 0, 236, -390, 114, 180, -4, 0, -568, -392, -420, 0, 14, -176, 198, 128, -318, 0, 0, 284, 230, -430, 164, -200], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 17, 3, 1, 4, 0]], "char_orbit_index": 6, "prim_orbit_index": 3, "minimal_twist": "731.2.f.d", "char_is_minimal": true, "conrey_index": 259, "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}