# Stored data for newform 4004.2.e.b, downloaded from the LMFDB on 16 April 2024.
{"label": "4004.2.e.b", "space_label": "4004.2.e", "level": 4004, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503874538835876, "dim": 48, "analytic_rank": 0, "is_twist_minimal": true, "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 77, "char_orbit_label": "e", "char_is_real": true, "Nk2": 16016, "analytic_conductor": 31.972100969320667, "level_radical": 2002, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [4004, 2, [2003, 3433, 365, 925], [2, 1, 1, 2]], "inner_twist_count": 2, "level_primes": [2, 7, 11, 13], "conrey_indexes": [3849], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 48, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 0, 0, 4], "traces": [48, 0, 0, 0, 0, 0, 4, 0, -48, 0, 2, 0, -48, 0, 8, 0, -4, 0, 0, 0, -10, 0, 4, 0, -44, 0, 0, 0, 0, 0, 0, 0, -10, 0, 14, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -8, 0, 12, 0, 0, 0, 0, 0, -16, 0, -16, 0, 0, 0, 4, 0, 0, 0, 0, 0, 16, 0, 0, 0, 22, 0, 0, 0, 64, 0, 4, 0, 0, 0, 12, 0, 0, 0, -4, 0, 36, 0, 0, 0, 0, 0, -40, 0, -12, 0, 0, 0, 74, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0, 48, 0, 14, 0, 28, 0, 0, 0, 0, 0, 0, 0, -76, 0, 12, 0, 4, 0, -88, 0, 0, 0, -92, 0, -48, 0, -2, 0, 36, 0, -14, 0, 0, 0, 0, 0, 48, 0, 8, 0, 0, 0, 0, 0, -4, 0, -8, 0, -28, 0, 8, 0, 48, 0, -120, 0, 136, 0, -84, 0, -4, 0, 84, 0, 0, 0, 0, 0, 0, 0, -70, 0, -38, 0, -32, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, -64, 0, 2, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 4, 0, 0, 0, 4, 0, 72, 0, 0, 0, -30, 0, 0, 0, 124, 0, -36, 0, 0, 0, 36, 0, 0, 0, -60, 0, 0, 0, 0, 0, 0, 0, -6, 0, -112, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 28, 0, 10, 0, -36, 0, 0, 0, 0, 0, 0, 0, -104, 0, -76, 0, -74, 0, 0, 0, -192, 0, -84, 0, 56, 0, 64, 0, -4, 0, -22, 0, 0, 0, 0, 0, 136, 0, -104, 0, 0, 0, 0, 0, -114, 0, 12, 0, -112, 0, 136, 0, 48, 0, 44, 0, 104, 0, -90, 0, 4, 0, 72, 0, 0, 0, 0, 0, 0, 0, -116, 0, 22, 0, -40, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 20, 0, 10, 0, 0, 0, 0, 0, -144, 0, -2, 0, 0, 0, -8, 0, 0, 0, -132, 0, 88, 0, 0, 0, 76, 0, 0, 0, 68, 0, 76, 0, 0, 0, 32, 0, 0, 0, -46, 0, 4, 0, 0, 0, 0, 0, 104, 0, -48, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 44, 0, 2, 0, 10, 0, 0, 0, 0, 0, 0, 0, -140, 0, -100, 0, 38, 0, -164, 0, -56, 0, -260, 0, -112, 0, 124, 0, -72, 0, -14, 0, 0, 0, 0, 0, 52, 0, -44, 0, 0, 0, 0, 0, -6, 0, 52, 0, -20, 0, 56, 0, 124, 0, -196, 0, 16, 0, -178, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, -142, 0, 36, 0, 4, 0, 0, 0, -164, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -116, 0, 62, 0, 0, 0, 0, 0, 12, 0, 82, 0, 0, 0, 124, 0, 0, 0, 0, 0, 324, 0, 0, 0, 92, 0, 0, 0, 172, 0, 112, 0, 0, 0, 176, 0, 0, 0, -56, 0, 60, 0, 0, 0, 0, 0, -30, 0, -64, 0, 0, 0, 86, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 244, 0, 22, 0, 26, 0, 0, 0, 0, 0, 0, 0, -172, 0, 24, 0, 32, 0, 64, 0, -96, 0, -16, 0, 132, 0, 230, 0, -92, 0, -110, 0, 0, 0, 0, 0, 248, 0, 160, 0, 0, 0, 0, 0, -194, 0, 216, 0, -24, 0, 108, 0, 32, 0, -44, 0, 340, 0, -10, 0, -184, 0, 188, 0, 0, 0, 0, 0, 0, 0, -266, 0, 114, 0, -116, 0, 0, 0, -40, 0, 0, 0, 0, 0, 0, 0, 114, 0, 0, 0, -100, 0, -16, 0, 0, 0, 0, 0, -92, 0, 124, 0, 0, 0, 60, 0, 0, 0, -84, 0, 8, 0, 0, 0, -56, 0, 0, 0, 4, 0, -4, 0, 0, 0, 192, 0, 0, 0, 12, 0, -36, 0, 0, 0, 0, 0, -12, 0, -168, 0, 0, 0, 220, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 48, 0, 294, 0, 92, 0, 0, 0, 0, 0, 0, 0, -216, 0, -336, 0, 52, 0, -136, 0, -244, 0, -28, 0, -52, 0, 162, 0, -88, 0, -124, 0, 0, 0, 0, 0, 40, 0, 40, 0, 0, 0, 0, 0, -152, 0, 52, 0, -24, 0, 128, 0, -4, 0, -240, 0, 308, 0, -174, 0, 16, 0, -48, 0, 0, 0, 0, 0, 0, 0, -122, 0, -60, 0, 0, 0, 0, 0, -52, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 192, 0, 284, 0, 0, 0, 0, 0, 220, 0, 42, 0, 0, 0, -144, 0, 0, 0, 116, 0, 172, 0, 0, 0, 100, 0, 0, 0, 260, 0, -44, 0, 0, 0, 304, 0, 0, 0, -114, 0, 116, 0, 0, 0, 0, 0, -76, 0, -4, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, -144, 0, 0, 0, 124, 0, -28, 0, 184, 0, 0, 0, 0, 0, 0, 0, -264, 0, 0, 0, -88, 0, -252, 0, -352, 0, -80, 0, -4, 0, 88, 0, 152, 0, 10, 0, 0, 0, 0, 0, 0, 0, 192, 0, 0, 0, 0, 0, -250, 0, 32, 0, -184, 0, 172, 0, 200, 0, -260, 0, 296, 0, -434, 0, 192, 0, -16, 0, 0, 0, 0, 0, 0, 0, -358, 0, 198, 0, -180, 0, 0, 0, -240, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 100, 0, 38, 0, 0, 0, 0, 0, -144, 0, 92, 0, 0, 0, 132, 0, 0, 0, -48, 0, 172, 0, 0, 0, -22, 0, 0, 0, 244, 0, 180, 0, 0, 0, 464, 0, 0, 0, -28, 0, 24, 0, 0, 0, 0, 0, -156, 0, -164, 0, 0, 0, 442, 0, 0, 0, 0, 0, 0, 0, -316, 0, 0, 0, -36, 0, 50, 0, 84, 0, 0, 0, 0, 0, 0, 0, -64, 0, -220, 0, 72, 0, -240, 0, -156, 0, -172, 0, 8, 0, 226, 0, 224, 0, -28, 0, 0, 0, 0, 0, -176, 0, -4, 0, 0, 0, 0, 0, -84, 0, 4, 0, 32, 0, 4, 0, -164, 0, -544, 0, 432, 0, -156, 0, -224, 0, 44, 0, 0, 0, 0, 0, 0, 0, -158, 0, -92, 0, -172, 0, 0, 0, -268, 0, 0, 0, 0, 0, 0, 0, -64, 0, 0, 0, -12, 0, 64, 0, 0, 0, 0, 0, -20, 0, 32, 0, 0, 0, -44, 0, 0, 0, 80, 0, 424, 0, 0, 0, 78, 0, 0, 0, 220, 0, 48, 0, 0, 0, 484, 0, 0, 0, -4, 0, 156, 0, 0, 0, 0, 0, -18, 0, -340, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 24, 0, -74, 0, -48, 0, 0, 0, 0, 0, 0, 0, -356, 0, -36, 0, 62, 0, 156, 0, 152, 0, -72, 0, 176, 0, 130, 0, -324, 0, -154, 0, 0, 0, 0, 0, 48, 0, -40, 0, 0, 0, 0, 0, -364, 0, 192, 0, 38, 0, 128, 0, 32, 0, -180, 0, 520, 0, -240, 0, 160, 0, 80, 0, 0, 0, 0, 0, 0, 0, -290, 0, 82, 0, 52, 0, 0, 0, -76, 0, 0, 0, 0, 0, 0, 0, 166, 0, 0, 0, -240, 0, 40, 0, 0, 0, 0, 0, -68, 0, 296, 0, 0, 0, -60, 0, 0, 0, -180, 0, 28, 0, 0, 0, -28, 0, 0, 0, 12, 0, 4, 0, 0, 0, 196, 0, 0, 0, -42, 0, 204, 0, 0, 0, 0, 0, -16, 0, -36, 0, 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, -32, 0, 50, 0, 76, 0, 0, 0, 0, 0, 0, 0, -384, 0, -464, 0, -74, 0, 108, 0, -212, 0, -4, 0, 96, 0, 110, 0, 192, 0, -108, 0, 0, 0, 0, 0, 12, 0, -172, 0, 0, 0, 0, 0, -106, 0, -292, 0, -242, 0, 8, 0, 40, 0, -552, 0, 596, 0, -172, 0, 112, 0, -180, 0, 0, 0, 0, 0, 0, 0, -326, 0, 118, 0, -40, 0, 0, 0, -468, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 0, -324, 0, 400, 0, 0, 0, 0, 0, 224, 0, 290, 0, 0, 0, 108, 0, 0, 0, -4, 0, 228, 0, 0, 0, -182, 0, 0, 0, -20, 0, 32, 0, 0, 0, 712, 0, 0, 0, -32, 0, 424, 0, 0, 0, 0, 0, -148, 0, 140, 0, 0, 0, 390, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 316, 0, -76, 0, -88, 0, 0, 0, 0, 0, 0, 0, -620, 0, -160, 0, -94, 0, -48, 0, 128, 0, -176, 0, -148, 0, 258, 0, -52, 0, 86, 0, 0, 0, 0, 0, 504, 0, 240, 0, 0, 0, 0, 0, -14, 0, 148, 0, -76, 0, -136, 0, 168, 0, -508, 0, 428, 0, -198, 0, -60, 0, 228, 0, 0, 0, 0, 0, 0, 0, -28, 0, 308, 0, -244, 0, 0, 0, -340, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, -44, 0, -164, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 16, 0, 0, 0, -68, 0, -8, 0, 0, 0, -326, 0, 0, 0, 72, 0, 152, 0, 0, 0, 336, 0, 0, 0, 60, 0, -204, 0, 0, 0, 0, 0, -24, 0, -64, 0, 0, 0, 432, 0, 0, 0, 0, 0, 0, 0, -88, 0, 0, 0, 196, 0, -98, 0, 48, 0, 0, 0, 0, 0, 0, 0, -740, 0, -412, 0, -52, 0, -28, 0, 76, 0, -176, 0, -68, 0, 490, 0, -180, 0, 118, 0, 0, 0, 0, 0, -252, 0, -216, 0, 0, 0, 0, 0, -178, 0, -12, 0, -102, 0, -180, 0, -184, 0, -548, 0, 664, 0, -384, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, -114, 0, -4, 0, -72, 0, 0, 0, -88, 0, 0, 0, 0, 0, 0, 0, 154, 0, 0, 0, 40, 0, 422, 0, 0, 0, 0, 0, 88, 0, 204, 0, 0, 0, 212, 0, 0, 0, 124, 0, 464, 0, 0, 0, 52, 0, 0, 0, 100, 0, -40, 0, 0, 0, 0, 0, 0, 0, -544, 0, -192, 0, 0, 0, 0, 0, 68, 0, -108, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, -156, 0, 48, 0, -54, 0, 0, 0, 0, 0, 0, 0, -420, 0, -120, 0, -210, 0, 16, 0, 48, 0, 48, 0, -244, 0, 134, 0, -304, 0, -342, 0, 0, 0, 0, 0, 456, 0, -32, 0, 0, 0, 0, 0, -402, 0, 408, 0, 2, 0, 164, 0, -48, 0, -400, 0, 448, 0, -384, 0, -120, 0, -68, 0, 0, 0, 0, 0, 0, 0, -392, 0, 412, 0, -36, 0, 0, 0, -96, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 160, 0, 146, 0, 0, 0, 0, 0, -8, 0, 14, 0, 0, 0, -260, 0, 0, 0, -28, 0, 400, 0, 0, 0, -418, 0, 0, 0, 32, 0, 148, 0, 0, 0, 648, 0, 0, 0, -138, 0, 272, 0, 0, 0, 0, 0, 68, 0, -76, 0, 0, 0, 462, 0, 0, 0, 0, 0, 0, 0, -124, 0, 0, 0, -132, 0, 60, 0, 108, 0, 0, 0, 0, 0, 0, 0, -1104, 0, -664, 0, 104, 0, 76, 0, 260, 0, 40, 0, -48, 0, 254, 0, 188, 0, -52, 0, 0, 0, 0, 0, -320, 0, -188, 0, 0, 0, 0, 0, -102, 0, 176, 0, -284, 0, -8, 0, 228, 0, -736, 0, 660, 0, -112, 0, 60, 0, 236, 0, 0, 0, 0, 0, 0, 0, -322, 0, -138, 0, 248, 0, 0, 0, -108, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 232, 0, 298, 0, 0, 0, 0, 0, 408, 0, 428, 0, 0, 0, -244, 0, 0, 0, 388, 0, 104, 0, 0, 0, 96, 0, 0, 0, -40, 0, -164, 0, 0, 0, 684, 0, 0, 0, 4, 0, 468, 0, 0, 0, 0, 0, -298, 0, 68, 0, 0, 0, 294, 0, 0, 0, 0, 0, 0, 0, -444, 0, 0, 0, 8, 0, 138, 0, -200, 0, 0, 0, 0, 0, 0, 0, -368, 0, -328, 0, -76, 0, -384, 0, 68, 0, 348, 0, -84, 0, 28, 0, -44, 0, 120, 0, 0, 0, 0, 0, 352, 0, 88, 0, 0, 0, 0, 0, -618, 0, 284, 0, -20, 0, -4, 0, -8, 0, -316, 0, 820, 0, -406, 0, -80, 0, 108, 0, 0, 0, 0, 0, 0, 0, -430, 0, 292, 0, -76, 0, 0, 0, -48, 0, 0, 0, 0, 0, 0, 0, 98, 0, 0, 0, 4, 0, 32, 0, 0, 0, 0, 0, 128, 0, 248, 0, 0, 0, 120, 0, 0, 0, -112, 0, 608, 0, 0, 0, -430, 0, 0, 0, -132, 0, 20, 0, 0, 0, 564, 0, 0, 0, 70, 0, -136, 0, 0, 0, 0, 0, 352, 0, -364, 0, 0, 0, 316, 0, 0, 0, 0, 0, 0, 0, 480, 0, 0, 0, -192, 0, 84, 0, -108, 0, 0, 0, 0, 0, 0, 0, -696, 0, -796, 0, 46, 0, -60, 0, -276, 0, 44, 0, 256, 0, 450, 0, 4, 0, -126, 0, 0, 0, 0, 0, -12, 0, -160, 0, 0, 0, 0, 0, -290, 0, -464, 0, -98, 0, -244, 0, 112, 0, -84, 0, 612, 0, -268, 0, -416, 0, -36, 0, 0, 0, 0, 0, 0, 0, -346, 0, 132, 0, 80, 0, 0, 0, -456, 0, 0, 0, 0, 0, 0, 0, -460, 0, 0, 0, -52, 0, 468, 0, 0, 0, 0, 0, 316, 0, 424, 0, 0, 0, 56, 0, 0, 0, -284, 0, 196, 0, 0, 0, -166, 0, 0, 0, 48, 0, 100, 0, 0, 0, 1344, 0, 0, 0, 182, 0, 8, 0, 0, 0, 0, 0, 60, 0, -60, 0, 0, 0, 218, 0, 0, 0, 0, 0, 0, 0, 260, 0, 0, 0, 88, 0, 258, 0, 70, 0, 0, 0, 0, 0, 0, 0, -1092, 0, -256, 0, 330, 0, -400, 0, -64, 0, -140, 0, 96, 0, 468, 0, -216, 0, 38, 0, 0, 0, 0, 0, 84, 0, -276, 0, 0, 0, 0, 0, -412, 0, 28, 0, 448, 0, -232, 0, -316, 0, -524, 0, 32, 0, -384, 0, 108, 0, -68, 0, 0, 0, 0, 0, 0, 0, -396, 0, 194, 0, 360, 0, 0, 0, -424, 0, 0, 0, 0, 0, 0, 0, 286, 0, 0, 0, -160, 0, -66, 0, 0, 0, 0, 0, 312, 0, 580, 0, 0, 0, -56, 0, 0, 0, 8, 0, 156, 0, 0, 0, -444, 0, 0, 0, -48, 0, -148, 0, 0, 0, 632, 0, 0, 0, 166, 0, -404, 0, 0, 0, 0, 0, 196, 0, 68, 0, 0, 0, 462, 0, 0, 0, 0, 0, 0, 0, -164, 0, 0, 0, -296, 0, 34, 0, 272, 0, 0, 0, 0, 0, 0, 0, -940, 0, -1120, 0, -178, 0, 176, 0, -312, 0, 120, 0, 108, 0, 362, 0, -24, 0, 30, 0, 0, 0, 0, 0, -288, 0, -168, 0, 0, 0, 0, 0, -296, 0, -188, 0, 196, 0, 100, 0, -372, 0, -700, 0, 852, 0, -24, 0, -468, 0, 76, 0, 0, 0, 0, 0, 0, 0, -20, 0, -60, 0, -312, 0, 0, 0, -164, 0, 0, 0, 0, 0, 0, 0, -430, 0, 0, 0, 28, 0, 430, 0, 0, 0, 0, 0, 612, 0, 266, 0, 0, 0, -76, 0, 0, 0, 208, 0, 64, 0, 0, 0, -428, 0, 0, 0, -300, 0, -216, 0, 0, 0, 992, 0, 0, 0, 12, 0, -92, 0, 0, 0, 0, 0, -2, 0, -40, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 248, 0, 0, 0, -132, 0, 62, 0, 24, 0, 0, 0, 0, 0, 0, 0, -476, 0, -364, 0, -298, 0, 104, 0, 168, 0, -4, 0, 232, 0, 354, 0, 40, 0, -60, 0, 0, 0, 0, 0, 220, 0, 256, 0, 0, 0, 0, 0, -362, 0, 232, 0, 144, 0, 28, 0, -72, 0, -716, 0, 468, 0, -482, 0, -24, 0, -220, 0, 0, 0, 0, 0, 0, 0, -814, 0, 384, 0, 280, 0, 0, 0, -476, 0, 0, 0, 0, 0, 0, 0, -24, 0, 0, 0, 720, 0, 6, 0, 0, 0, 0, 0, 4, 0, 496, 0, 0, 0, -116, 0, 0, 0, -340, 0, 264, 0, 0, 0, -212, 0, 0, 0, 356, 0, 280, 0, 0, 0, 672, 0, 0, 0, -120, 0, 36, 0, 0, 0, 0, 0, 206, 0, -4, 0, 0, 0, 638, 0, 0, 0, 0, 0, 0, 0, -736, 0, 0, 0, -600, 0, -64, 0, 104, 0, 0, 0, 0, 0, 0, 0, -908, 0, -288, 0, -148, 0, -168, 0, -80, 0, -8, 0, -360, 0, 518, 0, 272, 0, 146, 0, 0, 0, 0, 0, -4, 0, 140, 0, 0, 0, 0, 0, -52, 0, -356, 0, 0, 0, -200, 0, 236, 0, -880, 0, 824, 0, -130, 0, -300, 0, -72, 0, 0, 0, 0, 0, 0, 0, -40, 0, -184, 0, -92, 0, 0, 0, -244, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 240, 0, 112, 0, 0, 0, 0, 0, 472, 0, 560, 0, 0, 0, -188, 0, 0, 0, 316, 0, 784, 0], "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, 77, 2, 1, 2, 0]], "char_orbit_index": 5, "prim_orbit_index": 2, "minimal_twist": "4004.2.e.a", "char_is_minimal": true, "conrey_index": 3849, "id": null, "is_polredabs": null, "nf_label": null, "trace_hash": null, "hecke_cutters": 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}