# Stored data for newform 552.2.j.d, downloaded from the LMFDB on 19 April 2024. {"label": "552.2.j.d", "space_label": "552.2.j", "level": 552, "weight": 2, "hecke_orbit": 4, "hecke_orbit_code": 13511417390957096, "dim": 42, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[5, [24576, 81920, -1161728, -2604544, 1057792, 5175360, 695168, -4343136, -1357216, 1998768, 770480, -566000, -226032, 105136, 38152, -13112, -3716, 1064, 192, -50, -4, 1]]], "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 24, "char_orbit_label": "j", "char_is_real": true, "Nk2": 2208, "analytic_conductor": 4.407742191574677, "level_radical": 138, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [552, 2, [415, 277, 185, 97], [1, 1, 1, 2]], "inner_twist_count": 2, "level_primes": [2, 3, 23], "conrey_indexes": [323], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 42, "sato_tate_group": "1.2.3.c2", "trace_display": [0, 2, 8, 0], "traces": [42, 0, 2, 4, 8, 4, 0, -9, 2, -4, 0, -21, 0, -4, -8, -12, 0, -11, 4, -2, 8, 18, 42, 28, 22, 11, -16, 6, 0, 2, 0, -20, 12, 14, 0, -24, 0, -22, 8, 4, 0, -44, 28, 56, -8, 0, 0, 30, -50, 20, 28, -1, 24, 52, 0, -34, -8, -21, 0, -42, 0, -79, -16, 7, 0, -62, -4, 20, 2, -8, 0, 22, 4, 36, -6, 14, 32, 27, 0, -52, 18, 11, 0, -80, 0, -28, -48, -38, 0, -46, -8, 4, -22, 1, -16, 9, 20, 64, 0, 0, -52, 40, 0, -8, -32, -24, 0, -30, 0, -104, 8, 4, 0, -90, 8, 81, 74, -76, 32, 96, 6, 32, -50, 23, 96, 98, 0, -28, -32, 70, 0, -60, 0, -98, 72, 40, 0, 4, -36, 52, -54, -45, -64, 63, -24, 33, -22, -6, -32, 82, 0, -92, -32, -8, 0, -54, 0, -34, -24, 2, 0, -34, 12, 87, 40, 8, -96, 164, -14, 144, -20, -100, 76, 83, 0, -46, 12, -6, 0, -62, 0, -104, -48, -9, 0, -65, 8, 101, -108, -24, 48, 82, 4, 74, 32, 60, -112, 78, 0, -131, 8, -8, 0, -134, 0, -84, 2, -19, 0, -150, -16, 40, 62, 74, 32, 109, -8, 98, -22, 48, 56, 138, 0, -170, 22, 42, 0, -60, 0, -4, 64, 20, 0, -140, 32, 100, -120, -8, 48, 146, 4, 180, 42, 12, -232, 53, 0, -44, 4, -4, 0, -90, 0, -101, -32, 4, 0, -92, -32, 160, 78, 47, -64, 86, -88, 72, 48, 12, 112, 144, 0, -142, 32, -14, 0, -21, 0, -169, -64, 88, 0, -167, 28, 43, -136, 42, -32, 192, -38, 126, -36, 47, -64, 138, 0, -184, 36, 48, 0, -207, 0, -117, 16, -50, 0, -14, 16, 136, 192, -54, 32, 167, 68, 146, 84, 14, 220, 112, 0, -108, -28, -4, 0, -213, 0, -113, 16, 48, 0, -102, -52, 230, -172, 92, 16, 158, 20, 61, 4, 16, -144, 144, 0, -120, -8, -76, 0, -18, 0, -168, -16, 24, 0, -44, -128, 2, 152, 95, -16, 14, 50, 240, 2, 18, 64, 144, 0, -12, 56, -52, 0, -108, 0, -80, -104, -28, 0, -16, -132, 208, -66, 6, 0, 118, -96, 113, -12, -76, -264, 140, 0, -31, 12, 61, 0, -92, 0, -162, -16, -148, 0, -274, 76, 204, 172, -44, 112, 146, 68, 94, 76, -118, 96, -11, 0, -197, -8, -8, 0, -44, 0, -180, 168, -118, 0, 1, 56, 34, -156, -12, 48, 90, -108, 232, -132, -78, 4, 19, 0, -92, -26, -16, 0, -222, 0, 76, -24, 150, 0, -215, 96, 136, 94, -64, 16, 62, 4, 106, -72, -2, 320, 154, 0, -83, 112, 61, 0, -135, 0, -202, -104, -58, 0, -110, -52, 116, -200, 17, -32, 8, 0, 52, 8, 28, -176, 135, 0, -198, -32, -108, 0, -178, 0, -254, 128, -41, 0, -172, -36, -80, 136, -88, 32, 106, 8, 18, 96, -19, 160, 186, 0, -261, -56, 37, 0, -108, 0, 16, 80, -138, 0, -142, 28, 133, -172, -62, -32, 140, 42, 168, -36, -84, -260, 170, 0, 18, -12, -63, 0, -58, 0, -144, 24, 48, 0, -52, 156, 274, 228, 26, -192, 28, 56, 43, 20, -61, 184, 210, 0, -204, 64, -42, 0, -292, 0, -138, -16, 48, 0, -120, -36, 160, -264, -4, 22, 180, 84, 228, 110, -68, -144, 128, 0, -208, -80, 94, 0, -259, 0, -52, 56, 56, 0, -122, 40, 72, 168, 11, 240, -24, 132, 264, -72, -95, 224, 102, 0, 62, -48, -108, 0, -136, 0, -172, 184, 8, 0, -200, -140, 184, -16, 79, -64, 43, -174, -94, 56, 134, -192, 70, 0, -356, 8, -128, 0, 38, 0, -170, -64, 120, 0, -318, -116, 6, 288, -120, 32, 78, -72, 1, -24, -21, 144, 54, 0, -143, -28, -36, 0, -60, 0, -55, -168, -38, 0, -138, 0, 144, -232, -56, -16, 78, -44, 286, -32, 123, -296, 172, 0, 28, 4, 158, 0, -178, 0, -180, 8, 100, 0, 2, 160, 184, 232, 32, 128, -69, -112, 23, 86, 206, 40, 17, 0, -198, -8, -43, 0, -186, 0, -302, 56, 166, 0, -82, 248, -119, -270, -6, -176, 192, 104, 220, 88, -146, -240, -110, 0, -202, -70, -62, 0, -10, 0, 80, -32, -20, 0, -202, 124, 200, 288, -208, -144, 137, -72, 180, 96, 212, 560, -12, 0, 55, 36, -61, 0, -58, 0, -212, 12, -184, 0, -207, 120, 236, -256, 84, 112, 337, 100, -112, -122, 47, -136, 240, 0, -20, 8, 106, 0, -88, 0, 14, 96, 16, 0, -83, -100, -25, 296, 84, 192, 364, 96, 147, -48, 32, 136, 208, 0, -236, -8, -80, 0, 12, 0, 101, 184, 62, 0, -168, 156, 370, -240, 128, -64, -60, -32, 177, -108, -72, -372, 170, 0, 126, 140, 240, 0, -24, 0, -28, -80, 44, 0, -193, -248, 168, 328, 340, -128, 344, 102, -102, -8, -60, 72, -106, 0, -192, 24, 214, 0, -328, 0, -228, -272, 36, 0, 166, 100, -120, -212, -204, -32, 166, 104, 132, -106, 74, -240, 204, 0, -218, -140, -22, 0, 38, 0, 109, 32, 132, 0, -87, 16, 258, 320, 229, 112, 120, 88, 340, -44, 16, 288, 84, 0, 12, 8, -176, 0, -120, 0, -282, 32, -124, 0, 163, 92, 122, -304, 112, 0, -14, 8, -162, -32, -94, -256, 294, 0, 4, -24, 41, 0, -64, 0, -116, -72, 5, 0, 190, 60, -103, 206, 10, -352, -47, -44, 164, -132, -136, 208, 122, 0, -200, -16, -52, 0, -32, 0, 166, -32, -76, 0, -270, -232, 5, -264, -136, 96, 84, -98, 270, 36, -134, -552, -44, 0, 5, 64, 92, 0, 44, 0, -231, -8, -68, 0, 177, -176, 306, 256, 63, 80, 147, -8, -404, 168, 54, 28, -98, 0, -261, -48, 88, 0, -124, 0, -195, 176, 100], "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, 24, 6, 1, 2, 0]], "char_orbit_index": 10, "prim_orbit_index": 6, "minimal_twist": "552.2.j.c", "char_is_minimal": true, "conrey_index": 323, "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}