# Stored data for newform 1100.2.b.d, downloaded from the LMFDB on 10 September 2026.
{"Nk2": 4400, "analytic_conductor": 8.783544222340842, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 5, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": 1, "char_values": [1100, 2, [551, 177, 101], [2, 1, 2]], "cm_discs": [], "conrey_index": 749, "dim": 4, "field_disc": 7056, "field_disc_factorization": [[2, 4], [3, 2], [7, 2]], "field_poly": [25, 0, 11, 0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [[3, [25, 0, 11, 0, 1]], [7, [1, 0, 23, 0, 1]]], "hecke_orbit": 4, "hecke_orbit_code": 13510867635143756, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 5, 2, 1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "1100.2.b.d", "level": 1100, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 5, 11], "level_radical": 110, "minimal_twist": "1100.2.a.g", "nf_label": "4.0.7056.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{1}q^{3}+(\\beta _{1}+3\\beta _{2})q^{7}+(-3+\\beta _{3})q^{9}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "1.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "1100.2.b", "trace_display": [0, 0, 0, 0], "trace_hash": 149662928078069648, "trace_moments": [{"__RealLiteral__": 0, "data": "0.042", "prec": 7}, {"__RealLiteral__": 0, "data": "3.925", "prec": 14}, {"__RealLiteral__": 0, "data": "0.241", "prec": 10}, {"__RealLiteral__": 0, "data": "78.417", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "2138.934", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.515", "prec": 10}, "traces": [0, 4, 0, 0, 0, 0, 0, 0, 0, -10, 0, -4, 0, 0, 0, 0, 0, 0, 0, -8, 0, -16, 0, 0, 0, 0, 0, 0, 0, -18, 0, -16, 0, 0, 0, 0, 0, 0, 0, -2, 0, -24, 0, 0, 0, 0, 0, 0, 0, -18, 0, -18, 0, 0, 0, 0, 0, 0, 0, 24, 0, 26, 0, 0, 0, 0, 0, 0, 0, -24, 0, 12, 0, 0, 0, 0, 0, 0, 0, -2, 0, -20, 0, 0, 0, 0, 0, 0, 0, -6, 0, 10, 0, 0, 0, 0, 0, 0, 0, 10, 0, -42, 0, 0, 0, 0, 0, 0, 0, 10, 0, 38, 0, 0, 0, 0, 0, 0, 0, -36, 0, 4, 0, 0, 0, 0, 0, 0, 0, -20, 0, -30, 0, 0, 0, 0, 0, 0, 0, 16, 0, -30, 0, 0, 0, 0, 0, 0, 0, 24, 0, 20, 0, 0, 0, 0, 0, 0, 0, 72, 0, -6, 0, 0, 0, 0, 0, 0, 0, 48, 0, 62, 0, 0, 0, 0, 0, 0, 0, -6, 0, 14, 0, 0, 0, 0, 0, 0, 0, -50, 0, 78, 0, 0, 0, 0, 0, 0, 0, 34, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 20, 0, 0, 0, 0, 0, 0, 0, -32, 0, 6, 0, 0, 0, 0, 0, 0, 0, 58, 0, 16, 0, 0, 0, 0, 0, 0, 0, 18, 0, -10, 0, 0, 0, 0, 0, 0, 0, -102, 0, 18, 0, 0, 0, 0, 0, 0, 0, 62, 0, 66, 0, 0, 0, 0, 0, 0, 0, -18, 0, 8, 0, 0, 0, 0, 0, 0, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, -4, 0, 0, 0, 0, 0, 0, 0, -6, 0, 100, 0, 0, 0, 0, 0, 0, 0, 94, 0, -60, 0, 0, 0, 0, 0, 0, 0, 18, 0, -138, 0, 0, 0, 0, 0, 0, 0, -102, 0, -4, 0, 0, 0, 0, 0, 0, 0, -30, 0, 16, 0, 0, 0, 0, 0, 0, 0, 40, 0, 20, 0, 0, 0, 0, 0, 0, 0, 24, 0, 24, 0, 0, 0, 0, 0, 0, 0, 18, 0, 18, 0, 0, 0, 0, 0, 0, 0, 124, 0, -82, 0, 0, 0, 0, 0, 0, 0, 48, 0, -12, 0, 0, 0, 0, 0, 0, 0, -52, 0, -96, 0, 0, 0, 0, 0, 0, 0, -68, 0, 138, 0, 0, 0, 0, 0, 0, 0, -108, 0, 74, 0, 0, 0, 0, 0, 0, 0, 2, 0, -48, 0, 0, 0, 0, 0, 0, 0, -2, 0, -60, 0, 0, 0, 0, 0, 0, 0, -114, 0, 24, 0, 0, 0, 0, 0, 0, 0, -30, 0, 12, 0, 0, 0, 0, 0, 0, 0, -40, 0, -100, 0, 0, 0, 0, 0, 0, 0, 36, 0, -8, 0, 0, 0, 0, 0, 0, 0, -92, 0, -48, 0, 0, 0, 0, 0, 0, 0, -14, 0, 66, 0, 0, 0, 0, 0, 0, 0, 42, 0, 34, 0, 0, 0, 0, 0, 0, 0, -126, 0, -12, 0, 0, 0, 0, 0, 0, 0, 62, 0, -102, 0, 0, 0, 0, 0, 0, 0, 18, 0, -70, 0, 0, 0, 0, 0, 0, 0, -44, 0, 78, 0, 0, 0, 0, 0, 0, 0, -40, 0, 18, 0, 0, 0, 0, 0, 0, 0, -30, 0, -10, 0, 0, 0, 0, 0, 0, 0, -80, 0, -120, 0, 0, 0, 0, 0, 0, 0, 116, 0, -168, 0, 0, 0, 0, 0, 0, 0, -78, 0, 50, 0, 0, 0, 0, 0, 0, 0, 30, 0, 24, 0, 0, 0, 0, 0, 0, 0, -80, 0, 30, 0, 0, 0, 0, 0, 0, 0, 54, 0, -10, 0, 0, 0, 0, 0, 0, 0, 96, 0, -132, 0, 0, 0, 0, 0, 0, 0, -24, 0, -20, 0, 0, 0, 0, 0, 0, 0, -66, 0, 104, 0, 0, 0, 0, 0, 0, 0, -74, 0, -26, 0, 0, 0, 0, 0, 0, 0, -106, 0, -138, 0, 0, 0, 0, 0, 0, 0, 18, 0, -46, 0, 0, 0, 0, 0, 0, 0, 48, 0, 120, 0, 0, 0, 0, 0, 0, 0, -8, 0, -142, 0, 0, 0, 0, 0, 0, 0, 84, 0, 160, 0, 0, 0, 0, 0, 0, 0, 38, 0, 60, 0, 0, 0, 0, 0, 0, 0, -86, 0, 46, 0, 0, 0, 0, 0, 0, 0, -66, 0, 62, 0, 0, 0, 0, 0, 0, 0, 24, 0, 48, 0, 0, 0, 0, 0, 0, 0, 112, 0, -36, 0, 0, 0, 0, 0, 0, 0, -36, 0, -12, 0, 0, 0, 0, 0, 0, 0, 114, 0, -102, 0, 0, 0, 0, 0, 0, 0, -78, 0, -6, 0, 0, 0, 0, 0, 0, 0, 72, 0, -76, 0, 0, 0, 0, 0, 0, 0, -4, 0, 48, 0, 0, 0, 0, 0, 0, 0, 106, 0, 50, 0, 0, 0, 0, 0, 0, 0, -6, 0, -14, 0, 0, 0, 0, 0, 0, 0, -242, 0, 30, 0, 0, 0, 0, 0, 0, 0, 100, 0, 180, 0, 0, 0, 0, 0, 0, 0, 2, 0, 16, 0, 0, 0, 0, 0, 0, 0, 60, 0, 90, 0, 0, 0, 0, 0, 0, 0, 32, 0, 20, 0, 0, 0, 0, 0, 0, 0, 114, 0, 36, 0, 0, 0, 0, 0, 0, 0, 168, 0, 24, 0, 0, 0, 0, 0, 0, 0, -152, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, -174, 0, 0, 0, 0, 0, 0, 0, 112, 0, -72, 0, 0, 0, 0, 0, 0, 0, -22, 0, 66, 0, 0, 0, 0, 0, 0, 0, 192, 0, 24, 0, 0, 0, 0, 0, 0, 0, -6, 0, 30, 0, 0, 0, 0, 0, 0, 0, 6, 0, -46, 0, 0, 0, 0, 0, 0, 0, -60, 0, 86, 0, 0, 0, 0, 0, 0, 0, 40, 0, -10, 0, 0, 0, 0, 0, 0, 0, 148, 0, 44, 0, 0, 0, 0, 0, 0, 0, -138, 0, 74, 0, 0, 0, 0, 0, 0, 0, 170, 0, -150, 0, 0, 0, 0, 0, 0, 0, -68, 0, 24, 0, 0, 0, 0, 0, 0, 0, -48, 0, 8, 0, 0, 0, 0, 0, 0, 0, 102, 0, 180, 0, 0, 0, 0, 0, 0, 0, -32, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, -6, 0, 0, 0, 0, 0, 0, 0, -10, 0, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 32, 0, 0, 0, 0, 0, 0, 0, -12, 0, 42, 0, 0, 0, 0, 0, 0, 0, -170, 0, -132, 0, 0, 0, 0, 0, 0, 0, 64, 0, 30, 0, 0, 0, 0, 0, 0, 0, -24, 0, 82, 0, 0, 0, 0, 0, 0, 0, -36, 0, 216, 0, 0, 0, 0, 0, 0, 0, -10, 0, 200, 0, 0, 0, 0, 0, 0, 0, -78, 0, 80, 0, 0, 0, 0, 0, 0, 0, 12, 0, 30, 0, 0, 0, 0, 0, 0, 0, 66, 0, 2, 0, 0, 0, 0, 0, 0, 0, -10, 0, -76, 0, 0, 0, 0, 0, 0, 0, 50, 0, -126, 0, 0, 0, 0, 0, 0, 0, 90, 0, -38, 0, 0, 0, 0, 0, 0, 0, 102, 0, 14, 0, 0, 0, 0, 0, 0, 0, -12, 0, 12, 0, 0, 0, 0, 0, 0, 0, 10, 0, 86, 0, 0, 0, 0, 0, 0, 0, 168, 0, 34, 0, 0, 0, 0, 0, 0, 0, -120, 0, 12, 0, 0, 0, 0, 0, 0, 0, 64, 0, -146, 0, 0, 0, 0, 0, 0, 0, -24, 0, -82, 0, 0, 0, 0, 0, 0, 0, -158, 0, -24, 0, 0, 0, 0, 0, 0, 0, 36, 0, 132, 0, 0, 0, 0, 0, 0, 0, -144, 0, -76, 0, 0, 0, 0, 0, 0, 0, 12, 0, -4, 0, 0, 0, 0, 0, 0, 0, -22, 0, 24, 0, 0, 0, 0, 0, 0, 0, 228, 0, -104, 0, 0, 0, 0, 0, 0, 0, -50, 0, 90, 0, 0, 0, 0, 0, 0, 0, 48, 0, -76, 0, 0, 0, 0, 0, 0, 0, -42, 0, -202, 0, 0, 0, 0, 0, 0, 0, 94, 0, -24, 0, 0, 0, 0, 0, 0, 0, -44, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, -114, 0, 0, 0, 0, 0, 0, 0, 20, 0, -24, 0, 0, 0, 0, 0, 0, 0, 28, 0, -90, 0, 0, 0, 0, 0, 0, 0, -36, 0, 30, 0, 0, 0, 0, 0, 0, 0, -6, 0, -18, 0, 0, 0, 0, 0, 0, 0, -116, 0, 158, 0, 0, 0, 0, 0, 0, 0, 24, 0, -4, 0, 0, 0, 0, 0, 0, 0, 60, 0, 36, 0, 0, 0, 0, 0, 0, 0, -116, 0, -300, 0, 0, 0, 0, 0, 0, 0, -114, 0, -290, 0, 0, 0, 0, 0, 0, 0, 0, 0, 162, 0, 0, 0, 0, 0, 0, 0, -138, 0, -120, 0, 0, 0, 0, 0, 0, 0, -16, 0, -52, 0, 0, 0, 0, 0, 0, 0, -44, 0, 24, 0, 0, 0, 0, 0, 0, 0, -92, 0, 30, 0, 0, 0, 0, 0, 0, 0, -30, 0, 118, 0, 0, 0, 0, 0, 0, 0, -116, 0, 18, 0, 0, 0, 0, 0, 0, 0, -122, 0, 30, 0, 0, 0, 0, 0, 0, 0, -192, 0, -80, 0, 0, 0, 0, 0, 0, 0, -30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 148, 0, 204, 0, 0, 0, 0, 0, 0, 0, 156, 0, -112, 0, 0, 0, 0, 0, 0, 0, 28, 0, -114, 0, 0, 0, 0, 0, 0, 0, -24, 0, -64, 0, 0, 0, 0, 0, 0, 0, -72, 0, -38, 0, 0, 0, 0, 0, 0, 0, 302, 0, -20, 0, 0, 0, 0, 0, 0, 0, -128, 0, 354, 0, 0, 0, 0, 0, 0, 0, -54, 0, 64, 0, 0, 0, 0, 0, 0, 0, -228, 0, -30, 0, 0, 0, 0, 0, 0, 0, -44, 0, 14, 0, 0, 0, 0, 0, 0, 0, 108, 0, -150, 0, 0, 0, 0, 0, 0, 0, -174, 0, -246, 0, 0, 0, 0, 0, 0, 0, 22, 0, -106, 0, 0, 0, 0, 0, 0, 0, 132, 0, 164, 0, 0, 0, 0, 0, 0, 0, -72, 0, 138, 0, 0, 0, 0, 0, 0, 0, 16, 0, -114, 0, 0, 0, 0, 0, 0, 0, -96, 0, 6, 0, 0, 0, 0, 0, 0, 0, -78, 0, -18, 0, 0, 0, 0, 0, 0, 0, 10, 0, -22, 0, 0, 0, 0, 0, 0, 0, 180, 0, -82, 0, 0, 0, 0, 0, 0, 0, -80, 0, 108, 0, 0, 0, 0, 0, 0, 0, -90, 0, 68, 0, 0, 0, 0, 0, 0, 0, -180, 0, -208, 0, 0, 0, 0, 0, 0, 0, 346, 0, -66, 0, 0, 0, 0, 0, 0, 0, -228, 0, 156, 0, 0, 0, 0, 0, 0, 0, -48, 0, 116, 0, 0, 0, 0, 0, 0, 0, 66, 0, -24, 0, 0, 0, 0, 0, 0, 0, -98, 0, -62, 0, 0, 0, 0, 0, 0, 0, -6, 0, -62, 0, 0, 0, 0, 0, 0, 0, -50, 0, -204, 0, 0, 0, 0, 0, 0, 0, -96, 0, -96, 0, 0, 0, 0, 0, 0, 0, 210, 0, -78, 0, 0, 0, 0, 0, 0, 0, -284, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, -174, 0, 0, 0, 0, 0, 0, 0, -126, 0, -64, 0, 0, 0, 0, 0, 0, 0, 234, 0, -90, 0, 0, 0, 0, 0, 0, 0, 6, 0, 110, 0, 0, 0, 0, 0, 0, 0, 144, 0, -176, 0, 0, 0, 0, 0, 0, 0, 6, 0, -14, 0, 0, 0, 0, 0, 0, 0, -146, 0], "weight": 2, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "atkin_lehner_eigenvals": null, "atkin_lehner_string": null, "embedded_related_objects": null, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 3, 0], [0, 0, 0, 0], [-3, 0, 0, 1], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 2, 0], [0, 0, 0, 0], [-3, 0, 0, 2], [0, 0, 0, 0], [-3, 0, 0, -2], [0, 0, 0, 0], [0, 1, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 5, 0], [0, 0, 0, 0], [-5, 0, 0, 1], [0, 0, 0, 0], [-5, 0, 0, 2], [0, 0, 0, 0], [0, -1, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -2, -3, 0], [0, 0, 0, 0], [-1, 0, 0, 1], [0, 0, 0, 0], [-5, 0, 0, -2], [0, 0, 0, 0], [0, 0, -10, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 2, 7, 0], [0, 0, 0, 0], [-2, 0, 0, -5], [0, 0, 0, 0], [-4, 0, 0, -1], [0, 0, 0, 0], [0, -3, 3, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -3, 10, 0], [0, 0, 0, 0], [7, 0, 0, -2], [0, 0, 0, 0], [6, 0, 0, 1], [0, 0, 0, 0], [0, 0, -1, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 4, 0], [0, 0, 0, 0], [-7, 0, 0, 2], [0, 0, 0, 0], [0, 0, 0, 6], [0, 0, 0, 0], [0, 1, -5, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -1, -3, 0], [0, 0, 0, 0], [3, 0, 0, -7], [0, 0, 0, 0], [-4, 0, 0, -2], [0, 0, 0, 0], [0, 5, 4, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, -5, 5, 0], [0, 0, 0, 0], [-1, 0, 0, -1], [0, 0, 0, 0], [2, 0, 0, 1], [0, 0, 0, 0], [0, -5, 10, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 9, 0], [0, 0, 0, 0], [3, 0, 0, -1], [0, 0, 0, 0]]}