# Stored data for newform 241.2.a.b, downloaded from the LMFDB on 19 April 2024. {"label": "241.2.a.b", "space_label": "241.2.a", "level": 241, "weight": 2, "hecke_orbit": 2, "hecke_orbit_code": 4503599660925169, "dim": 12, "is_polredabs": true, "trace_hash": 1848781641771018309, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [-1, 18, -45, -328, 105, 444, -123, -219, 65, 44, -14, -3, 1]]], "qexp_display": "q+\\beta _{1}q^{2}+\\beta _{8}q^{3}+(1+\\beta _{2})q^{4}+(1-\\beta _{9}+\\cdots)q^{5}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 964, "fricke_eigenval": -1, "atkin_lehner_string": "-", "analytic_conductor": 1.9243946887128573, "hecke_ring_index": 1, "level_radical": 241, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": true, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "analytic_rank_proved": true, "char_values": [241, 1, [7], [1]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 1, "level_primes": [241], "conrey_indexes": [1], "field_disc": 32354823033956684288, "field_disc_factorization": [[2, 9], [97, 1], [651474368435017, 1]], "field_poly": [-1, 18, -45, -328, 105, 444, -123, -219, 65, 44, -14, -3, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.166", "prec": 17}, {"__RealLiteral__": 0, "data": "10.011", "prec": 20}, {"__RealLiteral__": 0, "data": "16.317", "prec": 20}, {"__RealLiteral__": 0, "data": "343.576", "prec": 24}, {"__RealLiteral__": 0, "data": "1481.083", "prec": 27}, {"__RealLiteral__": 0, "data": "22693.661", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 12, "sato_tate_group": "1.2.3.c1", "atkin_lehner_eigenvals": [[241, -1]], "trace_display": [3, 1, 6, 3], "traces": [0, 12, 3, 1, 13, 6, -1, 3, 9, 15, -7, 22, -7, -5, 6, 13, 15, -4, -1, -6, 10, -14, -12, 32, -15, 4, 8, -5, -11, 6, -19, 8, 1, -24, -19, 15, -8, -8, -10, 31, -52, -1, -49, -2, 42, -15, -25, 34, -49, -9, -27, -3, -41, 5, -40, -3, 1, -22, -33, 26, -57, -26, -17, -4, 13, -25, -2, 6, -35, -2, -4, 94, 17, -22, 26, 0, -20, -7, 54, 9, 19, 4, 15, -8, 2, 4, 9, 4, 6, -3, 11, -20, 36, 12, 48, 33, -23, -29, 28, 36, 6, 23, -18, -2, 1, -23, -22, 18, 60, 1, -17, 37, 27, 23, 22, 16, 2, -51, 48, 78, 14, -2, -16, -36, 21, 6, -31, 19, 26, -30, 54, 27, -96, 6, -8, 45, -32, 2, 108, 5, -9, 13, 8, -7, 38, -63, 17, -44, 105, 43, 93, -14, -21, -32, 38, 16, 3, -18, -2, -5, -32, -15, -12, -7, 61, -17, 44, 42, 63, -7, -41, -35, -32, -24, 78, -35, 91, -46, 11, 39, 30, -45, -12, -41, -75, -9, -43, -63, 54, -63, -15, 53, -110, -10, -24, -30, -93, -52, 50, 8, -53, -45, 36, -20, 156, -74, 55, 19, -137, -41, 2, 9, -62, -69, 39, 44, -87, -116, 81, -16, 172, -19, -40, -29, 16, -72, -40, -30, 7, -14, -138, 30, -13, 5, 37, -43, 12, -106, 7, 112, -72, 12, -124, -54, 20, -50, -55, -86, 21, -3, -42, -27, -47, 24, 98, -25, 47, -12, 52, -12, -86, -38, -38, 8, -59, -59, -57, 36, -39, -7, -11, 20, -88, 9, 124, -30, 67, -2, -27, 123, 42, -22, -59, 32, 116, 24, 16, -41, 142, 6, -52, 48, 43, -28, 74, -3, 1, 37, 54, 27, -25, 42, -61, -36, 65, 67, -101, -24, -35, -9, 102, 130, 14, 33, -62, -21, -4, -58, 135, 68, -16, 11, 36, 74, -52, -56, 7, 60, 226, 27, 13, -55, -24, 33, -34, 11, 27, -2, -38, -11, -26, -6, 32, -6, -66, 19, -41, -17, 169, -19, 74, 97, -22, 43, 166, 41, 24, -59, 60, 107, 60, -20, -135, -62, 37, 43, -9, 77, -1, 34, -148, -17, 40, -63, -13, 26, 141, -24, 25, 40, 36, 18, 129, 4, -14, 34, 79, -21, -8, 11, -22, 28, -120, 110, -5, -90, -9, 102, -1, -6, 93, -22, 164, -37, -85, -15, -12, 27, 222, -22, -54, -55, -149, -3, 77, 31, -103, 155, -21, 19, -24, 108, -136, 98, -81, -72, -67, -3, 12, 142, -41, 194, -160, -91, -139, -19, 8, -52, -83, -49, -173, 48, 21, -51, -35, 66, -196, -6, -62, 49, -56, -15, 38, 54, 26, 71, 70, 7, -72, -87, 2, 55, -117, 89, -59, 144, 92, -31, 18, -41, -21, -27, 2, 47, -124, 56, -20, 48, -45, 61, 46, -21, 3, -125, 49, -115, 104, 2, -163, -14, 194, -102, -51, 82, -90, -87, -151, 76, 7, 29, -151, -70, -93, -58, 34, -17, -221, -49, 194, 41, 17, 14, 37, -181, -82, -24, -130, 17, -81, 37, 56, 14, -202, -61, -183, 167, 182, -59, -185, 140, -39, -67, -72, -30, -166, 16, -242, 127, 90, -2, 181, 9, -146, -102, -76, -138, -106, -76, -51, -6, -227, 80, 128, 70, 137, -191, 54, 12, 46, -58, -111, 92, -130, -71, 52, 125, -38, 101, 10, 36, 156, -30, -244, -54, -73, 147, -12, -48, -10, -99, 81, -3, 28, 65, 94, 29, -100, 62, 105, 36, -36, 8, 126, 8, -90, -68, 49, 23, 221, 93, 163, -75, -65, 18, -28, 20, -3, 4, -70, 152, -9, -63, -159, 26, -66, -20, 3, 23, 56, -14, 154, 77, 21, -22, 275, 100, 33, -44, -72, -37, -70, 12, 134, 31, 118, -13, 126, 175, -215, 237, 123, 85, 19, -61, -25, -75, -6, 126, -99, -24, 68, -90, -47, -113, 118, 74, 162, -69, 98, -106, -98, -3, 47, -65, 51, -133, 54, -97, 47, 78, 98, 81, -3, 19, -47, -28, -67, 80, -211, -32, 63, -121, 124, 10, -168, 58, 84, 0, 224, -5, -13, 89, -78, 7, 77, 58, 286, 6, -105, -157, -4, 56, 212, -89, 163, 99, 55, 5, 12, 2, -77, 39, -14, -11, 153, -100, 232, 322, 78, 45, -15, -89, 60, 1, 1, -8, 60, 11, -7, 0, -54, 18, -196, -11, -41, 25, -111, 12, 165, -67, 76, 77, 7, -15, -365, 10, 102, -175, -196, 54, 105, -14, 103, 99, -11, -119, 114, -45, 123, -176, 59, -5, -58, -124, -10, -26, -169, 75, -4, -133, -26, 52, 114, -98, 182, -156, 39, -94, 189, 42, 154, 300, 44, -111, -312, 22, -181, -6, -59, -29, 171, 45, 224, -33, -1, 42, -86, 63, 196, -73, -111, 3, -77, -143, 222, 86, -6, -60, 175, 1, -38, -55, -83, -15, 41, 21, 160, 202, 129, -304, -134, 95, -44, -63, 201, -212, 6, 5, -150, -65, 192, 53, 68, -40, 159, -165, 91, 148, 95, 119, -93, 114, -2, -130, -189, 1, -184, -64, 22, -1, 263, -30, -177, -86, -70, -97, -13, -19, 56, -125, 129, 29, 57, 35, -43, 177, 16, -192, 1, -34, -16, -42, 228, 33, -276, 36, -151, 143, 154, 66, 213, -77, 50, -171, 188, -28, -144, -94, -19, -52, 247, -89, -193, -132, -143, 58, 47, 76, -206, -65, -150, -21, 167, -80, 127, 95, -64, -67, -112, 155, -15, 238, -36, 45, -210, -171, -247, 86, -43, -144, -424, 9, -81, -170, -20, -165, -79, 13, -248, 63, -38, -230, 83, -135, 60, 80, -187, 66, 84, -268, -251, 86, -127, 32, 14, 127, -56, 13, 294, -103, 22, -107, -33, -274, -67, 10, 101, 132, 108, 123, -107, 216, 114, -150, 13, -227, -248, -63, -113, -110, -145, 12, 230, -164, 196, -206, 109, 45, -235, -11, 12, -4, -127, -127, -307, -98, 253, 50, 65, -93, 121, 91, 160, 93, 201, -83, -268, -46, -29, 119, -107], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": true, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "241.2.a.b", "char_is_minimal": true, "conrey_index": 1, "id": null, "nf_label": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], [1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 1, -1], [0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0], [-1, 1, 0, 1, -1, -1, -1, 0, 0, 1, -1, 1], [1, 0, 0, 0, 0, -1, 1, -1, 0, 1, 0, 1], [-1, 1, -2, 1, -1, 0, 0, 1, -1, -1, -1, 0], [2, -1, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0], [-1, 0, 0, -2, 1, 0, 1, 0, 2, 1, 0, -1], [0, 0, -1, 0, 0, 1, 0, 1, 0, 0, 1, -1], [1, -1, 0, 0, 1, 0, 0, 1, -1, 0, 0, 0], [1, 0, -1, 0, -1, 0, 0, 0, 0, 0, -1, 1], [1, 0, 2, 1, 0, -1, -1, -2, -1, 1, 0, 2], [-1, 0, 0, -1, 1, -1, 0, 0, 1, 0, 0, -1], [1, 1, 0, 0, -1, 1, 0, -1, -2, 0, 2, 0], [-1, 1, 0, 0, -1, 0, -1, -1, 0, -1, -1, 0], [2, -2, 0, 1, 0, 0, 1, 0, -2, -2, 0, -1], [-2, -2, 0, 2, -1, 0, -2, 1, 0, 0, -2, 1], [-3, 3, -1, 1, -1, -2, 0, 0, 0, 0, -1, 1], [5, -1, 1, -3, 1, 2, 1, 0, 0, 1, 3, -1], [0, -2, 1, -2, 3, 1, 0, 0, 2, 0, 1, -2], [2, -1, 1, -1, 0, 2, -1, 0, 0, 0, 0, 1], [3, -2, 1, -2, 2, 1, 2, 0, 1, 0, 2, -1], [1, -2, 0, 0, 0, 1, 1, 2, 0, -1, 1, -1], [-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [-1, -1, 0, 1, 0, 0, -1, 0, 1, 0, -2, -1], [0, 0, 0, 0, 0, 1, 0, -1, -1, -2, 1, -1], [0, 1, -1, 0, -3, 0, 1, 0, 0, -1, -1, 0], [-2, 1, 1, 1, -1, -3, 0, -1, 0, 2, -1, 3], [-3, 0, -1, 1, 1, -1, 0, 0, 2, 0, 0, -1], [0, -2, 0, -1, 2, 2, 0, 1, 0, 0, 0, -1], [2, -1, -1, 0, 0, 1, 0, 2, -1, 0, 0, 0], [-2, 0, 0, 2, -2, -2, 0, 1, 0, 0, -1, 2], [-1, 0, 2, 0, 1, -1, 1, -1, 1, 1, 1, 0], [-3, 0, -1, 2, -2, -1, -1, 0, 1, -1, -4, 1], [3, 2, 0, 0, 0, 0, 1, -3, -2, 1, 2, 0], [-7, 3, -3, 2, -2, -3, 0, 0, 0, -1, -2, 1], [-2, 1, 1, 0, -2, -1, -1, -1, 0, 2, 0, 1], [-6, 0, 1, 1, 0, -2, -2, -1, 1, 0, -2, 1], [0, 1, 0, 1, 0, 0, -1, -2, -1, -1, 0, 0], [6, -1, 3, 0, -1, 1, 0, -1, -3, -2, 1, 1], [-2, 0, 1, 0, 0, -1, 0, 0, 2, 1, 0, 1], [-2, 2, 0, -3, 3, 0, 2, 0, 3, 4, 3, 0], [2, 0, 1, 0, 1, -1, 0, 0, 1, 2, -1, 2], [-3, -2, -2, -1, 2, 3, -2, 3, 2, 0, 0, -2], [2, 0, -2, -2, 2, 2, 3, 2, -2, 0, 3, -2], [-5, 1, 0, -1, 1, -2, -1, 0, 4, 2, -1, 0], [-2, -2, 1, 3, -2, -1, -2, 2, -1, 0, -3, 2], [-3, 2, -2, -3, 1, 1, 1, 0, 1, 1, 1, -1], [1, -1, 0, 0, 1, 1, 0, -1, 0, 1, 0, 0], [-2, 2, -3, 0, 0, 1, 1, 1, -2, -1, 2, -1], [1, -1, 3, -1, 2, 0, 1, -1, 0, -1, 2, -2], [0, 1, 1, 0, -1, 0, 0, -2, 1, 0, 1, 0], [-1, 0, -1, 1, -1, 2, -2, 3, -2, -2, -1, 0], [-5, 2, 0, -1, 0, 1, -2, 0, 4, -1, -3, -2], [4, 2, 0, -3, 0, 3, 0, 0, -1, 0, 3, -2], [-7, 0, -3, 2, -1, -2, 1, 2, 1, -1, -2, -1], [-1, 0, 0, 1, 0, 0, 1, -1, -2, -2, 1, -1], [0, 3, -2, 3, -4, 2, 0, -2, -4, -4, 0, 0], [-3, 0, 1, 1, 1, -4, -1, -3, 0, 1, -3, 2], [2, 0, 0, 1, -2, 1, 0, 1, -4, 0, 2, 0], [-3, 2, -1, -1, 1, -1, 1, 0, 0, 1, 1, -1], [4, -4, 0, -3, 1, 5, 1, 1, 0, -1, 2, -3], [3, 0, -1, -2, 1, 3, 2, 1, -1, -2, 0, -2], [-2, -2, -1, -2, 2, 2, 0, 2, 4, 0, 0, -2], [0, 4, 1, -2, -2, 1, 1, -1, 2, 1, 2, 1], [1, 0, 1, -1, 3, -1, 1, 0, 0, -1, 2, -1], [9, -2, 1, 1, 2, -1, 1, -1, -2, 1, 0, 2], [1, -1, 1, 4, -1, -2, -1, 0, -4, -1, -2, 3], [-1, 0, 2, -1, 0, 0, -1, 0, 0, 1, 0, 3], [1, 2, 0, 0, -2, 1, -1, 0, -1, 3, 1, 1], [-1, 4, 1, -1, 0, -2, -2, -2, 0, 0, -1, 3], [-1, -1, -1, 2, -1, 2, -1, 1, -1, -3, -1, -2], [-2, 1, 0, 1, 2, -3, 0, -1, 1, 0, 0, 0], [2, 2, 0, 1, -3, -3, 2, -1, 1, 2, -1, 3], [-2, 0, -1, 0, 0, -2, 0, 2, 0, 0, -4, 0], [6, -4, 1, 1, -2, 3, -1, -1, -4, -2, 1, 2], [-1, 2, 0, -3, 1, -2, 2, -2, 1, 0, 0, -2], [0, 0, 5, 2, -1, -2, -1, -4, -1, 4, 0, 5], [-1, 2, -3, 2, -2, 1, -1, 2, -2, -3, 1, -3], [0, 0, 1, -2, 1, -1, 1, -2, 0, 1, 0, 0], [0, -2, -2, 1, -1, 1, 0, 3, -1, 0, -1, -1], [-3, 0, -2, 2, -3, -3, 0, 1, 2, 0, -5, 2], [-4, 0, 1, 5, 1, -5, -2, 1, 0, 0, -3, 1], [-6, 5, -4, 6, -5, -5, -2, 1, -2, 2, -5, 5], [-1, 0, -2, 2, -1, -1, 1, 3, 0, -3, -3, 0], [3, -1, 2, -1, 0, 3, -1, -1, -2, 2, 3, 0], [-2, -2, 0, 2, 2, -1, -2, 3, 0, -2, -1, -1], [8, -7, 6, -4, 6, 4, 1, -1, 2, 3, 6, -3], [4, 0, 0, -5, 1, 1, 6, 1, 3, -2, 3, -3], [4, 2, 4, -2, 2, 1, -2, -1, 0, 2, 3, -1], [3, 0, 0, 1, -3, 3, -3, 0, 0, -1, -2, 1], [1, -6, 1, -5, 4, 2, 2, 2, 5, 0, 1, -3], [-4, -1, 2, -1, 1, -1, 0, -1, 3, 3, -1, 1], [8, -4, -1, -4, 5, 1, 5, 2, 0, -2, 6, -4], [1, 1, -1, 2, -1, -2, 0, -1, -1, 2, -1, 2], [3, -5, 4, -3, 5, 3, 1, -1, 1, 2, 4, -5]]}