# Stored data for newform 322.2.k.b, downloaded from the LMFDB on 13 May 2026. {"Nk2": 1288, "analytic_conductor": 2.571182945085228, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 161, "char_degree": 10, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 11, "char_orbit_label": "k", "char_order": 22, "char_parity": 1, "char_values": [322, 22, [185, 281], [11, 21]], "cm_discs": [], "conrey_index": 83, "dim": 80, "has_non_self_twist": 1, "hecke_cutters": [[3, [19790033062801, 0, -2101145953321670, 0, 136632663896613376, 0, 3747859951329840943, 0, 29264042843103784305, 0, -113061340014121535750, 0, 189056194952849955491, 0, -324586596144055026631, 0, 417381039309032515618, 0, -362997414764016552333, 0, 503791403296366106141, 0, -283598661929565387904, 0, 257786637998126140769, 0, -151588954255791083140, 0, 79782536142531587925, 0, -35094636994781669608, 0, 11067579301264927272, 0, -2731212966714569070, 0, 779302548790882337, 0, -281934128796340449, 0, 88214074475808402, 0, -23252972785608137, 0, 6385927118700743, 0, -1605174308719703, 0, 332897173957189, 0, -62325877068384, 0, 10454390873891, 0, -1584888307367, 0, 244820111796, 0, -34228358411, 0, 4933193705, 0, -716525689, 0, 123986588, 0, -16032845, 0, 1445331, 0, -84094, 0, 6522, 0, -1172, 0, 183, 0, -19, 0, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4504286855692610, "inner_twist_count": 4, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 7, 2, -1, 2, 0], [1, 1, 23, 4, -1, 22, 0], [1, 1, 161, 11, 1, 22, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "322.2.k.b", "level": 322, "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": true, "level_primes": [2, 7, 23], "level_radical": 322, "minimal_twist": "322.2.k.b", "prim_orbit_index": 11, "related_objects": [], "relative_dim": 8, "rm_discs": [], "sato_tate_group": "1.2.3.c22", "self_twist_discs": [], "self_twist_type": 0, "space_label": "322.2.k", "trace_display": [8, 0, 0, 11], "traces": [80, 8, 0, -8, 0, 0, 11, 8, 14, 0, 0, 0, 0, -11, 0, -8, 0, -14, 0, 0, -33, 0, 18, 0, 6, 0, 0, -11, 8, 22, 0, 8, 0, 0, -33, -8, -22, 0, 14, 0, 0, 22, -88, 0, 0, 4, 0, 0, 33, 16, 44, 0, -44, 0, 0, 11, -22, -52, 0, 0, 0, 0, -11, -8, -154, 0, 0, 0, 0, 22, -58, -36, 0, -22, 0, 0, 88, -58, -88, 0, 62, 0, 0, 33, 34, 88, 0, -22, 0, 0, 0, -4, -48, 0, 132, 0, 0, -33, 132, 6, 0, -88, 0, 0, -120, 66, -88, 0, -176, 0, 0, 0, 44, 0, 0, -36, 0, 0, -33, 0, 188, 0, -328, 0, 0, -55, 200, 8, 0, -66, 0, 0, -144, 44, 154, 0, 0, 0, 0, -33, -46, -8, 0, 14, 0, 0, 154, -22, 88, 0, 148, 0, 0, 44, 44, 58, 0, 66, 0, 0, -38, 136, 98, 0, 330, 0, 0, 33, -36, 54, 0, 44, 0, 0, -99, 0, 20, 0, 8, 0, 0, 99, 0, 26, 0, 136, 0, 0, -33, -44, -176, 0, 50, 0, 0, 33, -26, -66, 0, 38, 0, 0, 253, -22, -22, 0, -4, 0, 0, 120, -94, 66, 0, -198, 0, 0, 198, 0, -402, 0, 154, 0, 0, 0, -192, -44, 0, 22, 0, 0, -12, -52, -242, 0, 154, 0, 0, 77, -338, 22, 0, 76, 0, 0, 55, -68, 0, 0, -154, 0, 0, 0, 32, 20, 0, -8, 0, 0, 35, -66, 74, 0, 44, 0, 0, -43, -88, -132, 0, -66, 0, 0, 143, -286, 0, 0, 104, 0, 0, -11, -22, 68, 0, 8, 0, 0, -187, 8, -8, 0, 308, 0, 0, -154, 132, 0, 0, 0, 0, 0, -153, 6, -100, 0, -254, 0, 0, 33, -132, 0, 0, -14, 0, 0, -88, 22, 448, 0, -242, 0, 0, -237, 352, 62, 0, -98, 0, 0, -121, 44, 208, 0, 22, 0, 0, 11, 0, 36, 0, -54, 0, 0, 77, 0, 254, 0, 52, 0, 0, -99, 144, 44, 0, -86, 0, 0, -342, -140, -110, 0, -136, 0, 0, 44, -198, 110, 0, -26, 0, 0, -189, 18, -286, 0, -528, 0, 0, 99, 44, -154, 0, 264, 0, 0, 209, -50, -198, 0, 154, 0, 0, -22, -120, -238, 0, -66, 0, 0, 396, 6, -22, 0, 264, 0, 0, 99, 58, -66, 0, -286, 0, 0, 0, 400, -84, 0, 392, 0, 0, -32, 242, -126, 0, -44, 0, 0, -207, 66, -264, 0, -308, 0, 0, 22, -198, 0, 0, -148, 0, 0, -242, 154, 228, 0, -410, 0, 0, -11, 256, 148, 0, 110, 0, 0, -169, 154, 220, 0, 0, 0, 0, -54, 136, 8, 0, -110, 0, 0, 198, 154, 22, 0, 492, 0, 0, 132, 352, 338, 0, 0, 0, 0, -10, -164, 208, 0, 392, 0, 0, 308, 152, 222, 0, 286, 0, 0, 44, 22, 142, 0, -360, 0, 0, 55, 0, 56, 0, 200, 0, 0, 275, 8, 814, 0, 202, 0, 0, -46, 120, -110, 0, 212, 0, 0, 473, -110, 44, 0, 6, 0, 0, -100, -430, -88, 0, -22, 0, 0, 88, -66, -440, 0, 682, 0, 0, 0, -260, 0, 0, 66, 0, 0, -156, 28, -436, 0, -176, 0, 0, 44, -682, -22, 0, 152, 0, 0, -99, -30, -242, 0, -418, 0, 0, 0, -50, -96, 0, 184, 0, 0, 157, -352, 254, 0, -66, 0, 0, -66, -220, 0, 0, -66, 0, 0, 11, -88, 0, 0, 72, 0, 0, -232, 176, 126, 0, -230, 0, 0, -363, -98, 32, 0, 264, 0, 0, -33, -66, 176, 0, 0, 0, 0, -305, -8, -78, 0, -684, 0, 0, 0, 220, 22, 0, 36, 0, 0, -539, 0, 976, 0, -308, 0, 0, -137, 508, -220, 0, -18, 0, 0, 110, -188, -168, 0, -242, 0, 0, -253, -418, -198, 0, -208, 0, 0, 297, 0, 24, 0, 538, 0, 0, 11, 64, 110, 0, 8, 0, 0, -144, -34, -660, 0, 58, 0, 0, 132, -748, -44, 0, -56, 0, 0, 44, 36, -264, 0, -726, 0, 0, -11, 66, -320, 0, 0, 0, 0, 220, 86, 352, 0, -550, 0, 0, -164, 308, 74, 0, -110, 0, 0, 241, 180, -616, 0, 210, 0, 0, 99, 386, -44, 0, -396, 0, 0, 0, 4, -360, 0, 38, 0, 0, 90, 88, -62, 0, -352, 0, 0, -417, 550, -506, 0, -594, 0, 0, 11, 220, 0, 0, 264, 0, 0, -244, 264, 386, 0, -560, 0, 0, -242, 910, 50, 0, 330, 0, 0, -168, 176, 440, 0, 0, 0, 0, 33, 294, -34, 0, -180, 0, 0, -176, 132, 792, 0, 282, 0, 0, -88, 572, -6, 0, 242, 0, 0, -297, 396, -150, 0, 422, 0, 0, -11, 256, 118, 0, 88, 0, 0, 66, 66, -150, 0, -26, 0, 0, 385, 0, 40, 0, 260, 0, 0, 187, 92, 418, 0, 94, 0, 0, -89, -80, -110, 0, 60, 0, 0, 352, -22, 22, 0, 450, 0, 0, 97, -748, 66, 0, -88, 0, 0, 649, -484, -478, 0, 946, 0, 0, 209, -484, 264, 0, 0, 0, 0, -198, -402, -380, 0, -88, 0, 0, 374, -310, 0, 0, 344, 0, 0, 66, -514, -132, 0, -396, 0, 0, 0, -728, -80, 0, 248, 0, 0, 652, -198, 206, 0, -22, 0, 0, -84, -374, -22, 0, 110, 0, 0, 319, -484, 0, 0, 504, 0, 0, -342, -176, -70, 0, 14, 0, 0, -242, 198, 132, 0, 770, 0, 0, -198, -176, 22, 0, 0, 0, 0, -579, 168, 648, 0, -950, 0, 0, 22, -154, 22, 0, 102, 0, 0, 308, 22, 466, 0, -440, 0, 0, -441, 116, 76, 0, 342, 0, 0, 121, -128, 428, 0, 506, 0, 0, -66, 66, 112, 0, -222, 0, 0, 429, 0, 180, 0, 404, 0, 0, 44, 88, 286, 0, -186, 0, 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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}