# Stored data for newform 345.2.m.c, downloaded from the LMFDB on 23 April 2024. {"label": "345.2.m.c", "space_label": "345.2.m", "level": 345, "weight": 2, "hecke_orbit": 3, "hecke_orbit_code": 9008023922016601, "dim": 50, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[2, [64009, 364573, -3519043, -4510638, 195662687, 407118195, 3410662739, 5325232440, 18975880176, 14587767755, 24077164541, 12194697482, 17453480113, 7913620671, 11886234862, 1148011128, -51011979, 1395634790, 3480642009, -992560217, 5788881293, 3228638721, 3231483635, 1986208576, 2555488806, 142822944, 1062176923, -79502203, 362496123, -56587982, 97254873, -9336745, 23461614, -2819806, 3254260, -578567, 686053, -25168, 86116, -20548, 14050, 3201, 2314, 77, 325, 11, 54, 0, 7, 0, 1]]], "char_order": 11, "char_parity": 1, "char_degree": 10, "char_conductor": 23, "char_orbit_label": "m", "char_is_real": false, "Nk2": 1380, "analytic_conductor": 2.7548388697341735, "level_radical": 345, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "analytic_rank_proved": true, "char_values": [345, 11, [116, 277, 166], [11, 11, 4]], "inner_twist_count": 2, "level_primes": [3, 5, 23], "conrey_indexes": [16, 31, 121, 151, 196, 211, 256, 271, 301, 331], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 5, "sato_tate_group": "1.2.3.c11", "trace_display": [0, -5, 5, -3], "traces": [50, 0, -5, -4, 5, -11, -3, 0, -5, 0, 15, -4, -19, 55, 5, 12, 5, 0, -11, 4, 8, -18, 14, 66, -5, -18, -5, 10, -22, 0, 6, 33, 4, 18, -8, -15, 25, -97, -19, 22, -42, -11, -25, 25, -50, -44, 86, -10, -8, -11, -17, -67, -26, 0, -4, -132, 22, 8, -76, 4, 13, -8, 8, 76, 8, 4, 84, 66, 25, 22, 55, 0, -59, 17, -5, 82, -56, -7, 7, 10, -5, -150, 19, 10, 6, 44, -11, -62, -74, 0, -56, 41, 28, -161, 11, -44, -68, -198, 4, -4, 12, -4, 48, -84, 3, 227, 11, -15, 66, 18, -8, -16, 115, 46, -36, 188, 3, -12, 123, 11, -38, 58, -20, -28, 5, -11, -43, 0, 19, 18, -27, 25, 96, -110, 5, -70, 136, 77, -62, 12, 75, -76, -88, -10, -11, 91, -30, 119, 52, 0, -83, 197, 16, 44, -6, 21, 15, -42, -15, -154, -57, 22, -66, -47, 7, -6, -110, -132, 104, -40, 11, 229, -64, -25, -3, -105, -76, 157, 61, 4, 91, -33, -42, -297, 8, 47, -144, -82, -3, -2, 43, -78, -71, -171, -3, 37, -71, -18, 223, 0, -70, 202, 5, 99, -35, -130, -8, 120, 26, 22, 78, 108, -22, 106, 25, -11, 193, 337, -37, 19, 59, 28, -104, 385, -5, -14, 29, 137, -162, -33, 98, -174, 33, 48, 13, -265, 7, 330, -202, -12, 17, -110, -5, 47, 8, -150, 174, 14, -58, 0, 3, 10, -62, -62, 6, -226, 60, 99, 27, 89, 22, -70, 147, 37, 15, 124, 3, 10, -25, 11, -145, -279, 54, -173, -18, 118, 44, 43, 6, -55, -62, -18, 98, -10, 0, -47, 65, -11, 94, 58, -13, 13, -123, -88, -1, 366, 15, -294, -179, 62, -118, -191, -10, 240, -2, -4, -101, -229, -73, -47, 46, -150, -90, 48, 3, 77, 18, -92, 9, 1, 88, -88, 120, -4, -8, 92, 11, -260, -61, -4, -28, -127, -30, 8, 59, 83, 149, -303, 5, 110, -108, -97, 119, -44, 8, 26, -137, 67, 63, 55, -8, 15, 139, -133, 55, 10, -119, 178, -38, 0, -344, 40, -82, -265, -51, 3, -220, 112, 112, 38, -126, 104, -103, -118, 5, 235, -262, 0, 11, -137, 23, 204, 173, 0, 12, -207, 19, 262, 7, -70, -307, 154, -38, -182, 70, -96, -78, -270, -135, -10, 9, 44, 167, 147, 5, -38, -121, -290, 190, 7, 70, -38, 200, 77, -52, 235, 92, -278, 156, -54, 245, 132, -13, -301, -6, -153, -32, -179, 0, 99, -64, -10, -13, 264, 33, -68, 60, 80, 48, 29, -41, 226, 35, 119, 74, 94, 96, 355, 13, 0, 182, -35, -83, 309, 89, -45, 32, 177, 16, -8, 232, 286, -221, 541, 27, -250, 46, 43, -347, -158, 48, 260, 104, 90, -11, -661, 18, 20, -24, 55, -20, 274, 119, -160, -20, 0, 296, -167, 33, 0, -156, -102, 289, 100, -15, 57, -105, -94, -1, 4, 132, -99, 101, 55, -144, 205, 82, -397, 191, 92, -222, -231, 11, 60, -114, -189, 25, -30, -75, -70, -37, -25, -162, -21, 8, 291, 268, 170, -192, -84, 12, -195, -81, 223, -44, 88, -104, -4, 107, 4, 229, -57, -19, 425, -11, -66, -69, -113, 13, -29, 24, 253, -34, 176, 30, -167, 10, 14, 68, 16, -67, 3, -15, -313, 116, 15, -3, -205, 180, -2, 165, -93, 87, -374, -8, 142, 57, 511, 116, 219, 110, -171, 151, -552, 19, 406, 1, 70, -88, 12, -71, 63, 102, 15, 9, -38, 14, 205, -42, 0, -99, -55, 7, 232, 170, -238, -58, 302, -83, -3, -195, -110, -109, 136, 9, 28, -87, 57, 95, -38, 3, -372, -120, -144, -5, -231, -84, -129, -151, -55, 415, -28, 23, 113, 21, -79, -166, -190, 11, 165, -92, 128, -78, -363, -8, 13, -233, -22, -64, 48, 193, -89, -167, -125, 38, 164, -48, 374, 57, 19, -67, -258, -7, -89, -30, 94, -161, -104, -27, 66, 235, 143, -188, 96, -5, 100, -176, 85, 186, -29, -15, 71, -294, 16, 18, 297, 124, 128, -114, -22, -228, 150, -56, -30, 84, 101, 80, 197, -121, -67, 24, -18, 55, -131, -75, -42, -204, -221, 98, -78, -26, -668, 92, -242, -55, -89, -59, -7, -43, -12, 92, 349, -181, 4, -33, -220, 212, -93, -5, -3, -219, 201, -380, -200, -80, -121, 294, 70, -175, -75, -2, -341, -58, -74, 36, -150, -47, 293, 102, 0, 109, 183, -250, -42, -115, 10, 186, 152, -40, -164, -155, 180, 17, 422, -5, -92, -166, 203, -172, -286, -127, -93, -177, 33, 28, 118, 225, -248, -88, -43, -264, 367, 66, -316, -15, -26, -195, 495, 147, 42, 289, 114, 113, -459, 26, 366, -153, 124, 79, 33, 58, 30, 220, 76, -119, 242, 41, -469, 356, 0, 141, -145, -13, -66, -77, -180, 485, -333, -89, 47, -63, -129, -19, -124, -7, -228, 68, 74, -76, -104, 11, -117, -451, 98, 33, 276, -27, 168, -93, -55, 297, -5, -18, 468, 72, -84, 130, 85, 131, -26, -150, 12, -76, 214, 11, -246, 260, -47, -178, -108, 76, 419, -134, 0, 20, -466, 94, -216, 426, -30, -334, 205, 108, -277, 14, 178, -96, -262, 185, 17, 144, 154, 224, -478, -12, 150, -229, -272, 366, 8, -7, -82, 232, -151, -50, -44, -3, -214, -85, -4, -56, 327, -19, 24, -91, 7, 313, 375, -65, -33, 129, -431, 35, 522, 42, 184, -114, 18, -266, 165, 86, -69, 191, 266, 25, -18, -73, 344, -146, 8, 213, -29, 24, 184, 144, -150, 233, -264, -112, -215, 184, 92, 193, 116, -8, 22, 102, 231, 462, 68, -26, 841, -55, -103, -87, -392, -167, -151, 317, 122, -19, 199, 11, -371, -28, 407, -14, 22, 10, 39, -174, -4, 122, 45, 14, 186, -510, -161, -65, 172, -11, 189, -246, -18, -138, 202, -116, -142, -357, 18, 45, -19, -61, 272, 162, -127, 83, 117, 47, 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": true, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 23, 3, 1, 11, 0]], "char_orbit_index": 13, "prim_orbit_index": 3, "minimal_twist": "345.2.m.c", "char_is_minimal": true, "conrey_index": 16, "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}