# Stored data for newform 12.4.b.a, downloaded from the LMFDB on 25 April 2024.
{"label": "12.4.b.a", "space_label": "12.4.b", "level": 12, "weight": 4, "hecke_orbit": 1, "hecke_orbit_code": 68786585612, "dim": 4, "is_polredabs": true, "nf_label": "4.0.3600.1", "trace_hash": 253884373257674553, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [], "qexp_display": "q+\\beta _{1}q^{2}+(-\\beta _{1}-\\beta _{3})q^{3}+(-2+\\beta _{2}+\\cdots)q^{4}+\\cdots", "char_order": 2, "char_parity": 1, "char_degree": 1, "char_conductor": 12, "char_orbit_label": "b", "char_is_real": true, "Nk2": 192, "analytic_conductor": 0.7080229200688873, "hecke_ring_index": 16, "level_radical": 6, "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": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.759", "prec": 17}, "analytic_rank_proved": true, "char_values": [12, 2, [7, 5], [1, 1]], "hecke_ring_generator_nbound": 3, "inner_twist_count": 4, "level_primes": [2, 3], "conrey_indexes": [11], "field_disc": 3600, "field_disc_factorization": [[2, 4], [3, 2], [5, 2]], "field_poly": [4, 0, 1, 0, 1], "hecke_ring_index_factorization": [[2, 4]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "3.506", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "105.525", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4078.945", "prec": 27}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "3.2.3.c2", "trace_display": [0, 0, 0, 0], "traces": [0, 4, 0, 0, -8, 0, -24, 0, 0, -12, 80, 0, 120, -40, 0, 0, -224, 0, -240, 0, 0, 120, 240, 0, 288, 180, 0, 0, -240, 0, -240, 0, 0, -480, 320, 0, 24, -520, 0, 0, 320, 0, 240, 0, 0, 960, -672, 0, -480, 1132, 0, 0, 80, 0, 792, 0, 0, -1080, -1360, 0, -960, -1768, 0, 0, 1408, 0, 1200, 0, 0, 1344, 480, 0, -960, 1640, 0, 0, 2160, 0, 240, 0, 0, -2844, -1120, 0, -240, -1280, 0, 0, -2880, 0, -240, 0, 0, 3480, -1344, 0, 384, 3080, 0, 0, -360, 0, -960, 0, 0, -960, 4880, 0, 2520, -4264, 0, 0, 960, 0, -2160, 0, 0, 120, 1200, 0, 2880, -524, 0, 0, -6960, 0, -1440, 0, 0, -3480, -800, 0, 960, 2160, 0, 0, 1280, 0, -3360, 0, 0, 2688, 7200, 0, 672, 5440, 0, 0, 1040, 0, -1080, 0, 0, 3840, -2400, 0, -1200, -2920, 0, 0, -6400, 0, 1440, 0, 0, -4800, -8688, 0, 960, -8388, 0, 0, 6960, 0, 4080, 0, 0, -2400, 7520, 0, -1920, 5048, 0, 0, 8064, 0, 6960, 0, 0, 2520, -4320, 0, -5760, -760, 0, 0, -2264, 0, -720, 0, 0, 11400, -13360, 0, -3840, 4480, 0, 0, 2240, 0, 2400, 0, 0, -14400, 4464, 0, -9504, -6960, 0, 0, 9600, 0, 3120, 0, 0, -540, -9280, 0, 2160, 16376, 0, 0, -5440, 0, 2400, 0, 0, -1320, 1920, 0, 3840, -4792, 0, 0, 3536, 0, 3360, 0, 0, 17376, 13600, 0, 720, -13440, 0, 0, 8704, 0, -6960, 0, 0, -16320, -3120, 0, 4800, -19520, 0, 0, -22800, 0, -5040, 0, 0, -1200, 800, 0, -2688, 25400, 0, 0, -5760, 0, -6720, 0, 0, 8640, -2400, 0, 19200, 14532, 0, 0, -3280, 0, -6792, 0, 0, 15840, 14480, 0, 5400, 6960, 0, 0, -8640, 0, -960, 0, 0, -21000, 13920, 0, -2880, -28120, 0, 0, 2640, 0, -14640, 0, 0, -8928, 6720, 0, 5688, -1800, 0, 0, -4480, 0, -9600, 0, 0, 1560, -96, 0, -6720, 5960, 0, 0, 2560, 0, 12960, 0, 0, 13440, -10000, 0, 16320, -8296, 0, 0, -3840, 0, 6000, 0, 0, -3840, 9360, 0, -960, 7996, 0, 0, 2400, 0, 10608, 0, 0, -13440, -10400, 0, -6960, 19640, 0, 0, 16128, 0, -7920, 0, 0, 28440, -19200, 0, -19968, 9600, 0, 0, -6160, 0, 2400, 0, 0, 6240, -19120, 0, -28800, -42280, 0, 0, -10080, 0, 22800, 0, 0, -5760, -8160, 0, 11520, -14296, 0, 0, 42000, 0, 2016, 0, 0, -30360, 21600, 0, 1920, 14072, 0, 0, 19520, 0, 36000, 0, 0, 4800, -13920, 0, -10080, 57800, 0, 0, 8528, 0, -9840, 0, 0, -3396, -3200, 0, -15600, -30080, 0, 0, 11520, 0, -10800, 0, 0, 8760, -3504, 0, -8640, -13720, 0, 0, -26880, 0, 7200, 0, 0, -27840, -47200, 0, -240, -22800, 0, 0, -14400, 0, -2640, 0, 0, 58560, 39360, 0, 3840, 5200, 0, 0, 1048, 0, 12744, 0, 0, -3960, 22640, 0, 13440, 21760, 0, 0, 27840, 0, -43440, 0, 0, 192, -29520, 0, 17280, 53440, 0, 0, -56880, 0, 7680, 0, 0, -22680, 28160, 0, 6960, -26880, 0, 0, -3200, 0, 4080, 0, 0, 5400, 29472, 0, 26880, -11036, 0, 0, -4320, 0, -22560, 0, 0, -18720, -400, 0, 31680, -95848, 0, 0, -25600, 0, -2400, 0, 0, 5304, 10800, 0, -13440, 2640, 0, 0, 60720, 0, -41760, 0, 0, -19200, 49760, 0, -5376, 37120, 0, 0, -86400, 0, -21600, 0, 0, 38400, -6720, 0, -4224, 77960, 0, 0, -10880, 0, -18480, 0, 0, -9600, 5840, 0, 33960, 62640, 0, 0, 29120, 0, 25200, 0, 0, 3960, 6720, 0, 12960, -35032, 0, 0, -17520, 0, 40080, 0, 0, 16320, -35360, 0, -7680, -65800, 0, 0, -9600, 0, -42000, 0, 0, -44352, -22560, 0, 4800, -31900, 0, 0, 5840, 0, -1440, 0, 0, 8520, 4400, 0, -58560, -11320, 0, 0, 5120, 0, 22320, 0, 0, 27840, -17280, 0, 5760, 24000, 0, 0, 7920, 0, 25584, 0, 0, -4920, 13440, 0, 9600, 37688, 0, 0, 104256, 0, 31200, 0, 0, 7320, 45600, 0, -19200, -69880, 0, 0, 16776, 0, 27840, 0, 0, 7008, -69600, 0, -6480, -3200, 0, 0, -27840, 0, 26880, 0, 0, -28800, -13776, 0, -48960, 17920, 0, 0, -10800, 0, -7920, 0, 0, 26880, -77440, 0, 4800, 56696, 0, 0, 30080, 0, 9600, 0, 0, -78720, -56160, 0, -53760, 42000, 0, 0, -10096, 0, 3144, 0, 0, 25812, 32800, 0, -53040, 47000, 0, 0, 10752, 0, 3360, 0, 0, 10800, 29280, 0, 27840, -57920, 0, 0, 38400, 0, -40800, 0, 0, 59040, 13600, 0, -5040, -57160, 0, 0, 51840, 0, 56880, 0, 0, 3840, -43008, 0, 53760, -118264, 0, 0, 1520, 0, 41760, 0, 0, -15600, 84560, 0, 9600, 144000, 0, 0, -63392, 0, -15600, 0, 0, -58944, -5280, 0, 8640, 17680, 0, 0, -7920, 0, -12960, 0, 0, 90240, -15040, 0, -22800, -26880, 0, 0, -53440, 0, -56880, 0, 0, -135720, -31200, 0, 15360, -62640, 0, 0, -8960, 0, -2400, 0, 0, -21600, -12000, 0, 80640, -56296, 0, 0, -14080, 0, -60720, 0, 0, 73080, 106320, 0, 9600, 5076, 0, 0, -17040, 0, 4032, 0, 0, 105000, 14400, 0, 28800, 94520, 0, 0, -53568, 0, -12000, 0, 0, 13440, 89280, 0, -12672, 40000, 0, 0, 13920, 0, -32640, 0, 0, -9240, -60480, 0, 49200, 167000, 0, 0, -38400, 0, -67920, 0, 0, -24000, -21072, 0, -37440, -56880, 0, 0, -14640, 0, -43440, 0, 0, -13440, 128000, 0, 1080, -78080, 0, 0, -37120, 0, 17520, 0, 0, -160320, -4800, 0, 60480, -173760, 0, 0, -32752, 0, -20160, 0, 0, -24120, -34960, 0, 28800, -23400, 0, 0, 108800, 0, 69600, 0, 0, 45120, 12816, 0, 9600, 151400, 0, 0, -53760, 0, 17520, 0, 0, 31680, 69600, 0, 2640, -16400, 0, 0, -23040, 0, -14640, 0, 0, 81600, -105600, 0, 46080, -82676, 0, 0, 9584, 0, -20160, 0, 0, 34560, 61600, 0, -102600, 60720, 0, 0, 99008, 0, -7920, 0, 0, 12792, -47760, 0, -40320, 76480, 0, 0, -21600, 0, 57600, 0, 0, 65640, -72000, 0, -34752, -73480, 0, 0, 54400], "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, 3, 2, -1, 2, 0], [1, 1, 4, 2, -1, 2, 0], [1, 1, 12, 2, 1, 2, 0]], "char_orbit_index": 2, "prim_orbit_index": 2, "minimal_twist": "12.4.b.a", "char_is_minimal": true, "conrey_index": 11, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, -1, 0, -1], [-2, 0, 1, 1], [0, -2, -1, 1], [-6, 1, -3, 1], [0, 0, 1, 1], [0, -4, 4, -4], [-3, 6, 3, -3], [20, 0, -2, -2], [0, 10, -5, 5], [30, -4, -3, 5], [-10, 0, 0, 0], [0, -2, 4, -4], [0, -10, 9, -1], [-56, 0, -4, -4], [0, -8, -4, 4], [-60, -3, 6, 6], [0, 0, -9, -9], [0, 24, -8, 8], [30, -6, -3, 3], [60, 0, 10, 10], [0, -28, 14, -14], [72, 28, 0, -8], [45, 0, 0, 0], [0, -10, 0, 0], [0, 33, -27, 6], [-60, 0, -2, -2], [0, 34, 17, -17], [-60, -8, 6, -26], [0, 0, 29, 29], [0, -48, -16, 16], [-120, -30, -15, 15], [80, 0, -8, -8], [0, 20, -10, 10], [6, -72, 21, -27], [-130, 0, 0, 0], [0, 18, -36, 36], [0, 10, 0, 10], [80, 0, 24, 24], [0, 28, 14, -14], [60, 30, -6, -6], [0, 0, -29, -29], [0, 40, 40, -40], [240, 6, 3, -3], [-168, 0, -28, -28], [0, -56, 28, -28], [-120, 80, 12, 44], [283, 0, 0, 0], [0, 45, 0, 0], [0, -40, 36, -4], [20, 0, -10, -10], [0, -122, -61, 61], [198, 21, -9, 75], [0, 0, -40, -40], [0, -56, -8, 8], [-270, 54, 27, -27], [-340, 0, 34, 34], [0, 50, -25, 25], [-240, -40, -48, 32], [-442, 0, 0, 0], [0, -58, 116, -116], [0, -60, 27, -33], [352, 0, -48, -48], [0, 20, 10, -10], [300, -120, -30, -30], [0, 0, 95, 95], [0, 96, -32, 32], [336, 84, 42, -42], [120, 0, 20, 20], [0, 300, -150, 150], [-240, 12, -84, -60], [410, 0, 0, 0], [0, -130, 0, 0], [0, -45, 0, -45], [540, 0, 18, 18], [0, 60, 30, -30], [60, -10, 30, -10], [0, 0, -11, -11], [0, 32, 96, -96], [-711, -36, -18, 18], [-280, 0, 28, 28], [0, -362, 181, -181], [-60, 72, 6, 54], [-320, 0, 0, 0], [0, 58, -116, 116], [0, 170, -153, 17], [-720, 0, 40, 40], [0, -188, -94, 94], [-60, 240, 6, 6], [0, 0, -10, -10], [0, -112, -112, 112], [870, -174, -87, 87], [-336, 0, -56, -56], [0, -180, 90, -90], [96, -176, 192, -32], [770, 0, 0, 0], [0, 283, 0, 0], [0, -30, 135, 105], [-90, 0, 45, 45]]}