# Stored data for newform 225.4.a.j, downloaded from the LMFDB on 20 April 2024. {"label": "225.4.a.j", "space_label": "225.4.a", "level": 225, "weight": 4, "hecke_orbit": 10, "hecke_orbit_code": 40532396713443553, "dim": 2, "is_polredabs": true, "nf_label": "2.2.76.1", "trace_hash": 1862605499036191683, "analytic_rank": 1, "is_twist_minimal": false, "hecke_cutters": [[2, [-18, 2, 1]], [7, [-135, 26, 1]]], "qexp_display": "q+(-1+\\beta )q^{2}+(12-2\\beta )q^{4}+(-13+\\cdots)q^{7}+\\cdots", "char_order": 1, "char_parity": 1, "char_degree": 1, "char_conductor": 1, "char_orbit_label": "a", "char_is_real": true, "Nk2": 3600, "fricke_eigenval": -1, "atkin_lehner_string": "-+", "analytic_conductor": 13.275429751291638, "hecke_ring_index": 1, "level_radical": 15, "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": "0.002", "prec": 17}, "analytic_rank_proved": true, "char_values": [225, 1, [101, 127], [1, 1]], "hecke_ring_generator_nbound": 2, "inner_twist_count": 1, "level_primes": [3, 5], "conrey_indexes": [1], "field_disc": 76, "field_disc_factorization": [[2, 2], [19, 1]], "field_poly": [-19, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.939", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "9.342", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "62.565", "prec": 20}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 2, "sato_tate_group": "3.2.3.c1", "atkin_lehner_eigenvals": [[3, -1], [5, 1]], "trace_display": [-2, 0, 0, -26], "traces": [0, 2, -2, 0, 24, 0, 0, -26, -84, 0, 0, -28, 0, -18, -126, 0, 120, -68, 0, 6, 0, 0, -124, 132, 0, 0, 626, 0, -8, -92, 0, 122, -664, 0, -692, 0, 0, 284, -158, 0, 0, -392, 0, -690, -32, 0, -588, -620, 0, 260, 0, 0, -1432, -848, 0, 0, 180, 0, 1156, -124, 0, 750, 942, 0, 1376, 0, 0, 358, 704, 0, 0, -824, 0, 108, -1196, 0, 376, 972, 0, -880, 0, 0, 2368, 156, 0, 0, 842, 0, 264, 864, 0, -2198, 2496, 0, -596, 0, 0, -1042, 3692, 0, 0, -1008, 0, -760, 4404, 0, 1912, -1680, 0, 2026, 0, 0, 3304, -2984, 0, 0, -3232, 0, -2308, 3924, 0, -1662, 1378, 0, -664, 0, 0, -912, -624, 0, 0, 1920, 0, 530, -4158, 0, -1704, 2028, 0, -2216, 0, 0, 64, -2180, 0, 0, -412, 0, 5232, -2948, 0, -546, -1164, 0, 3132, 0, 0, -2038, 6960, 0, 0, 108, 0, -2134, -8656, 0, 7140, -2304, 0, 5496, 0, 0, -8584, -1884, 0, 0, 3184, 0, 4608, 3380, 0, -158, -4338, 0, -8280, 0, 0, 3992, -5008, 0, 0, 652, 0, 2714, 1042, 0, -4784, 2604, 0, -4602, 0, 0, 2376, -3060, 0, 0, 10792, 0, -20536, 524, 0, 3142, -12304, 0, -3336, 0, 0, -5842, -2938, 0, 0, -11548, 0, -3898, 1944, 0, -1880, -10984, 0, 2594, 0, 0, 10248, 3240, 0, 0, 3376, 0, 11124, 1424, 0, -462, 5918, 0, 4744, 0, 0, -2486, 1260, 0, 0, 6456, 0, -24, 2432, 0, 6944, 4200, 0, -44, 0, 0, -12408, 5624, 0, 0, 990, 0, 11896, -5236, 0, 2928, 20240, 0, -2940, 0, 0, 12406, -5992, 0, 0, -3156, 0, 322, -8368, 0, -4964, -2808, 0, 7686, 0, 0, 1904, 7404, 0, 0, -17400, 0, -15596, -8484, 0, 8362, 14986, 0, 5224, 0, 0, 1170, 3456, 0, 0, 5892, 0, 7466, 12070, 0, -22720, 8480, 0, -2968, 0, 0, -4212, 2836, 0, 0, -13826, 0, 28320, 12924, 0, 584, -12720, 0, 14616, 0, 0, 5646, -16440, 0, 0, -5964, 0, -10270, 29892, 0, -6780, -908, 0, -4668, 0, 0, 2608, -732, 0, 0, -576, 0, -23140, -12264, 0, -13092, -16258, 0, -13304, 0, 0, -12134, 22512, 0, 0, 6768, 0, -1830, 11816, 0, 18744, 17852, 0, -6030, 0, 0, 34156, 984, 0, 0, -14570, 0, -12504, -2184, 0, 4632, 12792, 0, -8988, 0, 0, 12450, -1934, 0, 0, 23040, 0, 15926, -14832, 0, -3780, -328, 0, -24326, 0, 0, -29184, 11340, 0, 0, 32728, 0, 1148, -21536, 0, -2484, -17278, 0, 42000, 0, 0, -18262, -10128, 0, 0, 6348, 0, 17466, -17262, 0, 26136, 2220, 0, 1050, 0, 0, -2284, -2112, 0, 0, -26654, 0, 352, 28232, 0, -2416, -26080, 0, 17216, 0, 0, -1836, -32082, 0, 0, -15264, 0, 12400, -39568, 0, 39168, -7540, 0, 10546, 0, 0, -9384, 9052, 0, 0, 16992, 0, -27112, -22860, 0, -17148, -18386, 0, -28456, 0, 0, 6698, -18732, 0, 0, 15760, 0, -18152, 5678, 0, -26728, 13752, 0, 5286, 0, 0, -29256, -33832, 0, 0, -3624, 0, -13984, 14756, 0, -188, 5344, 0, -25176, 0, 0, 13544, -9684, 0, 0, 25468, 0, 5970, 44016, 0, -27664, -25428, 0, -10150, 0, 0, 3320, 35144, 0, 0, -37836, 0, 6908, -19448, 0, 27002, -17216, 0, -10864, 0, 0, -8256, 26160, 0, 0, -4532, 0, -12880, 1578, 0, -10176, 5652, 0, 8642, 0, 0, 11820, 18036, 0, 0, 49686, 0, 30048, 11724, 0, 44758, -11872, 0, 6912, 0, 0, 11018, 43994, 0, 0, -31212, 0, 7616, -6360, 0, -25644, -720, 0, -3890, 0, 0, 46224, 6920, 0, 0, 1712, 0, 52716, -1448, 0, -42602, 42102, 0, -35432, 0, 0, -40512, -8680, 0, 0, -13876, 0, -36276, -8314, 0, -16200, 29568, 0, 18334, 0, 0, -15924, -33120, 0, 0, 33574, 0, -44520, 8584, 0, 12114, 73440, 0, 46544, 0, 0, 60892, -4936, 0, 0, -14472, 0, -17240, 9504, 0, 52, -22808, 0, 11464, 0, 0, 6312, 7844, 0, 0, -86752, 0, 50004, -18040, 0, 7044, 55656, 0, 37224, 0, 0, -18840, -52272, 0, 0, -19012, 0, 44068, 43298, 0, 87840, -36276, 0, 13546, 0, 0, -18204, -8976, 0, 0, -8730, 0, -46264, 24656, 0, -6432, -5280, 0, -11252, 0, 0, -26192, 15004, 0, 0, -45140, 0, 4500, -1024, 0, -46236, 7632, 0, 36546, 0, 0, -3456, -4716, 0, 0, 80080, 0, 18192, 5772, 0, -30248, 12180, 0, 30936, 0, 0, 33782, 53100, 0, 0, 20420, 0, -17740, -8082, 0, -63888, 10188, 0, -46536, 0, 0, 43848, -42920, 0, 0, -13978, 0, 16288, 41904, 0, 8688, 1712, 0, -55396, 0, 0, -12738, 61510, 0, 0, -2136, 0, -22690, -61792, 0, 85656, -37796, 0, -37322, 0, 0, 56280, 13464, 0, 0, 43764, 0, -73968, -9080, 0, 14576, -39288, 0, -110864, 0, 0, -27150, 44016, 0, 0, 58248, 0, 27298, -62914, 0, -42152, -18280, 0, 45400, 0, 0, 2952, -296, 0, 0, 11586, 0, 50544, -2960, 0, -346, -23040, 0, -8488, 0, 0, -2678, 25238, 0, 0, -33756, 0, -42226, 92112, 0, 29700, 8992, 0, 29300, 0, 0, -85344, -87880, 0, 0, 2944, 0, 62728, 42100, 0, -14754, -73820, 0, 65976, 0, 0, 4582, -84928, 0, 0, 29688, 0, 12346, -66402, 0, 40464, 66520, 0, -26400, 0, 0, -115332, -11440, 0, 0, -25066, 0, -23896, -12000, 0, -64022, -90564, 0, -13620, 0, 0, -32006, 58990, 0, 0, 12944, 0, 6350, -110912, 0, -15216, -28980, 0, 5776, 0, 0, 14328, 3004, 0, 0, -61200, 0, -68056, 24180, 0, 7552, 4544, 0, 96144, 0, 0, 12040, -144272, 0, 0, -38044, 0, -31368, -106996, 0, 90104, 16992, 0, -28530, 0, 0, 117864, -4744, 0, 0, 55392, 0, 77360, -6596, 0, -15028, -45936, 0, -53716, 0, 0, -15134, 11646, 0, 0, -23852, 0, -49584, 70384, 0, 41260, -7212, 0, -5836, 0, 0, -74520, -69392, 0, 0, 68464, 0, -4500, -22716, 0, -22348, 111692, 0, 32152, 0, 0, -48592, 95340, 0, 0, 18828, 0, 61640, 63982, 0, -23096, 27412, 0, -33984, 0, 0, 86992, 28872, 0, 0, 16936, 0, -36216, -47364, 0, -40526, 6312, 0, 58752, 0, 0, 27292, 44722, 0, 0], "weight_parity": 1, "has_non_self_twist": 0, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": true, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "char_orbit_index": 1, "prim_orbit_index": 1, "minimal_twist": "75.4.a.d", "char_is_minimal": true, "conrey_index": 1, "id": 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], [1, 0], [-1, 1], [0, 0], [12, -2], [0, 0], [0, 0], [-13, -4], [-42, 6], [0, 0], [0, 0], [-14, -4], [0, 0], [-9, 16], [-63, -9], [0, 0], [60, -32], [-34, -20], [0, 0], [3, -4], [0, 0], [0, 0], [-62, -10], [66, -12], [0, 0], [0, 0], [313, -25], [0, 0], [-4, -22], [-46, 28], [0, 0], [61, 28], [-332, 44], [0, 0], [-346, -14], [0, 0], [0, 0], [142, -24], [-79, 7], [0, 0], [0, 0], [-196, 52], [0, 0], [-345, 4], [-16, -20], [0, 0], [-294, 78], [-310, -32], [0, 0], [130, 104], [0, 0], [0, 0], [-716, 210], [-424, 28], [0, 0], [0, 0], [90, 90], [0, 0], [578, -74], [-62, -64], [0, 0], [375, 56], [471, 33], [0, 0], [688, -120], [0, 0], [0, 0], [179, -100], [352, -172], [0, 0], [0, 0], [-412, -20], [0, 0], [54, -8], [-598, 166], [0, 0], [188, -54], [486, 108], [0, 0], [-440, 160], [0, 0], [0, 0], [1184, -248], [78, 192], [0, 0], [0, 0], [421, -349], [0, 0], [132, 84], [432, 144], [0, 0], [-1099, -172], [1248, -276], [0, 0], [-298, -278], [0, 0], [0, 0], [-521, 0], [1846, 26], [0, 0], [0, 0]]}