# Stored data for newform 32.6.b.a, downloaded from the LMFDB on 11 July 2025.
{"Nk2": 1152, "analytic_conductor": 5.13228223401538, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 8, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 2, "char_orbit_label": "b", "char_order": 2, "char_parity": 1, "char_values": [32, 2, [31, 5], [2, 1]], "cm_discs": [], "conrey_index": 17, "dim": 4, "field_disc": 218489, "field_disc_factorization": [[41, 1], [73, 2]], "field_poly": [64, -8, -2, -1, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "has_non_self_twist": 1, "hecke_cutters": [], "hecke_orbit": 1, "hecke_orbit_code": 68820140064, "hecke_ring_generator_nbound": 5, "hecke_ring_index": 4096, "hecke_ring_index_factorization": [[2, 12]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 2, 1, 2, 0]], "is_cm": false, "is_largest": true, "is_maximal": true, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "32.6.b.a", "level": 32, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2], "level_radical": 2, "minimal_twist": "8.6.b.a", "nf_label": "4.0.218489.1", "prim_orbit_index": 2, "qexp_display": "q+\\beta _{1}q^{3}+\\beta _{2}q^{5}+(-24-\\beta _{3})q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "5.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "32.6.b", "trace_display": [0, 0, 0, -96], "trace_hash": 381009175449852716, "trace_moments": [{"__RealLiteral__": 0, "data": "0.003", "prec": 17}, {"__RealLiteral__": 0, "data": "3.740", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "69.482", "prec": 20}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1805.276", "prec": 27}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 17}, "traces": [0, 4, 0, 0, 0, 0, 0, -96, 0, -164, 0, 0, 0, 0, 0, 416, 0, 200, 0, 0, 0, 0, 0, -2336, 0, 1556, 0, 0, 0, 0, 0, 12928, 0, -2352, 0, 0, 0, 0, 0, -35104, 0, -4568, 0, 0, 0, 0, 0, 54720, 0, 9828, 0, 0, 0, 0, 0, -85472, 0, -2032, 0, 0, 0, 0, 0, 153440, 0, -19520, 0, 0, 0, 0, 0, -206688, 0, 39976, 0, 0, 0, 0, 0, 247872, 0, 29684, 0, 0, 0, 0, 0, -307872, 0, -84632, 0, 0, 0, 0, 0, 259744, 0, -99576, 0, 0, 0, 0, 0, -180448, 0, 64768, 0, 0, 0, 0, 0, 205472, 0, 303816, 0, 0, 0, 0, 0, -154304, 0, -51332, 0, 0, 0, 0, 0, -23040, 0, -498224, 0, 0, 0, 0, 0, 233536, 0, 194472, 0, 0, 0, 0, 0, -331680, 0, 555200, 0, 0, 0, 0, 0, 651488, 0, -307208, 0, 0, 0, 0, 0, -1108704, 0, -915712, 0, 0, 0, 0, 0, 933920, 0, 303284, 0, 0, 0, 0, 0, -1532384, 0, 1674320, 0, 0, 0, 0, 0, 2016864, 0, -690368, 0, 0, 0, 0, 0, -818432, 0, -1942904, 0, 0, 0, 0, 0, 1429152, 0, 1214352, 0, 0, 0, 0, 0, -1847776, 0, 2067792, 0, 0, 0, 0, 0, 700448, 0, -1207296, 0, 0, 0, 0, 0, -1863296, 0, -3053876, 0, 0, 0, 0, 0, 1401984, 0, 1715368, 0, 0, 0, 0, 0, 350400, 0, 3855944, 0, 0, 0, 0, 0, 714208, 0, -2625520, 0, 0, 0, 0, 0, -128704, 0, -4630008, 0, 0, 0, 0, 0, -2209888, 0, 1819712, 0, 0, 0, 0, 0, 1479488, 0, 5850880, 0, 0, 0, 0, 0, -2324096, 0, -892824, 0, 0, 0, 0, 0, 5192768, 0, -5370420, 0, 0, 0, 0, 0, -1994464, 0, 2215968, 0, 0, 0, 0, 0, 3392672, 0, 6351552, 0, 0, 0, 0, 0, -8352416, 0, -3538072, 0, 0, 0, 0, 0, 2902240, 0, -9727536, 0, 0, 0, 0, 0, -3079712, 0, 2723328, 0, 0, 0, 0, 0, 8102304, 0, 7609416, 0, 0, 0, 0, 0, -2210496, 0, -1214720, 0, 0, 0, 0, 0, 2925760, 0, -5846136, 0, 0, 0, 0, 0, -10681568, 0, 3684764, 0, 0, 0, 0, 0, 1269440, 0, 10353560, 0, 0, 0, 0, 0, -33216, 0, -8186304, 0, 0, 0, 0, 0, 10305024, 0, -9535232, 0, 0, 0, 0, 0, 1826752, 0, 4388240, 0, 0, 0, 0, 0, -2791808, 0, 5830344, 0, 0, 0, 0, 0, -4495584, 0, 1352424, 0, 0, 0, 0, 0, -6635872, 0, -5528368, 0, 0, 0, 0, 0, 5829696, 0, 3067880, 0, 0, 0, 0, 0, 2738112, 0, 6858056, 0, 0, 0, 0, 0, 11028320, 0, -7579140, 0, 0, 0, 0, 0, -18765792, 0, -9387384, 0, 0, 0, 0, 0, -1624576, 0, 3634856, 0, 0, 0, 0, 0, -15718848, 0, 447488, 0, 0, 0, 0, 0, 20479328, 0, 3112464, 0, 0, 0, 0, 0, 8557952, 0, 4504000, 0, 0, 0, 0, 0, 22817056, 0, -1906544, 0, 0, 0, 0, 0, -19668768, 0, 9221376, 0, 0, 0, 0, 0, -9861024, 0, -7210176, 0, 0, 0, 0, 0, -23534528, 0, -6091616, 0, 0, 0, 0, 0, 23705568, 0, 921000, 0, 0, 0, 0, 0, 2440448, 0, -11748060, 0, 0, 0, 0, 0, 19533856, 0, 17091344, 0, 0, 0, 0, 0, -20777696, 0, 16894400, 0, 0, 0, 0, 0, -11169696, 0, -12377600, 0, 0, 0, 0, 0, -13841824, 0, -2808672, 0, 0, 0, 0, 0, 23357728, 0, -5959320, 0, 0, 0, 0, 0, 18526816, 0, -5207288, 0, 0, 0, 0, 0, 9014176, 0, -3385792, 0, 0, 0, 0, 0, -9807968, 0, -32263608, 0, 0, 0, 0, 0, -38473760, 0, 22919528, 0, 0, 0, 0, 0, -16141440, 0, 42597120, 0, 0, 0, 0, 0, 4608064, 0, -4662616, 0, 0, 0, 0, 0, 48825920, 0, -3693916, 0, 0, 0, 0, 0, 2155104, 0, -12601328, 0, 0, 0, 0, 0, 16995936, 0, 12162440, 0, 0, 0, 0, 0, -43252320, 0, -7584112, 0, 0, 0, 0, 0, 1932704, 0, -46789224, 0, 0, 0, 0, 0, -11771968, 0, 29123840, 0, 0, 0, 0, 0, 60896736, 0, 57578504, 0, 0, 0, 0, 0, -18092224, 0, -27476336, 0, 0, 0, 0, 0, -12358496, 0, -30019392, 0, 0, 0, 0, 0, -51329504, 0, -10394672, 0, 0, 0, 0, 0, 15130528, 0, 9727488, 0, 0, 0, 0, 0, -23020096, 0, 4111360, 0, 0, 0, 0, 0, 76313152, 0, -58087168, 0, 0, 0, 0, 0, 10619360, 0, 63820492, 0, 0, 0, 0, 0, -2565984, 0, 70890192, 0, 0, 0, 0, 0, -72413920, 0, -28751296, 0, 0, 0, 0, 0, 4126912, 0, -21224880, 0, 0, 0, 0, 0, -16118400, 0, -39123352, 0, 0, 0, 0, 0, 47594848, 0, 9790344, 0, 0, 0, 0, 0, 22969472, 0, -24591104, 0, 0, 0, 0, 0, 8226240, 0, -70080320, 0, 0, 0, 0, 0, -59318976, 0, 83594304, 0, 0, 0, 0, 0, -5337216, 0, 97059416, 0, 0, 0, 0, 0, 66388704, 0, -22382040, 0, 0, 0, 0, 0, 26080160, 0, -13323184, 0, 0, 0, 0, 0, 25691488, 0, -27825648, 0, 0, 0, 0, 0, -43546592, 0, 7667592, 0, 0, 0, 0, 0, -62191456, 0, -19533836, 0, 0, 0, 0, 0, -84732832, 0, -83581616, 0, 0, 0, 0, 0, 60065888, 0, 67092456, 0, 0, 0, 0, 0, 1067904, 0, 78915008, 0, 0, 0, 0, 0, 63166176, 0, -36881480, 0, 0, 0, 0, 0, -30943584, 0, -4634936, 0, 0, 0, 0, 0, 37022304, 0, -52072448, 0, 0, 0, 0, 0, -59958112, 0, -44608256, 0, 0, 0, 0, 0, 71310464, 0, 18519104, 0, 0, 0, 0, 0, 11779392, 0, -66214576, 0, 0, 0, 0, 0, 25089248, 0, 116614416, 0, 0, 0, 0, 0, -117437472, 0, 116438024, 0, 0, 0, 0, 0, 18899520, 0, -19080280, 0, 0, 0, 0, 0, -63413056, 0, 25043456, 0, 0, 0, 0, 0, 58362464, 0, -121108632, 0, 0, 0, 0, 0, 24934464, 0, -61969020, 0, 0, 0, 0, 0, 125637280, 0, 5579552, 0, 0, 0, 0, 0, -113823136, 0, -51163192, 0, 0, 0, 0, 0, 11568608, 0, 101482816, 0, 0, 0, 0, 0, -26310272, 0, 85306576, 0, 0, 0, 0, 0, 2185792, 0], "weight": 6, "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, "fricke_eigenval": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 0], [0, 0, 1, 0], [0, 0, 0, 0], [-24, 0, 0, -1], [0, 0, 0, 0], [-41, 0, 0, -2], [0, 0, 0, 0], [0, 5, 8, 0], [0, 0, 0, 0], [0, 32, 3, 0], [0, 0, 0, 0], [104, 0, 0, -1], [0, 0, 0, 0], [50, 0, 0, 2], [0, 0, 0, 0], [0, -7, -24, 0], [0, 0, 0, 0], [0, -160, -12, 0], [0, 0, 0, 0], [-584, 0, 0, 13], [0, 0, 0, 0], [389, 0, 0, 20], [0, 0, 0, 0], [0, -70, -24, 0], [0, 0, 0, 0], [0, 256, -41, 0], [0, 0, 0, 0], [3232, 0, 0, 12], [0, 0, 0, 0], [-588, 0, 0, -18], [0, 0, 0, 0], [0, -16, 112, 0], [0, 0, 0, 0], [0, -160, 57, 0], [0, 0, 0, 0], [-8776, 0, 0, -67], [0, 0, 0, 0], [-1142, 0, 0, -68], [0, 0, 0, 0], [0, 421, -48, 0], [0, 0, 0, 0], [0, -32, 231, 0], [0, 0, 0, 0], [13680, 0, 0, -54], [0, 0, 0, 0], [2457, 0, 0, 48], [0, 0, 0, 0], [0, 322, 24, 0], [0, 0, 0, 0], [0, 928, -131, 0], [0, 0, 0, 0], [-21368, 0, 0, 155], [0, 0, 0, 0], [-508, 0, 0, 38], [0, 0, 0, 0], [0, -1427, 128, 0], [0, 0, 0, 0], [0, -2016, -657, 0], [0, 0, 0, 0], [38360, 0, 0, 89], [0, 0, 0, 0], [-4880, 0, 0, 28], [0, 0, 0, 0], [0, -1359, -792, 0], [0, 0, 0, 0], [0, 1184, 156, 0], [0, 0, 0, 0], [-51672, 0, 0, -57], [0, 0, 0, 0], [9994, 0, 0, 302], [0, 0, 0, 0], [0, 3109, 240, 0], [0, 0, 0, 0], [0, -928, 836, 0], [0, 0, 0, 0], [61968, 0, 0, 86], [0, 0, 0, 0], [7421, 0, 0, -322], [0, 0, 0, 0], [0, 2569, 704, 0], [0, 0, 0, 0], [0, 32, -222, 0], [0, 0, 0, 0], [-76968, 0, 0, -471], [0, 0, 0, 0], [-21158, 0, 0, -626], [0, 0, 0, 0], [0, -5168, -48, 0], [0, 0, 0, 0], [0, 4864, 144, 0], [0, 0, 0, 0], [64936, 0, 0, -473], [0, 0, 0, 0], [-24894, 0, 0, 274], [0, 0, 0, 0], [0, -1821, 1728, 0], [0, 0, 0, 0]]}