# Stored data for newform 256.7.d.g, downloaded from the LMFDB on 16 October 2026.
{"Nk2": 12544, "analytic_conductor": 58.893845406681855, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 8, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 4, "char_orbit_label": "d", "char_order": 2, "char_parity": -1, "char_values": [256, 2, [255, 5], [1, 1]], "cm_discs": [], "conrey_index": 127, "dim": 4, "field_disc": 2304, "field_disc_factorization": [[2, 8], [3, 2]], "field_poly": [9, 0, 0, 0, 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": [[3, [-1392, -24, 1]]], "hecke_orbit": 7, "hecke_orbit_code": 27021804040093952, "hecke_ring_generator_nbound": 7, "hecke_ring_index": 2048, "hecke_ring_index_factorization": [[2, 11]], "hecke_ring_index_proved": true, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": false, "label": "256.7.d.g", "level": 256, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": true, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2], "level_radical": 2, "minimal_twist": "32.7.c.b", "nf_label": "4.0.2304.2", "prim_orbit_index": 4, "qexp_display": "q+(12+\\beta _{2})q^{3}+(7\\beta _{1}-2\\beta _{3})q^{5}+(148\\beta _{1}+\\cdots)q^{7}+\\cdots", "related_objects": [], "relative_dim": 4, "rm_discs": [], "sato_tate_group": "6.2.3.c2", "self_twist_discs": [], "self_twist_type": 0, "space_label": "256.7.d", "trace_display": [0, 48, 0, 0], "trace_hash": 448186466338386129, "trace_moments": [0, {"__RealLiteral__": 0, "data": "3.646", "prec": 14}, 0, {"__RealLiteral__": 0, "data": "69.219", "prec": 17}, 0, {"__RealLiteral__": 0, "data": "1850.233", "prec": 24}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.507", "prec": 10}, "traces": [0, 4, 0, 48, 0, 0, 0, 0, 0, 3804, 0, -2768, 0, 0, 0, 0, 0, -5304, 0, -20112, 0, 0, 0, 0, 0, -36588, 0, 158112, 0, 0, 0, 0, 0, 71232, 0, -65728, 0, 0, 0, 0, 0, 209848, 0, -116816, 0, 0, 0, 0, 0, 95556, 0, 771936, 0, 0, 0, 0, 0, 526656, 0, -894608, 0, 0, 0, 0, 0, 613264, 0, -987088, 0, 0, 0, 0, 0, -219528, 0, 249072, 0, 0, 0, 0, 0, 2257668, 0, -54416, 0, 0, 0, 0, 0, 3723000, 0, 2819776, 0, 0, 0, 0, 0, 2918344, 0, -125616, 0, 0, 0, 0, 0, 6657792, 0, -2924112, 0, 0, 0, 0, 0, -110456, 0, -6378560, 0, 0, 0, 0, 0, -3395172, 0, 847008, 0, 0, 0, 0, 0, 7894080, 0, 9366320, 0, 0, 0, 0, 0, 2076856, 0, 10307120, 0, 0, 0, 0, 0, 12381584, 0, 8421168, 0, 0, 0, 0, 0, 15009912, 0, -22899968, 0, 0, 0, 0, 0, -10060544, 0, 6741168, 0, 0, 0, 0, 0, -2055468, 0, -694512, 0, 0, 0, 0, 0, -22746816, 0, -2925840, 0, 0, 0, 0, 0, -19971600, 0, 17875296, 0, 0, 0, 0, 0, -10081592, 0, -47789376, 0, 0, 0, 0, 0, -36808128, 0, -16228672, 0, 0, 0, 0, 0, 26973504, 0, -30782608, 0, 0, 0, 0, 0, -1203200, 0, 63376800, 0, 0, 0, 0, 0, -18280116, 0, 21332912, 0, 0, 0, 0, 0, 18304376, 0, -26478976, 0, 0, 0, 0, 0, -89552824, 0, 84794256, 0, 0, 0, 0, 0, -78921408, 0, -65036688, 0, 0, 0, 0, 0, -40210424, 0, 26213184, 0, 0, 0, 0, 0, -20327184, 0, 23786400, 0, 0, 0, 0, 0, -29249280, 0, 37017072, 0, 0, 0, 0, 0, -22437896, 0, -85769488, 0, 0, 0, 0, 0, 24122252, 0, -80732832, 0, 0, 0, 0, 0, -56145024, 0, 81917504, 0, 0, 0, 0, 0, 111975568, 0, -97306128, 0, 0, 0, 0, 0, 108829240, 0, 116209344, 0, 0, 0, 0, 0, 14314560, 0, 131116512, 0, 0, 0, 0, 0, 26619392, 0, 16933424, 0, 0, 0, 0, 0, -78391672, 0, -167655840, 0, 0, 0, 0, 0, 90696960, 0, -22762768, 0, 0, 0, 0, 0, 6365192, 0, 5784896, 0, 0, 0, 0, 0, 8939612, 0, -185298096, 0, 0, 0, 0, 0, 159457416, 0, -30007488, 0, 0, 0, 0, 0, 101311984, 0, 100348528, 0, 0, 0, 0, 0, 172074752, 0, 112008912, 0, 0, 0, 0, 0, 309698112, 0, 34752896, 0, 0, 0, 0, 0, 32911688, 0, 39900416, 0, 0, 0, 0, 0, -248429768, 0, -143865696, 0, 0, 0, 0, 0, 240673344, 0, -232512080, 0, 0, 0, 0, 0, 142101096, 0, -12856640, 0, 0, 0, 0, 0, 305596488, 0, 578069184, 0, 0, 0, 0, 0, 265461660, 0, -285527440, 0, 0, 0, 0, 0, -92645688, 0, -173624672, 0, 0, 0, 0, 0, 5710520, 0, 216491328, 0, 0, 0, 0, 0, -410754048, 0, 27746928, 0, 0, 0, 0, 0, 238866496, 0, 269980464, 0, 0, 0, 0, 0, -163680624, 0, 399694848, 0, 0, 0, 0, 0, -379408320, 0, 240737968, 0, 0, 0, 0, 0, 277548800, 0, 4405744, 0, 0, 0, 0, 0, -234206224, 0, 509616624, 0, 0, 0, 0, 0, -403307136, 0, -973619648, 0, 0, 0, 0, 0, 46023352, 0, -463187152, 0, 0, 0, 0, 0, 79008708, 0, -1139048688, 0, 0, 0, 0, 0, -398214336, 0, 57541680, 0, 0, 0, 0, 0, 618774672, 0, 239529904, 0, 0, 0, 0, 0, -403648000, 0, -933193920, 0, 0, 0, 0, 0, -502218624, 0, 177939952, 0, 0, 0, 0, 0, 10332728, 0, 58365040, 0, 0, 0, 0, 0, -1026757368, 0, 1393934688, 0, 0, 0, 0, 0, -740350992, 0, 1084402736, 0, 0, 0, 0, 0, -632280696, 0, 1099883136, 0, 0, 0, 0, 0, 45473528, 0, -1537834416, 0, 0, 0, 0, 0, -953036544, 0, -157788800, 0, 0, 0, 0, 0, 628787320, 0, -515462224, 0, 0, 0, 0, 0, -1136509228, 0, -732938496, 0, 0, 0, 0, 0, -2086190784, 0, -268738560, 0, 0, 0, 0, 0, 1574194888, 0, 385614128, 0, 0, 0, 0, 0, 414872896, 0, 1607970816, 0, 0, 0, 0, 0, 1375496136, 0, -327538576, 0, 0, 0, 0, 0, 1261296384, 0, 367148608, 0, 0, 0, 0, 0, 256416712, 0, -1095305184, 0, 0, 0, 0, 0, -282852288, 0, 799400880, 0, 0, 0, 0, 0, 246104976, 0, -280589584, 0, 0, 0, 0, 0, -505537296, 0, 1014292896, 0, 0, 0, 0, 0, -1065693696, 0, -363596992, 0, 0, 0, 0, 0, -1228125184, 0, -1361903936, 0, 0, 0, 0, 0, -766182656, 0, -406903968, 0, 0, 0, 0, 0, 2630782044, 0, 1419136608, 0, 0, 0, 0, 0, 258692672, 0, 168231856, 0, 0, 0, 0, 0, 231652336, 0, -1930191600, 0, 0, 0, 0, 0, 213296448, 0, 2889998272, 0, 0, 0, 0, 0, 397518904, 0, 77038272, 0, 0, 0, 0, 0, -359319352, 0, -719241120, 0, 0, 0, 0, 0, 1537435392, 0, -1264011744, 0, 0, 0, 0, 0, 2674721936, 0, -1272692624, 0, 0, 0, 0, 0, -58671376, 0, 245726016, 0, 0, 0, 0, 0, 3039222600, 0, 1274102688, 0, 0, 0, 0, 0, 2501339064, 0, 2004677808, 0, 0, 0, 0, 0, 1749334848, 0, 1167528768, 0, 0, 0, 0, 0, -987365568, 0, -3098516880, 0, 0, 0, 0, 0, 862624200, 0, -1524061120, 0, 0, 0, 0, 0, -970283436, 0, -845955168, 0, 0, 0, 0, 0, -2567857344, 0, -591577152, 0, 0, 0, 0, 0, 2493883192, 0, -1235097872, 0, 0, 0, 0, 0, 406866832, 0, -1926501744, 0, 0, 0, 0, 0, -2725896, 0, 408225152, 0, 0, 0, 0, 0, 1283891592, 0, -848326416, 0, 0, 0, 0, 0, -2922086400, 0, 1378113840, 0, 0, 0, 0, 0, -3033224448, 0, 3892933888, 0, 0, 0, 0, 0, 4479533040, 0, 4191671344, 0, 0, 0, 0, 0, -1292907200, 0, 2403718848, 0, 0, 0, 0, 0, 121810752, 0, -2028498752, 0, 0, 0, 0, 0, 2432358344, 0, 428856432, 0, 0, 0, 0, 0, -2796843144, 0, 1598405280, 0, 0, 0, 0, 0, 1199632896, 0, -3925493776, 0, 0, 0, 0, 0, 2792725560, 0, 4946255360, 0, 0, 0, 0, 0, -2332599036, 0, -1595136816, 0, 0, 0, 0, 0, -3646286208, 0, -3763691728, 0, 0, 0, 0, 0, -181545656, 0, -2931439200, 0, 0, 0, 0, 0, -617051408, 0, 1998071808, 0, 0, 0, 0, 0, -297356736, 0, 2924498240, 0, 0, 0, 0, 0], "weight": 7, "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], [12, 0, 1, 0], [0, 0, 0, 0], [0, 7, 0, -2], [0, 0, 0, 0], [0, 148, 0, -1], [0, 0, 0, 0], [951, 0, 24, 0], [0, 0, 0, 0], [-692, 0, 17, 0], [0, 0, 0, 0], [0, -1087, 0, 10], [0, 0, 0, 0], [0, -2988, 0, -17], [0, 0, 0, 0], [-1326, 0, 136, 0], [0, 0, 0, 0], [-5028, 0, 125, 0], [0, 0, 0, 0], [0, 240, 0, 136], [0, 0, 0, 0], [0, 2972, 0, -123], [0, 0, 0, 0], [-9147, 0, 112, 0], [0, 0, 0, 0], [39528, 0, 510, 0], [0, 0, 0, 0], [0, 9697, 0, 274], [0, 0, 0, 0], [0, -4432, 0, -476], [0, 0, 0, 0], [17808, 0, -488, 0], [0, 0, 0, 0], [-16432, 0, 1212, 0], [0, 0, 0, 0], [0, -15657, 0, -442], [0, 0, 0, 0], [0, 2316, 0, -967], [0, 0, 0, 0], [52462, 0, -272, 0], [0, 0, 0, 0], [-29204, 0, 1513, 0], [0, 0, 0, 0], [0, -67071, 0, -1734], [0, 0, 0, 0], [0, -17240, 0, -578], [0, 0, 0, 0], [23889, 0, 1184, 0], [0, 0, 0, 0], [192984, 0, 306, 0], [0, 0, 0, 0], [0, 8583, 0, -394], [0, 0, 0, 0], [0, -57068, 0, 1503], [0, 0, 0, 0], [131664, 0, -3528, 0], [0, 0, 0, 0], [-223652, 0, -1955, 0], [0, 0, 0, 0], [0, 29777, 0, 2346], [0, 0, 0, 0], [0, 103884, 0, 2601], [0, 0, 0, 0], [153316, 0, -8976, 0], [0, 0, 0, 0], [-246772, 0, -4063, 0], [0, 0, 0, 0], [0, -153264, 0, 1496], [0, 0, 0, 0], [0, -118796, 0, -153], [0, 0, 0, 0], [-54882, 0, 10744, 0], [0, 0, 0, 0], [62268, 0, -7803, 0], [0, 0, 0, 0], [0, -128528, 0, 3208], [0, 0, 0, 0], [0, 182104, 0, 1122], [0, 0, 0, 0], [564417, 0, 28152, 0], [0, 0, 0, 0], [-13604, 0, -12739, 0], [0, 0, 0, 0], [0, -427074, 0, 3604], [0, 0, 0, 0], [0, 537228, 0, 12985], [0, 0, 0, 0], [930750, 0, -3400, 0], [0, 0, 0, 0], [704944, 0, -10268, 0], [0, 0, 0, 0], [0, -784320, 0, -10144], [0, 0, 0, 0], [0, -419196, 0, 10931], [0, 0, 0, 0], [729586, 0, -18840, 0], [0, 0, 0, 0], [-31404, 0, -441, 0], [0, 0, 0, 0]]}