# Stored data for newform 675.2.l.f, downloaded from the LMFDB on 07 November 2025. {"Nk2": 2700, "analytic_conductor": 5.389902136436426, "analytic_rank": 0, "analytic_rank_proved": true, "char_conductor": 27, "char_degree": 6, "char_is_minimal": true, "char_is_real": false, "char_orbit_index": 12, "char_orbit_label": "l", "char_order": 9, "char_parity": 1, "char_values": [675, 9, [326, 352], [7, 9]], "cm_discs": [], "conrey_index": 76, "dim": 66, "has_non_self_twist": 1, "hecke_cutters": [[2, [23409, 16524, 3897639, 28863189, -41696451, -140686794, 3518239482, 1179503748, 9136826838, 57487534998, 125065101303, 489940996368, 1877945440117, 4497959520972, 7810655864226, 9155411572298, 6507999597789, 3607962891708, 7171706328503, 14136419166966, 15747064918974, 7703138828624, -4273951960188, -7186207751976, 2334492324995, 8353906106022, 5921505739029, 2012084989934, 339371746506, -419475552912, 264634440383, 1245838731246, 1112286544422, 386651642048, -7084413837, -55965868044, 35317343816, 115056264267, 114844841712, 67856622632, 28500048153, 8334216060, 1775045663, 1167514227, 1212909861, 734359355, 301707684, 82392354, 12264860, 7006212, 9270060, 5863523, 2559798, 783354, 113657, 11799, 25983, 17798, 7965, 2643, 527, 99, 84, 44, 18, 6, 1]]], "hecke_orbit": 6, "hecke_orbit_code": 22518754084651683, "inner_twist_count": 2, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 27, 5, 1, 9, 0]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_rm": false, "is_self_dual": false, "is_self_twist": false, "is_twist_minimal": true, "label": "675.2.l.f", "level": 675, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [3, 5], "level_radical": 15, "minimal_twist": "675.2.l.f", "prim_orbit_index": 5, "related_objects": [], "relative_dim": 11, "rm_discs": [], "sato_tate_group": "1.2.3.c9", "self_twist_discs": [], "self_twist_type": 0, "space_label": "675.2.l", "trace_display": [-6, 0, 0, -6], "traces": [66, -6, 0, 0, 0, -6, -6, -12, -6, 0, 15, -18, 0, 15, 0, 18, -30, 12, 12, 0, 12, 45, -36, -39, 0, 6, -51, 36, -15, 0, 3, -27, 3, 0, 0, 30, -6, 12, -15, 0, 39, -48, -12, 51, 0, 9, -30, 132, -6, 0, 0, -9, 24, 75, 0, 144, -33, -27, 45, 0, -54, -66, 120, -24, 0, 48, -9, 69, 51, 0, -15, -9, 15, 96, 0, -48, 36, 18, 48, 0, -54, 36, -30, 57, 0, -111, 33, -36, -12, 0, 9, 219, -63, 36, 0, -249, -57, -75, -48, 0, -99, 222, -18, -123, 0, -18, 84, -33, 30, 0, -84, -78, -6, -150, 0, -69, 156, -36, -87, 0, -45, 129, 0, 66, 0, 69, -3, 27, -6, 0, 24, 69, 36, -150, 0, 0, 72, -144, -12, 0, 60, -54, -117, -72, 0, 99, -12, -84, -129, 0, -27, -168, -135, -36, 0, 54, -21, -228, -66, 0, -30, -117, -12, -165, 0, -36, -87, 48, -108, 0, 12, 12, 102, -9, 0, 111, -84, -135, -24, 0, 24, -246, 108, -45, 0, 84, 18, 246, 93, 0, 36, -186, -54, 258, 0, 3, -78, 54, 69, 0, -42, 36, -12, 351, 0, -153, -21, 33, 69, 0, 72, -111, -111, -189, 0, -123, 96, -222, 156, 0, -189, 84, 84, 60, 0, 9, 153, -231, -114, 0, -195, 144, -81, -36, 0, -276, 216, 63, 54, 0, -108, 156, -45, -174, 0, -3, 66, 24, -24, 0, 30, 399, 54, -15, 0, -162, 171, 30, -54, 0, -9, 81, 9, -42, 0, 222, -84, -18, 54, 0, -12, 63, -84, 81, 0, 309, -33, 39, -30, 0, 144, -99, 3, -165, 0, 27, -168, -225, -69, 0, 267, 9, 177, -84, 0, 168, -210, -36, 15, 0, 162, -447, 180, 159, 0, 264, 51, 111, 120, 0, 108, -534, 279, 126, 0, -90, -189, 336, 108, 0, 204, -90, 210, 300, 0, 78, -96, 450, 177, 0, 165, -285, 258, -54, 0, -129, -135, 336, 99, 0, 3, -75, -48, 495, 0, 351, 30, 201, 60, 0, -153, -54, 45, 39, 0, -261, 150, 117, 39, 0, -21, 456, 24, 78, 0, -183, -135, -39, 24, 0, -198, 477, -3, -123, 0, 243, 360, -63, 150, 0, -108, -153, -39, -261, 0, -201, 240, -33, -171, 0, 135, 510, -69, 99, 0, -162, -54, -120, -249, 0, 51, 300, -3, -534, 0, -180, 0, -147, 9, 0, 93, 9, -78, -318, 0, 312, -132, 99, -210, 0, 15, -144, -105, 90, 0, 93, 15, -33, -342, 0, 288, -534, -114, -57, 0, 42, -291, -84, 27, 0, 135, -9, -63, 39, 0, 135, -405, -159, 75, 0, 0, -480, -120, 234, 0, 171, 72, 102, 87, 0, -45, -393, -150, 336, 0, -162, -246, 42, 18, 0, 51, 171, -51, 18, 0, -129, -9, -99, 63, 0, -159, 153, -147, 126, 0, -159, -48, -18, 72, 0, -114, 324, -198, 252, 0, -45, 120, -174, 0, 0, -12, -153, -147, -93, 0, -297, 264, -198, 120, 0, -129, 822, -159, 108, 0, -327, -153, -279, -69, 0, -51, 279, 15, -234, 0, -153, 258, -261, 90, 0, 18, 12, -138, -330, 0, 126, -33, -81, -300, 0, 0, 54, -42, -126, 0, 141, -27, -45, -288, 0, 246, -273, -240, 33, 0, -30, -93, 393, 24, 0, 453, -99, 120, 111, 0, 606, -285, -18, 12, 0, -87, -510, 147, -234, 0, 561, 60, 276, 129, 0, 216, -381, -54, 213, 0, 0, -327, 378, -162, 0, 78, -48, 294, 168, 0, -93, -264, -279, 234, 0, -183, -180, 153, 6, 0, -57, 213, 60, 189, 0, -105, 204, -57, 348, 0, -396, 327, 483, -270, 0, -378, -180, 204, 354, 0, -282, 333, -75, 117, 0, 15, 207, 132, -396, 0, -600, 465, 69, -111, 0, -255, 564, -27, -195, 0, -198, 612, -303, 162, 0, -486, 522, -264, -306, 0, -420, 324, -54, -150, 0, -144, 324, -282, -288, 0, -231, -45, -339, -363, 0, -279, 402, 21, -594, 0, 180, 204, -291, -36, 0, -144, 432, -114, -426, 0, -135, 111, 384, -333, 0, -81, -255, -234, 9, 0, 531, 63, -66, -126, 0, -84, -633, 324, 141, 0, 189, -288, 30, 51, 0, -93, -72, -207, -126, 0, 147, -186, 450, 84, 0, 72, -501, -252, 180, 0, -354, 63, -48, 285, 0, -165, -513, 288, 36, 0, 459, -138, -198, 51, 0, -432, -72, -42, 198, 0, -255, 141, 117, 174, 0, 60, 162, 15, 180, 0, -129, -192, -63, 408, 0, -351, 426, 270, 249, 0, -36, 147, -141, 36, 0, -135, -135, -162, 381, 0, -243, 99, 315, 96, 0, 351, 342, -18, -6, 0, -147, -9, -396, 3, 0, -123, 522, 102, -6, 0, 360, -45, -375, 27, 0, -141, -36, -252, -237, 0, -54, 207, 144, 90, 0, 90, -174, 102, 171, 0, 246, 69, -18, 249, 0, 276, -87, -90, -516, 0, 324, -243, 228, 18, 0, 324, 117, 594, -15, 0, 558, -453, 18, 336, 0, -63, -618, 450, 63, 0, 759, -108, 465, 186, 0, 528, -636, -225, 360, 0, 27, -426, 309, -66, 0, 273, 207, 354, 321, 0, 210, -318, -420, 270, 0, -207, -63, 456, -54, 0, -69, 93, 411, 477, 0, 6, -66, 93, 15, 0, -135, -66, 87, 249, 0, 225, 18, 576, 105, 0, -156, 249, -288, -54, 0, -36, 474, 519, 297, 0, -378, -132, 171, 57, 0, 207, 429, -378, -150, 0, -267, 96, -81, -228, 0, 45, -468, -219, -129, 0, -87, 384, -144, -354, 0, -3, 600, -402, -90, 0, 90, -72, -447, -312, 0, -39, 624, -252, -540, 0, 72, -111, -39, -162, 0, 306, -486, -129, -495, 0, 159, -165, -405, -249, 0, 21, -27, 189, -12, 0, 111, -243, -33, 0, 0, 408, -174, 84, -195, 0, -99, -342, -231, -333, 0, 177, -27, -177, 561, 0, -72, -555, -366, -189, 0, -48, -903, -264, -576, 0, 60, -54, -570, 36, 0], "weight": 2, "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, "field_disc": null, "field_disc_factorization": null, "field_poly": null, "field_poly_is_cyclotomic": null, "field_poly_is_real_cyclotomic": null, "field_poly_root_of_unity": null, "fricke_eigenval": null, "hecke_ring_generator_nbound": null, "hecke_ring_index": null, "hecke_ring_index_factorization": null, "hecke_ring_index_proved": null, "is_polredabs": null, "nf_label": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp_display": null, "trace_hash": null, "trace_moments": null, "trace_zratio": null}