๐ŸŒฟ Sagebrush Atlas
Atlas โ€บ Modular forms โ€บ Weight 2, level 501โ€“600

Search newform orbits

688 orbits; showing 1โ€“100 ยท JSON

LabelDimTrace formSignCMCurve
501.2.a.a1q+q2โˆ’q3โˆ’q4โˆ’4q5โˆ’q6+4q7+O(q8)q + q^{2} - q^{3} - q^{4} - 4q^{5} - q^{6} + 4q^{7} + O(q^{8})+1+1501a1 rank 0
501.2.a.b55qโˆ’4q2+5q3+4q4โˆ’9q5โˆ’4q6โˆ’4q7+O(q8)5q - 4q^{2} + 5q^{3} + 4q^{4} - 9q^{5} - 4q^{6} - 4q^{7} + O(q^{8})โˆ’1-1
501.2.a.c55qโˆ’5q3โˆ’q5โˆ’4q7+O(q8)5q - 5q^{3} - q^{5} - 4q^{7} + O(q^{8})โˆ’1-1
501.2.a.d88qโˆ’3q2โˆ’8q3+13q4+q5+3q6+O(q8)8q - 3q^{2} - 8q^{3} + 13q^{4} + q^{5} + 3q^{6} + O(q^{8})+1+1
501.2.a.e88q+3q2+8q3+9q4+7q5+3q6โˆ’4q7+O(q8)8q + 3q^{2} + 8q^{3} + 9q^{4} + 7q^{5} + 3q^{6} - 4q^{7} + O(q^{8})+1+1
502.2.a.a22q+2q2โˆ’2q3+2q4โˆ’3q5โˆ’2q6โˆ’4q7+O(q8)2q + 2q^{2} - 2q^{3} + 2q^{4} - 3q^{5} - 2q^{6} - 4q^{7} + O(q^{8})โˆ’1-1
502.2.a.b22q+2q2+2q3+2q4+5q5+2q6โˆ’2q7+O(q8)2q + 2q^{2} + 2q^{3} + 2q^{4} + 5q^{5} + 2q^{6} - 2q^{7} + O(q^{8})+1+1
502.2.a.c55qโˆ’5q2โˆ’q3+5q4โˆ’6q5+q6โˆ’q7+O(q8)5q - 5q^{2} - q^{3} + 5q^{4} - 6q^{5} + q^{6} - q^{7} + O(q^{8})โˆ’1-1
502.2.a.d55qโˆ’5q2+2q3+5q4+7q5โˆ’2q6+q7+O(q8)5q - 5q^{2} + 2q^{3} + 5q^{4} + 7q^{5} - 2q^{6} + q^{7} + O(q^{8})+1+1
502.2.a.e66q+6q2+q3+6q4โˆ’q5+q6+6q7+O(q8)6q + 6q^{2} + q^{3} + 6q^{4} - q^{5} + q^{6} + 6q^{7} + O(q^{8})+1+1
503.2.a.a1qโˆ’q2+q3โˆ’q4โˆ’4q5โˆ’q6โˆ’3q7+O(q8)q - q^{2} + q^{3} - q^{4} - 4q^{5} - q^{6} - 3q^{7} + O(q^{8})+1+1503c1 rank 0
503.2.a.b1q+q2+q3โˆ’q4โˆ’2q5+q6โˆ’3q7+O(q8)q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{7} + O(q^{8})โˆ’1-1503a1 rank 1
503.2.a.c1q+q2+3q3โˆ’q4โˆ’2q5+3q6+3q7+O(q8)q + q^{2} + 3q^{3} - q^{4} - 2q^{5} + 3q^{6} + 3q^{7} + O(q^{8})+1+1503b1 rank 0
503.2.a.d33q+q3+4q4+q6+q7+O(q8)3q + q^{3} + 4q^{4} + q^{6} + q^{7} + O(q^{8})+1+1
503.2.a.e1010qโˆ’4q2โˆ’8q3+4q4โˆ’q5โˆ’2q6โˆ’5q7+O(q8)10q - 4q^{2} - 8q^{3} + 4q^{4} - q^{5} - 2q^{6} - 5q^{7} + O(q^{8})โˆ’1-1
503.2.a.f2626q+4q2+4q3+36q4+9q5โˆ’4q6+11q7+O(q8)26q + 4q^{2} + 4q^{3} + 36q^{4} + 9q^{5} - 4q^{6} + 11q^{7} + O(q^{8})+1+1
504.2.a.a1qโˆ’2q5โˆ’q7+O(q8)q - 2q^{5} - q^{7} + O(q^{8})504a1 rank 1
504.2.a.b1qโˆ’2q5โˆ’q7+O(q8)q - 2q^{5} - q^{7} + O(q^{8})504f1 rank 1
504.2.a.c1qโˆ’2q5โˆ’q7+O(q8)q - 2q^{5} - q^{7} + O(q^{8})504c1 rank 0
504.2.a.d1qโˆ’2q5+q7+O(q8)q - 2q^{5} + q^{7} + O(q^{8})504e1 rank 1
504.2.a.e1qโˆ’2q5+q7+O(q8)q - 2q^{5} + q^{7} + O(q^{8})504g1 rank 0
504.2.a.f1q+2q5โˆ’q7+O(q8)q + 2q^{5} - q^{7} + O(q^{8})504d1 rank 0
504.2.a.g1q+2q5+q7+O(q8)q + 2q^{5} + q^{7} + O(q^{8})504b1 rank 0
504.2.a.h1q+4q5+q7+O(q8)q + 4q^{5} + q^{7} + O(q^{8})504h1 rank 0
505.2.a.a1q+q2โˆ’q4โˆ’q5+O(q8)q + q^{2} - q^{4} - q^{5} + O(q^{8})โˆ’1-1505a1 rank 1
505.2.a.b66qโˆ’3q2โˆ’q3+5q4โˆ’6q5โˆ’8q6โˆ’2q7+O(q8)6q - 3q^{2} - q^{3} + 5q^{4} - 6q^{5} - 8q^{6} - 2q^{7} + O(q^{8})โˆ’1-1
505.2.a.c88qโˆ’5q2โˆ’11q3+7q4+8q5+4q6โˆ’12q7+O(q8)8q - 5q^{2} - 11q^{3} + 7q^{4} + 8q^{5} + 4q^{6} - 12q^{7} + O(q^{8})โˆ’1-1
505.2.a.d99q+2q2+q3+10q4โˆ’9q5+4q6+O(q8)9q + 2q^{2} + q^{3} + 10q^{4} - 9q^{5} + 4q^{6} + O(q^{8})+1+1
505.2.a.e99q+2q2+7q3+6q4+9q5+4q6+6q7+O(q8)9q + 2q^{2} + 7q^{3} + 6q^{4} + 9q^{5} + 4q^{6} + 6q^{7} + O(q^{8})+1+1
506.2.a.a1qโˆ’q2โˆ’2q3+q4+q5+2q6โˆ’q7+O(q8)q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{7} + O(q^{8})โˆ’1-1506a1 rank 1
506.2.a.b1qโˆ’q2โˆ’2q3+q4+3q5+2q6+5q7+O(q8)q - q^{2} - 2q^{3} + q^{4} + 3q^{5} + 2q^{6} + 5q^{7} + O(q^{8})+1+1506c1 rank 0
506.2.a.c1qโˆ’q2+q4โˆ’3q5+3q7+O(q8)q - q^{2} + q^{4} - 3q^{5} + 3q^{7} + O(q^{8})+1+1506b1 rank 0
506.2.a.d1qโˆ’q2+q4โˆ’q5+q7+O(q8)q - q^{2} + q^{4} - q^{5} + q^{7} + O(q^{8})โˆ’1-1506d1 rank 1
506.2.a.e1q+q2โˆ’2q3+q4โˆ’q5โˆ’2q6โˆ’q7+O(q8)q + q^{2} - 2q^{3} + q^{4} - q^{5} - 2q^{6} - q^{7} + O(q^{8})โˆ’1-1506f1 rank 1
506.2.a.f1q+q2+q4โˆ’3q5โˆ’3q7+O(q8)q + q^{2} + q^{4} - 3q^{5} - 3q^{7} + O(q^{8})โˆ’1-1506e1 rank 1
506.2.a.g33qโˆ’3q2+3q3+3q4โˆ’7q5โˆ’3q6+O(q8)3q - 3q^{2} + 3q^{3} + 3q^{4} - 7q^{5} - 3q^{6} + O(q^{8})+1+1
506.2.a.h33qโˆ’3q2+3q3+3q4+3q5โˆ’3q6+O(q8)3q - 3q^{2} + 3q^{3} + 3q^{4} + 3q^{5} - 3q^{6} + O(q^{8})+1+1
506.2.a.i44q+4q2โˆ’q3+4q4+2q5โˆ’q6+3q7+O(q8)4q + 4q^{2} - q^{3} + 4q^{4} + 2q^{5} - q^{6} + 3q^{7} + O(q^{8})+1+1
506.2.a.j55q+5q2+q3+5q4+4q5+q6+q7+O(q8)5q + 5q^{2} + q^{3} + 5q^{4} + 4q^{5} + q^{6} + q^{7} + O(q^{8})+1+1
507.2.a.a1qโˆ’q2โˆ’q3โˆ’q4โˆ’2q5+q6+4q7+O(q8)q - q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} + 4q^{7} + O(q^{8})507c1 rank 1
507.2.a.b1qโˆ’q2โˆ’q3โˆ’q4+q5+q6โˆ’2q7+O(q8)q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2q^{7} + O(q^{8})507b1 rank 1
507.2.a.c1q+q2โˆ’q3โˆ’q4โˆ’q5โˆ’q6+2q7+O(q8)q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} + 2q^{7} + O(q^{8})507a1 rank 1
507.2.a.d22qโˆ’q2+2q3+5q4+3q5โˆ’q6+3q7+O(q8)2q - q^{2} + 2q^{3} + 5q^{4} + 3q^{5} - q^{6} + 3q^{7} + O(q^{8})
507.2.a.e22qโˆ’2q3โˆ’4q4+O(q8)2q - 2q^{3} - 4q^{4} + O(q^{8})
507.2.a.f22qโˆ’2q3+2q4+O(q8)2q - 2q^{3} + 2q^{4} + O(q^{8})
507.2.a.g22q+q2+2q3+5q4โˆ’3q5+q6โˆ’3q7+O(q8)2q + q^{2} + 2q^{3} + 5q^{4} - 3q^{5} + q^{6} - 3q^{7} + O(q^{8})
507.2.a.h22q+2q2+2q3+2q4+2q6+O(q8)2q + 2q^{2} + 2q^{3} + 2q^{4} + 2q^{6} + O(q^{8})
507.2.a.i33qโˆ’3q2โˆ’3q3+11q4โˆ’6q5+3q6โˆ’2q7+O(q8)3q - 3q^{2} - 3q^{3} + 11q^{4} - 6q^{5} + 3q^{6} - 2q^{7} + O(q^{8})
507.2.a.j33qโˆ’q2+3q3โˆ’q4โˆ’4q5โˆ’q6โˆ’10q7+O(q8)3q - q^{2} + 3q^{3} - q^{4} - 4q^{5} - q^{6} - 10q^{7} + O(q^{8})
507.2.a.k33q+q2+3q3โˆ’q4+4q5+q6+10q7+O(q8)3q + q^{2} + 3q^{3} - q^{4} + 4q^{5} + q^{6} + 10q^{7} + O(q^{8})
507.2.a.l33q+3q2โˆ’3q3+11q4+6q5โˆ’3q6+2q7+O(q8)3q + 3q^{2} - 3q^{3} + 11q^{4} + 6q^{5} - 3q^{6} + 2q^{7} + O(q^{8})
508.2.a.a22qโˆ’2q3โˆ’4q5+O(q8)2q - 2q^{3} - 4q^{5} + O(q^{8})
508.2.a.b22q+4q3+2q5โˆ’2q7+O(q8)2q + 4q^{3} + 2q^{5} - 2q^{7} + O(q^{8})
508.2.a.c33qโˆ’3q3โˆ’3q7+O(q8)3q - 3q^{3} - 3q^{7} + O(q^{8})
508.2.a.d33q+q3+4q5+7q7+O(q8)3q + q^{3} + 4q^{5} + 7q^{7} + O(q^{8})
509.2.a.a1414qโˆ’3q2โˆ’5q3+3q4โˆ’5q5โˆ’8q6โˆ’17q7+O(q8)14q - 3q^{2} - 5q^{3} + 3q^{4} - 5q^{5} - 8q^{6} - 17q^{7} + O(q^{8})โˆ’1-1
509.2.a.b2828q+3q2+5q3+41q4+q5+2q6+19q7+O(q8)28q + 3q^{2} + 5q^{3} + 41q^{4} + q^{5} + 2q^{6} + 19q^{7} + O(q^{8})+1+1
510.2.a.a1qโˆ’q2โˆ’q3+q4โˆ’q5+q6+2q7+O(q8)q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + O(q^{8})+1+1510a1 rank 0
510.2.a.b1qโˆ’q2+q3+q4+q5โˆ’q6โˆ’2q7+O(q8)q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + O(q^{8})+1+1510b1 rank 0
510.2.a.c1q+q2โˆ’q3+q4โˆ’q5โˆ’q6โˆ’4q7+O(q8)q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4q^{7} + O(q^{8})โˆ’1-1510d1 rank 1
510.2.a.d1q+q2โˆ’q3+q4โˆ’q5โˆ’q6+2q7+O(q8)q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} + O(q^{8})+1+1510c1 rank 0
510.2.a.e1q+q2โˆ’q3+q4+q5โˆ’q6+O(q8)q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + O(q^{8})+1+1510e1 rank 0
510.2.a.f1q+q2+q3+q4โˆ’q5+q6+O(q8)q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + O(q^{8})+1+1510f1 rank 0
510.2.a.g1q+q2+q3+q4+q5+q6+2q7+O(q8)q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + 2q^{7} + O(q^{8})+1+1510g1 rank 0
510.2.a.h22qโˆ’2q2โˆ’2q3+2q4+2q5+2q6+O(q8)2q - 2q^{2} - 2q^{3} + 2q^{4} + 2q^{5} + 2q^{6} + O(q^{8})+1+1
511.2.a.a33q+6q3+4q4+3q5+3q7+O(q8)3q + 6q^{3} + 4q^{4} + 3q^{5} + 3q^{7} + O(q^{8})+1+1
511.2.a.b33q+q2+3q4โˆ’q5โˆ’3q7+O(q8)3q + q^{2} + 3q^{4} - q^{5} - 3q^{7} + O(q^{8})+1+1
511.2.a.c66qโˆ’3q2โˆ’5q3+3q4โˆ’6q5+2q6+6q7+O(q8)6q - 3q^{2} - 5q^{3} + 3q^{4} - 6q^{5} + 2q^{6} + 6q^{7} + O(q^{8})โˆ’1-1
511.2.a.d66qโˆ’3q2+q3+3q4โˆ’2q5โˆ’4q6โˆ’6q7+O(q8)6q - 3q^{2} + q^{3} + 3q^{4} - 2q^{5} - 4q^{6} - 6q^{7} + O(q^{8})โˆ’1-1
511.2.a.e99q+2q2โˆ’q3+6q4+7q5+4q6+9q7+O(q8)9q + 2q^{2} - q^{3} + 6q^{4} + 7q^{5} + 4q^{6} + 9q^{7} + O(q^{8})+1+1
511.2.a.f1010q+4q2โˆ’q3+14q4+q5+2q6โˆ’10q7+O(q8)10q + 4q^{2} - q^{3} + 14q^{4} + q^{5} + 2q^{6} - 10q^{7} + O(q^{8})+1+1
512.2.a.a22qโˆ’4q3+O(q8)2q - 4q^{3} + O(q^{8})Q(โˆ’8)\mathbb{Q}(\sqrt{-8})
512.2.a.b22qโˆ’4q5+O(q8)2q - 4q^{5} + O(q^{8})
512.2.a.c22qโˆ’8q7+O(q8)2q - 8q^{7} + O(q^{8})
512.2.a.d22q+8q7+O(q8)2q + 8q^{7} + O(q^{8})
512.2.a.e22q+4q5+O(q8)2q + 4q^{5} + O(q^{8})
512.2.a.f22q+4q3+O(q8)2q + 4q^{3} + O(q^{8})Q(โˆ’8)\mathbb{Q}(\sqrt{-8})
512.2.a.g44q+O(q8)4q + O(q^{8})
513.2.a.a1qโˆ’q2โˆ’q4โˆ’2q7+O(q8)q - q^{2} - q^{4} - 2q^{7} + O(q^{8})513b1 rank 1
513.2.a.b1q+q2โˆ’q4โˆ’2q7+O(q8)q + q^{2} - q^{4} - 2q^{7} + O(q^{8})513a1 rank 1
513.2.a.c22q+2q4โˆ’8q7+O(q8)2q + 2q^{4} - 8q^{7} + O(q^{8})
513.2.a.d33qโˆ’3q2+3q4โˆ’3q5โˆ’3q7+O(q8)3q - 3q^{2} + 3q^{4} - 3q^{5} - 3q^{7} + O(q^{8})
513.2.a.e33qโˆ’q2+3q4โˆ’5q5+q7+O(q8)3q - q^{2} + 3q^{4} - 5q^{5} + q^{7} + O(q^{8})
513.2.a.f33q+q2+3q4+5q5+q7+O(q8)3q + q^{2} + 3q^{4} + 5q^{5} + q^{7} + O(q^{8})
513.2.a.g33q+3q2+3q4+3q5โˆ’3q7+O(q8)3q + 3q^{2} + 3q^{4} + 3q^{5} - 3q^{7} + O(q^{8})
513.2.a.h44q+4q4+8q7+O(q8)4q + 4q^{4} + 8q^{7} + O(q^{8})
513.2.a.i44q+8q4+12q7+O(q8)4q + 8q^{4} + 12q^{7} + O(q^{8})
514.2.a.a1q+q2โˆ’2q3+q4โˆ’2q5โˆ’2q6+2q7+O(q8)q + q^{2} - 2q^{3} + q^{4} - 2q^{5} - 2q^{6} + 2q^{7} + O(q^{8})โˆ’1-1514b1 rank 1
514.2.a.b1q+q2+q4โˆ’2q5โˆ’4q7+O(q8)q + q^{2} + q^{4} - 2q^{5} - 4q^{7} + O(q^{8})โˆ’1-1514a1 rank 1
514.2.a.c22qโˆ’2q2+2q4โˆ’4q7+O(q8)2q - 2q^{2} + 2q^{4} - 4q^{7} + O(q^{8})+1+1
514.2.a.d33qโˆ’3q2+2q3+3q4+4q5โˆ’2q6+6q7+O(q8)3q - 3q^{2} + 2q^{3} + 3q^{4} + 4q^{5} - 2q^{6} + 6q^{7} + O(q^{8})+1+1
514.2.a.e55qโˆ’5q2+5q4โˆ’4q5โˆ’4q7+O(q8)5q - 5q^{2} + 5q^{4} - 4q^{5} - 4q^{7} + O(q^{8})โˆ’1-1
514.2.a.f99q+9q2+2q3+9q4+4q5+2q6โˆ’4q7+O(q8)9q + 9q^{2} + 2q^{3} + 9q^{4} + 4q^{5} + 2q^{6} - 4q^{7} + O(q^{8})+1+1
515.2.a.a44qโˆ’q2โˆ’q3โˆ’q4+4q5โˆ’4q6โˆ’3q7+O(q8)4q - q^{2} - q^{3} - q^{4} + 4q^{5} - 4q^{6} - 3q^{7} + O(q^{8})โˆ’1-1
515.2.a.b88qโˆ’2q2โˆ’3q3+6q4โˆ’8q5โˆ’8q6โˆ’11q7+O(q8)8q - 2q^{2} - 3q^{3} + 6q^{4} - 8q^{5} - 8q^{6} - 11q^{7} + O(q^{8})โˆ’1-1
515.2.a.c99q+q2+3q3+11q4โˆ’9q5+9q7+O(q8)9q + q^{2} + 3q^{3} + 11q^{4} - 9q^{5} + 9q^{7} + O(q^{8})+1+1
515.2.a.d1414qโˆ’q2+q3+17q4+14q5+4q6+9q7+O(q8)14q - q^{2} + q^{3} + 17q^{4} + 14q^{5} + 4q^{6} + 9q^{7} + O(q^{8})+1+1
516.2.a.a1qโˆ’q3โˆ’2q5+2q7+O(q8)q - q^{3} - 2q^{5} + 2q^{7} + O(q^{8})516b1 rank 1
516.2.a.b1qโˆ’q3+3q5โˆ’q7+O(q8)q - q^{3} + 3q^{5} - q^{7} + O(q^{8})516a1 rank 0
516.2.a.c1q+q3+O(q8)q + q^{3} + O(q^{8})516c1 rank 0

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