๐ŸŒฟ Sagebrush Atlas
Atlas โ€บ Modular forms โ€บ Level 49

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20 orbits; showing 1โ€“20 ยท JSON

LabelDimTrace formSignCMCurve
49.2.a.a1q+q2โˆ’q4+O(q8)q + q^{2} - q^{4} + O(q^{8})Q(โˆ’7)\mathbb{Q}(\sqrt{-7})49a1 rank 0
49.4.a.a1qโˆ’5q2+17q4+O(q8)q - 5q^{2} + 17q^{4} + O(q^{8})Q(โˆ’7)\mathbb{Q}(\sqrt{-7})
49.4.a.b1qโˆ’q2+2q3โˆ’7q4โˆ’16q5โˆ’2q6+O(q8)q - q^{2} + 2q^{3} - 7q^{4} - 16q^{5} - 2q^{6} + O(q^{8})
49.4.a.c1q+2q2โˆ’7q3โˆ’4q4โˆ’7q5โˆ’14q6+O(q8)q + 2q^{2} - 7q^{3} - 4q^{4} - 7q^{5} - 14q^{6} + O(q^{8})
49.4.a.d1q+2q2+7q3โˆ’4q4+7q5+14q6+O(q8)q + 2q^{2} + 7q^{3} - 4q^{4} + 7q^{5} + 14q^{6} + O(q^{8})
49.4.a.e44q+2q2+34q4+O(q8)4q + 2q^{2} + 34q^{4} + O(q^{8})
49.6.a.a1qโˆ’10q2+14q3+68q4+56q5โˆ’140q6+O(q8)q - 10q^{2} + 14q^{3} + 68q^{4} + 56q^{5} - 140q^{6} + O(q^{8})
49.6.a.b1q+11q2+89q4+O(q8)q + 11q^{2} + 89q^{4} + O(q^{8})Q(โˆ’7)\mathbb{Q}(\sqrt{-7})
49.6.a.c22qโˆ’4q2โˆ’56q4+O(q8)2q - 4q^{2} - 56q^{4} + O(q^{8})
49.6.a.d22q+2q2โˆ’8q3+12q4โˆ’38q5โˆ’82q6+O(q8)2q + 2q^{2} - 8q^{3} + 12q^{4} - 38q^{5} - 82q^{6} + O(q^{8})
49.6.a.e22q+2q2+8q3+12q4+38q5+82q6+O(q8)2q + 2q^{2} + 8q^{3} + 12q^{4} + 38q^{5} + 82q^{6} + O(q^{8})
49.6.a.f22q+9q2+6q3+5q4+18q5+198q6+O(q8)2q + 9q^{2} + 6q^{3} + 5q^{4} + 18q^{5} + 198q^{6} + O(q^{8})
49.6.a.g44qโˆ’10q2+10q4+O(q8)4q - 10q^{2} + 10q^{4} + O(q^{8})
49.8.a.a1qโˆ’13q2+41q4+O(q8)q - 13q^{2} + 41q^{4} + O(q^{8})Q(โˆ’7)\mathbb{Q}(\sqrt{-7})
49.8.a.b1qโˆ’6q2+42q3โˆ’92q4+84q5โˆ’252q6+O(q8)q - 6q^{2} + 42q^{3} - 92q^{4} + 84q^{5} - 252q^{6} + O(q^{8})
49.8.a.c22qโˆ’3q2โˆ’94q3+181q4โˆ’330q5+1006q6+O(q8)2q - 3q^{2} - 94q^{3} + 181q^{4} - 330q^{5} + 1006q^{6} + O(q^{8})
49.8.a.d22q+20q2โˆ’56q4+O(q8)2q + 20q^{2} - 56q^{4} + O(q^{8})
49.8.a.e44qโˆ’6q2โˆ’28q3+348q4โˆ’252q5โˆ’1022q6+O(q8)4q - 6q^{2} - 28q^{3} + 348q^{4} - 252q^{5} - 1022q^{6} + O(q^{8})
49.8.a.f44qโˆ’6q2+28q3+348q4+252q5+1022q6+O(q8)4q - 6q^{2} + 28q^{3} + 348q^{4} + 252q^{5} + 1022q^{6} + O(q^{8})
49.8.a.g88q+30q2+458q4+O(q8)8q + 30q^{2} + 458q^{4} + O(q^{8})