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Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
1568.2.a.a \(1\) \(12.521\) \(\Q\) None \(0\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(q-2q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1568.2.a.b \(1\) \(12.521\) \(\Q\) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(q-2q^{3}+q^{9}+4q^{11}+4q^{13}+2q^{17}+\cdots\)
1568.2.a.d \(1\) \(12.521\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-4\) \(0\) \(+\) \(-\) \(q-4q^{5}-3q^{9}+4q^{13}-8q^{17}+11q^{25}+\cdots\)
1568.2.a.f \(1\) \(12.521\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(4\) \(0\) \(+\) \(-\) \(q+4q^{5}-3q^{9}-4q^{13}+8q^{17}+11q^{25}+\cdots\)
1568.2.a.h \(1\) \(12.521\) \(\Q\) None \(0\) \(2\) \(0\) \(0\) \(+\) \(-\) \(q+2q^{3}+q^{9}-4q^{11}+4q^{13}+2q^{17}+\cdots\)
1568.2.a.i \(1\) \(12.521\) \(\Q\) None \(0\) \(2\) \(2\) \(0\) \(+\) \(-\) \(q+2q^{3}+2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1568.2.a.t \(2\) \(12.521\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(6\) \(0\) \(+\) \(-\) \(q+\beta q^{3}+3q^{5}+4q^{9}+\beta q^{11}+4q^{13}+\cdots\)
1568.2.a.u \(2\) \(12.521\) \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(q+(1+\beta )q^{3}+(-1-2\beta )q^{5}+2\beta q^{9}+\cdots\)
1568.2.a.v \(2\) \(12.521\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+(3+2\beta )q^{9}+\cdots\)
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