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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2800.1.f.a \(1\) \(1.397\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{9}+q^{11}+q^{23}-q^{29}-q^{37}+\cdots\)
2800.1.f.b \(1\) \(1.397\) \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{9}+q^{11}-q^{23}-q^{29}+q^{37}+\cdots\)
2800.1.f.c \(2\) \(1.397\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}+q^{11}-iq^{13}+iq^{17}+\cdots\)
2800.1.p.a \(2\) \(1.397\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-q^{9}+q^{11}-iq^{23}+q^{29}+\cdots\)
2800.1.u.a \(4\) \(1.397\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
2800.1.u.b \(8\) \(1.397\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\)
2800.1.v.a \(4\) \(1.397\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-35}) \) \(\Q(\sqrt{7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{3}+\zeta_{8}^{3}q^{7}+3\zeta_{8}^{2}q^{9}+2q^{21}+\cdots\)
2800.1.v.b \(8\) \(1.397\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{3}+\zeta_{24}^{3}q^{7}+(-\zeta_{24}^{4}-\zeta_{24}^{8}+\cdots)q^{11}+\cdots\)
2800.1.z.a \(2\) \(1.397\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+iq^{9}+\cdots\)
2800.1.z.b \(4\) \(1.397\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots\)
2800.1.z.c \(4\) \(1.397\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
2800.1.bf.a \(2\) \(1.397\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-2\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+iq^{9}+(-1+\cdots)q^{11}+\cdots\)
2800.1.bf.b \(2\) \(1.397\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(2\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+iq^{9}+(-1+\cdots)q^{11}+\cdots\)
2800.1.bf.c \(4\) \(1.397\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(4\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+q^{7}+q^{8}+\cdots\)
2800.1.bf.d \(4\) \(1.397\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(2\) \(0\) \(0\) \(-4\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-q^{7}-q^{8}+\cdots\)
2800.1.bm.a \(4\) \(1.397\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}-\zeta_{8}^{3}q^{8}+\cdots\)
2800.1.bm.b \(8\) \(1.397\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}-\zeta_{24}^{9}q^{7}-\zeta_{24}^{3}q^{8}+\cdots\)
2800.1.ce.a \(2\) \(1.397\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-3\) \(0\) \(1\) \(q+(-1+\zeta_{6}^{2})q^{3}+\zeta_{6}q^{7}+(1-\zeta_{6}+\cdots)q^{9}+\cdots\)
2800.1.ce.b \(2\) \(1.397\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(3\) \(0\) \(-1\) \(q+(1-\zeta_{6}^{2})q^{3}-\zeta_{6}q^{7}+(1-\zeta_{6}-\zeta_{6}^{2}+\cdots)q^{9}+\cdots\)
2800.1.dc.a \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(-2\) \(0\) \(0\) \(2\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{7}+\cdots\)
2800.1.dc.b \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(-2\) \(q+\zeta_{12}^{5}q^{2}+(-\zeta_{12}+\zeta_{12}^{4})q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.dc.c \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(2\) \(q-\zeta_{12}^{5}q^{2}+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.dc.d \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{7}+\cdots\)
2800.1.di.a \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(-2\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(\zeta_{12}+\zeta_{12}^{4})q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.di.b \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{7}+\cdots\)
2800.1.di.c \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{7}+\cdots\)
2800.1.di.d \(4\) \(1.397\) \(\Q(\zeta_{12})\) None None \(2\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{4})q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
2800.1.dm.a \(8\) \(1.397\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{3}+\zeta_{24}q^{7}-\zeta_{24}^{8}q^{21}+\cdots\)
2800.2.a.a \(1\) \(22.358\) \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) \(+\) \(q-3q^{3}-q^{7}+6q^{9}-3q^{11}+q^{13}+\cdots\)
2800.2.a.b \(1\) \(22.358\) \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) \(-\) \(q-3q^{3}-q^{7}+6q^{9}+5q^{11}+6q^{13}+\cdots\)
2800.2.a.c \(1\) \(22.358\) \(\Q\) None None \(0\) \(-3\) \(0\) \(1\) \(-\) \(q-3q^{3}+q^{7}+6q^{9}+5q^{11}+5q^{13}+\cdots\)
2800.2.a.d \(1\) \(22.358\) \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) \(+\) \(q-2q^{3}-q^{7}+q^{9}-5q^{11}+8q^{17}+\cdots\)
2800.2.a.e \(1\) \(22.358\) \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) \(+\) \(q-2q^{3}+q^{7}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2800.2.a.f \(1\) \(22.358\) \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) \(+\) \(q-2q^{3}+q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
2800.2.a.g \(1\) \(22.358\) \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) \(+\) \(q-2q^{3}+q^{7}+q^{9}+4q^{13}-6q^{17}+\cdots\)
2800.2.a.h \(1\) \(22.358\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(q-q^{3}-q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
2800.2.a.i \(1\) \(22.358\) \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) \(+\) \(q-q^{3}-q^{7}-2q^{9}+5q^{11}-q^{13}+\cdots\)
2800.2.a.j \(1\) \(22.358\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(+\) \(q-q^{3}+q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots\)
2800.2.a.k \(1\) \(22.358\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(+\) \(q-q^{3}+q^{7}-2q^{9}+q^{11}-q^{13}-3q^{17}+\cdots\)
2800.2.a.l \(1\) \(22.358\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(-\) \(q-q^{3}+q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
2800.2.a.m \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}-3q^{9}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
2800.2.a.n \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}-3q^{9}-q^{11}-2q^{13}-4q^{17}+\cdots\)
2800.2.a.o \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-3q^{9}+4q^{13}+4q^{17}-4q^{19}+\cdots\)
2800.2.a.p \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(+\) \(q-q^{7}-3q^{9}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
2800.2.a.q \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) \(-\) \(q-q^{7}-3q^{9}+5q^{11}-6q^{13}+4q^{17}+\cdots\)
2800.2.a.r \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}-3q^{9}-q^{11}+2q^{13}+4q^{17}+\cdots\)
2800.2.a.s \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}-3q^{9}-4q^{13}-4q^{17}-4q^{19}+\cdots\)
2800.2.a.t \(1\) \(22.358\) \(\Q\) None None \(0\) \(0\) \(0\) \(1\) \(-\) \(q+q^{7}-3q^{9}+5q^{11}+6q^{13}-4q^{17}+\cdots\)
2800.2.a.u \(1\) \(22.358\) \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) \(-\) \(q+q^{3}-q^{7}-2q^{9}+q^{11}+q^{13}+3q^{17}+\cdots\)
2800.2.a.v \(1\) \(22.358\) \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots\)
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