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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3200.1.e.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-iq^{17}+q^{41}-q^{49}+iq^{73}+\cdots\)
3200.1.e.b \(4\) \(1.597\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
3200.1.g.a \(1\) \(1.597\) \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}+2q^{17}+2q^{41}+q^{49}+2q^{73}+\cdots\)
3200.1.g.b \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-iq^{13}-iq^{37}-q^{41}+q^{49}+\cdots\)
3200.1.g.c \(2\) \(1.597\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}+2q^{9}-\beta q^{11}-q^{17}+\beta q^{19}+\cdots\)
3200.1.g.d \(2\) \(1.597\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}+2q^{9}-\beta q^{11}+q^{17}+\beta q^{19}+\cdots\)
3200.1.g.e \(4\) \(1.597\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots\)
3200.1.m.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+(-1-i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.b \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+(1+i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.c \(4\) \(1.597\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\zeta_{8}q^{23}-q^{41}+\cdots\)
3200.1.m.d \(4\) \(1.597\) \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}-3\zeta_{8}^{2}q^{9}+2\zeta_{8}q^{27}+q^{41}+\cdots\)
3200.1.m.e \(8\) \(1.597\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{4}-\zeta_{24}^{8})q^{11}+\cdots\)
3200.1.bd.a \(4\) \(1.597\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(-\zeta_{10}+\zeta_{10}^{3}+\cdots)q^{13}+\cdots\)
3200.1.bd.b \(4\) \(1.597\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{13}+\cdots\)
3200.1.bi.a \(4\) \(1.597\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
3200.1.bi.b \(4\) \(1.597\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
3200.1.bz.a \(8\) \(1.597\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(\zeta_{20}^{3}-\zeta_{20}^{6}+\cdots)q^{13}+\cdots\)
3200.1.bz.b \(8\) \(1.597\) \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(-\zeta_{20}^{3}+\zeta_{20}^{6}+\cdots)q^{13}+\cdots\)
3200.2.a.a \(1\) \(25.552\) \(\Q\) None None \(0\) \(-3\) \(0\) \(-4\) \(-\) \(q-3q^{3}-4q^{7}+6q^{9}-3q^{11}-2q^{13}+\cdots\)
3200.2.a.b \(1\) \(25.552\) \(\Q\) None None \(0\) \(-3\) \(0\) \(-4\) \(-\) \(q-3q^{3}-4q^{7}+6q^{9}+3q^{11}+2q^{13}+\cdots\)
3200.2.a.c \(1\) \(25.552\) \(\Q\) None None \(0\) \(-3\) \(0\) \(4\) \(+\) \(q-3q^{3}+4q^{7}+6q^{9}-3q^{11}+2q^{13}+\cdots\)
3200.2.a.d \(1\) \(25.552\) \(\Q\) None None \(0\) \(-3\) \(0\) \(4\) \(-\) \(q-3q^{3}+4q^{7}+6q^{9}+3q^{11}-2q^{13}+\cdots\)
3200.2.a.e \(1\) \(25.552\) \(\Q\) None None \(0\) \(-2\) \(0\) \(-4\) \(+\) \(q-2q^{3}-4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3200.2.a.f \(1\) \(25.552\) \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) \(+\) \(q-2q^{3}+q^{9}+2q^{11}-2q^{13}-6q^{17}+\cdots\)
3200.2.a.g \(1\) \(25.552\) \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) \(-\) \(q-2q^{3}+q^{9}+2q^{11}+2q^{13}-6q^{17}+\cdots\)
3200.2.a.h \(1\) \(25.552\) \(\Q\) None None \(0\) \(-2\) \(0\) \(4\) \(+\) \(q-2q^{3}+4q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3200.2.a.i \(1\) \(25.552\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(-\) \(q-q^{3}-2q^{9}-q^{11}-2q^{13}-3q^{17}+\cdots\)
3200.2.a.j \(1\) \(25.552\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{3}-2q^{9}-q^{11}+2q^{13}-3q^{17}+\cdots\)
3200.2.a.k \(1\) \(25.552\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{3}-2q^{9}+q^{11}-2q^{13}+3q^{17}+\cdots\)
3200.2.a.l \(1\) \(25.552\) \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) \(+\) \(q-q^{3}-2q^{9}+q^{11}+2q^{13}+3q^{17}+\cdots\)
3200.2.a.m \(1\) \(25.552\) \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q-2q^{7}-3q^{9}-6q^{11}+2q^{13}+6q^{17}+\cdots\)
3200.2.a.n \(1\) \(25.552\) \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) \(-\) \(q-2q^{7}-3q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots\)
3200.2.a.o \(1\) \(25.552\) \(\Q\) None None \(0\) \(0\) \(0\) \(2\) \(+\) \(q+2q^{7}-3q^{9}-6q^{11}-2q^{13}+6q^{17}+\cdots\)
3200.2.a.p \(1\) \(25.552\) \(\Q\) None None \(0\) \(0\) \(0\) \(2\) \(-\) \(q+2q^{7}-3q^{9}+6q^{11}+2q^{13}+6q^{17}+\cdots\)
3200.2.a.q \(1\) \(25.552\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(+\) \(q+q^{3}-2q^{9}-q^{11}-2q^{13}+3q^{17}+\cdots\)
3200.2.a.r \(1\) \(25.552\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(-\) \(q+q^{3}-2q^{9}-q^{11}+2q^{13}+3q^{17}+\cdots\)
3200.2.a.s \(1\) \(25.552\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(+\) \(q+q^{3}-2q^{9}+q^{11}-2q^{13}-3q^{17}+\cdots\)
3200.2.a.t \(1\) \(25.552\) \(\Q\) None None \(0\) \(1\) \(0\) \(0\) \(+\) \(q+q^{3}-2q^{9}+q^{11}+2q^{13}-3q^{17}+\cdots\)
3200.2.a.u \(1\) \(25.552\) \(\Q\) None None \(0\) \(2\) \(0\) \(-4\) \(+\) \(q+2q^{3}-4q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3200.2.a.v \(1\) \(25.552\) \(\Q\) None None \(0\) \(2\) \(0\) \(0\) \(+\) \(q+2q^{3}+q^{9}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
3200.2.a.w \(1\) \(25.552\) \(\Q\) None None \(0\) \(2\) \(0\) \(0\) \(+\) \(q+2q^{3}+q^{9}-2q^{11}+2q^{13}-6q^{17}+\cdots\)
3200.2.a.x \(1\) \(25.552\) \(\Q\) None None \(0\) \(2\) \(0\) \(4\) \(-\) \(q+2q^{3}+4q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3200.2.a.y \(1\) \(25.552\) \(\Q\) None None \(0\) \(3\) \(0\) \(-4\) \(+\) \(q+3q^{3}-4q^{7}+6q^{9}-3q^{11}-2q^{13}+\cdots\)
3200.2.a.z \(1\) \(25.552\) \(\Q\) None None \(0\) \(3\) \(0\) \(-4\) \(-\) \(q+3q^{3}-4q^{7}+6q^{9}+3q^{11}+2q^{13}+\cdots\)
3200.2.a.ba \(1\) \(25.552\) \(\Q\) None None \(0\) \(3\) \(0\) \(4\) \(-\) \(q+3q^{3}+4q^{7}+6q^{9}-3q^{11}+2q^{13}+\cdots\)
3200.2.a.bb \(1\) \(25.552\) \(\Q\) None None \(0\) \(3\) \(0\) \(4\) \(-\) \(q+3q^{3}+4q^{7}+6q^{9}+3q^{11}-2q^{13}+\cdots\)
3200.2.a.bc \(2\) \(25.552\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(-4\) \(-\) \(q+(-1+\beta )q^{3}+(-2-2\beta )q^{7}-2\beta q^{9}+\cdots\)
3200.2.a.bd \(2\) \(25.552\) \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(-4\) \(-\) \(q+(-1+\beta )q^{3}+(-2-2\beta )q^{7}-2\beta q^{9}+\cdots\)
3200.2.a.be \(2\) \(25.552\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(-2\) \(+\) \(q+(-1-\beta )q^{3}+(-1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
3200.2.a.bf \(2\) \(25.552\) \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(2\) \(-\) \(q+(-1-\beta )q^{3}+(1-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
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