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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1344.1.e.a \(2\) \(0.671\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{21}) \) \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-iq^{5}-iq^{7}+q^{9}+2iq^{15}+\cdots\)
1344.1.e.b \(2\) \(0.671\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{9}-q^{13}-iq^{19}+\cdots\)
1344.1.e.c \(2\) \(0.671\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}+q^{13}+iq^{19}+\cdots\)
1344.1.e.d \(2\) \(0.671\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{21}) \) \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-iq^{5}+iq^{7}+q^{9}-2iq^{15}+\cdots\)
1344.1.o.a \(1\) \(0.671\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{7}) \) \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}-q^{7}+q^{9}+2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.o.b \(1\) \(0.671\) \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{7}) \) \(0\) \(1\) \(0\) \(1\) \(q+q^{3}+q^{7}+q^{9}-2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.z.a \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.z.b \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.a \(4\) \(0.671\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(-\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.b \(4\) \(0.671\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.bm.a \(4\) \(0.671\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bm.b \(4\) \(0.671\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}-q^{13}+\cdots\)
1344.1.bm.c \(4\) \(0.671\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+q^{13}+\cdots\)
1344.1.bm.d \(4\) \(0.671\) \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bn.a \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.1.bn.b \(2\) \(0.671\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.2.a.a \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(-4\) \(1\) \(+\) \(q-q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
1344.2.a.b \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(-1\) \(-\) \(q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{13}+2q^{15}+\cdots\)
1344.2.a.c \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(-1\) \(+\) \(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
1344.2.a.d \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(-2\) \(1\) \(+\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1344.2.a.e \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(-\) \(q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.f \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) \(-\) \(q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1344.2.a.g \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(2\) \(-1\) \(+\) \(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
1344.2.a.h \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(2\) \(-1\) \(-\) \(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1344.2.a.i \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(2\) \(1\) \(+\) \(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1344.2.a.j \(1\) \(10.732\) \(\Q\) None None \(0\) \(-1\) \(4\) \(1\) \(-\) \(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.k \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(-4\) \(-1\) \(-\) \(q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1344.2.a.l \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(-2\) \(-1\) \(+\) \(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
1344.2.a.m \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(-2\) \(1\) \(+\) \(q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots\)
1344.2.a.n \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(-2\) \(1\) \(-\) \(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
1344.2.a.o \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) \(+\) \(q+q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1344.2.a.p \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) \(-\) \(q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.q \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(2\) \(-1\) \(-\) \(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1344.2.a.r \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(2\) \(1\) \(-\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
1344.2.a.s \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(2\) \(1\) \(-\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1344.2.a.t \(1\) \(10.732\) \(\Q\) None None \(0\) \(1\) \(4\) \(-1\) \(-\) \(q+q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.u \(2\) \(10.732\) \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1344.2.a.v \(2\) \(10.732\) \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(2\) \(-\) \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
1344.2.b.a \(2\) \(10.732\) \(\Q(\sqrt{-6}) \) None None \(0\) \(-2\) \(0\) \(-2\) \(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
1344.2.b.b \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(4\) \(q-q^{3}+(2-\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
1344.2.b.c \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(-4\) \(q+q^{3}+(-2+\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
1344.2.b.d \(2\) \(10.732\) \(\Q(\sqrt{-6}) \) None None \(0\) \(2\) \(0\) \(2\) \(q+q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
1344.2.b.e \(4\) \(10.732\) 4.0.2312.1 None None \(0\) \(-4\) \(0\) \(-2\) \(q-q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.b.f \(4\) \(10.732\) 4.0.2312.1 None None \(0\) \(4\) \(0\) \(2\) \(q+q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.b.g \(8\) \(10.732\) 8.0.836829184.2 None None \(0\) \(-8\) \(0\) \(4\) \(q-q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1344.2.b.h \(8\) \(10.732\) 8.0.836829184.2 None None \(0\) \(8\) \(0\) \(-4\) \(q+q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots\)
1344.2.c.a \(2\) \(10.732\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.b \(2\) \(10.732\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.c \(2\) \(10.732\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
1344.2.c.d \(2\) \(10.732\) \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
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