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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3136.1.c.a 3136.c 7.b $4$ $1.565$ 4.0.2048.2 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}+q^{9}-\beta _{1}q^{13}-\beta _{1}q^{17}+\cdots\)
3136.1.d.a 3136.d 4.b $1$ $1.565$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-q^{25}+2q^{29}+2q^{37}-2q^{53}+\cdots\)
3136.1.d.b 3136.d 4.b $2$ $1.565$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{3}-q^{5}-iq^{11}-iq^{15}+q^{17}+\cdots\)
3136.1.d.c 3136.d 4.b $2$ $1.565$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+q^{9}+\beta q^{13}-\beta q^{17}+q^{25}+\cdots\)
3136.1.d.d 3136.d 4.b $2$ $1.565$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) \(q-iq^{3}+q^{5}-iq^{11}-iq^{15}-q^{17}+\cdots\)
3136.1.g.a 3136.g 8.d $4$ $1.565$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
3136.1.h.a 3136.h 56.h $8$ $1.565$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}^{3}-\zeta_{16}^{5})q^{3}+(1-\zeta_{16}^{2}+\zeta_{16}^{6}+\cdots)q^{9}+\cdots\)
3136.1.k.a 3136.k 16.f $2$ $1.565$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+(-1+i)q^{11}+q^{23}-iq^{25}+\cdots\)
3136.1.n.a 3136.n 56.j $16$ $1.565$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{48}^{17}-\zeta_{48}^{23})q^{3}+(-\zeta_{48}^{10}+\cdots)q^{9}+\cdots\)
3136.1.o.a 3136.o 56.k $8$ $1.565$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{3}+(-\zeta_{24}+\zeta_{24}^{7}+\cdots)q^{5}+\cdots\)
3136.1.r.a 3136.r 28.g $2$ $1.565$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{25}+q^{29}-\zeta_{6}q^{37}+\cdots\)
3136.1.r.b 3136.r 28.g $4$ $1.565$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{11}+\cdots\)
3136.1.r.c 3136.r 28.g $4$ $1.565$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{3})q^{5}+\beta _{2}q^{9}+\beta _{3}q^{13}-\beta _{1}q^{17}+\cdots\)
3136.1.s.a 3136.s 7.d $8$ $1.565$ 8.0.339738624.1 \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{5}+\beta _{4}q^{9}+\beta _{7}q^{13}+\beta _{3}q^{17}+\cdots\)
3136.1.z.a 3136.z 112.u $4$ $1.565$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{9}+(\zeta_{12}^{2}+\zeta_{12}^{5})q^{11}+\zeta_{12}^{4}q^{23}+\cdots\)
3136.1.bc.a 3136.bc 112.x $4$ $1.565$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{9}+(-\zeta_{12}+\zeta_{12}^{4})q^{11}+\cdots\)
3136.1.bm.a 3136.bm 64.j $8$ $1.565$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-\zeta_{16}q^{8}-\zeta_{16}q^{9}+\cdots\)
3136.1.ce.a 3136.ce 448.ak $16$ $1.565$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{48}^{11}q^{2}+\zeta_{48}^{22}q^{4}+\zeta_{48}^{9}q^{8}+\cdots\)
3136.1.cf.a 3136.cf 448.al $16$ $1.565$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}^{13}q^{2}-\zeta_{48}^{2}q^{4}-\zeta_{48}^{15}q^{8}+\cdots\)
3136.2.a.a 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-3\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+6q^{9}-q^{11}+2q^{13}+\cdots\)
3136.2.a.b 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-3\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+6q^{9}+q^{11}-2q^{13}+\cdots\)
3136.2.a.c 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}+q^{9}+8q^{15}+2q^{17}+\cdots\)
3136.2.a.d 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
3136.2.a.e 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}-4q^{13}-6q^{17}+2q^{19}+\cdots\)
3136.2.a.f 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+4q^{11}-4q^{13}+2q^{17}+\cdots\)
3136.2.a.g 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
3136.2.a.h 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
3136.2.a.i 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}-3q^{11}-6q^{13}+\cdots\)
3136.2.a.j 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+3q^{11}+6q^{13}+\cdots\)
3136.2.a.k 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(-1\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
3136.2.a.l 3136.a 1.a $1$ $25.041$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-4q^{5}-3q^{9}+4q^{13}+8q^{17}+11q^{25}+\cdots\)
3136.2.a.m 3136.a 1.a $1$ $25.041$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{5}-3q^{9}+6q^{13}-2q^{17}-q^{25}+\cdots\)
3136.2.a.n 3136.a 1.a $1$ $25.041$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-3q^{9}-4q^{11}+8q^{23}-5q^{25}-2q^{29}+\cdots\)
3136.2.a.o 3136.a 1.a $1$ $25.041$ \(\Q\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-3q^{9}+4q^{11}-8q^{23}-5q^{25}-2q^{29}+\cdots\)
3136.2.a.p 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-3q^{9}-4q^{11}+2q^{13}+6q^{17}+\cdots\)
3136.2.a.q 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-3q^{9}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
3136.2.a.r 3136.a 1.a $1$ $25.041$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+4q^{5}-3q^{9}-4q^{13}-8q^{17}+11q^{25}+\cdots\)
3136.2.a.s 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(1\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
3136.2.a.t 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}+3q^{11}-6q^{13}+\cdots\)
3136.2.a.u 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}-3q^{11}+6q^{13}+\cdots\)
3136.2.a.v 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(1\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
3136.2.a.w 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(2\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}+q^{9}-8q^{15}+2q^{17}+\cdots\)
3136.2.a.x 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
3136.2.a.y 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-4q^{11}-4q^{13}+2q^{17}+\cdots\)
3136.2.a.z 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
3136.2.a.ba 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
3136.2.a.bb 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(3\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+6q^{9}+q^{11}+2q^{13}+\cdots\)
3136.2.a.bc 3136.a 1.a $1$ $25.041$ \(\Q\) None None \(0\) \(3\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+6q^{9}-q^{11}-2q^{13}+\cdots\)
3136.2.a.bd 3136.a 1.a $2$ $25.041$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-1+2\beta )q^{5}-2\beta q^{9}+\cdots\)
3136.2.a.be 3136.a 1.a $2$ $25.041$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(1-2\beta )q^{5}-2\beta q^{9}+\cdots\)
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