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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3276.1.d.a 3276.d 1092.d $4$ $1.635$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-13}) \) None 3276.1.d.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{7}-\zeta_{8}^{2}q^{8}+\cdots\)
3276.1.d.b 3276.d 1092.d $4$ $1.635$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-13}) \) None 3276.1.d.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots\)
3276.1.k.a 3276.k 91.b $1$ $1.635$ \(\Q\) \(\Q(\sqrt{-91}) \) None 364.1.d.a \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}-q^{13}+q^{19}+q^{23}+q^{29}+\cdots\)
3276.1.k.b 3276.k 91.b $1$ $1.635$ \(\Q\) \(\Q(\sqrt{-91}) \) None 364.1.d.a \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}+q^{13}-q^{19}+q^{23}+q^{29}+\cdots\)
3276.1.k.c 3276.k 91.b $2$ $1.635$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-91}) \) None 3276.1.k.c \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{5}-q^{7}+q^{13}-q^{19}-\beta q^{23}+\cdots\)
3276.1.k.d 3276.k 91.b $2$ $1.635$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-91}) \) None 3276.1.k.c \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{5}+q^{7}-q^{13}+q^{19}+\beta q^{23}+\cdots\)
3276.1.bx.a 3276.bx 91.n $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.bx.a \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+\zeta_{6}^{2}q^{13}+q^{25}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{31}+\cdots\)
3276.1.bx.b 3276.bx 91.n $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.bx.a \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}+q^{25}+(-\zeta_{6}+\cdots)q^{31}+\cdots\)
3276.1.cz.a 3276.cz 91.p $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.cz.a \(0\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{7}-q^{13}+q^{19}+\zeta_{6}q^{25}+\cdots\)
3276.1.db.a 3276.db 3276.cb $4$ $1.635$ \(\Q(\zeta_{12})\) None None 3276.1.db.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-q^{6}+\cdots\)
3276.1.dv.a 3276.dv 91.l $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.cz.a \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}+q^{13}+\zeta_{6}q^{19}+\zeta_{6}q^{25}-\zeta_{6}q^{31}+\cdots\)
3276.1.dx.a 3276.dx 819.by $8$ $1.635$ \(\Q(\zeta_{24})\) None None 3276.1.dx.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{2}q^{3}+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{5}+\zeta_{24}^{7}q^{7}+\cdots\)
3276.1.ea.a 3276.ea 3276.da $4$ $1.635$ \(\Q(\zeta_{12})\) None None 3276.1.db.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{6}+\cdots\)
3276.1.ek.a 3276.ek 91.s $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.ek.a \(0\) \(0\) \(0\) \(-1\) \(q-\zeta_{6}q^{7}+\zeta_{6}q^{13}-\zeta_{6}q^{19}-\zeta_{6}^{2}q^{25}+\cdots\)
3276.1.ek.b 3276.ek 91.s $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.ek.a \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}+\zeta_{6}q^{19}-\zeta_{6}^{2}q^{25}+\cdots\)
3276.1.fl.a 3276.fl 273.am $4$ $1.635$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None 3276.1.fl.a \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{2}q^{7}-\beta _{3}q^{11}-q^{13}+(\beta _{1}-\beta _{3})q^{17}+\cdots\)
3276.1.fq.a 3276.fq 91.v $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.fq.a \(0\) \(0\) \(0\) \(-2\) \(q-q^{7}-q^{13}+(1-\zeta_{6}^{2})q^{19}-\zeta_{6}q^{25}+\cdots\)
3276.1.fx.a 3276.fx 364.al $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(-1\) \(0\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}+q^{8}-\zeta_{6}^{2}q^{11}+\cdots\)
3276.1.fx.b 3276.fx 364.al $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-13}) \) None 364.1.bl.a \(1\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots\)
3276.1.fx.c 3276.fx 364.al $4$ $1.635$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-13}) \) None 3276.1.fx.c \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}+q^{8}+\cdots\)
3276.1.fx.d 3276.fx 364.al $4$ $1.635$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-13}) \) None 3276.1.fx.c \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}-\zeta_{12}q^{7}-q^{8}+\cdots\)
3276.1.gn.a 3276.gn 273.s $4$ $1.635$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None 3276.1.fl.a \(0\) \(0\) \(0\) \(4\) \(q+q^{7}+(\beta _{1}-\beta _{3})q^{11}-q^{13}-\beta _{3}q^{17}+\cdots\)
3276.1.gs.a 3276.gs 1092.bt $8$ $1.635$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-13}) \) None 3276.1.gs.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{11}q^{7}+\cdots\)
3276.1.gs.b 3276.gs 1092.bt $8$ $1.635$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-13}) \) None 3276.1.gs.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{11}q^{7}+\cdots\)
3276.1.hq.a 3276.hq 91.m $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.fq.a \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+q^{13}+(-\zeta_{6}-\zeta_{6}^{2})q^{19}+\cdots\)
3276.1.il.a 3276.il 3276.hl $4$ $1.635$ \(\Q(\zeta_{12})\) None None 3276.1.db.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}-q^{6}+\cdots\)
3276.1.ip.a 3276.ip 91.t $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.ip.a \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{13}+\zeta_{6}^{2}q^{19}-q^{25}+\cdots\)
3276.1.ip.b 3276.ip 91.t $2$ $1.635$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None 3276.1.ip.a \(0\) \(0\) \(0\) \(2\) \(q+q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}^{2}q^{19}-q^{25}+\cdots\)
3276.1.iu.a 3276.iu 3276.hu $4$ $1.635$ \(\Q(\zeta_{12})\) None None 3276.1.db.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
3276.1.iy.a 3276.iy 91.x $4$ $1.635$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3276.1.iy.a \(0\) \(0\) \(0\) \(-4\) \(q-q^{7}-\zeta_{12}^{3}q^{13}+(-1-\zeta_{12})q^{19}+\cdots\)
3276.1.lw.a 3276.lw 91.ad $4$ $1.635$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3276.1.iy.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{7}+\zeta_{12}^{3}q^{13}+(-\zeta_{12}^{4}+\cdots)q^{19}+\cdots\)
3276.1.ma.a 3276.ma 91.z $4$ $1.635$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3276.1.ma.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{7}-\zeta_{12}^{5}q^{13}+(-1+\zeta_{12}+\cdots)q^{19}+\cdots\)
3276.1.ma.b 3276.ma 91.z $4$ $1.635$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None 3276.1.ma.a \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{2}q^{7}-\zeta_{12}q^{13}+(-\zeta_{12}^{3}-\zeta_{12}^{4}+\cdots)q^{19}+\cdots\)
3276.2.a.a 3276.a 1.a $1$ $26.159$ \(\Q\) None None 3276.2.a.a \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{11}+q^{13}+4q^{17}+\cdots\)
3276.2.a.b 3276.a 1.a $1$ $26.159$ \(\Q\) None None 364.2.a.a \(0\) \(0\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+4q^{11}+q^{13}+2q^{17}+\cdots\)
3276.2.a.c 3276.a 1.a $1$ $26.159$ \(\Q\) None None 1092.2.a.d \(0\) \(0\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+6q^{11}-q^{13}+8q^{17}+\cdots\)
3276.2.a.d 3276.a 1.a $1$ $26.159$ \(\Q\) None None 1092.2.a.c \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}+2q^{11}-q^{13}-4q^{17}+4q^{19}+\cdots\)
3276.2.a.e 3276.a 1.a $1$ $26.159$ \(\Q\) None None 3276.2.a.e \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}-q^{13}+4q^{17}-4q^{19}+\cdots\)
3276.2.a.f 3276.a 1.a $1$ $26.159$ \(\Q\) None None 3276.2.a.e \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}-q^{13}-4q^{17}-4q^{19}+\cdots\)
3276.2.a.g 3276.a 1.a $1$ $26.159$ \(\Q\) None None 1092.2.a.b \(0\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{11}+q^{13}+4q^{17}+\cdots\)
3276.2.a.h 3276.a 1.a $1$ $26.159$ \(\Q\) None None 3276.2.a.a \(0\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{11}+q^{13}-4q^{17}+\cdots\)
3276.2.a.i 3276.a 1.a $1$ $26.159$ \(\Q\) None None 1092.2.a.e \(0\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-q^{13}+4q^{17}-8q^{19}+\cdots\)
3276.2.a.j 3276.a 1.a $1$ $26.159$ \(\Q\) None None 1092.2.a.a \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-q^{13}-4q^{17}+6q^{23}+\cdots\)
3276.2.a.k 3276.a 1.a $1$ $26.159$ \(\Q\) None None 364.2.a.b \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}+2q^{11}-q^{13}+4q^{17}+\cdots\)
3276.2.a.l 3276.a 1.a $2$ $26.159$ \(\Q(\sqrt{5}) \) None None 1092.2.a.f \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}+(-1+\beta )q^{11}+\cdots\)
3276.2.a.m 3276.a 1.a $2$ $26.159$ \(\Q(\sqrt{33}) \) None None 1092.2.a.g \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+q^{7}-2q^{11}-q^{13}+(4-\beta )q^{19}+\cdots\)
3276.2.a.n 3276.a 1.a $2$ $26.159$ \(\Q(\sqrt{3}) \) None None 364.2.a.d \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
3276.2.a.o 3276.a 1.a $2$ $26.159$ \(\Q(\sqrt{3}) \) None None 3276.2.a.o \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+\beta q^{11}+q^{13}-4q^{19}+\cdots\)
3276.2.a.p 3276.a 1.a $2$ $26.159$ \(\Q(\sqrt{3}) \) None None 3276.2.a.p \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}-2\beta q^{11}+q^{13}+5q^{19}+\cdots\)
3276.2.a.q 3276.a 1.a $2$ $26.159$ \(\Q(\sqrt{6}) \) None None 364.2.a.c \(0\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-4-\beta )q^{11}-q^{13}+\cdots\)
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