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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3380.1.g.a 3380.g 260.g $2$ $1.687$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}+\zeta_{6}^{2}q^{5}-q^{8}-q^{9}-\zeta_{6}^{2}q^{10}+\cdots\)
3380.1.g.b 3380.g 260.g $2$ $1.687$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}-\zeta_{6}^{2}q^{5}+q^{8}-q^{9}-\zeta_{6}^{2}q^{10}+\cdots\)
3380.1.g.c 3380.g 260.g $6$ $1.687$ 6.0.153664.1 \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{5}q^{2}-\beta _{4}q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
3380.1.g.d 3380.g 260.g $6$ $1.687$ 6.0.153664.1 \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
3380.1.h.a 3380.h 20.d $2$ $1.687$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) \(\Q(\sqrt{65}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{5}-iq^{8}-q^{9}+q^{10}+\cdots\)
3380.1.h.b 3380.h 20.d $3$ $1.687$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-5}) \) None \(-3\) \(-1\) \(-3\) \(1\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
3380.1.h.c 3380.h 20.d $3$ $1.687$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-5}) \) None \(-3\) \(1\) \(3\) \(1\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
3380.1.h.d 3380.h 20.d $3$ $1.687$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-5}) \) None \(3\) \(-1\) \(3\) \(-1\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
3380.1.h.e 3380.h 20.d $3$ $1.687$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-5}) \) None \(3\) \(1\) \(-3\) \(-1\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
3380.1.h.f 3380.h 20.d $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.l.a 3380.l 260.l $2$ $1.687$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-iq^{2}-q^{4}-q^{5}+iq^{8}+iq^{9}+iq^{10}+\cdots\)
3380.1.l.b 3380.l 260.l $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.l.c 3380.l 260.l $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.s.a 3380.s 260.s $2$ $1.687$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-iq^{5}+q^{8}+iq^{9}-iq^{10}+\cdots\)
3380.1.s.b 3380.s 260.s $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\zeta_{12}q^{5}-q^{8}+\zeta_{12}^{3}q^{9}+\cdots\)
3380.1.s.c 3380.s 260.s $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+\zeta_{12}^{5}q^{5}+q^{8}+\zeta_{12}^{3}q^{9}+\cdots\)
3380.1.v.a 3380.v 260.v $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) \(\Q(\sqrt{65}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.v.b 3380.v 260.v $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.v.c 3380.v 260.v $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.v.d 3380.v 260.v $6$ $1.687$ 6.0.64827.1 \(\Q(\sqrt{-5}) \) None \(-3\) \(-1\) \(-6\) \(1\) \(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
3380.1.v.e 3380.v 260.v $6$ $1.687$ 6.0.64827.1 \(\Q(\sqrt{-5}) \) None \(-3\) \(1\) \(6\) \(1\) \(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
3380.1.v.f 3380.v 260.v $6$ $1.687$ 6.0.64827.1 \(\Q(\sqrt{-5}) \) None \(3\) \(-1\) \(6\) \(-1\) \(q+\beta _{5}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
3380.1.v.g 3380.v 260.v $6$ $1.687$ 6.0.64827.1 \(\Q(\sqrt{-5}) \) None \(3\) \(1\) \(-6\) \(-1\) \(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
3380.1.w.a 3380.w 260.w $2$ $1.687$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) \(\Q(\sqrt{65}) \) \(-1\) \(0\) \(-2\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots\)
3380.1.w.b 3380.w 260.w $2$ $1.687$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots\)
3380.1.w.c 3380.w 260.w $2$ $1.687$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}-q^{8}+\cdots\)
3380.1.w.d 3380.w 260.w $2$ $1.687$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-65}) \) \(\Q(\sqrt{65}) \) \(1\) \(0\) \(2\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots\)
3380.1.w.e 3380.w 260.w $12$ $1.687$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{10}q^{2}+(-1+\beta _{3}+\beta _{5}-\beta _{9})q^{3}+\cdots\)
3380.1.w.f 3380.w 260.w $12$ $1.687$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{9}q^{3}+\beta _{7}q^{4}+(\beta _{6}-\beta _{10}+\cdots)q^{5}+\cdots\)
3380.1.be.a 3380.be 260.ae $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
3380.1.be.b 3380.be 260.ae $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{5}+\cdots\)
3380.1.be.c 3380.be 260.ae $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}q^{5}+q^{8}+\cdots\)
3380.1.be.d 3380.be 260.ae $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{5}+\cdots\)
3380.1.be.e 3380.be 260.ae $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}q^{5}-q^{8}+\cdots\)
3380.1.bl.a 3380.bl 260.al $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-q^{5}+\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.bl.b 3380.bl 260.al $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
3380.1.bl.c 3380.bl 260.al $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{4}q^{5}+\cdots\)
3380.1.bl.d 3380.bl 260.al $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)
3380.1.bl.e 3380.bl 260.al $4$ $1.687$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+q^{5}-\zeta_{12}^{3}q^{8}+\cdots\)
3380.1.bq.a 3380.bq 3380.aq $12$ $1.687$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}-\zeta_{26}^{2}q^{5}+\cdots\)
3380.1.bq.b 3380.bq 3380.aq $12$ $1.687$ \(\Q(\zeta_{26})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}-\zeta_{26}^{9}q^{5}+\cdots\)
3380.1.bz.a 3380.bz 3380.az $24$ $1.687$ \(\Q(\zeta_{52})\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{52}^{16}q^{2}-\zeta_{52}^{6}q^{4}+\zeta_{52}^{11}q^{5}+\cdots\)
3380.1.cg.a 3380.cg 3380.bg $24$ $1.687$ \(\Q(\zeta_{52})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{52}^{23}q^{2}-\zeta_{52}^{20}q^{4}-\zeta_{52}^{22}q^{5}+\cdots\)
3380.1.co.a 3380.co 3380.bo $24$ $1.687$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-1}) \) None \(-1\) \(0\) \(1\) \(0\) \(q+\zeta_{78}^{17}q^{2}+\zeta_{78}^{34}q^{4}-\zeta_{78}q^{5}+\cdots\)
3380.1.co.b 3380.co 3380.bo $24$ $1.687$ \(\Q(\zeta_{39})\) \(\Q(\sqrt{-1}) \) None \(1\) \(0\) \(-1\) \(0\) \(q-\zeta_{78}^{17}q^{2}+\zeta_{78}^{34}q^{4}-\zeta_{78}^{32}q^{5}+\cdots\)
3380.1.cs.a 3380.cs 3380.bs $48$ $1.687$ \(\Q(\zeta_{156})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{156}^{41}q^{2}-\zeta_{156}^{4}q^{4}-\zeta_{156}^{46}q^{5}+\cdots\)
3380.1.cz.a 3380.cz 3380.bz $48$ $1.687$ \(\Q(\zeta_{156})\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\zeta_{156}^{46}q^{2}-\zeta_{156}^{14}q^{4}-\zeta_{156}^{43}q^{5}+\cdots\)
3380.2.a.a 3380.a 1.a $1$ $26.989$ \(\Q\) None None \(0\) \(-3\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}-3q^{7}+6q^{9}-3q^{11}+\cdots\)
3380.2.a.b 3380.a 1.a $1$ $26.989$ \(\Q\) None None \(0\) \(-3\) \(1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+3q^{7}+6q^{9}+3q^{11}+\cdots\)
3380.2.a.c 3380.a 1.a $1$ $26.989$ \(\Q\) None None \(0\) \(-2\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{15}+\cdots\)
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