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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2496.1.b.a 2496.b 312.b $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-26}) \) \(\Q(\sqrt{78}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}-q^{13}+2q^{21}+\cdots\)
2496.1.b.b 2496.b 312.b $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-26}) \) \(\Q(\sqrt{78}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{9}+q^{13}-2q^{21}+\cdots\)
2496.1.b.c 2496.b 312.b $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}+(\zeta_{12}^{2}+\zeta_{12}^{4})q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
2496.1.b.d 2496.b 312.b $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}+\cdots\)
2496.1.l.a 2496.l 39.d $1$ $1.246$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+q^{13}-q^{25}-q^{27}-q^{39}+\cdots\)
2496.1.l.b 2496.l 39.d $1$ $1.246$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}+q^{13}-q^{25}+q^{27}+q^{39}+\cdots\)
2496.1.l.c 2496.l 39.d $4$ $1.246$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{39}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
2496.1.bd.a 2496.bd 156.l $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}+(-1-i)q^{7}-q^{9}+iq^{13}+\cdots\)
2496.1.bd.b 2496.bd 156.l $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q-iq^{3}+(1+i)q^{7}-q^{9}+iq^{13}+(1+\cdots)q^{19}+\cdots\)
2496.1.be.a 2496.be 312.w $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q-q^{3}+(-1-i)q^{7}+q^{9}+iq^{13}+\cdots\)
2496.1.be.b 2496.be 312.w $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(2\) \(q-q^{3}+(1+i)q^{7}+q^{9}-iq^{13}+(1+\cdots)q^{19}+\cdots\)
2496.1.be.c 2496.be 312.w $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+q^{3}+(-1-i)q^{7}+q^{9}-iq^{13}+\cdots\)
2496.1.be.d 2496.be 312.w $2$ $1.246$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(2\) \(q+q^{3}+(1+i)q^{7}+q^{9}+iq^{13}+(-1+\cdots)q^{19}+\cdots\)
2496.1.bi.a 2496.bi 624.ai $8$ $1.246$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{2}q^{3}+(-\zeta_{16}+\zeta_{16}^{3})q^{5}+\zeta_{16}^{4}q^{9}+\cdots\)
2496.1.bs.a 2496.bs 39.i $2$ $1.246$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots\)
2496.1.bs.b 2496.bs 39.i $2$ $1.246$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{13}+\cdots\)
2496.1.bs.c 2496.bs 39.i $8$ $1.246$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{3}-\zeta_{24}^{6}q^{5}+(-\zeta_{24}-\zeta_{24}^{7}+\cdots)q^{7}+\cdots\)
2496.1.bw.a 2496.bw 312.ag $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{4}q^{13}+\cdots\)
2496.1.bw.b 2496.bw 312.ag $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{4}q^{13}+\cdots\)
2496.1.bx.a 2496.bx 312.ah $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(\zeta_{12}+\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2496.1.bx.b 2496.bx 312.ah $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+(-\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2496.1.cb.a 2496.cb 39.h $2$ $1.246$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-3\) \(q+\zeta_{6}^{2}q^{3}+(-1+\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}+\cdots\)
2496.1.cb.b 2496.cb 39.h $2$ $1.246$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(3\) \(q-\zeta_{6}^{2}q^{3}+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots\)
2496.1.de.a 2496.de 312.aq $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(-4\) \(q-\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
2496.1.de.b 2496.de 312.aq $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(4\) \(q-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
2496.1.de.c 2496.de 312.aq $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(-4\) \(q+\zeta_{12}^{2}q^{3}+(-1+\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
2496.1.de.d 2496.de 312.aq $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(4\) \(q+\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{5})q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
2496.1.df.a 2496.df 156.v $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{12}q^{3}+(-\zeta_{12}^{3}+\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2496.1.df.b 2496.df 156.v $4$ $1.246$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}q^{3}+(\zeta_{12}^{3}-\zeta_{12}^{4})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
2496.1.eh.a 2496.eh 2496.dh $32$ $1.246$ \(\Q(\zeta_{64})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{64}^{27}q^{2}-\zeta_{64}^{26}q^{3}-\zeta_{64}^{22}q^{4}+\cdots\)
2496.2.a.a 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
2496.2.a.b 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.c 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}-q^{13}+2q^{15}+\cdots\)
2496.2.a.d 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+2q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.e 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
2496.2.a.f 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
2496.2.a.g 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-6q^{11}+q^{13}+2q^{17}+\cdots\)
2496.2.a.h 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-q^{13}-6q^{17}+\cdots\)
2496.2.a.i 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-q^{13}+2q^{17}+\cdots\)
2496.2.a.j 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
2496.2.a.k 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
2496.2.a.l 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+4q^{11}-q^{13}+\cdots\)
2496.2.a.m 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
2496.2.a.n 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
2496.2.a.o 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(-1\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.p 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(1\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
2496.2.a.q 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
2496.2.a.r 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-2q^{7}+q^{9}-2q^{11}+\cdots\)
2496.2.a.s 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-q^{13}-2q^{15}+\cdots\)
2496.2.a.t 2496.a 1.a $1$ $19.931$ \(\Q\) None None \(0\) \(1\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
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