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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3744.1.l.a 3744.l 39.d $4$ $1.868$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{11}-q^{13}+(-\zeta_{8}+\cdots)q^{17}+\cdots\)
3744.1.l.b 3744.l 39.d $4$ $1.868$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{13}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{17}+\cdots\)
3744.1.l.c 3744.l 39.d $4$ $1.868$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\zeta_{8}^{3})q^{11}+q^{13}+\cdots\)
3744.1.o.a 3744.o 104.h $1$ $1.868$ \(\Q\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}-q^{13}+q^{17}+2q^{31}+\cdots\)
3744.1.o.b 3744.o 104.h $1$ $1.868$ \(\Q\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}+q^{13}+q^{17}-2q^{31}+\cdots\)
3744.1.o.c 3744.o 104.h $4$ $1.868$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{11}+\cdots\)
3744.1.bd.a 3744.bd 13.d $2$ $1.868$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}-iq^{13}+iq^{25}-q^{29}+\cdots\)
3744.1.bd.b 3744.bd 13.d $2$ $1.868$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-1-i)q^{5}+iq^{13}+iq^{17}+iq^{25}+\cdots\)
3744.1.bd.c 3744.bd 13.d $2$ $1.868$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(-1+i)q^{11}-q^{13}+iq^{23}-iq^{25}+\cdots\)
3744.1.bd.d 3744.bd 13.d $2$ $1.868$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+(1-i)q^{11}-q^{13}-iq^{23}-iq^{25}+\cdots\)
3744.1.bd.e 3744.bd 13.d $2$ $1.868$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(1+i)q^{5}-iq^{13}+iq^{25}+q^{29}+\cdots\)
3744.1.bv.a 3744.bv 39.i $8$ $1.868$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}+\zeta_{24}^{11})q^{5}+\zeta_{24}^{2}q^{13}+(-\zeta_{24}^{3}+\cdots)q^{17}+\cdots\)
3744.1.cc.a 3744.cc 468.v $4$ $1.868$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-q^{9}-\zeta_{12}^{5}q^{11}+\cdots\)
3744.1.ci.a 3744.ci 936.as $6$ $1.868$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{2}q^{3}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{5}+(\zeta_{18}^{7}+\cdots)q^{7}+\cdots\)
3744.1.ci.b 3744.ci 936.as $6$ $1.868$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{5}q^{3}+(\zeta_{18}-\zeta_{18}^{2})q^{5}+(\zeta_{18}^{2}+\cdots)q^{7}+\cdots\)
3744.1.ck.a 3744.ck 468.y $4$ $1.868$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{5}-\zeta_{12}^{4}q^{9}+\cdots\)
3744.1.dx.a 3744.dx 39.h $8$ $1.868$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{11})q^{5}-\zeta_{24}^{2}q^{13}+\cdots\)
3744.1.dy.a 3744.dy 52.j $4$ $1.868$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{7}-\zeta_{12}^{5}q^{11}+q^{13}-\zeta_{12}^{4}q^{17}+\cdots\)
3744.1.eh.a 3744.eh 416.ae $16$ $1.868$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{6}q^{4}+(-\zeta_{32}-\zeta_{32}^{11}+\cdots)q^{5}+\cdots\)
3744.1.gs.a 3744.gs 13.f $4$ $1.868$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{2})q^{5}-\zeta_{12}q^{13}+(1-\zeta_{12}^{4}+\cdots)q^{17}+\cdots\)
3744.1.gs.b 3744.gs 13.f $4$ $1.868$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}q^{13}+(-1+\cdots)q^{17}+\cdots\)
3744.1.gs.c 3744.gs 13.f $4$ $1.868$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}^{4}-\zeta_{12}^{5})q^{5}+\zeta_{12}q^{13}+\cdots\)
3744.2.a.a 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots\)
3744.2.a.b 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{11}+q^{13}+4q^{19}-4q^{23}+\cdots\)
3744.2.a.c 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{11}+q^{13}-4q^{19}+4q^{23}+\cdots\)
3744.2.a.d 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots\)
3744.2.a.e 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
3744.2.a.f 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(-1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
3744.2.a.g 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+q^{13}-2q^{17}+2q^{19}+8q^{23}+\cdots\)
3744.2.a.h 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+4q^{11}+q^{13}+6q^{17}-6q^{19}+\cdots\)
3744.2.a.i 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-4q^{11}+q^{13}+6q^{17}+6q^{19}+\cdots\)
3744.2.a.j 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}+q^{13}-2q^{17}-2q^{19}-8q^{23}+\cdots\)
3744.2.a.k 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-6q^{11}-q^{13}+2q^{17}+\cdots\)
3744.2.a.l 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{11}+q^{13}+6q^{17}-8q^{19}+\cdots\)
3744.2.a.m 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{11}+q^{13}-4q^{19}-4q^{23}+\cdots\)
3744.2.a.n 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{11}+q^{13}+4q^{19}+4q^{23}+\cdots\)
3744.2.a.o 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{11}+q^{13}+6q^{17}+8q^{19}+\cdots\)
3744.2.a.p 3744.a 1.a $1$ $29.896$ \(\Q\) None None \(0\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+6q^{11}-q^{13}+2q^{17}+\cdots\)
3744.2.a.q 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-\beta q^{7}-2\beta q^{11}-q^{13}+3q^{17}+\cdots\)
3744.2.a.r 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-1-\beta )q^{7}+2q^{11}+\cdots\)
3744.2.a.s 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(1+\beta )q^{7}-2q^{11}+\cdots\)
3744.2.a.t 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{7}-\beta q^{11}-q^{13}+\beta q^{19}-2\beta q^{23}+\cdots\)
3744.2.a.u 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{7}+\beta q^{11}-q^{13}+\beta q^{19}+2\beta q^{23}+\cdots\)
3744.2.a.v 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-3+\beta )q^{7}-2\beta q^{11}+\cdots\)
3744.2.a.w 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(3-\beta )q^{7}+2\beta q^{11}-q^{13}+\cdots\)
3744.2.a.x 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{17}) \) None None \(0\) \(0\) \(3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1-\beta )q^{7}+2q^{11}+\cdots\)
3744.2.a.y 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{17}) \) None None \(0\) \(0\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1+\beta )q^{7}-2q^{11}-q^{13}+\cdots\)
3744.2.a.z 3744.a 1.a $3$ $29.896$ 3.3.148.1 None None \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
3744.2.a.ba 3744.a 1.a $3$ $29.896$ 3.3.148.1 None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
3744.2.a.bb 3744.a 1.a $4$ $29.896$ \(\Q(\zeta_{20})^+\) None None \(0\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
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