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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3312.1.c.a $1$ $1.653$ \(\Q\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-q^{13}+q^{23}+q^{25}+q^{29}+q^{31}+\cdots\)
3312.1.w.a $2$ $1.653$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q-iq^{2}-q^{4}+iq^{8}+(-1-i)q^{13}+\cdots\)
3312.1.w.b $4$ $1.653$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{8}+\cdots\)
3312.1.bm.a $6$ $1.653$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{18}^{7}q^{3}-\zeta_{18}^{5}q^{9}+(\zeta_{18}^{4}+\zeta_{18}^{8}+\cdots)q^{13}+\cdots\)
3312.1.bp.a $12$ $1.653$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{36}^{5}q^{2}+\zeta_{36}^{8}q^{3}+\zeta_{36}^{10}q^{4}+\cdots\)
3312.1.bp.b $12$ $1.653$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{36}^{13}q^{2}-\zeta_{36}^{11}q^{3}-\zeta_{36}^{8}q^{4}+\cdots\)
3312.1.bw.a $12$ $1.653$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{36}^{13}q^{2}+\zeta_{36}^{11}q^{3}-\zeta_{36}^{8}q^{4}+\cdots\)
3312.1.bw.b $12$ $1.653$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\zeta_{36}^{11}q^{2}+\zeta_{36}^{14}q^{3}-\zeta_{36}^{4}q^{4}+\cdots\)
3312.2.a.a $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(-4\) \(-2\) $+$ \(q-4q^{5}-2q^{7}+2q^{13}+4q^{17}+6q^{19}+\cdots\)
3312.2.a.b $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(-4\) \(4\) $-$ \(q-4q^{5}+4q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
3312.2.a.c $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-2\) $-$ \(q-2q^{5}-2q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
3312.2.a.d $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $+$ \(q-2q^{5}-2q^{13}-2q^{17}+8q^{19}-q^{23}+\cdots\)
3312.2.a.e $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(-2\) \(4\) $+$ \(q-2q^{5}+4q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
3312.2.a.f $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $+$ \(q-4q^{7}+6q^{11}-2q^{13}-6q^{17}+6q^{19}+\cdots\)
3312.2.a.g $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ \(q-2q^{7}-q^{13}+6q^{17}-2q^{19}-q^{23}+\cdots\)
3312.2.a.h $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ \(q-2q^{7}+2q^{13}-2q^{19}-q^{23}-5q^{25}+\cdots\)
3312.2.a.i $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ \(q+2q^{7}-5q^{13}+6q^{17}-6q^{19}+q^{23}+\cdots\)
3312.2.a.j $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ \(q+2q^{7}+2q^{13}-8q^{17}-6q^{19}+q^{23}+\cdots\)
3312.2.a.k $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ \(q+2q^{7}+4q^{11}-6q^{13}-4q^{17}-2q^{19}+\cdots\)
3312.2.a.l $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) $+$ \(q+2q^{5}-2q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
3312.2.a.m $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) $-$ \(q+2q^{5}-2q^{7}-2q^{11}-2q^{13}+4q^{17}+\cdots\)
3312.2.a.n $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(2\) \(2\) $+$ \(q+2q^{5}+2q^{7}-6q^{11}-2q^{13}-q^{23}+\cdots\)
3312.2.a.o $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(2\) \(4\) $-$ \(q+2q^{5}+4q^{7}-2q^{11}+7q^{13}+4q^{17}+\cdots\)
3312.2.a.p $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(2\) \(4\) $-$ \(q+2q^{5}+4q^{7}-2q^{13}+2q^{17}+4q^{19}+\cdots\)
3312.2.a.q $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(2\) \(4\) $-$ \(q+2q^{5}+4q^{7}+2q^{11}-5q^{13}-4q^{17}+\cdots\)
3312.2.a.r $1$ $26.446$ \(\Q\) None None \(0\) \(0\) \(4\) \(-2\) $+$ \(q+4q^{5}-2q^{7}-4q^{11}-5q^{13}+2q^{17}+\cdots\)
3312.2.a.s $2$ $26.446$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-4\) \(0\) $-$ \(q+(-2+\beta )q^{5}+\beta q^{7}+4\beta q^{11}+4\beta q^{13}+\cdots\)
3312.2.a.t $2$ $26.446$ \(\Q(\sqrt{17}) \) None None \(0\) \(0\) \(-4\) \(0\) $-$ \(q-2q^{5}+(2-2\beta )q^{11}+(3-\beta )q^{13}+\cdots\)
3312.2.a.u $2$ $26.446$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-4\) \(4\) $+$ \(q+(-2+\beta )q^{5}+(2+\beta )q^{7}-2\beta q^{11}+\cdots\)
3312.2.a.v $2$ $26.446$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(-2\) \(-4\) $-$ \(q+(-1+\beta )q^{5}-2q^{7}+(-1+\beta )q^{11}+\cdots\)
3312.2.a.w $2$ $26.446$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-2\) \(-4\) $+$ \(q+(-1-\beta )q^{5}-2q^{7}+(1+\beta )q^{11}+\cdots\)
3312.2.a.x $2$ $26.446$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ \(q+(-1+\beta )q^{5}+(1-\beta )q^{7}+(-2+2\beta )q^{11}+\cdots\)
3312.2.a.y $2$ $26.446$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(0\) \(-4\) $+$ \(q+\beta q^{5}+(-2-\beta )q^{7}+4q^{13}+(-4+\cdots)q^{17}+\cdots\)
3312.2.a.z $2$ $26.446$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(2\) \(-4\) $+$ \(q+(1+\beta )q^{5}-2q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots\)
3312.2.a.ba $2$ $26.446$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(-2\) $-$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(-3+\beta )q^{11}+\cdots\)
3312.2.a.bb $2$ $26.446$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(-2\) $-$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+4q^{11}+\cdots\)
3312.2.a.bc $2$ $26.446$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ \(q+(1+\beta )q^{5}-2\beta q^{7}+(-3+\beta )q^{11}+\cdots\)
3312.2.a.bd $2$ $26.446$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(2\) $-$ \(q+(1+\beta )q^{5}+(1+\beta )q^{7}+(2+2\beta )q^{11}+\cdots\)
3312.2.a.be $2$ $26.446$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(4\) \(4\) $-$ \(q+(2+\beta )q^{5}+(2-\beta )q^{7}-2\beta q^{11}+(6+\cdots)q^{17}+\cdots\)
3312.2.a.bf $3$ $26.446$ 3.3.148.1 None None \(0\) \(0\) \(0\) \(-2\) $-$ \(q-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
3312.2.a.bg $4$ $26.446$ 4.4.44688.2 None None \(0\) \(0\) \(-4\) \(-2\) $+$ \(q+(-1-\beta _{2})q^{5}+\beta _{1}q^{7}+(\beta _{2}-\beta _{3})q^{11}+\cdots\)
3312.2.a.bh $4$ $26.446$ 4.4.44688.2 None None \(0\) \(0\) \(4\) \(-2\) $-$ \(q+(1+\beta _{2})q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3312.2.e.a $2$ $26.446$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta q^{5}+2\beta q^{7}-4q^{11}-4q^{13}+3\beta q^{17}+\cdots\)
3312.2.e.b $2$ $26.446$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+2\beta q^{5}-\beta q^{7}-2q^{11}+2q^{13}-5\beta q^{19}+\cdots\)
3312.2.e.c $2$ $26.446$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+3\beta q^{7}-2q^{11}+2q^{13}+2\beta q^{17}+\cdots\)
3312.2.e.d $2$ $26.446$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-3\beta q^{7}+2q^{11}+2q^{13}+2\beta q^{17}+\cdots\)
3312.2.e.e $2$ $26.446$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+2\beta q^{5}+\beta q^{7}+2q^{11}+2q^{13}+5\beta q^{19}+\cdots\)
3312.2.e.f $2$ $26.446$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q+\beta q^{5}-2\beta q^{7}+4q^{11}-4q^{13}+3\beta q^{17}+\cdots\)
3312.2.e.g $16$ $26.446$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{3}q^{5}-\beta _{8}q^{7}+\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)
3312.2.e.h $16$ $26.446$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ \(q-\beta _{3}q^{5}+\beta _{8}q^{7}-\beta _{10}q^{11}+(-1+\cdots)q^{13}+\cdots\)
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