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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3456.1.b.a 3456.b 8.d $4$ $1.725$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{3}q^{5}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{7}+\cdots\)
3456.1.e.a 3456.e 3.b $2$ $1.725$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{5}-q^{7}-\beta q^{11}-q^{13}-\beta q^{17}+\cdots\)
3456.1.e.b 3456.e 3.b $2$ $1.725$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{5}-q^{7}-\beta q^{11}+q^{13}+\beta q^{17}+\cdots\)
3456.1.e.c 3456.e 3.b $2$ $1.725$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{5}+q^{7}-\beta q^{11}-q^{13}+\beta q^{17}+\cdots\)
3456.1.e.d 3456.e 3.b $2$ $1.725$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(2\) \(q-\beta q^{5}+q^{7}-\beta q^{11}+q^{13}-\beta q^{17}+\cdots\)
3456.1.h.a 3456.h 24.h $2$ $1.725$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-\beta q^{7}-q^{11}+2q^{25}+\beta q^{31}+\cdots\)
3456.1.h.b 3456.h 24.h $2$ $1.725$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{5}-\beta q^{7}+q^{11}+2q^{25}+\beta q^{31}+\cdots\)
3456.1.j.a 3456.j 48.i $4$ $1.725$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}q^{11}+(1+\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
3456.1.j.b 3456.j 48.i $4$ $1.725$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}-\zeta_{8}q^{11}+(1+\zeta_{8}^{2}+\cdots)q^{13}+\cdots\)
3456.1.n.a 3456.n 72.j $2$ $1.725$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{11}+(-\zeta_{6}-\zeta_{6}^{2})q^{17}+(-\zeta_{6}+\cdots)q^{19}+\cdots\)
3456.1.n.b 3456.n 72.j $2$ $1.725$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{11}+(-\zeta_{6}-\zeta_{6}^{2})q^{17}+(\zeta_{6}+\cdots)q^{19}+\cdots\)
3456.1.t.a 3456.t 72.p $4$ $1.725$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{11}-q^{17}+(\zeta_{12}+\cdots)q^{19}+\cdots\)
3456.1.bh.a 3456.bh 216.r $12$ $1.725$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}q^{3}+\zeta_{36}^{2}q^{9}+(\zeta_{36}^{5}+\zeta_{36}^{15}+\cdots)q^{11}+\cdots\)
3456.1.bn.a 3456.bn 216.x $6$ $1.725$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{4}q^{3}+\zeta_{18}^{8}q^{9}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{11}+\cdots\)
3456.1.bn.b 3456.bn 216.x $6$ $1.725$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{4}q^{3}+\zeta_{18}^{8}q^{9}+(-\zeta_{18}^{2}-\zeta_{18}^{6}+\cdots)q^{11}+\cdots\)
3456.2.a.a 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-5q^{7}-q^{11}-6q^{13}-6q^{17}+\cdots\)
3456.2.a.b 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-5q^{7}-q^{11}+6q^{13}+6q^{17}+\cdots\)
3456.2.a.c 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+5q^{7}+q^{11}-6q^{13}-6q^{17}+\cdots\)
3456.2.a.d 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+5q^{7}+q^{11}+6q^{13}+6q^{17}+\cdots\)
3456.2.a.e 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+q^{11}-2q^{13}+2q^{17}+\cdots\)
3456.2.a.f 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+q^{11}+2q^{13}-2q^{17}+\cdots\)
3456.2.a.g 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-q^{11}-2q^{13}+2q^{17}+\cdots\)
3456.2.a.h 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-q^{11}+2q^{13}-2q^{17}+\cdots\)
3456.2.a.i 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-q^{11}-2q^{13}-2q^{17}+\cdots\)
3456.2.a.j 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-q^{11}+2q^{13}+2q^{17}+\cdots\)
3456.2.a.k 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+q^{11}-2q^{13}-2q^{17}+\cdots\)
3456.2.a.l 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+q^{11}+2q^{13}+2q^{17}+\cdots\)
3456.2.a.m 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(3\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-5q^{7}+q^{11}-6q^{13}+6q^{17}+\cdots\)
3456.2.a.n 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-5q^{7}+q^{11}+6q^{13}-6q^{17}+\cdots\)
3456.2.a.o 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+5q^{7}-q^{11}-6q^{13}+6q^{17}+\cdots\)
3456.2.a.p 3456.a 1.a $1$ $27.596$ \(\Q\) None None \(0\) \(0\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+5q^{7}-q^{11}+6q^{13}-6q^{17}+\cdots\)
3456.2.a.q 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(-1-\beta )q^{7}+(1+2\beta )q^{11}+\cdots\)
3456.2.a.r 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(-1+2\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
3456.2.a.s 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(-1+2\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
3456.2.a.t 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(-1-\beta )q^{7}+(1+2\beta )q^{11}+\cdots\)
3456.2.a.u 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}-q^{7}+(3+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
3456.2.a.v 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}-q^{7}+(3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
3456.2.a.w 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+q^{7}+(-3-\beta )q^{11}+\cdots\)
3456.2.a.x 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+q^{7}+(-3-\beta )q^{11}+\cdots\)
3456.2.a.y 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(1+\beta )q^{7}+(-1-2\beta )q^{11}+\cdots\)
3456.2.a.z 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(1-2\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
3456.2.a.ba 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(1-2\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
3456.2.a.bb 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+(1+\beta )q^{7}+(-1-2\beta )q^{11}+\cdots\)
3456.2.a.bc 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+(-1+\cdots)q^{13}+\cdots\)
3456.2.a.bd 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+(1+\cdots)q^{13}+\cdots\)
3456.2.a.be 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(-1+2\beta )q^{11}+\cdots\)
3456.2.a.bf 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1-2\beta )q^{7}+(-1-\beta )q^{11}+\cdots\)
3456.2.a.bg 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1-2\beta )q^{7}+(-1-\beta )q^{11}+\cdots\)
3456.2.a.bh 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1+\beta )q^{7}+(-1+2\beta )q^{11}+\cdots\)
3456.2.a.bi 3456.a 1.a $2$ $27.596$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1-\beta )q^{7}+(1-2\beta )q^{11}+\cdots\)
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