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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2312.1.e.a 2312.e 136.e $2$ $1.154$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}-q^{9}+\cdots\)
2312.1.e.b 2312.e 136.e $4$ $1.154$ 4.0.2048.2 \(\Q(\sqrt{-2}) \) None \(4\) \(0\) \(0\) \(0\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots\)
2312.1.f.a 2312.f 8.d $1$ $1.154$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}-q^{18}+\cdots\)
2312.1.f.b 2312.f 8.d $2$ $1.154$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}+q^{8}+q^{9}+\cdots\)
2312.1.f.c 2312.f 8.d $4$ $1.154$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-2}) \) None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{8}+\cdots\)
2312.1.j.a 2312.j 136.j $2$ $1.154$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{16}+\cdots\)
2312.1.j.b 2312.j 136.j $2$ $1.154$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+iq^{2}+(1-i)q^{3}-q^{4}+(1+i)q^{6}+\cdots\)
2312.1.j.c 2312.j 136.j $8$ $1.154$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{4}q^{2}+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{3}-q^{4}+\cdots\)
2312.1.p.a 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(-1-\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
2312.1.p.b 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
2312.1.p.c 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\)
2312.1.p.d 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8})q^{3}-\zeta_{8}^{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
2312.1.p.e 2312.p 136.p $8$ $1.154$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{6}q^{2}+(-\zeta_{16}^{3}-\zeta_{16}^{7})q^{3}+\cdots\)
2312.1.q.a 2312.q 136.q $16$ $1.154$ \(\Q(\zeta_{32})\) None \(\Q(\sqrt{34}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{2}q^{2}+(-\zeta_{32}^{3}-\zeta_{32}^{11})q^{3}+\cdots\)
2312.1.x.a 2312.x 2312.x $16$ $1.154$ \(\Q(\zeta_{34})\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q-\zeta_{34}q^{2}+(-\zeta_{34}^{5}-\zeta_{34}^{7})q^{3}+\zeta_{34}^{2}q^{4}+\cdots\)
2312.1.y.a 2312.y 2312.y $16$ $1.154$ \(\Q(\zeta_{34})\) \(\Q(\sqrt{-2}) \) None \(1\) \(0\) \(0\) \(0\) \(q+\zeta_{34}^{5}q^{2}+(\zeta_{34}+\zeta_{34}^{8})q^{3}+\zeta_{34}^{10}q^{4}+\cdots\)
2312.1.be.a 2312.be 2312.ae $32$ $1.154$ \(\Q(\zeta_{68})\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{68}^{13}q^{2}+(\zeta_{68}^{14}+\zeta_{68}^{23})q^{3}+\cdots\)
2312.1.bg.a 2312.bg 2312.ag $64$ $1.154$ \(\Q(\zeta_{136})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{136}^{35}q^{2}+(\zeta_{136}^{7}-\zeta_{136}^{22})q^{3}+\cdots\)
2312.2.a.a 2312.a 1.a $1$ $18.461$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}-2q^{11}-6q^{13}+4q^{19}+\cdots\)
2312.2.a.b 2312.a 1.a $1$ $18.461$ \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
2312.2.a.c 2312.a 1.a $1$ $18.461$ \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
2312.2.a.d 2312.a 1.a $1$ $18.461$ \(\Q\) None None \(0\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+2q^{7}+q^{9}+6q^{11}+\cdots\)
2312.2.a.e 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{13}) \) None None \(0\) \(-3\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+\beta q^{5}+\beta q^{7}+(1+3\beta )q^{9}+\cdots\)
2312.2.a.f 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(-1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-3\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
2312.2.a.g 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+\beta q^{7}-3q^{9}-2\beta q^{11}+2q^{13}+\cdots\)
2312.2.a.h 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-3\beta q^{5}-3\beta q^{7}-q^{9}-\beta q^{11}+\cdots\)
2312.2.a.i 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}+\beta q^{7}-q^{9}-\beta q^{11}+\cdots\)
2312.2.a.j 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2\beta q^{5}+2\beta q^{7}-q^{9}-\beta q^{11}+\cdots\)
2312.2.a.k 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+\beta q^{5}-2\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)
2312.2.a.l 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+3\beta )q^{5}+(3-\beta )q^{7}+\cdots\)
2312.2.a.m 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-2q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
2312.2.a.n 2312.a 1.a $2$ $18.461$ \(\Q(\sqrt{13}) \) None None \(0\) \(3\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-\beta q^{5}-\beta q^{7}+(1+3\beta )q^{9}+\cdots\)
2312.2.a.o 2312.a 1.a $3$ $18.461$ \(\Q(\zeta_{18})^+\) None None \(0\) \(-3\) \(-6\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(-1-2\beta _{1}+\beta _{2})q^{3}+(-2-\beta _{1}+\cdots)q^{5}+\cdots\)
2312.2.a.p 2312.a 1.a $3$ $18.461$ \(\Q(\zeta_{18})^+\) None None \(0\) \(-3\) \(6\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(2+\beta _{1}-\beta _{2})q^{5}+\cdots\)
2312.2.a.q 2312.a 1.a $3$ $18.461$ \(\Q(\zeta_{18})^+\) None None \(0\) \(3\) \(-6\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(-2-\beta _{1}+\beta _{2})q^{5}+\cdots\)
2312.2.a.r 2312.a 1.a $3$ $18.461$ \(\Q(\zeta_{18})^+\) None None \(0\) \(3\) \(6\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1+2\beta _{1}-\beta _{2})q^{3}+(2+\beta _{1})q^{5}+(2+\cdots)q^{7}+\cdots\)
2312.2.a.s 2312.a 1.a $4$ $18.461$ \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-2\beta _{1}-\beta _{3})q^{7}+\cdots\)
2312.2.a.t 2312.a 1.a $4$ $18.461$ \(\Q(\zeta_{16})^+\) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3})q^{3}+(-2\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
2312.2.a.u 2312.a 1.a $6$ $18.461$ 6.6.3418281.1 None None \(0\) \(0\) \(-6\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
2312.2.a.v 2312.a 1.a $6$ $18.461$ 6.6.3418281.1 None None \(0\) \(0\) \(6\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}+(\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
2312.2.a.w 2312.a 1.a $12$ $18.461$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{10}q^{5}+\beta _{6}q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots\)
2312.2.b.a 2312.b 17.b $2$ $18.461$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}+\beta q^{5}+2\beta q^{7}-5q^{9}+2\beta q^{11}+\cdots\)
2312.2.b.b 2312.b 17.b $2$ $18.461$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}-iq^{11}-6q^{13}-4q^{19}+\cdots\)
2312.2.b.c 2312.b 17.b $2$ $18.461$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{5}-iq^{7}-q^{9}-3iq^{11}+\cdots\)
2312.2.b.d 2312.b 17.b $2$ $18.461$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+2\beta q^{5}-2\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
2312.2.b.e 2312.b 17.b $2$ $18.461$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
2312.2.b.f 2312.b 17.b $2$ $18.461$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-3\beta q^{5}+3\beta q^{7}+q^{9}+\beta q^{11}+\cdots\)
2312.2.b.g 2312.b 17.b $4$ $18.461$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+(-3+\beta _{3})q^{9}+\cdots\)
2312.2.b.h 2312.b 17.b $4$ $18.461$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{1}q^{7}+(-4+\cdots)q^{9}+\cdots\)
2312.2.b.i 2312.b 17.b $4$ $18.461$ 4.0.2048.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{3})q^{3}+(\beta _{1}-2\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
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