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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1472.1.f.a 1472.f 23.b $1$ $0.735$ \(\Q\) \(\Q(\sqrt{-23}) \) None 23.1.b.a \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{13}-q^{23}+q^{25}+q^{27}+\cdots\)
1472.1.f.b 1472.f 23.b $1$ $0.735$ \(\Q\) \(\Q(\sqrt{-23}) \) None 23.1.b.a \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{13}+q^{23}+q^{25}-q^{27}+\cdots\)
1472.1.k.a 1472.k 368.k $2$ $0.735$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-23}) \) None 368.1.k.a \(0\) \(-2\) \(0\) \(0\) \(q+(-1-i)q^{3}+iq^{9}+(-1-i)q^{13}+\cdots\)
1472.1.k.b 1472.k 368.k $4$ $0.735$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-23}) \) None 368.1.k.b \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{3}+(\zeta_{12}^{2}-\zeta_{12}^{3}+\cdots)q^{9}+\cdots\)
1472.1.s.a 1472.s 1472.s $8$ $0.735$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-23}) \) None 1472.1.s.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}q^{2}+(\zeta_{16}-\zeta_{16}^{4})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)
1472.1.s.b 1472.s 1472.s $16$ $0.735$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-23}) \) None 1472.1.s.b \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{48}q^{2}+(-\zeta_{48}^{4}+\zeta_{48}^{17})q^{3}+\cdots\)
1472.2.a.a 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.d \(0\) \(-3\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots\)
1472.2.a.b 1472.a 1.a $1$ $11.754$ \(\Q\) None None 92.2.a.a \(0\) \(-3\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{5}+4q^{7}+6q^{9}+2q^{11}+\cdots\)
1472.2.a.c 1472.a 1.a $1$ $11.754$ \(\Q\) None None 92.2.a.b \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots\)
1472.2.a.d 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.b \(0\) \(-1\) \(2\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+4q^{7}-2q^{9}-2q^{11}+\cdots\)
1472.2.a.e 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.a \(0\) \(-1\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
1472.2.a.f 1472.a 1.a $1$ $11.754$ \(\Q\) None None 46.2.a.a \(0\) \(0\) \(-4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-4q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots\)
1472.2.a.g 1472.a 1.a $1$ $11.754$ \(\Q\) None None 46.2.a.a \(0\) \(0\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+4q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
1472.2.a.h 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.c \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-3q^{9}+6q^{11}+2q^{13}+6q^{17}+\cdots\)
1472.2.a.i 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.c \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}-6q^{11}+2q^{13}+6q^{17}+\cdots\)
1472.2.a.j 1472.a 1.a $1$ $11.754$ \(\Q\) None None 92.2.a.b \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots\)
1472.2.a.k 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.b \(0\) \(1\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-4q^{7}-2q^{9}+2q^{11}+\cdots\)
1472.2.a.l 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.a \(0\) \(1\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
1472.2.a.m 1472.a 1.a $1$ $11.754$ \(\Q\) None None 184.2.a.d \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots\)
1472.2.a.n 1472.a 1.a $1$ $11.754$ \(\Q\) None None 92.2.a.a \(0\) \(3\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{5}-4q^{7}+6q^{9}-2q^{11}+\cdots\)
1472.2.a.o 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{2}) \) None None 736.2.a.a \(0\) \(-2\) \(4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
1472.2.a.p 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{17}) \) None None 184.2.a.e \(0\) \(-1\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
1472.2.a.q 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{3}) \) None None 736.2.a.b \(0\) \(0\) \(-2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
1472.2.a.r 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{3}) \) None None 736.2.a.b \(0\) \(0\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}+(3+\beta )q^{7}+(-3+\cdots)q^{11}+\cdots\)
1472.2.a.s 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{5}) \) None None 23.2.a.a \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+(-1-\beta )q^{7}+2q^{9}+\cdots\)
1472.2.a.t 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{5}) \) None None 23.2.a.a \(0\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots\)
1472.2.a.u 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{17}) \) None None 184.2.a.e \(0\) \(1\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
1472.2.a.v 1472.a 1.a $2$ $11.754$ \(\Q(\sqrt{2}) \) None None 736.2.a.a \(0\) \(2\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(2+\beta )q^{7}+\cdots\)
1472.2.a.w 1472.a 1.a $3$ $11.754$ 3.3.316.1 None None 736.2.a.e \(0\) \(-4\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1472.2.a.x 1472.a 1.a $3$ $11.754$ 3.3.316.1 None None 736.2.a.e \(0\) \(4\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
1472.2.a.y 1472.a 1.a $4$ $11.754$ 4.4.13768.1 None None 736.2.a.g \(0\) \(-2\) \(-6\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1472.2.a.z 1472.a 1.a $4$ $11.754$ 4.4.13768.1 None None 736.2.a.g \(0\) \(2\) \(-6\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots\)
1472.2.b.a 1472.b 8.b $6$ $11.754$ 6.0.399424.1 None None 1472.2.b.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1472.2.b.b 1472.b 8.b $6$ $11.754$ 6.0.399424.1 None None 1472.2.b.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(\beta _{3}+\beta _{5})q^{5}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1472.2.b.c 1472.b 8.b $16$ $11.754$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 1472.2.b.c \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{11}q^{5}-\beta _{9}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
1472.2.b.d 1472.b 8.b $16$ $11.754$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 1472.2.b.c \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{11}q^{5}+\beta _{9}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
1472.2.c.a 1472.c 92.b $4$ $11.754$ \(\Q(\sqrt{2}, \sqrt{-5})\) None None 368.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}-2q^{9}+3\beta _{1}q^{11}+\cdots\)
1472.2.c.b 1472.c 92.b $4$ $11.754$ \(\Q(i, \sqrt{14})\) None None 92.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+2q^{9}-\beta _{3}q^{11}+\cdots\)
1472.2.c.c 1472.c 92.b $6$ $11.754$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None 92.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}+(-3-\beta _{2})q^{9}+(-\beta _{2}-\beta _{4}+\cdots)q^{13}+\cdots\)
1472.2.c.d 1472.c 92.b $8$ $11.754$ 8.0.303595776.1 None None 368.2.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{6}q^{7}+\beta _{7}q^{9}+\cdots\)
1472.2.c.e 1472.c 92.b $24$ $11.754$ None None 736.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1472.2.h.a 1472.h 184.h $8$ $11.754$ 8.0.\(\cdots\).3 \(\Q(\sqrt{-46}) \) None 1472.2.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{5}-3q^{9}-\beta _{4}q^{11}+\beta _{7}q^{19}+\cdots\)
1472.2.h.b 1472.h 184.h $8$ $11.754$ 8.0.157351936.1 None None 1472.2.h.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+\beta _{3}q^{5}+\beta _{7}q^{7}+4q^{9}-\beta _{5}q^{11}+\cdots\)
1472.2.h.c 1472.h 184.h $32$ $11.754$ None None 1472.2.h.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1472.2.i.a 1472.i 368.i $12$ $11.754$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) None 368.2.i.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{3}q^{3}+(-3\beta _{1}-\beta _{3}+\beta _{4}+\beta _{11})q^{9}+\cdots\)
1472.2.i.b 1472.i 368.i $80$ $11.754$ None None 368.2.i.b \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1472.2.j.a 1472.j 16.e $2$ $11.754$ \(\Q(\sqrt{-1}) \) None None 368.2.j.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+4iq^{7}+iq^{9}+(-4+\cdots)q^{11}+\cdots\)
1472.2.j.b 1472.j 16.e $4$ $11.754$ \(\Q(\zeta_{12})\) None None 368.2.j.b \(0\) \(6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
1472.2.j.c 1472.j 16.e $12$ $11.754$ 12.0.\(\cdots\).1 None None 368.2.j.c \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{2}+\beta _{3}+\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\)
1472.2.j.d 1472.j 16.e $24$ $11.754$ None None 368.2.j.d \(0\) \(4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
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