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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1248.1.b.a 1248.b 312.b $4$ $0.623$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-39}) \) None 312.1.b.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{9}+\cdots\)
1248.1.l.a 1248.l 39.d $4$ $0.623$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{39}) \) 1248.1.l.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
1248.1.bs.a 1248.bs 39.i $8$ $0.623$ \(\Q(\zeta_{24})\) None None 1248.1.bs.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{3}-\zeta_{24}^{6}q^{5}+(\zeta_{24}+\zeta_{24}^{7}+\cdots)q^{7}+\cdots\)
1248.1.cm.a 1248.cm 1248.bm $16$ $0.623$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-39}) \) None 1248.1.cm.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{10}q^{3}+\zeta_{32}^{6}q^{4}+\cdots\)
1248.2.a.a 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.a \(0\) \(-1\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-2q^{7}+q^{9}+6q^{11}+\cdots\)
1248.2.a.b 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.b \(0\) \(-1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+4q^{11}+q^{13}+\cdots\)
1248.2.a.c 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.c \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+q^{13}+2q^{17}+\cdots\)
1248.2.a.d 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.d \(0\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1248.2.a.e 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.e \(0\) \(-1\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-2q^{7}+q^{9}+2q^{11}+\cdots\)
1248.2.a.f 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.b \(0\) \(1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-4q^{11}+q^{13}+\cdots\)
1248.2.a.g 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.a \(0\) \(1\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+2q^{7}+q^{9}-6q^{11}+\cdots\)
1248.2.a.h 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.d \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
1248.2.a.i 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.c \(0\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}+q^{9}+q^{13}+2q^{17}+\cdots\)
1248.2.a.j 1248.a 1.a $1$ $9.965$ \(\Q\) None None 1248.2.a.e \(0\) \(1\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
1248.2.a.k 1248.a 1.a $2$ $9.965$ \(\Q(\sqrt{5}) \) None None 1248.2.a.k \(0\) \(-2\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+(3-\beta )q^{7}+q^{9}+\cdots\)
1248.2.a.l 1248.a 1.a $2$ $9.965$ \(\Q(\sqrt{5}) \) None None 1248.2.a.l \(0\) \(-2\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+(-1-\beta )q^{7}+q^{9}+\cdots\)
1248.2.a.m 1248.a 1.a $2$ $9.965$ \(\Q(\sqrt{5}) \) None None 1248.2.a.k \(0\) \(2\) \(-2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
1248.2.a.n 1248.a 1.a $2$ $9.965$ \(\Q(\sqrt{5}) \) None None 1248.2.a.l \(0\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}+(1+\beta )q^{7}+q^{9}+\cdots\)
1248.2.a.o 1248.a 1.a $3$ $9.965$ 3.3.148.1 None None 1248.2.a.o \(0\) \(-3\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta _{1})q^{5}+\beta _{2}q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1248.2.a.p 1248.a 1.a $3$ $9.965$ 3.3.148.1 None None 1248.2.a.o \(0\) \(3\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
1248.2.c.a 1248.c 13.b $6$ $9.965$ 6.0.153664.1 None None 1248.2.c.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
1248.2.c.b 1248.c 13.b $6$ $9.965$ 6.0.153664.1 None None 1248.2.c.a \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1248.2.c.c 1248.c 13.b $8$ $9.965$ 8.0.134560000.4 None None 1248.2.c.c \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta _{1}q^{5}-\beta _{6}q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1248.2.c.d 1248.c 13.b $8$ $9.965$ 8.0.134560000.4 None None 1248.2.c.c \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta _{1}q^{5}+\beta _{6}q^{7}+q^{9}+(\beta _{1}+\beta _{3}+\cdots)q^{11}+\cdots\)
1248.2.d.a 1248.d 12.b $4$ $9.965$ \(\Q(\zeta_{8})\) None None 1248.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+(\zeta_{8}-\zeta_{8}^{2})q^{7}+(1+\zeta_{8}^{3})q^{9}+\cdots\)
1248.2.d.b 1248.d 12.b $8$ $9.965$ \(\Q(\zeta_{24})\) None None 1248.2.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{6}q^{3}+\zeta_{24}^{2}q^{5}+\zeta_{24}^{5}q^{7}+\cdots\)
1248.2.d.c 1248.d 12.b $16$ $9.965$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 1248.2.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}-\beta _{4}q^{5}-\beta _{2}q^{7}+(-1-\beta _{4}+\cdots)q^{9}+\cdots\)
1248.2.d.d 1248.d 12.b $20$ $9.965$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None 1248.2.d.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+\beta _{15}q^{5}+\beta _{7}q^{7}-\beta _{16}q^{9}+\cdots\)
1248.2.g.a 1248.g 8.b $8$ $9.965$ \(\Q(\zeta_{20})\) None None 312.2.g.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{20}q^{3}+(-\zeta_{20}+\zeta_{20}^{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1248.2.g.b 1248.g 8.b $16$ $9.965$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 312.2.g.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+\beta _{12}q^{5}-\beta _{5}q^{7}-q^{9}+\beta _{10}q^{11}+\cdots\)
1248.2.h.a 1248.h 312.h $8$ $9.965$ 8.0.\(\cdots\).21 \(\Q(\sqrt{-39}) \) None 312.2.h.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+3q^{9}+(-\beta _{3}+\beta _{6}+\cdots)q^{11}+\cdots\)
1248.2.h.b 1248.h 312.h $12$ $9.965$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) \(\Q(\sqrt{-26}) \) None 312.2.h.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{5}q^{3}+\beta _{9}q^{5}+(-\beta _{1}+\beta _{11})q^{7}+\cdots\)
1248.2.h.c 1248.h 312.h $32$ $9.965$ None None 312.2.h.c \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1248.2.j.a 1248.j 24.f $48$ $9.965$ None None 312.2.j.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1248.2.m.a 1248.m 104.e $2$ $9.965$ \(\Q(\sqrt{-1}) \) None None 312.2.m.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}-2q^{5}-q^{9}+4q^{11}+(3-2i)q^{13}+\cdots\)
1248.2.m.b 1248.m 104.e $2$ $9.965$ \(\Q(\sqrt{-1}) \) None None 312.2.m.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{5}-q^{9}-4q^{11}+(-3+\cdots)q^{13}+\cdots\)
1248.2.m.c 1248.m 104.e $24$ $9.965$ None None 312.2.m.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1248.2.n.a 1248.n 156.h $4$ $9.965$ \(\Q(\zeta_{8})\) None None 1248.2.n.a \(0\) \(-4\) \(-8\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{8}^{2})q^{3}+(-2+\zeta_{8}^{3})q^{5}+\cdots\)
1248.2.n.b 1248.n 156.h $4$ $9.965$ \(\Q(\zeta_{8})\) None None 1248.2.n.a \(0\) \(-4\) \(8\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\zeta_{8}^{2})q^{3}+(2+\zeta_{8}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1248.2.n.c 1248.n 156.h $4$ $9.965$ \(\Q(\zeta_{8})\) None None 1248.2.n.a \(0\) \(4\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{8}^{2})q^{3}+(-2+\zeta_{8}^{3})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1248.2.n.d 1248.n 156.h $4$ $9.965$ \(\Q(\zeta_{8})\) None None 1248.2.n.a \(0\) \(4\) \(8\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\zeta_{8}^{2})q^{3}+(2-\zeta_{8}^{3})q^{5}+(2-\zeta_{8}^{3})q^{7}+\cdots\)
1248.2.n.e 1248.n 156.h $40$ $9.965$ None None 1248.2.n.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1248.2.q.a 1248.q 13.c $2$ $9.965$ \(\Q(\sqrt{-3}) \) None None 1248.2.q.a \(0\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+(6+\cdots)q^{11}+\cdots\)
1248.2.q.b 1248.q 13.c $2$ $9.965$ \(\Q(\sqrt{-3}) \) None None 1248.2.q.b \(0\) \(-1\) \(6\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+3q^{5}+2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.c 1248.q 13.c $2$ $9.965$ \(\Q(\sqrt{-3}) \) None None 1248.2.q.c \(0\) \(-1\) \(8\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+4q^{5}-3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.d 1248.q 13.c $2$ $9.965$ \(\Q(\sqrt{-3}) \) None None 1248.2.q.a \(0\) \(1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+(-6+\cdots)q^{11}+\cdots\)
1248.2.q.e 1248.q 13.c $2$ $9.965$ \(\Q(\sqrt{-3}) \) None None 1248.2.q.b \(0\) \(1\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3q^{5}-2\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.f 1248.q 13.c $2$ $9.965$ \(\Q(\sqrt{-3}) \) None None 1248.2.q.c \(0\) \(1\) \(8\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+4q^{5}+3\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1248.2.q.g 1248.q 13.c $4$ $9.965$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None 1248.2.q.g \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1248.2.q.h 1248.q 13.c $4$ $9.965$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None 1248.2.q.h \(0\) \(-2\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{3}+\beta _{3}q^{5}+(\beta _{1}-3\beta _{2}+\cdots)q^{7}+\cdots\)
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