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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1122.2.a.a 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.a \(-1\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
1122.2.a.b 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.b \(-1\) \(-1\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.c 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.c \(-1\) \(-1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.d 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.d \(-1\) \(1\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.e 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.e \(1\) \(-1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.f 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.f \(1\) \(-1\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.g 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.g \(1\) \(-1\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.h 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.h \(1\) \(-1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
1122.2.a.i 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.i \(1\) \(1\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
1122.2.a.j 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.j \(1\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.k 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.k \(1\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.l 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.l \(1\) \(1\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.m 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.m \(1\) \(1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.n 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.n \(1\) \(1\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.o 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{5}) \) None 1122.2.a.o \(-2\) \(-2\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
1122.2.a.p 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{2}) \) None 1122.2.a.p \(-2\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1122.2.a.q 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{2}) \) None 1122.2.a.q \(-2\) \(2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
1122.2.a.r 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{5}) \) None 1122.2.a.r \(-2\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
1122.2.a.s 1122.a 1.a $3$ $8.959$ 3.3.148.1 None 1122.2.a.s \(3\) \(-3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
1122.2.b.a 1122.b 33.d $16$ $8.959$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1122.2.b.a \(-16\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{9}q^{3}+q^{4}+\beta _{13}q^{5}+\beta _{9}q^{6}+\cdots\)
1122.2.b.b 1122.b 33.d $16$ $8.959$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1122.2.b.b \(-16\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\)
1122.2.b.c 1122.b 33.d $16$ $8.959$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1122.2.b.a \(16\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{9}q^{3}+q^{4}+\beta _{13}q^{5}-\beta _{9}q^{6}+\cdots\)
1122.2.b.d 1122.b 33.d $16$ $8.959$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1122.2.b.b \(16\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
1122.2.c.a 1122.c 17.b $2$ $8.959$ \(\Q(\sqrt{-1}) \) None 1122.2.c.a \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-iq^{3}+q^{4}+4iq^{5}+iq^{6}+\cdots\)
1122.2.c.b 1122.c 17.b $2$ $8.959$ \(\Q(\sqrt{-1}) \) None 1122.2.c.b \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+iq^{3}+q^{4}-iq^{6}-q^{8}-q^{9}+\cdots\)
1122.2.c.c 1122.c 17.b $2$ $8.959$ \(\Q(\sqrt{-1}) \) None 1122.2.c.c \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-iq^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
1122.2.c.d 1122.c 17.b $2$ $8.959$ \(\Q(\sqrt{-1}) \) None 1122.2.c.d \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-iq^{3}+q^{4}+2iq^{5}-iq^{6}+\cdots\)
1122.2.c.e 1122.c 17.b $4$ $8.959$ \(\Q(i, \sqrt{13})\) None 1122.2.c.e \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1122.2.c.f 1122.c 17.b $4$ $8.959$ \(\Q(\zeta_{8})\) None 1122.2.c.f \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\zeta_{8}q^{3}+q^{4}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
1122.2.c.g 1122.c 17.b $6$ $8.959$ 6.0.419904.1 None 1122.2.c.g \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
1122.2.c.h 1122.c 17.b $10$ $8.959$ 10.0.\(\cdots\).1 None 1122.2.c.h \(-10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-\beta _{1}+\beta _{7})q^{5}+\cdots\)
1122.2.h.a 1122.h 561.h $2$ $8.959$ \(\Q(\sqrt{-2}) \) None 1122.2.h.a \(-2\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1122.2.h.b 1122.h 561.h $2$ $8.959$ \(\Q(\sqrt{-2}) \) None 1122.2.h.a \(-2\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1122.2.h.c 1122.h 561.h $2$ $8.959$ \(\Q(\sqrt{-2}) \) None 1122.2.h.a \(2\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1122.2.h.d 1122.h 561.h $2$ $8.959$ \(\Q(\sqrt{-2}) \) None 1122.2.h.a \(2\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1122.2.h.e 1122.h 561.h $4$ $8.959$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 1122.2.h.e \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}-2\beta _{2}q^{7}+\cdots\)
1122.2.h.f 1122.h 561.h $4$ $8.959$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 1122.2.h.e \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{2}q^{6}-2\beta _{2}q^{7}+\cdots\)
1122.2.h.g 1122.h 561.h $28$ $8.959$ None 1122.2.h.g \(-28\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1122.2.h.h 1122.h 561.h $28$ $8.959$ None 1122.2.h.g \(28\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1122.2.l.a 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None 1122.2.l.a \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.b 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None 1122.2.l.b \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.c 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None 1122.2.l.c \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1122.2.l.d 1122.l 17.c $4$ $8.959$ \(\Q(\zeta_{8})\) None 1122.2.l.d \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+(2+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1122.2.l.e 1122.l 17.c $12$ $8.959$ 12.0.\(\cdots\).1 None 1122.2.l.e \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1122.2.l.f 1122.l 17.c $16$ $8.959$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 1122.2.l.f \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{10}q^{2}-\beta _{6}q^{3}-q^{4}+\beta _{15}q^{5}+\cdots\)
1122.2.l.g 1122.l 17.c $20$ $8.959$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 1122.2.l.g \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{8}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
1122.3.d.a 1122.d 187.b $72$ $30.572$ None 1122.3.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1122.3.f.a 1122.f 11.b $64$ $30.572$ None 1122.3.f.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1122.4.a.a 1122.a 1.a $1$ $66.200$ \(\Q\) None 1122.4.a.a \(-2\) \(-3\) \(-18\) \(26\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-18q^{5}+6q^{6}+\cdots\)
1122.4.a.b 1122.a 1.a $3$ $66.200$ 3.3.2636.1 None 1122.4.a.b \(6\) \(9\) \(-20\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(-6+\beta _{1}+2\beta _{2})q^{5}+\cdots\)
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