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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1650.2.a.a 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.b 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.c 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.d 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.e 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-4q^{7}-q^{8}+\cdots\)
1650.2.a.f 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
1650.2.a.g 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1650.2.a.h 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
1650.2.a.i 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.j 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
1650.2.a.k 1650.a 1.a $1$ $13.175$ \(\Q\) None \(-1\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
1650.2.a.l 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.m 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.n 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.o 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1650.2.a.p 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.q 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
1650.2.a.r 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
1650.2.a.s 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
1650.2.a.t 1650.a 1.a $1$ $13.175$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+4q^{7}+q^{8}+\cdots\)
1650.2.a.u 1650.a 1.a $2$ $13.175$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.v 1650.a 1.a $2$ $13.175$ \(\Q(\sqrt{73}) \) None \(-2\) \(-2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
1650.2.a.w 1650.a 1.a $2$ $13.175$ \(\Q(\sqrt{10}) \) None \(-2\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
1650.2.a.x 1650.a 1.a $2$ $13.175$ \(\Q(\sqrt{10}) \) None \(2\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-2+\beta )q^{7}+\cdots\)
1650.2.a.y 1650.a 1.a $2$ $13.175$ \(\Q(\sqrt{73}) \) None \(2\) \(2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-\beta q^{7}+q^{8}+\cdots\)
1650.2.a.z 1650.a 1.a $2$ $13.175$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta )q^{7}+\cdots\)
1650.2.c.a 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.b 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
1650.2.c.c 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.d 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.e 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1650.2.c.f 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
1650.2.c.g 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.h 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1650.2.c.i 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
1650.2.c.j 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1650.2.c.k 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
1650.2.c.l 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
1650.2.c.m 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.n 1650.c 5.b $2$ $13.175$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1650.2.c.o 1650.c 5.b $4$ $13.175$ \(\Q(i, \sqrt{73})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+q^{6}+\beta _{1}q^{7}+\cdots\)
1650.2.d.a 1650.d 33.d $2$ $13.175$ \(\Q(\sqrt{-2}) \) None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1650.2.d.b 1650.d 33.d $2$ $13.175$ \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{6}+\cdots\)
1650.2.d.c 1650.d 33.d $8$ $13.175$ 8.0.2051727616.3 None \(-8\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1650.2.d.d 1650.d 33.d $8$ $13.175$ 8.0.\(\cdots\).1 None \(-8\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.e 1650.d 33.d $8$ $13.175$ 8.0.\(\cdots\).1 None \(-8\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.f 1650.d 33.d $8$ $13.175$ 8.0.2051727616.3 None \(8\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(-\beta _{3}-\beta _{4})q^{3}+q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
1650.2.d.g 1650.d 33.d $8$ $13.175$ 8.0.\(\cdots\).1 None \(8\) \(-1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.h 1650.d 33.d $8$ $13.175$ 8.0.\(\cdots\).1 None \(8\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{4}q^{3}+q^{4}-\beta _{4}q^{6}-\beta _{7}q^{7}+\cdots\)
1650.2.d.i 1650.d 33.d $12$ $13.175$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-\beta _{3}q^{7}+\cdots\)
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