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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1690.2.a.a 1690.a 1.a $1$ $13.495$ \(\Q\) None \(-1\) \(-2\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}-q^{7}+\cdots\)
1690.2.a.b 1690.a 1.a $1$ $13.495$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
1690.2.a.c 1690.a 1.a $1$ $13.495$ \(\Q\) None \(-1\) \(0\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}-3q^{9}+\cdots\)
1690.2.a.d 1690.a 1.a $1$ $13.495$ \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots\)
1690.2.a.e 1690.a 1.a $1$ $13.495$ \(\Q\) None \(-1\) \(2\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}+4q^{7}+\cdots\)
1690.2.a.f 1690.a 1.a $1$ $13.495$ \(\Q\) None \(1\) \(-2\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+4q^{7}+\cdots\)
1690.2.a.g 1690.a 1.a $1$ $13.495$ \(\Q\) None \(1\) \(-2\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
1690.2.a.h 1690.a 1.a $1$ $13.495$ \(\Q\) None \(1\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}-3q^{9}+\cdots\)
1690.2.a.i 1690.a 1.a $1$ $13.495$ \(\Q\) None \(1\) \(2\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
1690.2.a.j 1690.a 1.a $2$ $13.495$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(6\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
1690.2.a.k 1690.a 1.a $2$ $13.495$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+q^{7}+\cdots\)
1690.2.a.l 1690.a 1.a $2$ $13.495$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
1690.2.a.m 1690.a 1.a $2$ $13.495$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
1690.2.a.n 1690.a 1.a $2$ $13.495$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots\)
1690.2.a.o 1690.a 1.a $2$ $13.495$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(1+\beta )q^{6}+\cdots\)
1690.2.a.p 1690.a 1.a $3$ $13.495$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-1\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1690.2.a.q 1690.a 1.a $3$ $13.495$ \(\Q(\zeta_{14})^+\) None \(-3\) \(1\) \(3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1690.2.a.r 1690.a 1.a $3$ $13.495$ \(\Q(\zeta_{14})^+\) None \(3\) \(-1\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
1690.2.a.s 1690.a 1.a $3$ $13.495$ \(\Q(\zeta_{14})^+\) None \(3\) \(1\) \(-3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
1690.2.a.t 1690.a 1.a $4$ $13.495$ 4.4.4752.1 None \(-4\) \(2\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+q^{4}-q^{5}+\cdots\)
1690.2.a.u 1690.a 1.a $4$ $13.495$ 4.4.4752.1 None \(4\) \(2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)
1690.2.a.v 1690.a 1.a $6$ $13.495$ 6.6.20439713.1 None \(-6\) \(-2\) \(-6\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
1690.2.a.w 1690.a 1.a $6$ $13.495$ 6.6.20439713.1 None \(6\) \(-2\) \(6\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1690.2.b.a 1690.b 5.b $6$ $13.495$ 6.0.3534400.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(\beta _{3}-\beta _{4})q^{3}-q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
1690.2.b.b 1690.b 5.b $6$ $13.495$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(\beta _{1}+\beta _{4})q^{5}+\cdots\)
1690.2.b.c 1690.b 5.b $6$ $13.495$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+(-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
1690.2.b.d 1690.b 5.b $8$ $13.495$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{2}q^{3}-q^{4}+(\beta _{4}-\beta _{7})q^{5}+\cdots\)
1690.2.b.e 1690.b 5.b $16$ $13.495$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}+\beta _{12}q^{3}-q^{4}-\beta _{10}q^{5}+\cdots\)
1690.2.b.f 1690.b 5.b $18$ $13.495$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(\beta _{4}-\beta _{15})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
1690.2.b.g 1690.b 5.b $18$ $13.495$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{4}-\beta _{15})q^{3}-q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
1690.2.c.a 1690.c 65.d $6$ $13.495$ 6.0.3534400.1 None \(-6\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(-\beta _{2}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
1690.2.c.b 1690.c 65.d $6$ $13.495$ 6.0.350464.1 None \(-6\) \(0\) \(2\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{5}q^{3}+q^{4}+(-\beta _{2}+\beta _{5})q^{5}+\cdots\)
1690.2.c.c 1690.c 65.d $6$ $13.495$ 6.0.350464.1 None \(6\) \(0\) \(-2\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\beta _{5}q^{3}+q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
1690.2.c.d 1690.c 65.d $6$ $13.495$ 6.0.3534400.1 None \(6\) \(0\) \(4\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(-\beta _{2}+\beta _{3})q^{3}+q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
1690.2.c.e 1690.c 65.d $8$ $13.495$ 8.0.\(\cdots\).1 None \(-8\) \(0\) \(-3\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
1690.2.c.f 1690.c 65.d $8$ $13.495$ 8.0.\(\cdots\).1 None \(8\) \(0\) \(3\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)
1690.2.c.g 1690.c 65.d $18$ $13.495$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-18\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+(\beta _{4}-\beta _{15})q^{3}+q^{4}+(\beta _{6}+\beta _{10}+\cdots)q^{5}+\cdots\)
1690.2.c.h 1690.c 65.d $18$ $13.495$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(18\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(\beta _{4}-\beta _{15})q^{3}+q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
1690.2.d.a 1690.d 13.b $2$ $13.495$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{3}-q^{4}+iq^{5}-2iq^{6}+\cdots\)
1690.2.d.b 1690.d 13.b $2$ $13.495$ \(\Q(\sqrt{-1}) \) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{3}-q^{4}-iq^{5}-2iq^{6}+\cdots\)
1690.2.d.c 1690.d 13.b $2$ $13.495$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}+3iq^{7}-iq^{8}+\cdots\)
1690.2.d.d 1690.d 13.b $2$ $13.495$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+iq^{5}-iq^{8}-3q^{9}+\cdots\)
1690.2.d.e 1690.d 13.b $2$ $13.495$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2q^{3}-q^{4}-iq^{5}+2iq^{6}+\cdots\)
1690.2.d.f 1690.d 13.b $4$ $13.495$ \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}+(-1+\zeta_{12}^{3})q^{3}-q^{4}+\cdots\)
1690.2.d.g 1690.d 13.b $4$ $13.495$ \(\Q(i, \sqrt{10})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
1690.2.d.h 1690.d 13.b $4$ $13.495$ \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}+(1+\zeta_{12}^{3})q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots\)
1690.2.d.i 1690.d 13.b $6$ $13.495$ 6.0.153664.1 None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{2}q^{3}-q^{4}-\beta _{5}q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)
1690.2.d.j 1690.d 13.b $6$ $13.495$ 6.0.153664.1 None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{4}q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{1}q^{6}+\cdots\)
1690.2.d.k 1690.d 13.b $8$ $13.495$ 8.0.22581504.2 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{3}q^{6}+\cdots\)
1690.2.d.l 1690.d 13.b $12$ $13.495$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{5}+\beta _{8})q^{3}-q^{4}+\cdots\)
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