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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1530.2.a.a 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.b 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
1530.2.a.c 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.d 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.e 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.f 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots\)
1530.2.a.g 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.h 1530.a 1.a $1$ $12.217$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
1530.2.a.i 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.j 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.k 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.l 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.m 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.n 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.o 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.p 1530.a 1.a $1$ $12.217$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\)
1530.2.a.q 1530.a 1.a $2$ $12.217$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\)
1530.2.a.r 1530.a 1.a $2$ $12.217$ \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+2\beta q^{7}-q^{8}+q^{10}+\cdots\)
1530.2.a.s 1530.a 1.a $2$ $12.217$ \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\)
1530.2.a.t 1530.a 1.a $2$ $12.217$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\)
1530.2.c.a 1530.c 17.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-iq^{5}+2iq^{7}-q^{8}+iq^{10}+\cdots\)
1530.2.c.b 1530.c 17.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+iq^{5}+4iq^{7}-q^{8}-iq^{10}+\cdots\)
1530.2.c.c 1530.c 17.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-iq^{5}+2iq^{7}-q^{8}+iq^{10}+\cdots\)
1530.2.c.d 1530.c 17.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-iq^{5}+q^{8}-iq^{10}-6iq^{11}+\cdots\)
1530.2.c.e 1530.c 17.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}-iq^{5}+q^{8}-iq^{10}+4iq^{11}+\cdots\)
1530.2.c.f 1530.c 17.b $4$ $12.217$ \(\Q(\zeta_{8})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-\zeta_{8}q^{5}+(2\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots\)
1530.2.c.g 1530.c 17.b $4$ $12.217$ \(\Q(i, \sqrt{13})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
1530.2.c.h 1530.c 17.b $6$ $12.217$ 6.0.5089536.1 None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
1530.2.c.i 1530.c 17.b $6$ $12.217$ 6.0.5089536.1 None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
1530.2.d.a 1530.d 5.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-2+i)q^{5}+iq^{8}+\cdots\)
1530.2.d.b 1530.d 5.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{8}+\cdots\)
1530.2.d.c 1530.d 5.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2+i)q^{5}+4iq^{7}-iq^{8}+\cdots\)
1530.2.d.d 1530.d 5.b $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(2+i)q^{5}+iq^{8}+(1+\cdots)q^{10}+\cdots\)
1530.2.d.e 1530.d 5.b $4$ $12.217$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
1530.2.d.f 1530.d 5.b $4$ $12.217$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1530.2.d.g 1530.d 5.b $6$ $12.217$ 6.0.5161984.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1530.2.d.h 1530.d 5.b $6$ $12.217$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1530.2.d.i 1530.d 5.b $6$ $12.217$ 6.0.5161984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-q^{4}-\beta _{4}q^{5}+(\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
1530.2.d.j 1530.d 5.b $6$ $12.217$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1530.2.f.a 1530.f 85.c $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(-2+i)q^{5}-4q^{7}+\cdots\)
1530.2.f.b 1530.f 85.c $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2-i)q^{5}+2q^{7}+\cdots\)
1530.2.f.c 1530.f 85.c $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2+i)q^{5}+4q^{7}+\cdots\)
1530.2.f.d 1530.f 85.c $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{4}+(2+i)q^{5}-4q^{7}+iq^{8}+\cdots\)
1530.2.f.e 1530.f 85.c $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2+i)q^{5}-2q^{7}-iq^{8}+\cdots\)
1530.2.f.f 1530.f 85.c $2$ $12.217$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2+i)q^{5}+4q^{7}-iq^{8}+\cdots\)
1530.2.f.g 1530.f 85.c $4$ $12.217$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1530.2.f.h 1530.f 85.c $4$ $12.217$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+(3\zeta_{8}+\cdots)q^{7}+\cdots\)
1530.2.f.i 1530.f 85.c $4$ $12.217$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+(2+\cdots)q^{7}+\cdots\)
1530.2.f.j 1530.f 85.c $6$ $12.217$ 6.0.350464.1 None \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{5})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1530.2.f.k 1530.f 85.c $6$ $12.217$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{4}+(-\beta _{1}-\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
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