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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1848.1.b.a 1848.b 1848.b $2$ $0.922$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{154}) \) \(0\) \(0\) \(0\) \(-2\) \(q-iq^{2}-iq^{3}-q^{4}-iq^{5}-q^{6}-q^{7}+\cdots\)
1848.1.b.b 1848.b 1848.b $2$ $0.922$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-231}) \) \(\Q(\sqrt{154}) \) \(0\) \(0\) \(0\) \(2\) \(q+iq^{2}-iq^{3}-q^{4}-iq^{5}+q^{6}+q^{7}+\cdots\)
1848.1.b.c 1848.b 1848.b $4$ $0.922$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
1848.1.b.d 1848.b 1848.b $4$ $0.922$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-231}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{4}q^{4}+\cdots\)
1848.1.br.a 1848.br 1848.ar $2$ $0.922$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(-1\) \(-1\) \(-1\) \(1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)
1848.1.br.b 1848.br 1848.ar $2$ $0.922$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(-1\) \(-1\) \(1\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
1848.1.br.c 1848.br 1848.ar $2$ $0.922$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(1\) \(-1\) \(-1\) \(-1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\cdots\)
1848.1.br.d 1848.br 1848.ar $2$ $0.922$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-66}) \) None \(1\) \(-1\) \(1\) \(1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\cdots\)
1848.1.br.e 1848.br 1848.ar $4$ $0.922$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(-2\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
1848.1.br.f 1848.br 1848.ar $4$ $0.922$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-66}) \) None \(2\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)
1848.1.ce.a 1848.ce 1848.be $4$ $0.922$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}+\cdots\)
1848.1.ce.b 1848.ce 1848.be $4$ $0.922$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}+\cdots\)
1848.1.dq.a 1848.dq 1848.cq $8$ $0.922$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\zeta_{20}^{9}q^{2}+\zeta_{20}^{7}q^{3}-\zeta_{20}^{8}q^{4}+\cdots\)
1848.1.dq.b 1848.dq 1848.cq $8$ $0.922$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{20}^{9}q^{2}+\zeta_{20}^{7}q^{3}-\zeta_{20}^{8}q^{4}+\cdots\)
1848.1.ec.a 1848.ec 1848.dc $16$ $0.922$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(2\) \(q-\zeta_{60}^{13}q^{2}+\zeta_{60}^{29}q^{3}+\zeta_{60}^{26}q^{4}+\cdots\)
1848.1.ec.b 1848.ec 1848.dc $16$ $0.922$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(-2\) \(q-\zeta_{60}^{13}q^{2}-\zeta_{60}^{29}q^{3}+\zeta_{60}^{26}q^{4}+\cdots\)
1848.1.er.a 1848.er 1848.dr $8$ $0.922$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-\zeta_{30}^{2}q^{2}+\zeta_{30}q^{3}+\zeta_{30}^{4}q^{4}+(-\zeta_{30}^{4}+\cdots)q^{5}+\cdots\)
1848.1.er.b 1848.er 1848.dr $8$ $0.922$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-\zeta_{30}^{2}q^{2}+\zeta_{30}q^{3}+\zeta_{30}^{4}q^{4}+(\zeta_{30}^{7}+\cdots)q^{5}+\cdots\)
1848.1.er.c 1848.er 1848.dr $8$ $0.922$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(-1\) \(1\) \(q+\zeta_{30}^{2}q^{2}-\zeta_{30}q^{3}+\zeta_{30}^{4}q^{4}+(-\zeta_{30}^{7}+\cdots)q^{5}+\cdots\)
1848.1.er.d 1848.er 1848.dr $8$ $0.922$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(-1\) \(1\) \(q+\zeta_{30}^{2}q^{2}-\zeta_{30}q^{3}+\zeta_{30}^{4}q^{4}+(\zeta_{30}^{4}+\cdots)q^{5}+\cdots\)
1848.2.a.a 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
1848.2.a.b 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
1848.2.a.c 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-q^{11}+2q^{13}-8q^{17}+\cdots\)
1848.2.a.d 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(-1\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-6q^{13}+\cdots\)
1848.2.a.e 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(-4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
1848.2.a.f 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
1848.2.a.g 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
1848.2.a.h 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
1848.2.a.i 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
1848.2.a.j 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-5q^{13}+\cdots\)
1848.2.a.k 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-q^{11}+3q^{13}+\cdots\)
1848.2.a.l 1848.a 1.a $1$ $14.756$ \(\Q\) None None \(0\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}+q^{11}+6q^{13}+\cdots\)
1848.2.a.m 1848.a 1.a $2$ $14.756$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.n 1848.a 1.a $2$ $14.756$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}-q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.o 1848.a 1.a $2$ $14.756$ \(\Q(\sqrt{33}) \) None None \(0\) \(-2\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}-q^{11}+\cdots\)
1848.2.a.p 1848.a 1.a $2$ $14.756$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots\)
1848.2.a.q 1848.a 1.a $2$ $14.756$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}-q^{11}+\cdots\)
1848.2.a.r 1848.a 1.a $2$ $14.756$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+q^{11}+\cdots\)
1848.2.a.s 1848.a 1.a $2$ $14.756$ \(\Q(\sqrt{41}) \) None None \(0\) \(2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+q^{11}-\beta q^{13}+\cdots\)
1848.2.a.t 1848.a 1.a $3$ $14.756$ 3.3.961.1 None None \(0\) \(3\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{5}+q^{7}+q^{9}-q^{11}+(1+\cdots)q^{13}+\cdots\)
1848.2.a.u 1848.a 1.a $3$ $14.756$ 3.3.568.1 None None \(0\) \(3\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{2}q^{5}+q^{7}+q^{9}+q^{11}+\beta _{1}q^{13}+\cdots\)
1848.2.f.a 1848.f 33.d $36$ $14.756$ None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1848.2.f.b 1848.f 33.d $36$ $14.756$ None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1848.2.q.a 1848.q 77.b $24$ $14.756$ None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$
1848.2.q.b 1848.q 77.b $24$ $14.756$ None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$
1848.2.v.a 1848.v 21.c $8$ $14.756$ 8.0.\(\cdots\).10 None None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{7})q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
1848.2.v.b 1848.v 21.c $8$ $14.756$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{5}-\beta _{6})q^{3}+\beta _{2}q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)
1848.2.v.c 1848.v 21.c $16$ $14.756$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{3}+(\beta _{6}+\beta _{9}-\beta _{12})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1848.2.v.d 1848.v 21.c $16$ $14.756$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}-\beta _{15})q^{3}+(\beta _{5}-\beta _{6}-\beta _{10}+\cdots)q^{5}+\cdots\)
1848.2.v.e 1848.v 21.c $32$ $14.756$ None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$
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