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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4680.2.a.a 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-5q^{7}-q^{11}+q^{13}+3q^{17}+\cdots\)
4680.2.a.b 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}-3q^{11}+q^{13}+3q^{17}+\cdots\)
4680.2.a.c 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+3q^{11}-q^{13}+q^{17}+\cdots\)
4680.2.a.d 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+q^{13}+4q^{17}+6q^{19}+\cdots\)
4680.2.a.e 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{11}+q^{13}-2q^{17}+2q^{19}+\cdots\)
4680.2.a.f 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{13}+6q^{17}-8q^{19}-6q^{23}+\cdots\)
4680.2.a.g 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}+q^{13}-2q^{17}-4q^{19}+\cdots\)
4680.2.a.h 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-4q^{11}-q^{13}-8q^{17}+\cdots\)
4680.2.a.i 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-4q^{11}-q^{13}+2q^{19}+\cdots\)
4680.2.a.j 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+5q^{11}-q^{13}-3q^{17}+\cdots\)
4680.2.a.k 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-4q^{11}+q^{13}-6q^{17}+\cdots\)
4680.2.a.l 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+q^{13}-2q^{17}+q^{25}+\cdots\)
4680.2.a.m 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-4q^{11}+q^{13}+6q^{17}+\cdots\)
4680.2.a.n 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{7}+3q^{11}+q^{13}-3q^{17}+\cdots\)
4680.2.a.o 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+5q^{11}+q^{13}-3q^{17}+\cdots\)
4680.2.a.p 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}+q^{13}+2q^{17}-4q^{19}+\cdots\)
4680.2.a.q 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{13}-2q^{17}-4q^{23}+q^{25}+\cdots\)
4680.2.a.r 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{13}-6q^{17}-8q^{19}+6q^{23}+\cdots\)
4680.2.a.s 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{13}+6q^{17}+4q^{19}+q^{25}+\cdots\)
4680.2.a.t 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}-q^{13}+6q^{17}+4q^{19}+\cdots\)
4680.2.a.u 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+4q^{11}-q^{13}+8q^{17}+\cdots\)
4680.2.a.v 4680.a 1.a $1$ $37.370$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-5q^{11}-q^{13}+3q^{17}+\cdots\)
4680.2.a.w 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3\beta q^{11}-q^{13}+(2+2\beta )q^{17}+\cdots\)
4680.2.a.x 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-q^{13}+(2-\beta )q^{17}+2q^{19}+\cdots\)
4680.2.a.y 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+(4-\beta )q^{11}+q^{13}+(2+\cdots)q^{17}+\cdots\)
4680.2.a.z 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+(2-\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
4680.2.a.ba 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-q^{13}+(-2-\beta )q^{17}+\cdots\)
4680.2.a.bb 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{41}) \) None \(0\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+(2+\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
4680.2.a.bc 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+(-3-\beta )q^{11}-q^{13}-2q^{17}+\cdots\)
4680.2.a.bd 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2\beta q^{7}+(-1-\beta )q^{11}+q^{13}+\cdots\)
4680.2.a.be 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2\beta q^{7}+(3+\beta )q^{11}+q^{13}+\cdots\)
4680.2.a.bf 4680.a 1.a $2$ $37.370$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+\beta q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
4680.2.a.bg 4680.a 1.a $3$ $37.370$ 3.3.1016.1 None \(0\) \(0\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta _{2}q^{7}+(2-\beta _{1})q^{11}-q^{13}+\cdots\)
4680.2.a.bh 4680.a 1.a $3$ $37.370$ 3.3.940.1 None \(0\) \(0\) \(-3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta _{2}q^{7}+(-2-\beta _{1})q^{11}-q^{13}+\cdots\)
4680.2.a.bi 4680.a 1.a $3$ $37.370$ 3.3.621.1 None \(0\) \(0\) \(-3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta _{2})q^{7}+(-1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
4680.2.a.bj 4680.a 1.a $3$ $37.370$ 3.3.1016.1 None \(0\) \(0\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta _{2}q^{7}+(-2+\beta _{1})q^{11}-q^{13}+\cdots\)
4680.2.a.bk 4680.a 1.a $3$ $37.370$ 3.3.621.1 None \(0\) \(0\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta _{2})q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4680.2.a.bl 4680.a 1.a $3$ $37.370$ 3.3.1849.1 None \(0\) \(0\) \(3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(2-\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
4680.2.g.a 4680.g 13.b $2$ $37.370$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+4iq^{7}-4iq^{11}+(-3-2i)q^{13}+\cdots\)
4680.2.g.b 4680.g 13.b $2$ $37.370$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+2iq^{7}+4iq^{11}+(-3+2i)q^{13}+\cdots\)
4680.2.g.c 4680.g 13.b $2$ $37.370$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{5}+2iq^{7}+(-3+2i)q^{13}+6q^{17}+\cdots\)
4680.2.g.d 4680.g 13.b $2$ $37.370$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{5}+6iq^{11}+(-2-3i)q^{13}+\cdots\)
4680.2.g.e 4680.g 13.b $2$ $37.370$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+3iq^{7}+3iq^{11}+(-2-3i)q^{13}+\cdots\)
4680.2.g.f 4680.g 13.b $4$ $37.370$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+(1-\zeta_{12}^{2})q^{13}+\cdots\)
4680.2.g.g 4680.g 13.b $4$ $37.370$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
4680.2.g.h 4680.g 13.b $4$ $37.370$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
4680.2.g.i 4680.g 13.b $6$ $37.370$ 6.0.3356224.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(-2\beta _{1}+\beta _{4})q^{7}+(-2\beta _{4}+\cdots)q^{11}+\cdots\)
4680.2.g.j 4680.g 13.b $6$ $37.370$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}+(\beta _{3}-\beta _{4}+\beta _{5})q^{7}+(\beta _{3}+\beta _{4}+\cdots)q^{11}+\cdots\)
4680.2.g.k 4680.g 13.b $8$ $37.370$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5})q^{7}+\beta _{4}q^{11}+\cdots\)
4680.2.g.l 4680.g 13.b $12$ $37.370$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}-\beta _{2}q^{7}+\beta _{6}q^{11}+(-1-\beta _{7}+\cdots)q^{13}+\cdots\)
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