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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4600.2.a.a 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(-3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{7}+6q^{9}+5q^{13}+6q^{17}+\cdots\)
4600.2.a.b 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(-2\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{7}+q^{9}-6q^{13}-7q^{17}+\cdots\)
4600.2.a.c 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
4600.2.a.d 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(-2\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{7}+q^{9}+5q^{11}+5q^{13}+\cdots\)
4600.2.a.e 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
4600.2.a.f 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}-q^{13}+4q^{17}+\cdots\)
4600.2.a.g 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-3q^{9}+6q^{11}+2q^{13}-6q^{17}+\cdots\)
4600.2.a.h 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}-6q^{11}+2q^{13}+3q^{17}+\cdots\)
4600.2.a.i 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}-4q^{11}+5q^{13}+\cdots\)
4600.2.a.j 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}+2q^{11}+5q^{13}+4q^{17}+\cdots\)
4600.2.a.k 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}-2q^{9}-2q^{11}-7q^{13}+\cdots\)
4600.2.a.l 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
4600.2.a.m 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(2\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots\)
4600.2.a.n 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
4600.2.a.o 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(2\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{7}+q^{9}+6q^{13}+7q^{17}+\cdots\)
4600.2.a.p 4600.a 1.a $1$ $36.731$ \(\Q\) None \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}-q^{13}+6q^{21}+\cdots\)
4600.2.a.q 4600.a 1.a $2$ $36.731$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(2+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
4600.2.a.r 4600.a 1.a $2$ $36.731$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
4600.2.a.s 4600.a 1.a $2$ $36.731$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1+\beta )q^{9}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4600.2.a.t 4600.a 1.a $2$ $36.731$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}-2q^{11}+\cdots\)
4600.2.a.u 4600.a 1.a $2$ $36.731$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
4600.2.a.v 4600.a 1.a $3$ $36.731$ 3.3.229.1 None \(0\) \(-2\) \(0\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-2+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
4600.2.a.w 4600.a 1.a $3$ $36.731$ \(\Q(\zeta_{14})^+\) None \(0\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4600.2.a.x 4600.a 1.a $3$ $36.731$ 3.3.2597.1 None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
4600.2.a.y 4600.a 1.a $3$ $36.731$ 3.3.621.1 None \(0\) \(0\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
4600.2.a.z 4600.a 1.a $3$ $36.731$ \(\Q(\zeta_{14})^+\) None \(0\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(2-2\beta _{1})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
4600.2.a.ba 4600.a 1.a $4$ $36.731$ 4.4.15529.1 None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
4600.2.a.bb 4600.a 1.a $4$ $36.731$ 4.4.15529.1 None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4600.2.a.bc 4600.a 1.a $5$ $36.731$ 5.5.791953.1 None \(0\) \(-3\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
4600.2.a.bd 4600.a 1.a $5$ $36.731$ 5.5.521397.1 None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
4600.2.a.be 4600.a 1.a $5$ $36.731$ 5.5.13955077.1 None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\beta _{4})q^{9}+\cdots\)
4600.2.a.bf 4600.a 1.a $5$ $36.731$ 5.5.521397.1 None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
4600.2.a.bg 4600.a 1.a $5$ $36.731$ 5.5.791953.1 None \(0\) \(3\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
4600.2.a.bh 4600.a 1.a $7$ $36.731$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
4600.2.a.bi 4600.a 1.a $7$ $36.731$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(3\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\beta _{6})q^{9}+\cdots\)
4600.2.a.bj 4600.a 1.a $8$ $36.731$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(0\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)
4600.2.a.bk 4600.a 1.a $8$ $36.731$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(3\) \(0\) \(7\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)
4600.2.e.a 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+2iq^{7}-6q^{9}-5iq^{13}+\cdots\)
4600.2.e.b 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-2iq^{7}-6q^{9}-iq^{13}+6q^{21}+\cdots\)
4600.2.e.c 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+iq^{7}-q^{9}-5q^{11}-iq^{13}+\cdots\)
4600.2.e.d 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-5iq^{13}+\cdots\)
4600.2.e.e 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}+2q^{9}-4q^{11}+5iq^{13}+\cdots\)
4600.2.e.f 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-4iq^{7}+2q^{9}-2q^{11}-7iq^{13}+\cdots\)
4600.2.e.g 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}+2q^{9}+iq^{13}+4iq^{17}+\cdots\)
4600.2.e.h 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{9}+2q^{11}+5iq^{13}-4iq^{17}+\cdots\)
4600.2.e.i 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-4iq^{7}+2q^{9}+3q^{11}-2iq^{13}+\cdots\)
4600.2.e.j 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}-6q^{11}+2iq^{13}-3iq^{17}+\cdots\)
4600.2.e.k 4600.e 5.b $2$ $36.731$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}+3q^{9}+6q^{11}+2iq^{13}+\cdots\)
4600.2.e.l 4600.e 5.b $4$ $36.731$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
4600.2.e.m 4600.e 5.b $4$ $36.731$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-2\beta _{1}q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
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