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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4560.2.a.a 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
4560.2.a.b 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
4560.2.a.c 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
4560.2.a.d 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
4560.2.a.e 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.f 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
4560.2.a.g 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.h 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}+q^{15}+\cdots\)
4560.2.a.i 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
4560.2.a.j 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
4560.2.a.k 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
4560.2.a.l 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
4560.2.a.m 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
4560.2.a.n 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
4560.2.a.o 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
4560.2.a.p 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
4560.2.a.q 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(-1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
4560.2.a.r 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}+6q^{11}-q^{15}+\cdots\)
4560.2.a.s 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.t 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
4560.2.a.u 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
4560.2.a.v 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
4560.2.a.w 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.x 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-6q^{13}+q^{15}+\cdots\)
4560.2.a.y 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
4560.2.a.z 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
4560.2.a.ba 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
4560.2.a.bb 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-2q^{13}+q^{15}-6q^{17}+\cdots\)
4560.2.a.bc 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}+6q^{13}+q^{15}+\cdots\)
4560.2.a.bd 4560.a 1.a $1$ $36.412$ \(\Q\) None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
4560.2.a.be 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-3-\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4560.2.a.bf 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
4560.2.a.bg 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
4560.2.a.bh 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4560.2.a.bi 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(3+\beta )q^{7}+q^{9}+(1-3\beta )q^{11}+\cdots\)
4560.2.a.bj 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
4560.2.a.bk 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4560.2.a.bl 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4560.2.a.bm 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4560.2.a.bn 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
4560.2.a.bo 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4560.2.a.bp 4560.a 1.a $2$ $36.412$ \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(3+\beta )q^{11}+\cdots\)
4560.2.a.bq 4560.a 1.a $3$ $36.412$ 3.3.1016.1 None \(0\) \(-3\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta _{2}q^{7}+q^{9}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
4560.2.a.br 4560.a 1.a $3$ $36.412$ 3.3.564.1 None \(0\) \(-3\) \(3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
4560.2.a.bs 4560.a 1.a $3$ $36.412$ 3.3.1772.1 None \(0\) \(-3\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}+(-2-\beta _{2})q^{11}+\cdots\)
4560.2.a.bt 4560.a 1.a $3$ $36.412$ 3.3.568.1 None \(0\) \(3\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4560.2.a.bu 4560.a 1.a $3$ $36.412$ 3.3.1524.1 None \(0\) \(3\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
4560.2.a.bv 4560.a 1.a $3$ $36.412$ 3.3.316.1 None \(0\) \(3\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
4560.2.d.a 4560.d 76.d $2$ $36.412$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-q^{5}-2\zeta_{6}q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
4560.2.d.b 4560.d 76.d $2$ $36.412$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+q^{5}+q^{9}-2\zeta_{6}q^{11}-q^{15}+\cdots\)
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