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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 13
6240.2.a.a 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
6240.2.a.b 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
6240.2.a.c 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-4q^{11}+q^{13}+q^{15}+\cdots\)
6240.2.a.d 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-q^{13}+q^{15}+2q^{17}+\cdots\)
6240.2.a.e 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots\)
6240.2.a.f 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6240.2.a.g 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.h 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+5q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6240.2.a.i 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6240.2.a.j 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.k 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.l 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
6240.2.a.m 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
6240.2.a.n 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
6240.2.a.o 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
6240.2.a.p 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+q^{13}-q^{15}+\cdots\)
6240.2.a.q 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(-5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-5q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6240.2.a.r 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.s 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6240.2.a.t 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots\)
6240.2.a.u 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots\)
6240.2.a.v 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}-q^{15}+\cdots\)
6240.2.a.w 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
6240.2.a.x 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
6240.2.a.y 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}+q^{13}+q^{15}+\cdots\)
6240.2.a.z 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
6240.2.a.ba 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
6240.2.a.bb 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
6240.2.a.bc 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
6240.2.a.bd 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.be 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.bf 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6240.2.a.bg 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(-2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
6240.2.a.bh 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bi 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bj 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-2\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
6240.2.a.bk 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-2\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6240.2.a.bl 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-6\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-3-\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6240.2.a.bm 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(2\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(4+\beta )q^{11}+\cdots\)
6240.2.a.bn 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
6240.2.a.bo 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-2\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
6240.2.a.bp 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
6240.2.a.bq 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-2\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\cdots\)
6240.2.a.br 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bs 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(-2\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6240.2.a.bt 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
6240.2.a.bu 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(-4-\beta )q^{11}+\cdots\)
6240.2.a.bv 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(3+\beta )q^{7}+q^{9}+(2-2\beta )q^{11}+\cdots\)
6240.2.a.bw 6240.a 1.a $3$ $49.827$ 3.3.229.1 None \(0\) \(-3\) \(-3\) \(-5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-2-\beta _{2})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
6240.2.a.bx 6240.a 1.a $3$ $49.827$ 3.3.229.1 None \(0\) \(-3\) \(-3\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
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