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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 7
5040.2.a.a 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-5q^{11}-5q^{13}+7q^{17}+\cdots\)
5040.2.a.b 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.c 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.d 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-6q^{13}-2q^{17}+8q^{19}+\cdots\)
5040.2.a.e 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
5040.2.a.f 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.g 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{13}+6q^{17}-8q^{19}+\cdots\)
5040.2.a.h 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+3q^{11}-q^{13}+3q^{17}+\cdots\)
5040.2.a.i 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.j 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.k 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.l 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.m 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}+2q^{17}+6q^{19}+\cdots\)
5040.2.a.n 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.o 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-2q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.p 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+2q^{13}-2q^{17}+q^{25}+\cdots\)
5040.2.a.q 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.r 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.s 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.t 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.u 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
5040.2.a.v 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots\)
5040.2.a.w 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-4q^{13}+6q^{17}-2q^{19}+\cdots\)
5040.2.a.x 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
5040.2.a.y 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
5040.2.a.z 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.ba 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{13}+6q^{17}+4q^{19}+\cdots\)
5040.2.a.bb 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
5040.2.a.bc 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+6q^{11}-4q^{13}-6q^{17}+\cdots\)
5040.2.a.bd 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-5q^{11}-3q^{13}+q^{17}+\cdots\)
5040.2.a.be 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
5040.2.a.bf 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bg 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bh 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.bi 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
5040.2.a.bj 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
5040.2.a.bk 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+2q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bl 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+2q^{11}+4q^{13}-6q^{17}+\cdots\)
5040.2.a.bm 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.bn 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bo 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}-2q^{17}+6q^{19}+\cdots\)
5040.2.a.bp 5040.a 1.a $1$ $40.245$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.bq 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
5040.2.a.br 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
5040.2.a.bs 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+(1+\beta )q^{11}+2q^{13}+(-1+\cdots)q^{17}+\cdots\)
5040.2.a.bt 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+\beta q^{11}+(2+\beta )q^{13}+(2+\cdots)q^{17}+\cdots\)
5040.2.a.bu 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+(2+\beta )q^{11}+(-2+\beta )q^{13}+\cdots\)
5040.2.a.bv 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+(-1-\beta )q^{11}+2q^{13}+\cdots\)
5040.2.a.bw 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+(2+\beta )q^{11}+\beta q^{13}+2q^{17}+\cdots\)
5040.2.a.bx 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+(-2+\beta )q^{11}+(-2-\beta )q^{13}+\cdots\)
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