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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 7 11
5082.2.a.a 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.b 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.c 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.d 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.e 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
5082.2.a.f 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.g 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.h 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.i 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(-1\) \(4\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.j 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.k 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.l 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
5082.2.a.m 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(1\) \(2\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.n 5082.a 1.a $1$ $40.580$ \(\Q\) None \(-1\) \(1\) \(2\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.o 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.p 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(-3\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.q 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.r 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.s 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.t 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.u 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.v 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.w 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.x 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(-1\) \(4\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.y 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.z 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.ba 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
5082.2.a.bb 5082.a 1.a $1$ $40.580$ \(\Q\) None \(1\) \(1\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bc 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-4\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.bd 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-3\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.be 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bf 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(1\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{7}+\cdots\)
5082.2.a.bg 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(4\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bh 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(-5\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bi 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(-4\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bj 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(-1\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.bk 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bl 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{33}) \) None \(-2\) \(2\) \(3\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bm 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-4\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.bn 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(-3\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.bo 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
5082.2.a.bp 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(1\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
5082.2.a.bq 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(4\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
5082.2.a.br 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-5\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bs 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-4\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bt 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bu 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
5082.2.a.bv 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bw 5082.a 1.a $2$ $40.580$ \(\Q(\sqrt{33}) \) None \(2\) \(2\) \(3\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
5082.2.a.bx 5082.a 1.a $4$ $40.580$ 4.4.8000.1 None \(-4\) \(-4\) \(2\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
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