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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 11
7623.2.a.a 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.b 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.c 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.d 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-2\) \(0\) \(3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{5}-q^{7}-6q^{10}+\cdots\)
7623.2.a.e 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}-q^{7}+3q^{8}+q^{10}+\cdots\)
7623.2.a.f 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.g 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-2q^{10}+\cdots\)
7623.2.a.h 7623.a 1.a $1$ $60.870$ \(\Q\) None \(-1\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{5}+q^{7}+3q^{8}-3q^{10}+\cdots\)
7623.2.a.i 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.j 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.k 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-q^{7}+4q^{13}+4q^{16}+\cdots\)
7623.2.a.l 7623.a 1.a $1$ $60.870$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}+q^{7}-4q^{13}+4q^{16}+\cdots\)
7623.2.a.m 7623.a 1.a $1$ $60.870$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
7623.2.a.n 7623.a 1.a $1$ $60.870$ \(\Q\) None \(1\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots\)
7623.2.a.o 7623.a 1.a $1$ $60.870$ \(\Q\) None \(1\) \(0\) \(3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{5}-q^{7}-3q^{8}+3q^{10}+\cdots\)
7623.2.a.p 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.q 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(-1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-q^{7}-2q^{10}+\cdots\)
7623.2.a.r 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots\)
7623.2.a.s 7623.a 1.a $1$ $60.870$ \(\Q\) None \(2\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots\)
7623.2.a.t 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+\cdots\)
7623.2.a.u 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}-\beta q^{5}+q^{7}+\cdots\)
7623.2.a.v 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}-q^{7}+\cdots\)
7623.2.a.w 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+(-2+3\beta )q^{5}-q^{7}+3q^{8}+\cdots\)
7623.2.a.x 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)
7623.2.a.y 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.z 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.ba 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bb 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(4\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.bc 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bd 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.be 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+q^{7}+(-4+\cdots)q^{8}+\cdots\)
7623.2.a.bf 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{21}) \) None \(-1\) \(0\) \(-6\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(3+\beta )q^{4}-3q^{5}-q^{7}+(-5+\cdots)q^{8}+\cdots\)
7623.2.a.bg 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{5}-q^{7}+2q^{13}+4q^{16}+\cdots\)
7623.2.a.bh 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-\beta q^{5}+q^{7}-2q^{13}+4q^{16}+\cdots\)
7623.2.a.bi 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+2\beta q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bj 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+3q^{4}-\beta q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bk 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+3q^{4}+(-1+\beta )q^{5}+\cdots\)
7623.2.a.bl 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}+2q^{5}-q^{7}-\beta q^{8}+\cdots\)
7623.2.a.bm 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bn 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(-1+2\beta )q^{5}+\cdots\)
7623.2.a.bo 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1-\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bp 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}-q^{7}+\cdots\)
7623.2.a.bq 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+2\beta )q^{5}+\cdots\)
7623.2.a.br 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}+3q^{8}+\cdots\)
7623.2.a.bs 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(1-2\beta )q^{5}+q^{7}+\cdots\)
7623.2.a.bt 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}-q^{5}-q^{7}+(4+\beta )q^{8}+\cdots\)
7623.2.a.bu 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+(-2+3\beta )q^{5}+q^{7}-3q^{8}+\cdots\)
7623.2.a.bv 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
7623.2.a.bw 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
7623.2.a.bx 7623.a 1.a $2$ $60.870$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)
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