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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 19
9576.2.a.a 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-4\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-q^{7}+2q^{11}+2q^{13}+q^{19}+\cdots\)
9576.2.a.b 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-6q^{11}-2q^{13}+8q^{17}+\cdots\)
9576.2.a.c 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-4q^{11}-6q^{13}-6q^{17}+\cdots\)
9576.2.a.d 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{11}-4q^{13}+4q^{17}+\cdots\)
9576.2.a.e 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
9576.2.a.f 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+6q^{11}-2q^{13}+q^{19}+\cdots\)
9576.2.a.g 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9576.2.a.h 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+6q^{11}-4q^{17}-q^{19}+\cdots\)
9576.2.a.i 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-6q^{11}+4q^{13}-q^{19}+2q^{23}+\cdots\)
9576.2.a.j 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}-2q^{13}+q^{19}-4q^{23}-5q^{25}+\cdots\)
9576.2.a.k 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}+2q^{13}+2q^{17}+q^{19}+\cdots\)
9576.2.a.l 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}-4q^{13}+q^{19}+6q^{23}+\cdots\)
9576.2.a.m 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}+6q^{13}-q^{19}-6q^{23}+\cdots\)
9576.2.a.n 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{13}+8q^{17}-q^{19}+4q^{23}+\cdots\)
9576.2.a.o 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}+6q^{13}-q^{19}+6q^{23}+\cdots\)
9576.2.a.p 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}+2q^{13}-2q^{17}+q^{19}+\cdots\)
9576.2.a.q 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}+2q^{13}+q^{19}-5q^{25}+\cdots\)
9576.2.a.r 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{11}-4q^{13}-4q^{17}+\cdots\)
9576.2.a.s 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{13}-2q^{17}+q^{19}+\cdots\)
9576.2.a.t 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
9576.2.a.u 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-6q^{11}+4q^{17}-q^{19}+\cdots\)
9576.2.a.v 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-2q^{13}-6q^{17}-q^{19}+\cdots\)
9576.2.a.w 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+2q^{11}+2q^{13}-2q^{17}+\cdots\)
9576.2.a.x 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
9576.2.a.y 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots\)
9576.2.a.z 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-2q^{11}+2q^{13}+q^{19}+\cdots\)
9576.2.a.ba 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-2q^{13}-4q^{17}+q^{19}+\cdots\)
9576.2.a.bb 9576.a 1.a $1$ $76.465$ \(\Q\) None \(0\) \(0\) \(4\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}-2q^{11}-4q^{13}-4q^{17}+\cdots\)
9576.2.a.bc 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-5\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta )q^{5}+q^{7}+(1+3\beta )q^{11}+\cdots\)
9576.2.a.bd 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-4\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{11}+(1+\beta )q^{13}+\cdots\)
9576.2.a.be 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+2\beta q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bf 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}-q^{7}+2\beta q^{11}+4q^{13}+\cdots\)
9576.2.a.bg 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(3-\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
9576.2.a.bh 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+q^{7}-2q^{11}-4q^{13}+\cdots\)
9576.2.a.bi 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}-2q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bj 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{5}+q^{7}+(-2+2\beta )q^{13}+\cdots\)
9576.2.a.bk 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}-2q^{13}-\beta q^{17}-q^{19}+\cdots\)
9576.2.a.bl 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}-2q^{11}+(2-\beta )q^{13}+\cdots\)
9576.2.a.bm 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{5}+q^{7}+(-1+3\beta )q^{11}+\cdots\)
9576.2.a.bn 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{5}+q^{7}+(-1+3\beta )q^{11}+\cdots\)
9576.2.a.bo 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+2q^{11}+(2+\beta )q^{13}+\cdots\)
9576.2.a.bp 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+(-3+\cdots)q^{13}+\cdots\)
9576.2.a.bq 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}-2\beta q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.br 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+2\beta q^{11}+4q^{13}+\cdots\)
9576.2.a.bs 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+\beta q^{11}+(1-2\beta )q^{13}+\cdots\)
9576.2.a.bt 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+(-1+3\beta )q^{11}+(3-4\beta )q^{13}+\cdots\)
9576.2.a.bu 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+2q^{11}-4q^{13}+\cdots\)
9576.2.a.bv 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+2q^{11}+2\beta q^{13}+\cdots\)
9576.2.a.bw 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+4q^{11}+(2+2\beta )q^{13}+\cdots\)
9576.2.a.bx 9576.a 1.a $2$ $76.465$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(4\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-2q^{11}+(1+\beta )q^{13}+\cdots\)
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