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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7
315.4.a.i 315.a 1.a $2$ $18.586$ \(\Q(\sqrt{65}) \) None 105.4.a.f \(-1\) \(0\) \(-10\) \(-14\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(8+\beta )q^{4}-5q^{5}-7q^{7}+(-2^{4}+\cdots)q^{8}+\cdots\)
315.4.a.k 315.a 1.a $2$ $18.586$ \(\Q(\sqrt{2}) \) None 105.4.a.e \(2\) \(0\) \(-10\) \(-14\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-5q^{5}-7q^{7}+\cdots\)
  displayed columns for results