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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.b 315.a 1.a $1$ $18.586$ \(\Q\) None 315.4.a.b \(-3\) \(0\) \(-5\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+q^{4}-5q^{5}+7q^{7}+21q^{8}+\cdots\)
315.4.a.n 315.a 1.a $3$ $18.586$ 3.3.22952.1 None 315.4.a.n \(-2\) \(0\) \(-15\) \(21\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
  displayed columns for results