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