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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 23
115.4.a.a 115.a 1.a $1$ $6.785$ \(\Q\) None 115.4.a.a \(1\) \(4\) \(-5\) \(-32\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+4q^{3}-7q^{4}-5q^{5}+4q^{6}+\cdots\)
115.4.a.d 115.a 1.a $5$ $6.785$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 115.4.a.d \(-5\) \(-6\) \(-25\) \(-15\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots\)
  displayed columns for results