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Results (9 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
347.1.b.a 347.b 347.b $2$ $0.173$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-347}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{9}-\beta q^{11}+\cdots\)
1388.1.d.a 1388.d 347.b $1$ $0.693$ \(\Q\) \(\Q(\sqrt{-347}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{11}+2q^{13}+q^{25}+q^{27}+\cdots\)
1388.1.d.b 1388.d 347.b $4$ $0.693$ \(\Q(\zeta_{15})^+\) \(\Q(\sqrt{-347}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{9}+(-\beta _{2}-\beta _{3})q^{11}+\cdots\)
3123.1.b.a 3123.b 347.b $2$ $1.559$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-347}) \) None \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+(1-\beta )q^{11}+(-1+\beta )q^{13}+\cdots\)
3123.1.h.a 3123.h 3123.h $2$ $1.559$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-347}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
3123.1.h.b 3123.h 3123.h $8$ $1.559$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-347}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{30}^{11}q^{3}+\zeta_{30}^{10}q^{4}-\zeta_{30}^{7}q^{9}+\cdots\)
3817.1.h.a 3817.h 3817.h $20$ $1.905$ \(\Q(\zeta_{50})\) \(\Q(\sqrt{-347}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{50}^{16}-\zeta_{50}^{19})q^{3}+\zeta_{50}^{20}q^{4}+\cdots\)
347.3.b.a 347.b 347.b $5$ $9.455$ 5.5.15051125.1 \(\Q(\sqrt{-347}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{3}+4q^{4}+(9+4\beta _{1}-\beta _{4})q^{9}+\cdots\)
1388.3.d.a 1388.d 347.b $10$ $37.820$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) \(\Q(\sqrt{-347}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+(9+2\beta _{4}+\beta _{6})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
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