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Results (14 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
407.1.d.a 407.d 407.d $1$ $0.203$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-407}) \) \(\Q(\sqrt{37}) \) \(0\) \(-2\) \(0\) \(0\) \(q-2q^{3}-q^{4}+3q^{9}+q^{11}+2q^{12}+\cdots\)
407.1.d.b 407.d 407.d $2$ $0.203$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+q^{4}-q^{9}+q^{11}+\beta q^{13}+\cdots\)
407.1.d.c 407.d 407.d $4$ $0.203$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
3256.1.f.e 3256.f 3256.f $16$ $1.625$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{2}+(-\zeta_{32}^{2}-\zeta_{32}^{14})q^{3}+\cdots\)
3663.1.g.a 3663.g 407.d $1$ $1.828$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-407}) \) \(\Q(\sqrt{37}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-q^{11}+q^{16}+q^{25}+q^{37}+\cdots\)
3663.1.g.b 3663.g 407.d $2$ $1.828$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}+q^{4}-q^{11}-\beta q^{13}-q^{16}+\cdots\)
3663.1.g.d 3663.g 407.d $4$ $1.828$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+(\beta _{1}-\beta _{3})q^{8}+\cdots\)
3663.1.bb.a 3663.bb 3663.ab $2$ $1.828$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-407}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+q^{6}-q^{8}-\zeta_{6}q^{9}+\cdots\)
3663.1.bb.d 3663.bb 3663.ab $2$ $1.828$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-407}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}-q^{6}+q^{8}-\zeta_{6}q^{9}+\cdots\)
3663.1.bb.e 3663.bb 3663.ab $4$ $1.828$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-407}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+\zeta_{12}^{2}q^{3}+\cdots\)
3663.1.bb.f 3663.bb 3663.ab $8$ $1.828$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{2}-\zeta_{24}^{10}q^{3}+(-\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
3663.1.bb.g 3663.bb 3663.ab $16$ $1.828$ \(\Q(\zeta_{48})\) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{48}^{15}-\zeta_{48}^{17})q^{2}-\zeta_{48}^{2}q^{3}+\cdots\)
407.3.d.b 407.d 407.d $8$ $11.090$ 8.8.\(\cdots\).2 \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+\beta _{3}q^{3}+(4+\beta _{3}-\beta _{6})q^{4}+\cdots\)
407.3.d.c 407.d 407.d $8$ $11.090$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) \(\Q(\sqrt{-407}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{5}q^{2}+\beta _{3}q^{3}+(4-\beta _{3}-\beta _{6})q^{4}+\cdots\)
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