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Results (24 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
356.1.d.a 356.d 356.d $1$ $0.178$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-89}) \) \(\Q(\sqrt{89}) \) \(-1\) \(0\) \(2\) \(0\) \(q-q^{2}+q^{4}+2q^{5}-q^{8}-q^{9}-2q^{10}+\cdots\)
356.1.d.b 356.d 356.d $1$ $0.178$ \(\Q\) \(\Q(\sqrt{-89}) \) None \(1\) \(-1\) \(-1\) \(2\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
356.1.d.c 356.d 356.d $1$ $0.178$ \(\Q\) \(\Q(\sqrt{-89}) \) None \(1\) \(1\) \(-1\) \(-2\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\)
356.1.d.d 356.d 356.d $2$ $0.178$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-89}) \) None \(-2\) \(0\) \(-2\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-q^{8}+\cdots\)
1424.1.h.a 1424.h 356.d $2$ $0.711$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta q^{3}-2q^{5}-\beta q^{7}+q^{9}+2\beta q^{15}+\cdots\)
1424.1.h.b 1424.h 356.d $4$ $0.711$ \(\Q(\zeta_{24})^+\) \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\beta _{1}q^{3}+q^{5}+(\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
1780.1.b.c 1780.b 1780.b $4$ $0.888$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
1780.1.b.d 1780.b 1780.b $8$ $0.888$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{24}^{6}q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{7})q^{3}+\cdots\)
2492.1.n.a 2492.n 2492.n $6$ $1.244$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-89}) \) None \(-3\) \(0\) \(0\) \(-3\) \(q+\zeta_{18}^{6}q^{2}+(-\zeta_{18}-\zeta_{18}^{5})q^{3}-\zeta_{18}^{3}q^{4}+\cdots\)
2492.1.n.b 2492.n 2492.n $6$ $1.244$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-89}) \) None \(-3\) \(0\) \(0\) \(3\) \(q+\zeta_{18}^{6}q^{2}+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{3}+\cdots\)
2492.1.n.c 2492.n 2492.n $12$ $1.244$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-89}) \) None \(6\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{12}q^{2}+(\zeta_{36}^{5}+\zeta_{36}^{7})q^{3}-\zeta_{36}^{6}q^{4}+\cdots\)
3204.1.h.a 3204.h 356.d $1$ $1.599$ \(\Q\) \(\Q(\sqrt{-89}) \) None \(-1\) \(0\) \(1\) \(-2\) \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\)
3204.1.h.b 3204.h 356.d $1$ $1.599$ \(\Q\) \(\Q(\sqrt{-89}) \) None \(-1\) \(0\) \(1\) \(2\) \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
3204.1.h.c 3204.h 356.d $1$ $1.599$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-89}) \) \(\Q(\sqrt{89}) \) \(1\) \(0\) \(-2\) \(0\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+q^{16}+\cdots\)
3204.1.h.d 3204.h 356.d $2$ $1.599$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-89}) \) None \(2\) \(0\) \(2\) \(0\) \(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+q^{16}+\cdots\)
3204.1.n.a 3204.n 3204.n $6$ $1.599$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-89}) \) None \(-3\) \(0\) \(0\) \(-3\) \(q-\zeta_{18}^{3}q^{2}-\zeta_{18}^{2}q^{3}+\zeta_{18}^{6}q^{4}+\cdots\)
3204.1.n.b 3204.n 3204.n $6$ $1.599$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-89}) \) None \(-3\) \(0\) \(0\) \(3\) \(q-\zeta_{18}^{3}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{6}q^{4}+\cdots\)
3204.1.n.c 3204.n 3204.n $12$ $1.599$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-89}) \) None \(6\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{6}q^{2}-\zeta_{36}q^{3}+\zeta_{36}^{12}q^{4}+\cdots\)
356.3.d.a 356.d 356.d $6$ $9.700$ 6.6.\(\cdots\).1 \(\Q(\sqrt{-89}) \) None \(-12\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
356.3.d.b 356.d 356.d $6$ $9.700$ 6.6.\(\cdots\).1 \(\Q(\sqrt{-89}) \) None \(12\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}-\beta _{1}q^{3}+4q^{4}+(\beta _{2}+\beta _{5})q^{5}+\cdots\)
2848.2.e.c 2848.e 89.b $12$ $22.741$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{3}+\beta _{5}q^{5}+\beta _{6}q^{7}+(-3-\beta _{2}+\cdots)q^{9}+\cdots\)
2848.2.e.d 2848.e 89.b $12$ $22.741$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{3}q^{7}+(-3+\beta _{2}+\cdots)q^{9}+\cdots\)
1424.3.h.b 1424.h 356.d $6$ $38.801$ 6.6.8222758416.1 \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(0\) \(-18\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(-3-\beta _{1}+\cdots)q^{7}+\cdots\)
1424.3.h.c 1424.h 356.d $6$ $38.801$ 6.6.8222758416.1 \(\Q(\sqrt{-89}) \) None \(0\) \(0\) \(0\) \(18\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{3}+(\beta _{2}-\beta _{3})q^{5}+(3+\beta _{1})q^{7}+\cdots\)
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