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Results (22 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
395.1.c.a 395.c 395.c $1$ $0.197$ \(\Q\) \(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-395}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{4}+q^{5}-q^{9}-2q^{11}+q^{16}-2q^{19}+\cdots\)
395.1.c.b 395.c 395.c $2$ $0.197$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}+q^{4}-q^{5}+\beta q^{7}+q^{9}-\beta q^{12}+\cdots\)
1580.1.h.a 1580.h 395.c $1$ $0.789$ \(\Q\) \(\Q(\sqrt{-395}) \) None \(0\) \(-1\) \(1\) \(-1\) \(q-q^{3}+q^{5}-q^{7}-q^{11}-q^{15}+2q^{17}+\cdots\)
1580.1.h.b 1580.h 395.c $1$ $0.789$ \(\Q\) \(\Q(\sqrt{-395}) \) None \(0\) \(1\) \(1\) \(1\) \(q+q^{3}+q^{5}+q^{7}-q^{11}+q^{15}-2q^{17}+\cdots\)
1580.1.h.c 1580.h 395.c $2$ $0.789$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{3}+q^{5}+\beta q^{7}+2q^{9}+q^{11}+\cdots\)
1580.1.h.d 1580.h 395.c $4$ $0.789$ \(\Q(\zeta_{24})^+\) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1975.1.d.a 1975.d 79.b $1$ $0.986$ \(\Q\) \(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-395}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{4}+q^{9}-2q^{11}+q^{16}+2q^{19}+\cdots\)
1975.1.d.b 1975.d 79.b $2$ $0.986$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}-q^{4}-\beta q^{7}-q^{9}+\beta q^{12}+\cdots\)
2765.1.bf.a 2765.bf 2765.af $2$ $1.380$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(-2\) \(-1\) \(-1\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
2765.1.bf.b 2765.bf 2765.af $2$ $1.380$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(2\) \(-1\) \(1\) \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
2765.1.bf.c 2765.bf 2765.af $4$ $1.380$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}+\cdots\)
2765.1.bf.d 2765.bf 2765.af $8$ $1.380$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{24}+\zeta_{24}^{7})q^{3}-\zeta_{24}^{4}q^{4}-\zeta_{24}^{8}q^{5}+\cdots\)
3555.1.e.a 3555.e 395.c $1$ $1.774$ \(\Q\) \(\Q(\sqrt{-79}) \), \(\Q(\sqrt{-395}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}+2q^{11}+q^{16}-2q^{19}+\cdots\)
3555.1.e.c 3555.e 395.c $2$ $1.774$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(2\) \(0\) \(q+q^{4}+q^{5}-\beta q^{7}+q^{16}+\beta q^{17}+\cdots\)
3555.1.bg.a 3555.bg 3555.ag $2$ $1.774$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(-1\) \(-1\) \(1\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots\)
3555.1.bg.b 3555.bg 3555.ag $2$ $1.774$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-395}) \) None \(0\) \(1\) \(-1\) \(-1\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots\)
3555.1.bg.c 3555.bg 3555.ag $4$ $1.774$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+(\zeta_{12}^{3}+\cdots)q^{7}+\cdots\)
3555.1.bg.d 3555.bg 3555.ag $8$ $1.774$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{24}^{5}q^{3}-\zeta_{24}^{4}q^{4}+\zeta_{24}^{4}q^{5}+\cdots\)
395.3.c.a 395.c 395.c $4$ $10.763$ 4.4.7988480.1 \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(-20\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}+4q^{4}-5q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
395.3.c.b 395.c 395.c $4$ $10.763$ 4.4.31600.1 \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+4q^{4}+5q^{5}+(-2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1580.3.h.a 1580.h 395.c $8$ $43.052$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(-40\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}-5q^{5}+(-\beta _{1}-\beta _{6})q^{7}+(9+\cdots)q^{9}+\cdots\)
1580.3.h.b 1580.h 395.c $8$ $43.052$ 8.8.\(\cdots\).1 \(\Q(\sqrt{-395}) \) None \(0\) \(0\) \(40\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{6}q^{3}+5q^{5}+(-\beta _{5}+\beta _{6})q^{7}+(9+\cdots)q^{9}+\cdots\)
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