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Results (27 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
303.1.d.a 303.d 303.d $2$ $0.151$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-303}) \) None \(-1\) \(2\) \(0\) \(0\) \(q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
303.1.d.b 303.d 303.d $2$ $0.151$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-303}) \) None \(1\) \(-2\) \(0\) \(0\) \(q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
2424.1.j.e 2424.j 2424.j $2$ $1.210$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-303}) \) \(\Q(\sqrt{202}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+iq^{8}-q^{9}+\cdots\)
2424.1.j.f 2424.j 2424.j $8$ $1.210$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-303}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{5}q^{3}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{6}q^{6}+\cdots\)
2727.1.d.a 2727.d 303.d $1$ $1.361$ \(\Q\) \(\Q(\sqrt{-303}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-2q^{2}+3q^{4}-4q^{8}+q^{11}-q^{13}+\cdots\)
2727.1.d.b 2727.d 303.d $1$ $1.361$ \(\Q\) \(\Q(\sqrt{-303}) \) None \(2\) \(0\) \(0\) \(0\) \(q+2q^{2}+3q^{4}+4q^{8}-q^{11}-q^{13}+\cdots\)
2727.1.d.c 2727.d 303.d $4$ $1.361$ \(\Q(\zeta_{15})^+\) \(\Q(\sqrt{-303}) \) None \(-2\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{3}q^{4}-q^{8}+\beta _{1}q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
2727.1.d.d 2727.d 303.d $4$ $1.361$ \(\Q(\zeta_{15})^+\) \(\Q(\sqrt{-303}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}-\beta _{3}q^{4}+q^{8}-\beta _{1}q^{11}+(-\beta _{2}+\cdots)q^{13}+\cdots\)
3333.1.be.a 3333.be 3333.ae $20$ $1.663$ \(\Q(\zeta_{50})\) \(\Q(\sqrt{-303}) \) None \(0\) \(-5\) \(0\) \(0\) \(q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+\zeta_{50}^{20}q^{3}+\cdots\)
3333.1.be.b 3333.be 3333.ae $20$ $1.663$ \(\Q(\zeta_{50})\) \(\Q(\sqrt{-303}) \) None \(0\) \(5\) \(0\) \(0\) \(q+(\zeta_{50}^{9}+\zeta_{50}^{21})q^{2}-\zeta_{50}^{20}q^{3}+\cdots\)
3636.1.h.a 3636.h 404.d $2$ $1.815$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-303}) \) \(\Q(\sqrt{303}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-q^{13}+q^{16}+\cdots\)
3636.1.h.d 3636.h 404.d $8$ $1.815$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-303}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{8}+(-\zeta_{20}^{3}+\cdots)q^{11}+\cdots\)
3939.1.e.a 3939.e 3939.e $1$ $1.966$ \(\Q\) \(\Q(\sqrt{-303}) \), \(\Q(\sqrt{-3939}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{4}+q^{9}-q^{12}+q^{13}+q^{16}+\cdots\)
3939.1.e.b 3939.e 3939.e $1$ $1.966$ \(\Q\) \(\Q(\sqrt{-303}) \), \(\Q(\sqrt{-3939}) \) \(\Q(\sqrt{13}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{4}+q^{9}+q^{12}+q^{13}+q^{16}+\cdots\)
3939.1.e.e 3939.e 3939.e $4$ $1.966$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-303}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+(\zeta_{10}+\zeta_{10}^{4})q^{2}-q^{3}+(-1+\zeta_{10}^{2}+\cdots)q^{4}+\cdots\)
3939.1.e.f 3939.e 3939.e $4$ $1.966$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-303}) \) None \(0\) \(4\) \(0\) \(0\) \(q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+q^{3}+(-1+\zeta_{10}^{2}+\cdots)q^{4}+\cdots\)
3939.1.x.a 3939.x 3939.x $2$ $1.966$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-303}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}-q^{8}+\cdots\)
3939.1.x.b 3939.x 3939.x $2$ $1.966$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-303}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{6}+q^{8}+\cdots\)
3939.1.x.c 3939.x 3939.x $8$ $1.966$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-303}) \) None \(-1\) \(-4\) \(0\) \(0\) \(q+(\zeta_{30}^{4}+\zeta_{30}^{6})q^{2}-\zeta_{30}^{5}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots\)
3939.1.x.d 3939.x 3939.x $8$ $1.966$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-303}) \) None \(1\) \(4\) \(0\) \(0\) \(q+(-\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}+\zeta_{30}^{5}q^{3}+\cdots\)
3939.1.bb.a 3939.bb 3939.ab $2$ $1.966$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-303}) \) None \(-3\) \(-1\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}^{2}q^{3}+(1+\zeta_{6}+\cdots)q^{4}+\cdots\)
3939.1.bb.b 3939.bb 3939.ab $2$ $1.966$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-303}) \) None \(3\) \(1\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}-\zeta_{6}^{2}q^{3}+(1+\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
3939.1.bb.c 3939.bb 3939.ab $8$ $1.966$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-303}) \) None \(-3\) \(4\) \(0\) \(0\) \(q+(\zeta_{30}-\zeta_{30}^{9})q^{2}+\zeta_{30}^{5}q^{3}+(\zeta_{30}^{2}+\cdots)q^{4}+\cdots\)
3939.1.bb.d 3939.bb 3939.ab $8$ $1.966$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-303}) \) None \(3\) \(-4\) \(0\) \(0\) \(q+(\zeta_{30}^{4}-\zeta_{30}^{6})q^{2}-\zeta_{30}^{5}q^{3}+(\zeta_{30}^{8}+\cdots)q^{4}+\cdots\)
909.2.c.d 909.c 101.b $10$ $7.258$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) \(\Q(\sqrt{-303}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-2\beta _{1}+\beta _{3}+\cdots)q^{8}+\cdots\)
303.3.d.a 303.d 303.d $5$ $8.256$ 5.5.286903125.1 \(\Q(\sqrt{-303}) \) None \(0\) \(-15\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-3q^{3}+(4+\beta _{2}-\beta _{3})q^{4}+\cdots\)
303.3.d.b 303.d 303.d $5$ $8.256$ 5.5.286903125.1 \(\Q(\sqrt{-303}) \) None \(0\) \(15\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+3q^{3}+(4+\beta _{2}-\beta _{3})q^{4}+\cdots\)
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