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Results (47 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1045.1.k.a 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{209}) \) \(-2\) \(0\) \(0\) \(0\) \(q+(-1-i)q^{2}+iq^{4}-iq^{5}-q^{8}+\cdots\)
1045.1.k.b 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(-2\) \(q-iq^{4}+q^{5}+(-1+i)q^{7}-iq^{9}+\cdots\)
1045.1.k.c 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(2\) \(q-iq^{4}+q^{5}+(1-i)q^{7}-iq^{9}+iq^{11}+\cdots\)
1045.1.k.d 1045.k 1045.k $2$ $0.522$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{209}) \) \(2\) \(0\) \(0\) \(0\) \(q+(1+i)q^{2}+iq^{4}-iq^{5}+q^{8}-iq^{9}+\cdots\)
1045.1.w.a 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-95}) \) None \(-2\) \(-2\) \(-1\) \(0\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
1045.1.w.b 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-5\) \(q+\zeta_{10}q^{4}-\zeta_{10}q^{5}+(-1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
1045.1.w.c 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(5\) \(q+\zeta_{10}q^{4}-\zeta_{10}^{3}q^{5}+(1-\zeta_{10}^{2})q^{7}+\cdots\)
1045.1.w.d 1045.w 1045.w $4$ $0.522$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-95}) \) None \(2\) \(2\) \(-1\) \(0\) \(q+(-\zeta_{10}^{2}-\zeta_{10}^{4})q^{2}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
1045.1.w.e 1045.w 1045.w $8$ $0.522$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{20}^{3}-\zeta_{20}^{9})q^{2}+(\zeta_{20}^{7}+\zeta_{20}^{9}+\cdots)q^{3}+\cdots\)
1045.1.w.f 1045.w 1045.w $16$ $0.522$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(4\) \(0\) \(q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots\)
1045.1.br.a 1045.br 1045.ar $8$ $0.522$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-8\) \(q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{4}q^{5}+(-1-\zeta_{20}+\cdots)q^{7}+\cdots\)
1045.1.br.b 1045.br 1045.ar $8$ $0.522$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-2\) \(q-\zeta_{20}^{3}q^{4}+\zeta_{20}^{8}q^{5}+(\zeta_{20}^{5}-\zeta_{20}^{6}+\cdots)q^{7}+\cdots\)
1045.2.a.a 1045.a 1.a $1$ $8.344$ \(\Q\) None None \(-1\) \(-2\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-2q^{7}+\cdots\)
1045.2.a.b 1045.a 1.a $1$ $8.344$ \(\Q\) None None \(1\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-3q^{8}-3q^{9}+q^{10}+\cdots\)
1045.2.a.c 1045.a 1.a $2$ $8.344$ \(\Q(\sqrt{2}) \) None None \(2\) \(4\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+q^{5}+\cdots\)
1045.2.a.d 1045.a 1.a $5$ $8.344$ \(\Q(\zeta_{22})^+\) None None \(-3\) \(-7\) \(5\) \(-11\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}-\beta _{4})q^{2}+(-2-\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
1045.2.a.e 1045.a 1.a $5$ $8.344$ 5.5.36497.1 None None \(-1\) \(-3\) \(-5\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(-1+\beta _{1})q^{3}+\beta _{3}q^{4}-q^{5}+\cdots\)
1045.2.a.f 1045.a 1.a $6$ $8.344$ 6.6.7281497.1 None None \(-2\) \(-1\) \(-6\) \(5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(\beta _{4}+\beta _{5})q^{4}-q^{5}+\cdots\)
1045.2.a.g 1045.a 1.a $6$ $8.344$ 6.6.131947641.1 None None \(0\) \(3\) \(6\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1045.2.a.h 1045.a 1.a $7$ $8.344$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(1\) \(3\) \(-7\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1045.2.a.i 1045.a 1.a $8$ $8.344$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-6\) \(-7\) \(8\) \(-11\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{6})q^{3}+(2+\cdots)q^{4}+\cdots\)
1045.2.a.j 1045.a 1.a $9$ $8.344$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(3\) \(3\) \(-9\) \(-9\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{8})q^{4}+\cdots\)
1045.2.a.k 1045.a 1.a $9$ $8.344$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(3\) \(3\) \(9\) \(13\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
1045.2.b.a 1045.b 5.b $4$ $8.344$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
1045.2.b.b 1045.b 5.b $16$ $8.344$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{13}+\cdots)q^{5}+\cdots\)
1045.2.b.c 1045.b 5.b $20$ $8.344$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2})q^{4}-\beta _{11}q^{5}+\cdots\)
1045.2.b.d 1045.b 5.b $22$ $8.344$ None None \(0\) \(0\) \(7\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1045.2.b.e 1045.b 5.b $30$ $8.344$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1045.2.f.a 1045.f 209.d $40$ $8.344$ None None \(0\) \(0\) \(-40\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1045.2.f.b 1045.f 209.d $40$ $8.344$ None None \(0\) \(0\) \(40\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1045.4.a.a 1045.a 1.a $1$ $61.657$ \(\Q\) None None \(-5\) \(-1\) \(-5\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}-q^{3}+17q^{4}-5q^{5}+5q^{6}+\cdots\)
1045.4.a.b 1045.a 1.a $20$ $61.657$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-12\) \(-21\) \(100\) \(-131\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(4+\cdots)q^{4}+\cdots\)
1045.4.a.c 1045.a 1.a $20$ $61.657$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-1\) \(-8\) \(-100\) \(49\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(3+\beta _{2})q^{4}-5q^{5}+\cdots\)
1045.4.a.d 1045.a 1.a $22$ $61.657$ None None \(-4\) \(-21\) \(110\) \(-41\) $-$ $\mathrm{SU}(2)$
1045.4.a.e 1045.a 1.a $22$ $61.657$ None None \(12\) \(21\) \(110\) \(93\) $+$ $\mathrm{SU}(2)$
1045.4.a.f 1045.a 1.a $23$ $61.657$ None None \(-2\) \(-9\) \(-115\) \(13\) $-$ $\mathrm{SU}(2)$
1045.4.a.g 1045.a 1.a $23$ $61.657$ None None \(6\) \(9\) \(-115\) \(-37\) $+$ $\mathrm{SU}(2)$
1045.4.a.h 1045.a 1.a $24$ $61.657$ None None \(4\) \(21\) \(120\) \(71\) $+$ $\mathrm{SU}(2)$
1045.4.a.i 1045.a 1.a $25$ $61.657$ None None \(2\) \(9\) \(-125\) \(-15\) $+$ $\mathrm{SU}(2)$
1045.6.a.a 1045.a 1.a $35$ $167.601$ None None \(-4\) \(-27\) \(-875\) \(117\) $+$ $\mathrm{SU}(2)$
1045.6.a.b 1045.a 1.a $36$ $167.601$ None None \(-8\) \(-63\) \(900\) \(-509\) $+$ $\mathrm{SU}(2)$
1045.6.a.c 1045.a 1.a $37$ $167.601$ None None \(-12\) \(-27\) \(-925\) \(337\) $+$ $\mathrm{SU}(2)$
1045.6.a.d 1045.a 1.a $37$ $167.601$ None None \(4\) \(27\) \(-925\) \(-79\) $-$ $\mathrm{SU}(2)$
1045.6.a.e 1045.a 1.a $38$ $167.601$ None None \(-24\) \(-63\) \(950\) \(-729\) $+$ $\mathrm{SU}(2)$
1045.6.a.f 1045.a 1.a $38$ $167.601$ None None \(8\) \(63\) \(950\) \(275\) $-$ $\mathrm{SU}(2)$
1045.6.a.g 1045.a 1.a $39$ $167.601$ None None \(12\) \(27\) \(-975\) \(-251\) $-$ $\mathrm{SU}(2)$
1045.6.a.h 1045.a 1.a $40$ $167.601$ None None \(24\) \(63\) \(1000\) \(839\) $-$ $\mathrm{SU}(2)$
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