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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1040.1.l.a 1040.l 260.g $2$ $0.519$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-65}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}-q^{5}+q^{9}-\beta q^{11}+q^{13}+\cdots\)
1040.1.l.b 1040.l 260.g $2$ $0.519$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-65}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{3}+q^{5}+q^{9}+\beta q^{11}-q^{13}+\cdots\)
1040.1.bf.a 1040.bf 260.l $2$ $0.519$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}-iq^{9}-iq^{13}+(-1+i)q^{17}+\cdots\)
1040.1.cb.a 1040.cb 1040.bb $4$ $0.519$ \(\Q(\zeta_{8})\) None \(\Q(\sqrt{65}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
1040.1.ce.a 1040.ce 260.s $2$ $0.519$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-iq^{9}+q^{13}+(1-i)q^{17}+q^{25}+\cdots\)
1040.1.cx.a 1040.cx 260.v $2$ $0.519$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}-\zeta_{6}q^{13}+(1+\zeta_{6}+\cdots)q^{17}+\cdots\)
1040.1.cx.b 1040.cx 260.v $2$ $0.519$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{5}-\zeta_{6}^{2}q^{9}+\zeta_{6}q^{13}+(-1+\cdots)q^{17}+\cdots\)
1040.1.ea.a 1040.ea 260.ae $4$ $0.519$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{4}q^{5}-\zeta_{12}q^{9}-\zeta_{12}^{2}q^{13}+\cdots\)
1040.1.ez.a 1040.ez 260.al $4$ $0.519$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}-\zeta_{12}q^{13}+(-\zeta_{12}^{3}+\cdots)q^{17}+\cdots\)
1040.2.a.a 1040.a 1.a $1$ $8.304$ \(\Q\) None None \(0\) \(-2\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
1040.2.a.b 1040.a 1.a $1$ $8.304$ \(\Q\) None None \(0\) \(-2\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
1040.2.a.c 1040.a 1.a $1$ $8.304$ \(\Q\) None None \(0\) \(-2\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
1040.2.a.d 1040.a 1.a $1$ $8.304$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+4q^{11}-q^{13}-6q^{17}+\cdots\)
1040.2.a.e 1040.a 1.a $1$ $8.304$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+q^{13}+2q^{17}+8q^{19}+\cdots\)
1040.2.a.f 1040.a 1.a $1$ $8.304$ \(\Q\) None None \(0\) \(2\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
1040.2.a.g 1040.a 1.a $1$ $8.304$ \(\Q\) None None \(0\) \(2\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots\)
1040.2.a.h 1040.a 1.a $2$ $8.304$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}-2q^{7}+(1-2\beta )q^{9}+\cdots\)
1040.2.a.i 1040.a 1.a $2$ $8.304$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots\)
1040.2.a.j 1040.a 1.a $2$ $8.304$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(-2-2\beta )q^{7}-q^{9}+\cdots\)
1040.2.a.k 1040.a 1.a $2$ $8.304$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-2q^{7}+3q^{9}+(2+\beta )q^{11}+\cdots\)
1040.2.a.l 1040.a 1.a $2$ $8.304$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
1040.2.a.m 1040.a 1.a $2$ $8.304$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
1040.2.a.n 1040.a 1.a $2$ $8.304$ \(\Q(\sqrt{2}) \) None None \(0\) \(4\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+q^{5}+2q^{7}+(3+4\beta )q^{9}+\cdots\)
1040.2.a.o 1040.a 1.a $3$ $8.304$ 3.3.564.1 None None \(0\) \(-2\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
1040.2.d.a 1040.d 5.b $2$ $8.304$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-i)q^{5}-4iq^{7}+3q^{9}+2q^{11}+\cdots\)
1040.2.d.b 1040.d 5.b $6$ $8.304$ 6.0.3534400.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{4})q^{3}+(\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
1040.2.d.c 1040.d 5.b $6$ $8.304$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{4})q^{3}+(\beta _{1}+\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1040.2.d.d 1040.d 5.b $6$ $8.304$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-\beta _{1}+\beta _{4})q^{5}+(\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1040.2.d.e 1040.d 5.b $6$ $8.304$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}+\beta _{4})q^{3}+(\beta _{1}-\beta _{4})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1040.2.d.f 1040.d 5.b $10$ $8.304$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{9}q^{3}+\beta _{2}q^{5}-\beta _{4}q^{7}+(-4-\beta _{5}+\cdots)q^{9}+\cdots\)
1040.2.f.a 1040.f 65.d $2$ $8.304$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-i)q^{5}-q^{9}+iq^{11}+\cdots\)
1040.2.f.b 1040.f 65.d $2$ $8.304$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1+i)q^{5}-q^{9}-iq^{11}+(-3+\cdots)q^{13}+\cdots\)
1040.2.f.c 1040.f 65.d $4$ $8.304$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
1040.2.f.d 1040.f 65.d $4$ $8.304$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(1-\beta _{1})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
1040.2.f.e 1040.f 65.d $8$ $8.304$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{4}+\beta _{7})q^{7}+\cdots\)
1040.2.f.f 1040.f 65.d $10$ $8.304$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}-\beta _{5}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1040.2.f.g 1040.f 65.d $10$ $8.304$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(3\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
1040.2.k.a 1040.k 13.b $2$ $8.304$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}-iq^{5}+q^{9}+(2+3i)q^{13}+\cdots\)
1040.2.k.b 1040.k 13.b $6$ $8.304$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
1040.2.k.c 1040.k 13.b $6$ $8.304$ 6.0.9144576.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
1040.2.k.d 1040.k 13.b $6$ $8.304$ 6.0.5089536.1 None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1040.2.k.e 1040.k 13.b $8$ $8.304$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots\)
1040.2.q.a 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}-q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1040.2.q.b 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+q^{5}+3\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
1040.2.q.c 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
1040.2.q.d 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.e 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.f 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-q^{5}+5\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.g 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+q^{5}-3\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
1040.2.q.h 1040.q 13.c $2$ $8.304$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}-3\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-3+3\zeta_{6})q^{11}+\cdots\)
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