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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2640.1.l.a 2640.l 660.g $1$ $1.318$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) \(\Q(\sqrt{15}) \) \(0\) \(-1\) \(-1\) \(0\) \(q-q^{3}-q^{5}+q^{9}-q^{11}+q^{15}+q^{25}+\cdots\)
2640.1.l.b 2640.l 660.g $1$ $1.318$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) \(\Q(\sqrt{15}) \) \(0\) \(-1\) \(1\) \(0\) \(q-q^{3}+q^{5}+q^{9}+q^{11}-q^{15}+q^{25}+\cdots\)
2640.1.l.c 2640.l 660.g $1$ $1.318$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) \(\Q(\sqrt{15}) \) \(0\) \(1\) \(-1\) \(0\) \(q+q^{3}-q^{5}+q^{9}+q^{11}-q^{15}+q^{25}+\cdots\)
2640.1.l.d 2640.l 660.g $1$ $1.318$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-165}) \) \(\Q(\sqrt{15}) \) \(0\) \(1\) \(1\) \(0\) \(q+q^{3}+q^{5}+q^{9}-q^{11}+q^{15}+q^{25}+\cdots\)
2640.1.l.e 2640.l 660.g $2$ $1.318$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}-q^{11}+\cdots\)
2640.1.l.f 2640.l 660.g $2$ $1.318$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}+q^{11}+\cdots\)
2640.1.l.g 2640.l 660.g $2$ $1.318$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+q^{11}+\cdots\)
2640.1.l.h 2640.l 660.g $2$ $1.318$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(1\) \(0\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{9}-q^{11}+\cdots\)
2640.1.ch.a 2640.ch 165.l $2$ $1.318$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+iq^{5}-q^{9}+iq^{11}+q^{15}+\cdots\)
2640.1.ch.b 2640.ch 165.l $2$ $1.318$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-iq^{5}+q^{9}-iq^{11}-iq^{15}+\cdots\)
2640.1.ch.c 2640.ch 165.l $4$ $1.318$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{9}+\cdots\)
2640.1.ch.d 2640.ch 165.l $4$ $1.318$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{4}q^{9}+\zeta_{12}^{3}q^{11}+\cdots\)
2640.2.a.a 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+q^{15}+\cdots\)
2640.2.a.b 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
2640.2.a.c 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}+q^{15}+\cdots\)
2640.2.a.d 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.e 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+q^{15}+\cdots\)
2640.2.a.f 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+4q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.g 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}-q^{15}+\cdots\)
2640.2.a.h 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}-q^{15}+\cdots\)
2640.2.a.i 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(-1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}-q^{11}-6q^{13}+\cdots\)
2640.2.a.j 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.k 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.l 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.m 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-q^{11}-4q^{13}-q^{15}+\cdots\)
2640.2.a.n 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-q^{11}+2q^{13}-q^{15}+\cdots\)
2640.2.a.o 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
2640.2.a.p 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
2640.2.a.q 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.r 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-q^{11}+2q^{13}+\cdots\)
2640.2.a.s 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-q^{11}-6q^{13}+q^{15}+\cdots\)
2640.2.a.t 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-q^{11}+6q^{13}+q^{15}+\cdots\)
2640.2.a.u 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}+q^{11}-2q^{13}+q^{15}+\cdots\)
2640.2.a.v 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
2640.2.a.w 2640.a 1.a $1$ $21.081$ \(\Q\) None None \(0\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
2640.2.a.x 2640.a 1.a $2$ $21.081$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots\)
2640.2.a.y 2640.a 1.a $2$ $21.081$ \(\Q(\sqrt{13}) \) None None \(0\) \(-2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}+q^{11}+\cdots\)
2640.2.a.z 2640.a 1.a $2$ $21.081$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta q^{7}+q^{9}-q^{11}+(2+\cdots)q^{13}+\cdots\)
2640.2.a.ba 2640.a 1.a $2$ $21.081$ \(\Q(\sqrt{17}) \) None None \(0\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-q^{11}+\cdots\)
2640.2.a.bb 2640.a 1.a $2$ $21.081$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(2+\beta )q^{7}+q^{9}+q^{11}+\cdots\)
2640.2.a.bc 2640.a 1.a $2$ $21.081$ \(\Q(\sqrt{13}) \) None None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}-q^{11}+\cdots\)
2640.2.a.bd 2640.a 1.a $2$ $21.081$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+q^{11}+(2+\cdots)q^{13}+\cdots\)
2640.2.a.be 2640.a 1.a $3$ $21.081$ 3.3.148.1 None None \(0\) \(-3\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}-q^{11}+(-1+\cdots)q^{13}+\cdots\)
2640.2.d.a 2640.d 5.b $2$ $21.081$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-2i)q^{5}+2iq^{7}-q^{9}+\cdots\)
2640.2.d.b 2640.d 5.b $2$ $21.081$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(1-2i)q^{5}-q^{9}-q^{11}-4iq^{13}+\cdots\)
2640.2.d.c 2640.d 5.b $4$ $21.081$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{5}+(-\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
2640.2.d.d 2640.d 5.b $4$ $21.081$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2640.2.d.e 2640.d 5.b $4$ $21.081$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{3}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
2640.2.d.f 2640.d 5.b $6$ $21.081$ 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
2640.2.d.g 2640.d 5.b $6$ $21.081$ 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+(\beta _{1}+\beta _{5})q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)
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