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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
6480.2.a.a 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-5q^{7}-q^{13}-6q^{17}-5q^{19}+\cdots\)
6480.2.a.b 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{11}-4q^{13}+6q^{17}+\cdots\)
6480.2.a.c 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+3q^{11}-4q^{13}-6q^{17}+\cdots\)
6480.2.a.d 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{11}+7q^{19}-6q^{23}+q^{25}+\cdots\)
6480.2.a.e 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+5q^{11}+3q^{17}-5q^{19}-6q^{23}+\cdots\)
6480.2.a.f 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+5q^{11}+4q^{13}+4q^{17}+5q^{19}+\cdots\)
6480.2.a.g 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-6q^{11}+2q^{13}+4q^{19}+\cdots\)
6480.2.a.h 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{13}+6q^{17}-2q^{19}+\cdots\)
6480.2.a.i 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+5q^{13}+6q^{17}-5q^{19}+\cdots\)
6480.2.a.j 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{11}-2q^{17}-q^{19}+\cdots\)
6480.2.a.k 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}+2q^{11}-2q^{13}+4q^{17}+\cdots\)
6480.2.a.l 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+3q^{11}-4q^{13}-3q^{17}+\cdots\)
6480.2.a.m 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+3q^{11}-4q^{13}-5q^{19}+\cdots\)
6480.2.a.n 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-5q^{7}-q^{13}+6q^{17}-5q^{19}+\cdots\)
6480.2.a.o 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{11}-4q^{13}+6q^{17}+\cdots\)
6480.2.a.p 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+3q^{11}-4q^{13}-6q^{17}+\cdots\)
6480.2.a.q 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-5q^{11}-3q^{17}-5q^{19}+6q^{23}+\cdots\)
6480.2.a.r 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-5q^{11}+4q^{13}-4q^{17}+5q^{19}+\cdots\)
6480.2.a.s 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{11}+7q^{19}+6q^{23}+q^{25}+\cdots\)
6480.2.a.t 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
6480.2.a.u 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+5q^{13}-6q^{17}-5q^{19}+\cdots\)
6480.2.a.v 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+6q^{11}+2q^{13}+4q^{19}+\cdots\)
6480.2.a.w 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+3q^{11}+2q^{17}-q^{19}+\cdots\)
6480.2.a.x 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+3q^{7}-2q^{11}-2q^{13}-4q^{17}+\cdots\)
6480.2.a.y 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{11}-4q^{13}-5q^{19}+\cdots\)
6480.2.a.z 6480.a 1.a $1$ $51.743$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{11}-4q^{13}+3q^{17}+\cdots\)
6480.2.a.ba 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-2+\beta )q^{7}+(-2+2\beta )q^{11}+\cdots\)
6480.2.a.bb 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-2+\beta )q^{7}+2\beta q^{11}+(2-\beta )q^{13}+\cdots\)
6480.2.a.bc 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta )q^{7}-2q^{17}+(2-2\beta )q^{19}+\cdots\)
6480.2.a.bd 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+(-1+\beta )q^{11}-\beta q^{13}+\cdots\)
6480.2.a.be 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+(1+\beta )q^{11}-2\beta q^{13}+\cdots\)
6480.2.a.bf 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}+(3-\beta )q^{11}+(2+\beta )q^{13}+\cdots\)
6480.2.a.bg 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+(-2+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.bh 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}-\beta q^{11}+(2+2\beta )q^{13}+\cdots\)
6480.2.a.bi 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-2\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(3+\beta )q^{7}+(-4-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.bj 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-2+\beta )q^{7}-2\beta q^{11}+(2-\beta )q^{13}+\cdots\)
6480.2.a.bk 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-2+\beta )q^{7}+(2-2\beta )q^{11}+\cdots\)
6480.2.a.bl 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta )q^{7}+2q^{17}+(2-2\beta )q^{19}+\cdots\)
6480.2.a.bm 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{57}) \) None \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+(-3+\beta )q^{11}+(2+\beta )q^{13}+\cdots\)
6480.2.a.bn 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+(-1-\beta )q^{11}-2\beta q^{13}+\cdots\)
6480.2.a.bo 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+(1-\beta )q^{11}-\beta q^{13}+\cdots\)
6480.2.a.bp 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+\beta q^{11}+(2+2\beta )q^{13}+\cdots\)
6480.2.a.bq 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+(2-\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.br 6480.a 1.a $2$ $51.743$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(2\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(3+\beta )q^{7}+(4+\beta )q^{11}+(-2+\cdots)q^{13}+\cdots\)
6480.2.a.bs 6480.a 1.a $3$ $51.743$ 3.3.564.1 None \(0\) \(0\) \(-3\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-2+\beta _{1})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
6480.2.a.bt 6480.a 1.a $3$ $51.743$ 3.3.564.1 None \(0\) \(0\) \(-3\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1+\beta _{1})q^{7}+\beta _{2}q^{11}+(2+\cdots)q^{13}+\cdots\)
6480.2.a.bu 6480.a 1.a $3$ $51.743$ 3.3.564.1 None \(0\) \(0\) \(-3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(-1-\beta _{2})q^{11}+\cdots\)
6480.2.a.bv 6480.a 1.a $3$ $51.743$ 3.3.564.1 None \(0\) \(0\) \(3\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-2+\beta _{1})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
6480.2.a.bw 6480.a 1.a $3$ $51.743$ 3.3.564.1 None \(0\) \(0\) \(3\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1+\beta _{1})q^{7}-\beta _{2}q^{11}+(2+\cdots)q^{13}+\cdots\)
6480.2.a.bx 6480.a 1.a $3$ $51.743$ 3.3.564.1 None \(0\) \(0\) \(3\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+(1+\beta _{2})q^{11}+\cdots\)
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