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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 13
7800.2.a.a 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}-q^{13}-2q^{17}+\cdots\)
7800.2.a.b 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}+3q^{11}+q^{13}+7q^{17}+\cdots\)
7800.2.a.c 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{11}+q^{13}+8q^{17}+\cdots\)
7800.2.a.d 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-q^{13}-2q^{17}-4q^{19}+\cdots\)
7800.2.a.e 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+q^{13}-2q^{17}-4q^{23}+\cdots\)
7800.2.a.f 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+6q^{11}+q^{13}-2q^{17}+\cdots\)
7800.2.a.g 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-5q^{11}-q^{13}-3q^{17}+\cdots\)
7800.2.a.h 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}-q^{13}+4q^{17}+\cdots\)
7800.2.a.i 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
7800.2.a.j 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
7800.2.a.k 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7800.2.a.l 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(-1\) \(0\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+5q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
7800.2.a.m 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(-5\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-5q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
7800.2.a.n 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}-q^{13}-2q^{17}+\cdots\)
7800.2.a.o 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
7800.2.a.p 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
7800.2.a.q 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{11}-q^{13}-8q^{17}+\cdots\)
7800.2.a.r 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{11}-q^{13}-2q^{17}+\cdots\)
7800.2.a.s 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-2q^{11}+q^{13}-2q^{17}+\cdots\)
7800.2.a.t 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-q^{13}+6q^{17}+4q^{19}+\cdots\)
7800.2.a.u 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{11}-q^{13}+2q^{17}+\cdots\)
7800.2.a.v 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+3q^{11}-q^{13}-7q^{17}+\cdots\)
7800.2.a.w 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
7800.2.a.x 7800.a 1.a $1$ $62.283$ \(\Q\) None \(0\) \(1\) \(0\) \(5\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+5q^{7}+q^{9}+q^{11}-q^{13}+3q^{17}+\cdots\)
7800.2.a.y 7800.a 1.a $2$ $62.283$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
7800.2.a.z 7800.a 1.a $2$ $62.283$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{7}+q^{9}+(-1+\beta )q^{11}+\cdots\)
7800.2.a.ba 7800.a 1.a $2$ $62.283$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta )q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
7800.2.a.bb 7800.a 1.a $2$ $62.283$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\cdots\)
7800.2.a.bc 7800.a 1.a $2$ $62.283$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
7800.2.a.bd 7800.a 1.a $2$ $62.283$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
7800.2.a.be 7800.a 1.a $2$ $62.283$ \(\Q(\sqrt{41}) \) None \(0\) \(2\) \(0\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
7800.2.a.bf 7800.a 1.a $3$ $62.283$ 3.3.1849.1 None \(0\) \(-3\) \(0\) \(-5\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2+\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
7800.2.a.bg 7800.a 1.a $3$ $62.283$ 3.3.788.1 None \(0\) \(-3\) \(0\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots\)
7800.2.a.bh 7800.a 1.a $3$ $62.283$ 3.3.3732.1 None \(0\) \(-3\) \(0\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{2}q^{7}+q^{9}+(2-\beta _{1})q^{11}+\cdots\)
7800.2.a.bi 7800.a 1.a $3$ $62.283$ 3.3.940.1 None \(0\) \(-3\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{2}q^{7}+q^{9}+(2+\beta _{1})q^{11}+\cdots\)
7800.2.a.bj 7800.a 1.a $3$ $62.283$ 3.3.568.1 None \(0\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+(-2-\beta _{1})q^{11}-q^{13}+\cdots\)
7800.2.a.bk 7800.a 1.a $3$ $62.283$ 3.3.2700.1 None \(0\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{1}q^{7}+q^{9}-\beta _{1}q^{11}-q^{13}+\cdots\)
7800.2.a.bl 7800.a 1.a $3$ $62.283$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(\beta _{1}+2\beta _{2})q^{7}+q^{9}+(-1+\beta _{2})q^{11}+\cdots\)
7800.2.a.bm 7800.a 1.a $3$ $62.283$ 3.3.568.1 None \(0\) \(-3\) \(0\) \(2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{7}+q^{9}+(1+\beta _{1}+2\beta _{2})q^{11}+\cdots\)
7800.2.a.bn 7800.a 1.a $3$ $62.283$ 3.3.568.1 None \(0\) \(3\) \(0\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
7800.2.a.bo 7800.a 1.a $3$ $62.283$ 3.3.148.1 None \(0\) \(3\) \(0\) \(-1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-\beta _{1}-2\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
7800.2.a.bp 7800.a 1.a $3$ $62.283$ 3.3.568.1 None \(0\) \(3\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+(-2-\beta _{1})q^{11}+q^{13}+\cdots\)
7800.2.a.bq 7800.a 1.a $3$ $62.283$ 3.3.2700.1 None \(0\) \(3\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta _{1}q^{7}+q^{9}-\beta _{1}q^{11}+q^{13}+\cdots\)
7800.2.a.br 7800.a 1.a $3$ $62.283$ 3.3.788.1 None \(0\) \(3\) \(0\) \(1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\beta _{2})q^{11}+\cdots\)
7800.2.a.bs 7800.a 1.a $3$ $62.283$ 3.3.3732.1 None \(0\) \(3\) \(0\) \(1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{7}+q^{9}+(2-\beta _{1})q^{11}+\cdots\)
7800.2.a.bt 7800.a 1.a $4$ $62.283$ 4.4.30056.1 None \(0\) \(-4\) \(0\) \(-7\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2-\beta _{1})q^{7}+q^{9}+(\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
7800.2.a.bu 7800.a 1.a $4$ $62.283$ 4.4.461844.1 None \(0\) \(-4\) \(0\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
7800.2.a.bv 7800.a 1.a $4$ $62.283$ 4.4.10304.1 None \(0\) \(-4\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{3}q^{7}+q^{9}+(-2-\beta _{1})q^{11}+\cdots\)
7800.2.a.bw 7800.a 1.a $4$ $62.283$ 4.4.10304.1 None \(0\) \(4\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{3}q^{7}+q^{9}+(-2-\beta _{1})q^{11}+\cdots\)
7800.2.a.bx 7800.a 1.a $4$ $62.283$ 4.4.461844.1 None \(0\) \(4\) \(0\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1-\beta _{1})q^{7}+q^{9}+(1+\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
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