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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7 13
6825.2.a.a 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-2\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
6825.2.a.b 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
6825.2.a.c 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.d 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.e 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.f 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.g 6825.a 1.a $1$ $54.498$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+q^{7}+3q^{8}+\cdots\)
6825.2.a.h 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.i 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.j 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.k 6825.a 1.a $1$ $54.498$ \(\Q\) None \(1\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-q^{7}-3q^{8}+\cdots\)
6825.2.a.l 6825.a 1.a $1$ $54.498$ \(\Q\) None \(2\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
6825.2.a.m 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
6825.2.a.n 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{13}) \) None \(-1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
6825.2.a.o 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.p 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.q 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-\beta q^{6}+q^{7}+\cdots\)
6825.2.a.r 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.s 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
6825.2.a.t 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{13}) \) None \(1\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(1+\beta )q^{4}-\beta q^{6}-q^{7}+\cdots\)
6825.2.a.u 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
6825.2.a.v 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
6825.2.a.w 6825.a 1.a $2$ $54.498$ \(\Q(\sqrt{5}) \) None \(3\) \(-2\) \(0\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots\)
6825.2.a.x 6825.a 1.a $3$ $54.498$ 3.3.229.1 None \(0\) \(-3\) \(0\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.y 6825.a 1.a $3$ $54.498$ 3.3.621.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.z 6825.a 1.a $3$ $54.498$ 3.3.837.1 None \(0\) \(-3\) \(0\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.ba 6825.a 1.a $3$ $54.498$ 3.3.229.1 None \(0\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bb 6825.a 1.a $3$ $54.498$ 3.3.229.1 None \(0\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bc 6825.a 1.a $3$ $54.498$ 3.3.621.1 None \(0\) \(3\) \(0\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bd 6825.a 1.a $3$ $54.498$ 3.3.316.1 None \(2\) \(3\) \(0\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
6825.2.a.be 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{20})^+\) None \(-2\) \(4\) \(0\) \(4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
6825.2.a.bf 6825.a 1.a $4$ $54.498$ 4.4.14013.1 None \(-1\) \(-4\) \(0\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bg 6825.a 1.a $4$ $54.498$ 4.4.17428.1 None \(-1\) \(-4\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bh 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{15})^+\) None \(-1\) \(4\) \(0\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3})q^{2}+q^{3}+\beta _{1}q^{4}+(\beta _{2}+\beta _{3})q^{6}+\cdots\)
6825.2.a.bi 6825.a 1.a $4$ $54.498$ 4.4.3981.1 None \(-1\) \(4\) \(0\) \(4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bj 6825.a 1.a $4$ $54.498$ 4.4.3981.1 None \(1\) \(-4\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bk 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{15})^+\) None \(1\) \(-4\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{2}-\beta _{3})q^{2}-q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
6825.2.a.bl 6825.a 1.a $4$ $54.498$ 4.4.14013.1 None \(1\) \(4\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bm 6825.a 1.a $4$ $54.498$ \(\Q(\zeta_{20})^+\) None \(2\) \(-4\) \(0\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-q^{3}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{6}+\cdots\)
6825.2.a.bn 6825.a 1.a $4$ $54.498$ 4.4.2225.1 None \(3\) \(-4\) \(0\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6825.2.a.bo 6825.a 1.a $5$ $54.498$ 5.5.255877.1 None \(0\) \(5\) \(0\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(2+\beta _{1})q^{4}-\beta _{2}q^{6}+\cdots\)
6825.2.a.bp 6825.a 1.a $6$ $54.498$ 6.6.259521624.1 None \(-3\) \(6\) \(0\) \(-6\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
6825.2.a.bq 6825.a 1.a $6$ $54.498$ 6.6.55102497.1 None \(-2\) \(6\) \(0\) \(6\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.br 6825.a 1.a $6$ $54.498$ 6.6.78539816.1 None \(-1\) \(-6\) \(0\) \(-6\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bs 6825.a 1.a $6$ $54.498$ 6.6.78539816.1 None \(1\) \(6\) \(0\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bt 6825.a 1.a $6$ $54.498$ 6.6.55102497.1 None \(2\) \(-6\) \(0\) \(-6\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bu 6825.a 1.a $6$ $54.498$ 6.6.259521624.1 None \(3\) \(-6\) \(0\) \(6\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
6825.2.a.bv 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(-8\) \(0\) \(8\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
6825.2.a.bw 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-2\) \(8\) \(0\) \(-8\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
6825.2.a.bx 6825.a 1.a $8$ $54.498$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-8\) \(0\) \(-8\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
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