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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6552.2.a.a 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}-6q^{11}-q^{13}-6q^{17}+\cdots\)
6552.2.a.b 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+q^{7}+4q^{11}+q^{13}-6q^{17}+\cdots\)
6552.2.a.c 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-q^{13}+2q^{17}+5q^{19}+\cdots\)
6552.2.a.d 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}+3q^{11}-q^{13}-q^{17}+\cdots\)
6552.2.a.e 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+q^{13}+6q^{17}-4q^{19}+\cdots\)
6552.2.a.f 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-4q^{11}-q^{13}-6q^{17}+\cdots\)
6552.2.a.g 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+2q^{11}-q^{13}+6q^{17}+\cdots\)
6552.2.a.h 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+4q^{11}-q^{13}-2q^{17}+\cdots\)
6552.2.a.i 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-q^{11}+q^{13}+3q^{17}+\cdots\)
6552.2.a.j 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
6552.2.a.k 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{7}-2q^{11}-q^{13}+2q^{17}-5q^{25}+\cdots\)
6552.2.a.l 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}+2q^{11}-q^{13}+2q^{17}+8q^{23}+\cdots\)
6552.2.a.m 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{11}-q^{13}-4q^{17}+2q^{19}+\cdots\)
6552.2.a.n 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-q^{13}-2q^{17}-4q^{19}-2q^{23}+\cdots\)
6552.2.a.o 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-q^{13}+2q^{17}-4q^{19}+2q^{23}+\cdots\)
6552.2.a.p 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}+2q^{11}-q^{13}+6q^{17}-8q^{19}+\cdots\)
6552.2.a.q 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{11}+q^{13}-7q^{19}+\cdots\)
6552.2.a.r 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+q^{11}+q^{13}-3q^{17}+\cdots\)
6552.2.a.s 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{11}-q^{13}+6q^{17}+\cdots\)
6552.2.a.t 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots\)
6552.2.a.u 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+4q^{11}+q^{13}-2q^{17}+\cdots\)
6552.2.a.v 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}+4q^{11}+q^{13}+6q^{17}+\cdots\)
6552.2.a.w 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}-6q^{11}-q^{13}+8q^{17}+\cdots\)
6552.2.a.x 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}-3q^{11}-q^{13}+q^{17}+\cdots\)
6552.2.a.y 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}+2q^{11}-q^{13}+7q^{19}+\cdots\)
6552.2.a.z 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+q^{7}+5q^{11}-q^{13}-3q^{17}+\cdots\)
6552.2.a.ba 6552.a 1.a $1$ $52.318$ \(\Q\) None \(0\) \(0\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}-4q^{11}+q^{13}+6q^{17}+\cdots\)
6552.2.a.bb 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(-3+\beta )q^{11}+\cdots\)
6552.2.a.bc 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+\cdots\)
6552.2.a.bd 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}-q^{7}+(2-\beta )q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
6552.2.a.be 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+q^{7}+2q^{11}-q^{13}+(-2+\cdots)q^{17}+\cdots\)
6552.2.a.bf 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(1-\beta )q^{11}-q^{13}+(-1+\cdots)q^{17}+\cdots\)
6552.2.a.bg 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(-3+\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bh 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(-2+\beta )q^{11}-q^{13}+\cdots\)
6552.2.a.bi 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(1+\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bj 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+(2-3\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bk 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bl 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+q^{13}+\cdots\)
6552.2.a.bm 6552.a 1.a $2$ $52.318$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(3-\beta )q^{11}-q^{13}+\cdots\)
6552.2.a.bn 6552.a 1.a $3$ $52.318$ 3.3.316.1 None \(0\) \(0\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}+q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
6552.2.a.bo 6552.a 1.a $3$ $52.318$ 3.3.961.1 None \(0\) \(0\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{5}-q^{7}+(-3+\beta _{1}-\beta _{2})q^{11}+\cdots\)
6552.2.a.bp 6552.a 1.a $3$ $52.318$ 3.3.2089.1 None \(0\) \(0\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+(-\beta _{1}-\beta _{2})q^{11}-q^{13}+\cdots\)
6552.2.a.bq 6552.a 1.a $4$ $52.318$ 4.4.19664.1 None \(0\) \(0\) \(-4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}-q^{7}+(-1-\beta _{1})q^{11}+\cdots\)
6552.2.a.br 6552.a 1.a $4$ $52.318$ 4.4.64268.1 None \(0\) \(0\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{5}-q^{7}+(\beta _{1}+2\beta _{3})q^{11}+\cdots\)
6552.2.a.bs 6552.a 1.a $4$ $52.318$ 4.4.138892.1 None \(0\) \(0\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}-q^{7}+(1-\beta _{2})q^{11}+\cdots\)
6552.2.a.bt 6552.a 1.a $4$ $52.318$ 4.4.183064.1 None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{5}+q^{7}-\beta _{1}q^{11}+q^{13}+(-1+\cdots)q^{17}+\cdots\)
6552.2.a.bu 6552.a 1.a $4$ $52.318$ 4.4.19664.1 None \(0\) \(0\) \(4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{5}-q^{7}+(1+\beta _{1})q^{11}-q^{13}+\cdots\)
6552.2.a.bv 6552.a 1.a $5$ $52.318$ 5.5.9654428.1 None \(0\) \(0\) \(-1\) \(5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{5}+q^{7}+(-2-\beta _{3})q^{11}+q^{13}+\cdots\)
6552.2.a.bw 6552.a 1.a $5$ $52.318$ 5.5.9654428.1 None \(0\) \(0\) \(1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+(2+\beta _{3})q^{11}+q^{13}+\cdots\)
6552.2.v.a 6552.v 21.c $48$ $52.318$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$
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