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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4368.2.a.a 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.b 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.c 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}-q^{13}+2q^{15}+\cdots\)
4368.2.a.d 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.e 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
4368.2.a.f 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}+q^{9}+2q^{11}-q^{13}-6q^{17}+\cdots\)
4368.2.a.g 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
4368.2.a.h 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
4368.2.a.i 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.j 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
4368.2.a.k 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
4368.2.a.l 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(-1\) \(3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
4368.2.a.m 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
4368.2.a.n 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
4368.2.a.o 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-q^{13}-2q^{15}+\cdots\)
4368.2.a.p 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
4368.2.a.q 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+2q^{11}+q^{13}+\cdots\)
4368.2.a.r 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-2q^{11}+q^{13}+\cdots\)
4368.2.a.s 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
4368.2.a.t 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
4368.2.a.u 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}+q^{9}+2q^{11}-q^{13}+4q^{17}+\cdots\)
4368.2.a.v 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
4368.2.a.w 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}+6q^{11}-q^{13}+\cdots\)
4368.2.a.x 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
4368.2.a.y 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{13}+2q^{15}+\cdots\)
4368.2.a.z 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
4368.2.a.ba 4368.a 1.a $1$ $34.879$ \(\Q\) None \(0\) \(1\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-q^{7}+q^{9}-6q^{11}-q^{13}+\cdots\)
4368.2.a.bb 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
4368.2.a.bc 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
4368.2.a.bd 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
4368.2.a.be 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1+\beta )q^{5}+q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bf 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
4368.2.a.bg 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{41}) \) None \(0\) \(2\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
4368.2.a.bh 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}-q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4368.2.a.bi 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
4368.2.a.bj 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-2q^{11}-q^{13}+(2+\cdots)q^{17}+\cdots\)
4368.2.a.bk 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}-q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
4368.2.a.bl 4368.a 1.a $2$ $34.879$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bm 4368.a 1.a $3$ $34.879$ 3.3.2089.1 None \(0\) \(-3\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta _{1}q^{5}-q^{7}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4368.2.a.bn 4368.a 1.a $3$ $34.879$ 3.3.1373.1 None \(0\) \(-3\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta _{2}q^{5}+q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
4368.2.a.bo 4368.a 1.a $3$ $34.879$ 3.3.961.1 None \(0\) \(-3\) \(2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}+q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
4368.2.a.bp 4368.a 1.a $3$ $34.879$ 3.3.316.1 None \(0\) \(-3\) \(3\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-\beta _{1})q^{5}-q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
4368.2.a.bq 4368.a 1.a $3$ $34.879$ 3.3.316.1 None \(0\) \(3\) \(-3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta _{1})q^{5}+q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
4368.2.a.br 4368.a 1.a $4$ $34.879$ 4.4.17428.1 None \(0\) \(-4\) \(-3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta _{2})q^{5}-q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
4368.2.a.bs 4368.a 1.a $4$ $34.879$ 4.4.138892.1 None \(0\) \(4\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta _{1})q^{5}+q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
4368.2.e.a 4368.e 28.d $16$ $34.879$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{12}q^{5}+\beta _{13}q^{7}+q^{9}+(\beta _{7}+\cdots)q^{11}+\cdots\)
4368.2.e.b 4368.e 28.d $16$ $34.879$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{12}q^{5}-\beta _{13}q^{7}+q^{9}+(-\beta _{7}+\cdots)q^{11}+\cdots\)
4368.2.e.c 4368.e 28.d $32$ $34.879$ None \(0\) \(-32\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
4368.2.e.d 4368.e 28.d $32$ $34.879$ None \(0\) \(32\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
4368.2.h.a 4368.h 13.b $2$ $34.879$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+4iq^{5}-iq^{7}+q^{9}+(-3+2i)q^{13}+\cdots\)
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