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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
184.1.e.a 184.e 184.e $1$ $0.092$ \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-46}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots\)
184.1.e.b 184.e 184.e $2$ $0.092$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{4}+\cdots\)
184.2.a.a 184.a 1.a $1$ $1.469$ \(\Q\) None None \(0\) \(-1\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
184.2.a.b 184.a 1.a $1$ $1.469$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-4q^{7}-2q^{9}-2q^{11}+\cdots\)
184.2.a.c 184.a 1.a $1$ $1.469$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots\)
184.2.a.d 184.a 1.a $1$ $1.469$ \(\Q\) None None \(0\) \(3\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{7}+6q^{9}-5q^{13}-6q^{17}+\cdots\)
184.2.a.e 184.a 1.a $2$ $1.469$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
184.2.b.a 184.b 8.b $2$ $1.469$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2\beta q^{3}-2q^{4}-\beta q^{5}+4q^{6}+\cdots\)
184.2.b.b 184.b 8.b $8$ $1.469$ 8.0.5198736512.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-\beta _{4}q^{3}+\beta _{1}q^{4}-\beta _{6}q^{5}+\cdots\)
184.2.b.c 184.b 8.b $12$ $1.469$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
184.2.h.a 184.h 184.h $4$ $1.469$ \(\Q(i, \sqrt{14})\) None None \(4\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}-2q^{3}-2\beta _{1}q^{4}+\beta _{3}q^{5}+\cdots\)
184.2.h.b 184.h 184.h $6$ $1.469$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{5})q^{3}+\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
184.2.h.c 184.h 184.h $12$ $1.469$ 12.0.\(\cdots\).2 None None \(-4\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(1-\beta _{2}-\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
184.2.i.a 184.i 23.c $30$ $1.469$ None None \(0\) \(-2\) \(2\) \(13\) $\mathrm{SU}(2)[C_{11}]$
184.2.i.b 184.i 23.c $30$ $1.469$ None None \(0\) \(2\) \(0\) \(-13\) $\mathrm{SU}(2)[C_{11}]$
184.2.j.a 184.j 184.j $220$ $1.469$ None None \(-11\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
184.2.p.a 184.p 184.p $220$ $1.469$ None None \(-11\) \(0\) \(0\) \(-22\) $\mathrm{SU}(2)[C_{22}]$
184.3.e.a 184.e 184.e $2$ $5.014$ \(\Q(\sqrt{23}) \) \(\Q(\sqrt{-46}) \) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+\beta q^{5}-8q^{8}+9q^{9}+\cdots\)
184.3.e.b 184.e 184.e $2$ $5.014$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-46}) \) None \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+\beta q^{5}+8q^{8}+9q^{9}+\cdots\)
184.3.e.c 184.e 184.e $6$ $5.014$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{2}+(-\beta _{3}-\beta _{4}+2\beta _{5})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
184.3.e.d 184.e 184.e $36$ $5.014$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.3.f.a 184.f 23.b $12$ $5.014$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{9}q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
184.3.g.a 184.g 8.d $44$ $5.014$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.3.k.a 184.k 184.k $460$ $5.014$ None None \(-7\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
184.3.l.a 184.l 23.d $120$ $5.014$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
184.3.m.a 184.m 184.m $460$ $5.014$ None None \(-7\) \(0\) \(0\) \(-22\) $\mathrm{SU}(2)[C_{22}]$
184.4.a.a 184.a 1.a $1$ $10.856$ \(\Q\) None None \(0\) \(-4\) \(22\) \(8\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}+22q^{5}+8q^{7}-11q^{9}-20q^{11}+\cdots\)
184.4.a.b 184.a 1.a $1$ $10.856$ \(\Q\) None None \(0\) \(8\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+8q^{3}-4q^{5}-4q^{7}+37q^{9}+26q^{11}+\cdots\)
184.4.a.c 184.a 1.a $3$ $10.856$ 3.3.761.1 None None \(0\) \(-3\) \(2\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
184.4.a.d 184.a 1.a $3$ $10.856$ 3.3.761.1 None None \(0\) \(1\) \(16\) \(18\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(5+2\beta _{1}+\beta _{2})q^{5}+(5+3\beta _{1}+\cdots)q^{7}+\cdots\)
184.4.a.e 184.a 1.a $4$ $10.856$ 4.4.167313.1 None None \(0\) \(1\) \(-20\) \(-10\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-5+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
184.4.a.f 184.a 1.a $4$ $10.856$ 4.4.2822449.1 None None \(0\) \(5\) \(-2\) \(-32\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
184.4.b.a 184.b 8.b $30$ $10.856$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.4.b.b 184.b 8.b $36$ $10.856$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.4.h.a 184.h 184.h $2$ $10.856$ \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{-23}) \) None \(3\) \(-8\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1+\beta )q^{2}-4q^{3}+(-5+3\beta )q^{4}+\cdots\)
184.4.h.b 184.h 184.h $4$ $10.856$ \(\Q(\sqrt{-3}, \sqrt{-23})\) \(\Q(\sqrt{-23}) \) None \(-3\) \(8\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1-\beta _{2}-\beta _{3})q^{2}+(2-2\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
184.4.h.c 184.h 184.h $64$ $10.856$ None None \(-4\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.4.i.a 184.i 23.c $90$ $10.856$ None None \(0\) \(-2\) \(0\) \(-87\) $\mathrm{SU}(2)[C_{11}]$
184.4.i.b 184.i 23.c $90$ $10.856$ None None \(0\) \(2\) \(-10\) \(87\) $\mathrm{SU}(2)[C_{11}]$
184.4.j.a 184.j 184.j $700$ $10.856$ None None \(-7\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
184.4.p.a 184.p 184.p $700$ $10.856$ None None \(-7\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{22}]$
184.5.e.a 184.e 184.e $1$ $19.020$ \(\Q\) \(\Q(\sqrt{-46}) \) None \(4\) \(0\) \(-42\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}+2^{4}q^{4}-42q^{5}+2^{6}q^{8}+3^{4}q^{9}+\cdots\)
184.5.e.b 184.e 184.e $1$ $19.020$ \(\Q\) \(\Q(\sqrt{-46}) \) None \(4\) \(0\) \(42\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}+2^{4}q^{4}+42q^{5}+2^{6}q^{8}+3^{4}q^{9}+\cdots\)
184.5.e.c 184.e 184.e $2$ $19.020$ \(\Q(\sqrt{46}) \) \(\Q(\sqrt{-46}) \) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}+2^{4}q^{4}+\beta q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)
184.5.e.d 184.e 184.e $6$ $19.020$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-\beta _{4}-\beta _{5})q^{2}+(-4\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
184.5.e.e 184.e 184.e $84$ $19.020$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.5.f.a 184.f 23.b $24$ $19.020$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.5.g.a 184.g 8.d $88$ $19.020$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
184.6.a.a 184.a 1.a $6$ $29.511$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-15\) \(-26\) \(72\) $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{3})q^{3}+(-4-\beta _{3}+\beta _{4})q^{5}+\cdots\)
184.6.a.b 184.a 1.a $7$ $29.511$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(0\) \(-23\) \(-50\) \(-146\) $+$ $\mathrm{SU}(2)$ \(q+(-3+\beta _{1})q^{3}+(-7+\beta _{2})q^{5}+(-22+\cdots)q^{7}+\cdots\)
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