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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2300.1.f.a 2300.f 23.b $2$ $1.148$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-q^{9}-iq^{17}-iq^{23}+q^{29}+\cdots\)
2300.1.k.a 2300.k 460.k $4$ $1.148$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{115}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+2q^{6}+\cdots\)
2300.1.k.b 2300.k 460.k $8$ $1.148$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}q^{2}-\zeta_{24}^{3}q^{3}+\zeta_{24}^{2}q^{4}+\zeta_{24}^{4}q^{6}+\cdots\)
2300.1.k.c 2300.k 460.k $24$ $1.148$ \(\Q(\zeta_{72})\) \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{72}^{19}q^{2}+(\zeta_{72}^{25}-\zeta_{72}^{29})q^{3}+\cdots\)
2300.1.bf.a 2300.bf 92.g $20$ $1.148$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{44}^{7}q^{2}+(-\zeta_{44}^{5}+\zeta_{44}^{19})q^{3}+\cdots\)
2300.1.bh.a 2300.bh 460.v $40$ $1.148$ \(\Q(\zeta_{88})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{88}q^{2}+(-\zeta_{88}^{7}-\zeta_{88}^{31})q^{3}+\cdots\)
2300.2.a.a 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}+3q^{13}-4q^{17}+\cdots\)
2300.2.a.b 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-3q^{11}+5q^{13}+\cdots\)
2300.2.a.c 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}+q^{13}+6q^{17}+\cdots\)
2300.2.a.d 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(-1\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{7}-2q^{9}-6q^{11}+q^{13}+\cdots\)
2300.2.a.e 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+6q^{11}-6q^{13}-7q^{17}+\cdots\)
2300.2.a.f 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}-4q^{11}-q^{13}+\cdots\)
2300.2.a.g 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}-3q^{11}-5q^{13}+\cdots\)
2300.2.a.h 2300.a 1.a $1$ $18.366$ \(\Q\) None None \(0\) \(3\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{7}+6q^{9}+2q^{11}+5q^{13}+\cdots\)
2300.2.a.i 2300.a 1.a $2$ $18.366$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots\)
2300.2.a.j 2300.a 1.a $3$ $18.366$ 3.3.321.1 None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-2\beta _{1}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
2300.2.a.k 2300.a 1.a $3$ $18.366$ 3.3.321.1 None None \(0\) \(2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+2\beta _{1}q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
2300.2.a.l 2300.a 1.a $4$ $18.366$ 4.4.53121.1 None None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.2.a.m 2300.a 1.a $4$ $18.366$ 4.4.53121.1 None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
2300.2.a.n 2300.a 1.a $6$ $18.366$ 6.6.143376304.1 None None \(0\) \(-4\) \(0\) \(-9\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
2300.2.a.o 2300.a 1.a $6$ $18.366$ 6.6.143376304.1 None None \(0\) \(4\) \(0\) \(9\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(2-\beta _{3})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
2300.2.c.a 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-2iq^{7}-6q^{9}-3iq^{13}+\cdots\)
2300.2.c.b 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-4iq^{7}-6q^{9}+2q^{11}+5iq^{13}+\cdots\)
2300.2.c.c 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-iq^{7}-q^{9}-3q^{11}-5iq^{13}+\cdots\)
2300.2.c.d 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}+2q^{9}-6q^{11}-iq^{13}+\cdots\)
2300.2.c.e 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{7}+2q^{9}-4q^{11}-iq^{13}+\cdots\)
2300.2.c.f 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{7}+2q^{9}-iq^{13}+6iq^{17}+\cdots\)
2300.2.c.g 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}+6q^{11}+6iq^{13}-7iq^{17}+\cdots\)
2300.2.c.h 2300.c 5.b $4$ $18.366$ \(\Q(i, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2300.2.c.i 2300.c 5.b $6$ $18.366$ 6.0.6594624.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{4})q^{3}+2\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.2.c.j 2300.c 5.b $8$ $18.366$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.2.i.a 2300.i 115.e $8$ $18.366$ 8.0.\(\cdots\).122 \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{1}q^{7}-3\beta _{2}q^{9}+(\beta _{1}-2\beta _{5})q^{17}+\cdots\)
2300.2.i.b 2300.i 115.e $8$ $18.366$ 8.0.157351936.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}-\beta _{5}q^{7}+4\beta _{3}q^{9}-\beta _{1}q^{11}+\cdots\)
2300.2.i.c 2300.i 115.e $8$ $18.366$ 8.0.\(\cdots\).3 None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3})q^{3}+\beta _{2}q^{7}-\beta _{3}q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2300.2.i.d 2300.i 115.e $16$ $18.366$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{3}+(\beta _{10}-\beta _{12}-\beta _{15})q^{7}+(\beta _{3}+\cdots)q^{9}+\cdots\)
2300.2.i.e 2300.i 115.e $16$ $18.366$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{5}-\beta _{9})q^{7}+(\beta _{6}-\beta _{7}+\cdots)q^{9}+\cdots\)
2300.2.i.f 2300.i 115.e $16$ $18.366$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{9})q^{7}+(\beta _{6}+\cdots)q^{9}+\cdots\)
2300.3.d.a 2300.d 115.c $8$ $62.670$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{5})q^{7}+(-2+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.3.d.b 2300.d 115.c $32$ $62.670$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2300.3.d.c 2300.d 115.c $32$ $62.670$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2300.3.f.a 2300.f 23.b $4$ $62.670$ 4.0.53792.1 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{2})q^{7}+(1+\beta _{3})q^{9}+\cdots\)
2300.3.f.b 2300.f 23.b $4$ $62.670$ \(\Q(i, \sqrt{345})\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-4\beta _{2})q^{7}-9q^{9}+(-3\beta _{1}+4\beta _{2}+\cdots)q^{17}+\cdots\)
2300.3.f.c 2300.f 23.b $16$ $62.670$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{7}+(4+\beta _{3})q^{9}-\beta _{8}q^{11}+\cdots\)
2300.3.f.d 2300.f 23.b $16$ $62.670$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{1}q^{7}+(4+\beta _{3})q^{9}+\beta _{8}q^{11}+\cdots\)
2300.3.f.e 2300.f 23.b $16$ $62.670$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{7}q^{7}+(4-\beta _{1})q^{9}+(\beta _{4}+\cdots)q^{11}+\cdots\)
2300.3.f.f 2300.f 23.b $20$ $62.670$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}-\beta _{16}q^{7}+(4+\beta _{2})q^{9}-\beta _{12}q^{11}+\cdots\)
2300.4.a.a 2300.a 1.a $3$ $135.704$ 3.3.28669.1 None None \(0\) \(-8\) \(0\) \(-42\) $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{2})q^{3}+(-14+\beta _{1})q^{7}+(28+\cdots)q^{9}+\cdots\)
2300.4.a.b 2300.a 1.a $3$ $135.704$ 3.3.1229.1 None None \(0\) \(4\) \(0\) \(46\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(18-5\beta _{1}-3\beta _{2})q^{7}+\cdots\)
2300.4.a.c 2300.a 1.a $5$ $135.704$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(3\) \(0\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
2300.4.a.d 2300.a 1.a $5$ $135.704$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(7\) \(0\) \(20\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3})q^{3}+(5+\beta _{1}+2\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
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