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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.1.c.a 108.c 3.b $1$ $0.054$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots\)
108.2.a.a 108.a 1.a $1$ $0.862$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) $-$ $N(\mathrm{U}(1))$ \(q+5q^{7}-7q^{13}-q^{19}-5q^{25}-4q^{31}+\cdots\)
108.2.b.a 108.b 12.b $4$ $0.862$ \(\Q(\sqrt{3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
108.2.b.b 108.b 12.b $4$ $0.862$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
108.2.e.a 108.e 9.c $2$ $0.862$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
108.2.h.a 108.h 36.h $8$ $0.862$ 8.0.170772624.1 None None \(3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{4}+\cdots\)
108.2.i.a 108.i 27.e $18$ $0.862$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{12}q^{3}+(-1+\beta _{1}-\beta _{4}-\beta _{6}-\beta _{7}+\cdots)q^{5}+\cdots\)
108.2.l.a 108.l 108.l $96$ $0.862$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
108.3.c.a 108.c 3.b $1$ $2.943$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(11\) $\mathrm{U}(1)[D_{2}]$ \(q+11q^{7}+23q^{13}-37q^{19}+5^{2}q^{25}+\cdots\)
108.3.c.b 108.c 3.b $2$ $2.943$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-7q^{7}+iq^{11}+14q^{13}+2iq^{17}+\cdots\)
108.3.d.a 108.d 4.b $2$ $2.943$ \(\Q(\sqrt{-3}) \) None None \(-2\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+7q^{5}+\cdots\)
108.3.d.b 108.d 4.b $2$ $2.943$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(-14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}-7q^{5}+\cdots\)
108.3.d.c 108.d 4.b $4$ $2.943$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(3+\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
108.3.d.d 108.d 4.b $8$ $2.943$ 8.0.207360000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{5})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
108.3.f.a 108.f 36.f $2$ $2.943$ \(\Q(\sqrt{-3}) \) None None \(-4\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-2q^{2}+4q^{4}+(4-4\zeta_{6})q^{5}+(-4+\cdots)q^{7}+\cdots\)
108.3.f.b 108.f 36.f $2$ $2.943$ \(\Q(\sqrt{-3}) \) None None \(2\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-2\zeta_{6})q^{2}-4\zeta_{6}q^{4}+(4-4\zeta_{6})q^{5}+\cdots\)
108.3.f.c 108.f 36.f $16$ $2.943$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(3\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{3})q^{4}+(-\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
108.3.g.a 108.g 9.d $4$ $2.943$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(-9\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}-2\beta _{3})q^{7}+\cdots\)
108.3.j.a 108.j 108.j $204$ $2.943$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
108.3.k.a 108.k 27.f $36$ $2.943$ None None \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{18}]$
108.4.a.a 108.a 1.a $1$ $6.372$ \(\Q\) None None \(0\) \(0\) \(-9\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-9q^{5}-q^{7}-63q^{11}-28q^{13}-72q^{17}+\cdots\)
108.4.a.b 108.a 1.a $1$ $6.372$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-37\) $-$ $N(\mathrm{U}(1))$ \(q-37q^{7}-19q^{13}-163q^{19}-5^{3}q^{25}+\cdots\)
108.4.a.c 108.a 1.a $1$ $6.372$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(17\) $+$ $N(\mathrm{U}(1))$ \(q+17q^{7}+89q^{13}+107q^{19}-5^{3}q^{25}+\cdots\)
108.4.a.d 108.a 1.a $1$ $6.372$ \(\Q\) None None \(0\) \(0\) \(9\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+9q^{5}-q^{7}+63q^{11}-28q^{13}+72q^{17}+\cdots\)
108.4.b.a 108.b 12.b $12$ $6.372$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(-1-\beta _{4})q^{4}-\beta _{9}q^{5}+(\beta _{2}+\cdots)q^{7}+\cdots\)
108.4.b.b 108.b 12.b $12$ $6.372$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{6}q^{4}+\beta _{5}q^{5}-\beta _{4}q^{7}+\cdots\)
108.4.e.a 108.e 9.c $6$ $6.372$ 6.0.6831243.2 None None \(0\) \(0\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\beta _{1}+\beta _{5})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
108.4.h.a 108.h 36.h $8$ $6.372$ 8.0.\(\cdots\).1 None None \(3\) \(0\) \(-66\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{7}q^{2}+(2\beta _{2}-2\beta _{3}-2\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
108.4.h.b 108.h 36.h $24$ $6.372$ None None \(0\) \(0\) \(72\) \(0\) $\mathrm{SU}(2)[C_{6}]$
108.4.i.a 108.i 27.e $54$ $6.372$ None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{9}]$
108.4.l.a 108.l 108.l $312$ $6.372$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
108.5.c.a 108.c 3.b $1$ $11.164$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(23\) $\mathrm{U}(1)[D_{2}]$ \(q+23q^{7}+191q^{13}+647q^{19}+5^{4}q^{25}+\cdots\)
108.5.c.b 108.c 3.b $2$ $11.164$ \(\Q(\sqrt{-6}) \) None None \(0\) \(0\) \(0\) \(-62\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{5}-31q^{7}-5\beta q^{11}-241q^{13}+\cdots\)
108.5.c.c 108.c 3.b $2$ $11.164$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+5q^{7}+13iq^{11}-34q^{13}+\cdots\)
108.5.d.a 108.d 4.b $16$ $11.164$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}-\beta _{7}+\cdots)q^{5}+\cdots\)
108.5.d.b 108.d 4.b $16$ $11.164$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(2+\beta _{2})q^{4}+(-\beta _{7}+\beta _{9}+\cdots)q^{5}+\cdots\)
108.5.f.a 108.f 36.f $44$ $11.164$ None None \(1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
108.5.g.a 108.g 9.d $8$ $11.164$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(0\) \(0\) \(9\) \(13\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{2}+\beta _{4}+\beta _{7})q^{5}+(3-\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
108.5.j.a 108.j 108.j $420$ $11.164$ None None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$
108.5.k.a 108.k 27.f $72$ $11.164$ None None \(0\) \(0\) \(9\) \(0\) $\mathrm{SU}(2)[C_{18}]$
108.6.a.a 108.a 1.a $1$ $17.321$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-25\) $+$ $N(\mathrm{U}(1))$ \(q-5^{2}q^{7}-427q^{13}-1711q^{19}-5^{5}q^{25}+\cdots\)
108.6.a.b 108.a 1.a $2$ $17.321$ \(\Q(\sqrt{41}) \) None None \(0\) \(0\) \(0\) \(-32\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(-2^{4}+3\beta )q^{7}+(-3^{5}+8\beta )q^{11}+\cdots\)
108.6.a.c 108.a 1.a $2$ $17.321$ \(\Q(\sqrt{41}) \) None None \(0\) \(0\) \(0\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+(-2^{4}-3\beta )q^{7}+(3^{5}+8\beta )q^{11}+\cdots\)
108.6.a.d 108.a 1.a $2$ $17.321$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(0\) \(58\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+29q^{7}+\beta q^{11}+329q^{13}+\cdots\)
108.6.b.a 108.b 12.b $4$ $17.321$ \(\Q(\sqrt{3}, \sqrt{-29})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(-26-2\beta _{3})q^{4}+\cdots\)
108.6.b.b 108.b 12.b $16$ $17.321$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(6-\beta _{4})q^{4}+(-3\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
108.6.b.c 108.b 12.b $20$ $17.321$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+(1+\beta _{2})q^{4}+\beta _{15}q^{5}-\beta _{5}q^{7}+\cdots\)
108.6.e.a 108.e 9.c $10$ $17.321$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(21\) \(29\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{1}+\beta _{7})q^{5}+(6\beta _{1}+\beta _{2}+\beta _{7}+\cdots)q^{7}+\cdots\)
108.6.h.a 108.h 36.h $56$ $17.321$ None None \(3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
108.6.i.a 108.i 27.e $90$ $17.321$ None None \(0\) \(0\) \(-87\) \(0\) $\mathrm{SU}(2)[C_{9}]$
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