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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
154.2.a.a 154.a 1.a $1$ $1.230$ \(\Q\) None \(-1\) \(0\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
154.2.a.b 154.a 1.a $1$ $1.230$ \(\Q\) None \(-1\) \(2\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-q^{7}+\cdots\)
154.2.a.c 154.a 1.a $1$ $1.230$ \(\Q\) None \(1\) \(0\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
154.2.a.d 154.a 1.a $2$ $1.230$ \(\Q(\sqrt{5}) \) None \(2\) \(-2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)
154.2.c.a 154.c 77.b $8$ $1.230$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}-\beta _{3}q^{6}+\cdots\)
154.2.e.a 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.b 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.c 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.d 154.e 7.c $2$ $1.230$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.e 154.e 7.c $4$ $1.230$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
154.2.e.f 154.e 7.c $4$ $1.230$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
154.2.f.a 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
154.2.f.b 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(-1\) \(5\) \(3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
154.2.f.c 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
154.2.f.d 154.f 11.c $4$ $1.230$ \(\Q(\zeta_{10})\) None \(1\) \(5\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2\zeta_{10}+\cdots)q^{3}+\cdots\)
154.2.f.e 154.f 11.c $8$ $1.230$ 8.0.58140625.2 None \(2\) \(-1\) \(5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots\)
154.2.i.a 154.i 77.i $16$ $1.230$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-\beta _{3}+\beta _{4}+\beta _{13})q^{3}+\beta _{10}q^{4}+\cdots\)
154.2.k.a 154.k 77.l $32$ $1.230$ None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{10}]$
154.2.m.a 154.m 77.m $8$ $1.230$ \(\Q(\zeta_{15})\) None \(-1\) \(1\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{15}]$ \(q-\zeta_{15}^{7}q^{2}+(2\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
154.2.m.b 154.m 77.m $24$ $1.230$ None \(-3\) \(-3\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{15}]$
154.2.m.c 154.m 77.m $32$ $1.230$ None \(4\) \(2\) \(-2\) \(7\) $\mathrm{SU}(2)[C_{15}]$
154.2.n.a 154.n 77.n $64$ $1.230$ None \(0\) \(0\) \(12\) \(-10\) $\mathrm{SU}(2)[C_{30}]$
154.3.b.a 154.b 7.b $16$ $4.196$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{1}q^{3}+2q^{4}+\beta _{8}q^{5}+\beta _{9}q^{6}+\cdots\)
154.3.d.a 154.d 11.b $12$ $4.196$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+\beta _{2}q^{3}-2q^{4}+(1-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)
154.3.g.a 154.g 77.h $32$ $4.196$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$
154.3.h.a 154.h 7.d $24$ $4.196$ None \(0\) \(12\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{6}]$
154.3.j.a 154.j 11.d $48$ $4.196$ None \(0\) \(4\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{10}]$
154.3.l.a 154.l 77.j $64$ $4.196$ None \(0\) \(0\) \(0\) \(-26\) $\mathrm{SU}(2)[C_{10}]$
154.3.o.a 154.o 77.p $128$ $4.196$ None \(0\) \(0\) \(12\) \(26\) $\mathrm{SU}(2)[C_{30}]$
154.3.p.a 154.p 77.o $128$ $4.196$ None \(0\) \(0\) \(-4\) \(30\) $\mathrm{SU}(2)[C_{30}]$
154.4.a.a 154.a 1.a $1$ $9.086$ \(\Q\) None \(-2\) \(-5\) \(-1\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}+4q^{4}-q^{5}+10q^{6}+\cdots\)
154.4.a.b 154.a 1.a $1$ $9.086$ \(\Q\) None \(-2\) \(0\) \(2\) \(-7\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+2q^{5}-7q^{7}-8q^{8}+\cdots\)
154.4.a.c 154.a 1.a $1$ $9.086$ \(\Q\) None \(2\) \(-10\) \(-14\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-10q^{3}+4q^{4}-14q^{5}-20q^{6}+\cdots\)
154.4.a.d 154.a 1.a $1$ $9.086$ \(\Q\) None \(2\) \(-2\) \(18\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+4q^{4}+18q^{5}-4q^{6}+\cdots\)
154.4.a.e 154.a 1.a $1$ $9.086$ \(\Q\) None \(2\) \(7\) \(3\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+7q^{3}+4q^{4}+3q^{5}+14q^{6}+\cdots\)
154.4.a.f 154.a 1.a $2$ $9.086$ \(\Q(\sqrt{137}) \) None \(-4\) \(-5\) \(-7\) \(14\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
154.4.a.g 154.a 1.a $2$ $9.086$ \(\Q(\sqrt{37}) \) None \(-4\) \(6\) \(26\) \(14\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(3+\beta )q^{3}+4q^{4}+(13-\beta )q^{5}+\cdots\)
154.4.a.h 154.a 1.a $2$ $9.086$ \(\Q(\sqrt{57}) \) None \(4\) \(-5\) \(-17\) \(-14\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2-\beta )q^{3}+4q^{4}+(-10+\cdots)q^{5}+\cdots\)
154.4.a.i 154.a 1.a $3$ $9.086$ 3.3.7636.1 None \(6\) \(6\) \(26\) \(-21\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2-\beta _{1})q^{3}+4q^{4}+(9-\beta _{2})q^{5}+\cdots\)
154.4.c.a 154.c 77.b $24$ $9.086$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
154.4.e.a 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-11\) \(-20\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{3}q^{2}+(-2+\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{3}+\cdots\)
154.4.e.b 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(7\) \(10\) \(62\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{1}q^{2}+(1-\beta _{1}+\beta _{4})q^{3}+(-4+\cdots)q^{4}+\cdots\)
154.4.e.c 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-7\) \(-20\) \(-20\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{6})q^{2}+(\beta _{1}-\beta _{2}+\beta _{6})q^{3}+\cdots\)
154.4.e.d 154.e 7.c $10$ $9.086$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-1\) \(10\) \(48\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{3})q^{2}-\beta _{2}q^{3}-4\beta _{3}q^{4}+(2+\cdots)q^{5}+\cdots\)
154.4.f.a 154.f 11.c $4$ $9.086$ \(\Q(\zeta_{10})\) None \(2\) \(-13\) \(-21\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
154.4.f.b 154.f 11.c $4$ $9.086$ \(\Q(\zeta_{10})\) None \(2\) \(2\) \(24\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)
154.4.f.c 154.f 11.c $8$ $9.086$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(20\) \(-21\) \(14\) $\mathrm{SU}(2)[C_{5}]$ \(q-2\beta _{3}q^{2}+(3+\beta _{2}+3\beta _{3})q^{3}+(-4+\cdots)q^{4}+\cdots\)
154.4.f.d 154.f 11.c $16$ $9.086$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(-21\) \(26\) \(-28\) $\mathrm{SU}(2)[C_{5}]$ \(q+2\beta _{2}q^{2}+(-2-\beta _{1}+2\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)
154.4.f.e 154.f 11.c $20$ $9.086$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-10\) \(-11\) \(-28\) \(-35\) $\mathrm{SU}(2)[C_{5}]$ \(q+2\beta _{7}q^{2}+(\beta _{1}-2\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
154.4.f.f 154.f 11.c $20$ $9.086$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-10\) \(19\) \(36\) \(35\) $\mathrm{SU}(2)[C_{5}]$ \(q+2\beta _{3}q^{2}+(1+\beta _{3}+\beta _{8})q^{3}+4\beta _{5}q^{4}+\cdots\)
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