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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.2.a.a 138.a 1.a $1$ $1.102$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-2q^{7}+\cdots\)
138.2.a.b 138.a 1.a $1$ $1.102$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
138.2.a.c 138.a 1.a $1$ $1.102$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
138.2.a.d 138.a 1.a $2$ $1.102$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
138.2.d.a 138.d 69.c $8$ $1.102$ 8.0.\(\cdots\).3 None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}-q^{4}+\beta _{3}q^{5}+\cdots\)
138.2.e.a 138.e 23.c $10$ $1.102$ \(\Q(\zeta_{22})\) None \(-1\) \(-1\) \(8\) \(8\) $\mathrm{SU}(2)[C_{11}]$ \(q-\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
138.2.e.b 138.e 23.c $10$ $1.102$ \(\Q(\zeta_{22})\) None \(-1\) \(1\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{11}]$ \(q-\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
138.2.e.c 138.e 23.c $10$ $1.102$ \(\Q(\zeta_{22})\) None \(1\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{11}]$ \(q+\zeta_{22}q^{2}+\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(1+\cdots)q^{5}+\cdots\)
138.2.e.d 138.e 23.c $10$ $1.102$ \(\Q(\zeta_{22})\) None \(1\) \(1\) \(2\) \(2\) $\mathrm{SU}(2)[C_{11}]$ \(q+\zeta_{22}q^{2}-\zeta_{22}^{8}q^{3}+\zeta_{22}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
138.2.f.a 138.f 69.g $80$ $1.102$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
138.3.b.a 138.b 23.b $8$ $3.760$ 8.0.1358954496.3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+\beta _{1}q^{3}+2q^{4}+(-\beta _{2}+2\beta _{3}+\cdots)q^{5}+\cdots\)
138.3.c.a 138.c 3.b $16$ $3.760$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-2q^{4}-\beta _{7}q^{5}+\beta _{11}q^{6}+\cdots\)
138.3.g.a 138.g 69.h $160$ $3.760$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
138.3.h.a 138.h 23.d $80$ $3.760$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
138.4.a.a 138.a 1.a $1$ $8.142$ \(\Q\) None \(-2\) \(-3\) \(-10\) \(32\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-10q^{5}+6q^{6}+\cdots\)
138.4.a.b 138.a 1.a $1$ $8.142$ \(\Q\) None \(-2\) \(3\) \(2\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
138.4.a.c 138.a 1.a $1$ $8.142$ \(\Q\) None \(2\) \(-3\) \(-2\) \(-34\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
138.4.a.d 138.a 1.a $2$ $8.142$ \(\Q(\sqrt{277}) \) None \(-4\) \(6\) \(2\) \(28\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(1-\beta )q^{5}-6q^{6}+\cdots\)
138.4.a.e 138.a 1.a $2$ $8.142$ \(\Q(\sqrt{2}) \) None \(4\) \(-6\) \(8\) \(12\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+(4+\beta )q^{5}-6q^{6}+\cdots\)
138.4.a.f 138.a 1.a $3$ $8.142$ 3.3.16372.1 None \(6\) \(9\) \(20\) \(10\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(7+\beta _{2})q^{5}+\cdots\)
138.4.d.a 138.d 69.c $24$ $8.142$ None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
138.4.e.a 138.e 23.c $30$ $8.142$ None \(-6\) \(-9\) \(-20\) \(-10\) $\mathrm{SU}(2)[C_{11}]$
138.4.e.b 138.e 23.c $30$ $8.142$ None \(-6\) \(9\) \(-6\) \(22\) $\mathrm{SU}(2)[C_{11}]$
138.4.e.c 138.e 23.c $30$ $8.142$ None \(6\) \(-9\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{11}]$
138.4.e.d 138.e 23.c $30$ $8.142$ None \(6\) \(9\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{11}]$
138.4.f.a 138.f 69.g $240$ $8.142$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
138.5.b.a 138.b 23.b $16$ $14.265$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+8q^{4}+\beta _{4}q^{5}+\beta _{7}q^{6}+\cdots\)
138.5.c.a 138.c 3.b $28$ $14.265$ None \(0\) \(-8\) \(0\) \(-104\) $\mathrm{SU}(2)[C_{2}]$
138.5.g.a 138.g 69.h $320$ $14.265$ None \(0\) \(20\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
138.5.h.a 138.h 23.d $160$ $14.265$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
138.6.a.a 138.a 1.a $1$ $22.133$ \(\Q\) None \(-4\) \(-9\) \(-44\) \(-70\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}-44q^{5}+6^{2}q^{6}+\cdots\)
138.6.a.b 138.a 1.a $1$ $22.133$ \(\Q\) None \(-4\) \(-9\) \(76\) \(210\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+76q^{5}+6^{2}q^{6}+\cdots\)
138.6.a.c 138.a 1.a $1$ $22.133$ \(\Q\) None \(4\) \(-9\) \(-10\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-10q^{5}-6^{2}q^{6}+\cdots\)
138.6.a.d 138.a 1.a $1$ $22.133$ \(\Q\) None \(4\) \(9\) \(-46\) \(-136\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}-46q^{5}+6^{2}q^{6}+\cdots\)
138.6.a.e 138.a 1.a $2$ $22.133$ \(\Q(\sqrt{154}) \) None \(-8\) \(18\) \(-4\) \(-40\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-2+3\beta )q^{5}+\cdots\)
138.6.a.f 138.a 1.a $2$ $22.133$ \(\Q(\sqrt{514}) \) None \(8\) \(-18\) \(40\) \(-100\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+(20+3\beta )q^{5}+\cdots\)
138.6.a.g 138.a 1.a $3$ $22.133$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(-27\) \(-18\) \(-50\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-6-\beta _{2})q^{5}+\cdots\)
138.6.a.h 138.a 1.a $3$ $22.133$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-12\) \(27\) \(-4\) \(-34\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
138.6.a.i 138.a 1.a $4$ $22.133$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(16\) \(36\) \(54\) \(348\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(13-\beta _{1})q^{5}+\cdots\)
138.6.d.a 138.d 69.c $40$ $22.133$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
138.7.b.a 138.b 23.b $24$ $31.747$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
138.7.c.a 138.c 3.b $44$ $31.747$ None \(0\) \(-20\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
138.8.a.a 138.a 1.a $1$ $43.109$ \(\Q\) None \(8\) \(27\) \(-230\) \(106\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}-230q^{5}+\cdots\)
138.8.a.b 138.a 1.a $3$ $43.109$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-24\) \(-81\) \(160\) \(-364\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(55+5\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.c 138.a 1.a $3$ $43.109$ 3.3.3351293.1 None \(-24\) \(81\) \(-162\) \(-296\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-55-5\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.d 138.a 1.a $3$ $43.109$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(24\) \(-81\) \(92\) \(-858\) $-$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(31+\beta _{2})q^{5}+\cdots\)
138.8.a.e 138.a 1.a $4$ $43.109$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(-108\) \(-90\) \(-222\) $-$ $\mathrm{SU}(2)$ \(q-8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(-23+\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.f 138.a 1.a $4$ $43.109$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-32\) \(108\) \(-162\) \(1218\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(-40-\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.g 138.a 1.a $4$ $43.109$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(-108\) \(342\) \(-30\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}-3^{3}q^{3}+2^{6}q^{4}+(85+\beta _{1}+\cdots)q^{5}+\cdots\)
138.8.a.h 138.a 1.a $4$ $43.109$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(32\) \(108\) \(270\) \(2022\) $+$ $\mathrm{SU}(2)$ \(q+8q^{2}+3^{3}q^{3}+2^{6}q^{4}+(68-\beta _{1}+\cdots)q^{5}+\cdots\)
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