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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
115.2.a.a 115.a 1.a $1$ $0.918$ \(\Q\) None \(2\) \(0\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+q^{7}-3q^{9}-2q^{10}+\cdots\)
115.2.a.b 115.a 1.a $2$ $0.918$ \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}-q^{5}+\cdots\)
115.2.a.c 115.a 1.a $4$ $0.918$ 4.4.15317.1 None \(2\) \(-2\) \(4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
115.2.b.a 115.b 5.b $2$ $0.918$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2iq^{3}-2q^{4}+(2+i)q^{5}+\cdots\)
115.2.b.b 115.b 5.b $8$ $0.918$ 8.0.527896576.2 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
115.2.e.a 115.e 115.e $20$ $0.918$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+\beta _{4}q^{4}+\beta _{18}q^{5}+\cdots\)
115.2.g.a 115.g 23.c $10$ $0.918$ \(\Q(\zeta_{22})\) None \(5\) \(1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{11}]$ \(q+(\zeta_{22}+\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\)
115.2.g.b 115.g 23.c $20$ $0.918$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(1\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{2}+\cdots\)
115.2.g.c 115.g 23.c $50$ $0.918$ None \(-5\) \(-2\) \(-5\) \(-5\) $\mathrm{SU}(2)[C_{11}]$
115.2.j.a 115.j 115.j $100$ $0.918$ None \(0\) \(0\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{22}]$
115.2.l.a 115.l 115.l $200$ $0.918$ None \(-18\) \(-14\) \(-22\) \(-22\) $\mathrm{SU}(2)[C_{44}]$
115.3.c.a 115.c 115.c $1$ $3.134$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(-5\) \(9\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}-5q^{5}+9q^{7}+9q^{9}+2^{4}q^{16}+\cdots\)
115.3.c.b 115.c 115.c $1$ $3.134$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(5\) \(-9\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{4}+5q^{5}-9q^{7}+9q^{9}+2^{4}q^{16}+\cdots\)
115.3.c.c 115.c 115.c $20$ $3.134$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-3+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\)
115.3.d.a 115.d 23.b $6$ $3.134$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{4}q^{3}-3q^{4}-\beta _{3}q^{5}-\beta _{4}q^{6}+\cdots\)
115.3.d.b 115.d 23.b $10$ $3.134$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{7}q^{3}+(3+\beta _{6})q^{4}+\beta _{5}q^{5}+\cdots\)
115.3.f.a 115.f 5.c $44$ $3.134$ None \(-4\) \(0\) \(-8\) \(-16\) $\mathrm{SU}(2)[C_{4}]$
115.3.h.a 115.h 23.d $160$ $3.134$ None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
115.3.i.a 115.i 115.i $220$ $3.134$ None \(0\) \(0\) \(-11\) \(0\) $\mathrm{SU}(2)[C_{22}]$
115.3.k.a 115.k 115.k $440$ $3.134$ None \(-18\) \(-22\) \(-14\) \(-6\) $\mathrm{SU}(2)[C_{44}]$
115.4.a.a 115.a 1.a $1$ $6.785$ \(\Q\) None \(1\) \(4\) \(-5\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+4q^{3}-7q^{4}-5q^{5}+4q^{6}+\cdots\)
115.4.a.b 115.a 1.a $1$ $6.785$ \(\Q\) None \(2\) \(-3\) \(5\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}-4q^{4}+5q^{5}-6q^{6}+\cdots\)
115.4.a.c 115.a 1.a $2$ $6.785$ \(\Q(\sqrt{109}) \) None \(-6\) \(-3\) \(10\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-3q^{2}+(-1-\beta )q^{3}+q^{4}+5q^{5}+\cdots\)
115.4.a.d 115.a 1.a $5$ $6.785$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-5\) \(-6\) \(-25\) \(-15\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2}-\beta _{3}-\beta _{4})q^{3}+\cdots\)
115.4.a.e 115.a 1.a $5$ $6.785$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(6\) \(4\) \(-25\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
115.4.a.f 115.a 1.a $8$ $6.785$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(0\) \(40\) \(11\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+\cdots\)
115.4.b.a 115.b 5.b $34$ $6.785$ None \(0\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{2}]$
115.4.e.a 115.e 115.e $68$ $6.785$ None \(-4\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
115.4.g.a 115.g 23.c $110$ $6.785$ None \(-2\) \(6\) \(-55\) \(-10\) $\mathrm{SU}(2)[C_{11}]$
115.4.g.b 115.g 23.c $130$ $6.785$ None \(6\) \(-6\) \(65\) \(38\) $\mathrm{SU}(2)[C_{11}]$
115.4.j.a 115.j 115.j $340$ $6.785$ None \(0\) \(0\) \(-25\) \(0\) $\mathrm{SU}(2)[C_{22}]$
115.4.l.a 115.l 115.l $680$ $6.785$ None \(-18\) \(-26\) \(-22\) \(-22\) $\mathrm{SU}(2)[C_{44}]$
115.5.c.a 115.c 115.c $1$ $11.888$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(-25\) \(17\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{4}-5^{2}q^{5}+17q^{7}+3^{4}q^{9}+\cdots\)
115.5.c.b 115.c 115.c $1$ $11.888$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(25\) \(-17\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{4}q^{4}+5^{2}q^{5}-17q^{7}+3^{4}q^{9}+\cdots\)
115.5.c.c 115.c 115.c $44$ $11.888$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
115.5.d.a 115.d 23.b $32$ $11.888$ None \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
115.5.f.a 115.f 5.c $88$ $11.888$ None \(0\) \(0\) \(-48\) \(160\) $\mathrm{SU}(2)[C_{4}]$
115.5.h.a 115.h 23.d $320$ $11.888$ None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
115.5.i.a 115.i 115.i $460$ $11.888$ None \(0\) \(0\) \(-11\) \(0\) $\mathrm{SU}(2)[C_{22}]$
115.5.k.a 115.k 115.k $920$ $11.888$ None \(-18\) \(2\) \(-54\) \(-78\) $\mathrm{SU}(2)[C_{44}]$
115.6.a.a 115.a 1.a $2$ $18.444$ \(\Q(\sqrt{1821}) \) None \(4\) \(3\) \(-50\) \(53\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2-\beta )q^{3}-28q^{4}-5^{2}q^{5}+\cdots\)
115.6.a.b 115.a 1.a $7$ $18.444$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-12\) \(4\) \(175\) \(-275\) $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+(1-\beta _{1}-\beta _{6})q^{3}+\cdots\)
115.6.a.c 115.a 1.a $7$ $18.444$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(-3\) \(-175\) \(33\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+\cdots\)
115.6.a.d 115.a 1.a $10$ $18.444$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-12\) \(-18\) \(-250\) \(-15\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(-2+\beta _{3})q^{3}+(14+\cdots)q^{4}+\cdots\)
115.6.a.e 115.a 1.a $12$ $18.444$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(8\) \(22\) \(300\) \(16\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}-\beta _{4})q^{3}+(5^{2}+\cdots)q^{4}+\cdots\)
115.6.b.a 115.b 5.b $54$ $18.444$ None \(0\) \(0\) \(98\) \(0\) $\mathrm{SU}(2)[C_{2}]$
115.7.c.a 115.c 115.c $1$ $26.456$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(-125\) \(-594\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{6}q^{4}-5^{3}q^{5}-594q^{7}+3^{6}q^{9}+\cdots\)
115.7.c.b 115.c 115.c $1$ $26.456$ \(\Q\) \(\Q(\sqrt{-115}) \) \(0\) \(0\) \(125\) \(594\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{6}q^{4}+5^{3}q^{5}+594q^{7}+3^{6}q^{9}+\cdots\)
115.7.c.c 115.c 115.c $68$ $26.456$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
115.7.d.a 115.d 23.b $48$ $26.456$ None \(-20\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
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