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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1305.1.b.a 1305.b 435.b $4$ $0.651$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{5}+\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{8}+\cdots\)
1305.1.b.b 1305.b 435.b $4$ $0.651$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{7}+\zeta_{8}^{2}q^{8}+\cdots\)
1305.1.l.a 1305.l 145.f $2$ $0.651$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{4}-iq^{5}+(1-i)q^{11}-q^{16}+\cdots\)
1305.1.o.a 1305.o 145.h $2$ $0.651$ \(\Q(\sqrt{-1}) \) None \(\Q(\sqrt{29}) \) \(0\) \(0\) \(0\) \(-2\) \(q-iq^{4}+iq^{5}+(-1+i)q^{7}+(1+i+\cdots)q^{13}+\cdots\)
1305.2.a.a 1305.a 1.a $1$ $10.420$ \(\Q\) None None \(-2\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-2q^{7}-2q^{10}+\cdots\)
1305.2.a.b 1305.a 1.a $1$ $10.420$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
1305.2.a.c 1305.a 1.a $1$ $10.420$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-2q^{7}-q^{11}+6q^{13}+\cdots\)
1305.2.a.d 1305.a 1.a $1$ $10.420$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+2q^{7}-3q^{11}+2q^{13}+\cdots\)
1305.2.a.e 1305.a 1.a $1$ $10.420$ \(\Q\) None None \(1\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-4q^{7}-3q^{8}-q^{10}+\cdots\)
1305.2.a.f 1305.a 1.a $1$ $10.420$ \(\Q\) None None \(1\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
1305.2.a.g 1305.a 1.a $1$ $10.420$ \(\Q\) None None \(2\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-2q^{7}-2q^{10}+\cdots\)
1305.2.a.h 1305.a 1.a $2$ $10.420$ \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(-1-2\beta )q^{7}+\cdots\)
1305.2.a.i 1305.a 1.a $2$ $10.420$ \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(2-2\beta )q^{7}+\cdots\)
1305.2.a.j 1305.a 1.a $2$ $10.420$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{4}+q^{5}+2q^{7}-\beta q^{8}+\cdots\)
1305.2.a.k 1305.a 1.a $2$ $10.420$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}-3q^{7}+\cdots\)
1305.2.a.l 1305.a 1.a $2$ $10.420$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-1-2\beta )q^{7}+\cdots\)
1305.2.a.m 1305.a 1.a $2$ $10.420$ \(\Q(\sqrt{21}) \) None None \(1\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(3+\beta )q^{4}-q^{5}+q^{7}+(5+2\beta )q^{8}+\cdots\)
1305.2.a.n 1305.a 1.a $2$ $10.420$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}-q^{5}+(-2+\cdots)q^{7}+\cdots\)
1305.2.a.o 1305.a 1.a $3$ $10.420$ 3.3.148.1 None None \(-3\) \(0\) \(3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1305.2.a.p 1305.a 1.a $3$ $10.420$ 3.3.148.1 None None \(-1\) \(0\) \(-3\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1305.2.a.q 1305.a 1.a $3$ $10.420$ 3.3.469.1 None None \(-1\) \(0\) \(-3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
1305.2.a.r 1305.a 1.a $4$ $10.420$ 4.4.2225.1 None None \(3\) \(0\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
1305.2.a.s 1305.a 1.a $7$ $10.420$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(-1\) \(0\) \(-7\) \(10\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
1305.2.a.t 1305.a 1.a $7$ $10.420$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(1\) \(0\) \(7\) \(10\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1-\beta _{5}+\cdots)q^{7}+\cdots\)
1305.2.c.a 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+(2-i)q^{5}-2iq^{7}+\cdots\)
1305.2.c.b 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+(-1-2i)q^{5}+2iq^{7}+\cdots\)
1305.2.c.c 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}+\beta q^{5}-2\beta q^{7}-5q^{11}-2\beta q^{13}+\cdots\)
1305.2.c.d 1305.c 5.b $2$ $10.420$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-\beta q^{5}-2\beta q^{7}+5q^{11}-2\beta q^{13}+\cdots\)
1305.2.c.e 1305.c 5.b $4$ $10.420$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}+(1-\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
1305.2.c.f 1305.c 5.b $4$ $10.420$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
1305.2.c.g 1305.c 5.b $4$ $10.420$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+q^{4}+(1+2\zeta_{8})q^{5}+\zeta_{8}^{2}q^{7}+\cdots\)
1305.2.c.h 1305.c 5.b $6$ $10.420$ 6.0.84345856.2 None None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-3+\beta _{3}+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
1305.2.c.i 1305.c 5.b $10$ $10.420$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2}+\beta _{9})q^{2}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1305.2.c.j 1305.c 5.b $10$ $10.420$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{4}+\beta _{6})q^{2}+(-1-\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
1305.2.c.k 1305.c 5.b $12$ $10.420$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)
1305.2.c.l 1305.c 5.b $12$ $10.420$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+\beta _{7}q^{5}+\beta _{3}q^{7}+\cdots\)
1305.2.d.a 1305.d 29.b $4$ $10.420$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
1305.2.d.b 1305.d 29.b $6$ $10.420$ 6.0.16516096.1 None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}-\beta _{2}q^{7}+\cdots\)
1305.2.d.c 1305.d 29.b $10$ $10.420$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-10\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
1305.2.d.d 1305.d 29.b $10$ $10.420$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}-\beta _{5}q^{7}+\cdots\)
1305.2.d.e 1305.d 29.b $10$ $10.420$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(-10\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+\beta _{7}q^{7}+\cdots\)
1305.2.d.f 1305.d 29.b $10$ $10.420$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(10\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)
1305.2.f.a 1305.f 145.d $2$ $10.420$ \(\Q(\sqrt{-1}) \) None None \(-4\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}+2q^{4}+(-2-i)q^{5}+4iq^{7}+\cdots\)
1305.2.f.b 1305.f 145.d $2$ $10.420$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{4}+(1-i)q^{5}+iq^{7}+3q^{8}+\cdots\)
1305.2.f.c 1305.f 145.d $2$ $10.420$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-q^{4}+(1-i)q^{5}+iq^{7}-3q^{8}+\cdots\)
1305.2.f.d 1305.f 145.d $2$ $10.420$ \(\Q(\sqrt{-1}) \) None None \(4\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}+2q^{4}+(-2-i)q^{5}+4iq^{7}+\cdots\)
1305.2.f.e 1305.f 145.d $4$ $10.420$ \(\Q(\sqrt{-3}, \sqrt{17})\) None None \(-4\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{4}+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+\cdots\)
1305.2.f.f 1305.f 145.d $4$ $10.420$ \(\Q(\sqrt{5}, \sqrt{-6})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{4}+\beta _{2}q^{5}+\beta _{1}q^{7}+3q^{8}+\cdots\)
1305.2.f.g 1305.f 145.d $4$ $10.420$ \(\Q(\sqrt{-5}, \sqrt{-29})\) \(\Q(\sqrt{-435}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{4}-\beta _{1}q^{5}-\beta _{2}q^{11}+4q^{16}+\cdots\)
1305.2.f.h 1305.f 145.d $4$ $10.420$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+3q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{7}+\cdots\)
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