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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1456.1.f.a 1456.f 91.b $1$ $0.727$ \(\Q\) \(\Q(\sqrt{-91}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}+q^{13}+q^{19}+q^{23}+\cdots\)
1456.1.f.b 1456.f 91.b $1$ $0.727$ \(\Q\) \(\Q(\sqrt{-91}) \) None \(0\) \(0\) \(1\) \(1\) \(q+q^{5}+q^{7}+q^{9}-q^{13}-q^{19}+q^{23}+\cdots\)
1456.1.bb.a 1456.bb 1456.ab $4$ $0.727$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+\zeta_{8}q^{6}+\cdots\)
1456.1.bc.a 1456.bc 1456.ac $4$ $0.727$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1456.1.bc.b 1456.bc 1456.ac $4$ $0.727$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1456.1.bl.a 1456.bl 1456.al $4$ $0.727$ \(\Q(\zeta_{8})\) None None \(-4\) \(0\) \(0\) \(0\) \(q-q^{2}-\zeta_{8}^{3}q^{3}+q^{4}+\zeta_{8}^{3}q^{6}+\zeta_{8}q^{7}+\cdots\)
1456.1.bs.a 1456.bs 364.q $4$ $0.727$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}-\zeta_{12}^{5}q^{7}+\cdots\)
1456.1.dg.a 1456.dg 364.ai $4$ $0.727$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1456.1.dj.a 1456.dj 364.al $4$ $0.727$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{7}+\zeta_{12}^{4}q^{9}+(-\zeta_{12}-\zeta_{12}^{3}+\cdots)q^{11}+\cdots\)
1456.1.fx.a 1456.fx 1456.ex $8$ $0.727$ \(\Q(\zeta_{24})\) None None \(-4\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{8}q^{2}-\zeta_{24}^{5}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
1456.2.a.a 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(-3\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{5}+q^{7}+6q^{9}-q^{11}+\cdots\)
1456.2.a.b 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{7}+6q^{9}+5q^{11}-q^{13}+\cdots\)
1456.2.a.c 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(-2\) \(3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{5}-q^{7}+q^{9}-q^{13}-6q^{15}+\cdots\)
1456.2.a.d 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
1456.2.a.e 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(-1\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
1456.2.a.f 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(0\) \(-3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
1456.2.a.g 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(0\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-3q^{9}+6q^{11}-q^{13}+\cdots\)
1456.2.a.h 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(0\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
1456.2.a.i 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
1456.2.a.j 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
1456.2.a.k 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(2\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{5}-q^{7}+q^{9}+q^{13}-6q^{15}+\cdots\)
1456.2.a.l 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(2\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
1456.2.a.m 1456.a 1.a $1$ $11.626$ \(\Q\) None None \(0\) \(2\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1456.2.a.n 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+\beta q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
1456.2.a.o 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
1456.2.a.p 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{6}) \) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}+q^{7}+3q^{9}+\cdots\)
1456.2.a.q 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(6\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(3+\beta )q^{5}-q^{7}-q^{9}+3\beta q^{11}+\cdots\)
1456.2.a.r 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+\beta q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots\)
1456.2.a.s 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{2}) \) None None \(0\) \(4\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
1456.2.a.t 1456.a 1.a $3$ $11.626$ 3.3.316.1 None None \(0\) \(2\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+q^{7}+\cdots\)
1456.2.a.u 1456.a 1.a $4$ $11.626$ 4.4.183064.1 None None \(0\) \(-1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1456.2.a.v 1456.a 1.a $4$ $11.626$ 4.4.64268.1 None None \(0\) \(-1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)
1456.2.j.a 1456.j 28.d $16$ $11.626$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{10}q^{3}+\beta _{14}q^{5}+(-\beta _{2}+\beta _{13}+\cdots)q^{7}+\cdots\)
1456.2.j.b 1456.j 28.d $32$ $11.626$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1456.2.k.a 1456.k 13.b $2$ $11.626$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2iq^{5}-iq^{7}-2q^{9}-5iq^{11}+\cdots\)
1456.2.k.b 1456.k 13.b $6$ $11.626$ 6.0.30647296.1 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots\)
1456.2.k.c 1456.k 13.b $6$ $11.626$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{3}-\beta _{5})q^{5}+\beta _{3}q^{7}+\cdots\)
1456.2.k.d 1456.k 13.b $8$ $11.626$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{3}+\beta _{4})q^{5}+\beta _{3}q^{7}+(1+\cdots)q^{9}+\cdots\)
1456.2.k.e 1456.k 13.b $8$ $11.626$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+\beta _{5}q^{7}+\cdots\)
1456.2.k.f 1456.k 13.b $12$ $11.626$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}-\beta _{5}-\beta _{7})q^{5}-\beta _{4}q^{7}+\cdots\)
1456.2.p.a 1456.p 364.h $2$ $11.626$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-4\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}-3q^{5}+(-2+\zeta_{6})q^{7}+q^{9}+\cdots\)
1456.2.p.b 1456.p 364.h $2$ $11.626$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-4\) \(6\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}+3q^{5}+(2+\zeta_{6})q^{7}+q^{9}-6q^{11}+\cdots\)
1456.2.p.c 1456.p 364.h $2$ $11.626$ \(\Q(\sqrt{-3}) \) None None \(0\) \(4\) \(-6\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}-3q^{5}+(2+\zeta_{6})q^{7}+q^{9}-6q^{11}+\cdots\)
1456.2.p.d 1456.p 364.h $2$ $11.626$ \(\Q(\sqrt{-3}) \) None None \(0\) \(4\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{3}+3q^{5}+(-2+\zeta_{6})q^{7}+q^{9}+\cdots\)
1456.2.p.e 1456.p 364.h $4$ $11.626$ \(\Q(\sqrt{-2}, \sqrt{-13})\) \(\Q(\sqrt{-13}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{7}-3q^{9}+(2\beta _{1}-\beta _{2})q^{11}+\beta _{3}q^{13}+\cdots\)
1456.2.p.f 1456.p 364.h $4$ $11.626$ \(\Q(\sqrt{-7}, \sqrt{13})\) \(\Q(\sqrt{-91}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{5}-\beta _{1}q^{7}-3q^{9}-\beta _{2}q^{13}+\cdots\)
1456.2.p.g 1456.p 364.h $8$ $11.626$ 8.0.5554571841.1 \(\Q(\sqrt{-91}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{4}q^{5}+\beta _{2}q^{7}-3q^{9}+(\beta _{4}-\beta _{7})q^{13}+\cdots\)
1456.2.p.h 1456.p 364.h $8$ $11.626$ 8.0.3317760000.6 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{5})q^{7}+3q^{9}+\cdots\)
1456.2.p.i 1456.p 364.h $24$ $11.626$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1456.2.r.a 1456.r 7.c $2$ $11.626$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
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