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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2576.1.p.a 2576.p 644.h $4$ $1.286$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-161}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{3}q^{3}-\beta _{1}q^{5}-q^{7}+(1-\beta _{2})q^{9}+\cdots\)
2576.1.p.b 2576.p 644.h $4$ $1.286$ \(\Q(\zeta_{16})^+\) \(\Q(\sqrt{-161}) \) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{3}q^{3}-\beta _{1}q^{5}+q^{7}+(1-\beta _{2})q^{9}+\cdots\)
2576.1.y.a 2576.y 2576.y $2$ $1.286$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+iq^{9}+\cdots\)
2576.1.y.b 2576.y 2576.y $2$ $1.286$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+iq^{9}+\cdots\)
2576.1.cj.a 2576.cj 161.l $10$ $1.286$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(1\) \(q+\zeta_{22}^{5}q^{7}-\zeta_{22}^{9}q^{9}+(-\zeta_{22}^{6}-\zeta_{22}^{8}+\cdots)q^{11}+\cdots\)
2576.1.cn.a 2576.cn 2576.bn $20$ $1.286$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{44}^{7}q^{2}+\zeta_{44}^{14}q^{4}-\zeta_{44}^{5}q^{7}+\cdots\)
2576.1.cn.b 2576.cn 2576.bn $20$ $1.286$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{44}q^{2}+\zeta_{44}^{2}q^{4}+\zeta_{44}^{5}q^{7}-\zeta_{44}^{3}q^{8}+\cdots\)
2576.1.cq.a 2576.cq 2576.bq $20$ $1.286$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{44}^{15}q^{2}-\zeta_{44}^{8}q^{4}-\zeta_{44}^{9}q^{7}+\cdots\)
2576.1.cq.b 2576.cq 2576.bq $20$ $1.286$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{44}^{17}q^{2}-\zeta_{44}^{12}q^{4}-\zeta_{44}^{9}q^{7}+\cdots\)
2576.2.a.a 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-3\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{5}+q^{7}+6q^{9}-2q^{11}+\cdots\)
2576.2.a.b 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-2\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-q^{7}+q^{9}-6q^{11}+\cdots\)
2576.2.a.c 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-4q^{11}+6q^{17}+\cdots\)
2576.2.a.d 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
2576.2.a.e 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-2\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
2576.2.a.f 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-2\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
2576.2.a.g 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}-2q^{9}+2q^{11}+\cdots\)
2576.2.a.h 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}+6q^{11}-3q^{13}+\cdots\)
2576.2.a.i 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
2576.2.a.j 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-3q^{9}-4q^{11}+6q^{13}+\cdots\)
2576.2.a.k 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(0\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{9}-4q^{13}-4q^{17}+\cdots\)
2576.2.a.l 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}+2q^{11}-3q^{13}+\cdots\)
2576.2.a.m 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(2\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)
2576.2.a.n 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}-6q^{17}-6q^{19}+\cdots\)
2576.2.a.o 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(3\) \(-4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{5}+q^{7}+6q^{9}-2q^{11}+\cdots\)
2576.2.a.p 2576.a 1.a $1$ $20.569$ \(\Q\) None None \(0\) \(3\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{7}+6q^{9}+6q^{11}+q^{13}+\cdots\)
2576.2.a.q 2576.a 1.a $2$ $20.569$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}+q^{7}-q^{9}-2q^{11}+\cdots\)
2576.2.a.r 2576.a 1.a $2$ $20.569$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+q^{7}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
2576.2.a.s 2576.a 1.a $2$ $20.569$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+q^{7}-2q^{9}-2\beta q^{11}+\cdots\)
2576.2.a.t 2576.a 1.a $2$ $20.569$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
2576.2.a.u 2576.a 1.a $2$ $20.569$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
2576.2.a.v 2576.a 1.a $3$ $20.569$ 3.3.148.1 None None \(0\) \(-2\) \(2\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{1})q^{5}+q^{7}+\cdots\)
2576.2.a.w 2576.a 1.a $3$ $20.569$ 3.3.316.1 None None \(0\) \(-2\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(1-\beta _{2})q^{5}+q^{7}+\cdots\)
2576.2.a.x 2576.a 1.a $3$ $20.569$ 3.3.568.1 None None \(0\) \(-1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
2576.2.a.y 2576.a 1.a $3$ $20.569$ 3.3.148.1 None None \(0\) \(0\) \(4\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(2-2\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots\)
2576.2.a.z 2576.a 1.a $4$ $20.569$ 4.4.34196.1 None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
2576.2.a.ba 2576.a 1.a $4$ $20.569$ 4.4.8468.1 None None \(0\) \(3\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-\beta _{2}+\beta _{3})q^{5}-q^{7}+\cdots\)
2576.2.a.bb 2576.a 1.a $5$ $20.569$ 5.5.6963152.1 None None \(0\) \(-3\) \(2\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
2576.2.a.bc 2576.a 1.a $5$ $20.569$ 5.5.8580816.1 None None \(0\) \(-1\) \(4\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{4})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
2576.2.a.bd 2576.a 1.a $5$ $20.569$ 5.5.2147108.1 None None \(0\) \(0\) \(-4\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(-1-\beta _{4})q^{5}-q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
2576.2.a.be 2576.a 1.a $5$ $20.569$ 5.5.3385684.1 None None \(0\) \(3\) \(2\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{3}+\beta _{1}q^{5}-q^{7}+(3-\beta _{4})q^{9}+\cdots\)
2576.2.e.a 2576.e 92.b $12$ $20.569$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{9}q^{5}-q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
2576.2.e.b 2576.e 92.b $12$ $20.569$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{9}q^{5}+q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
2576.2.e.c 2576.e 92.b $24$ $20.569$ None None \(0\) \(0\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{2}]$
2576.2.e.d 2576.e 92.b $24$ $20.569$ None None \(0\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$
2576.2.f.a 2576.f 161.c $2$ $20.569$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{7}+3q^{9}-2\beta q^{11}+(-4-\beta )q^{23}+\cdots\)
2576.2.f.b 2576.f 161.c $4$ $20.569$ 4.0.2312.1 None None \(0\) \(0\) \(-8\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-2q^{5}+(1-\beta _{1})q^{7}+(-2+\cdots)q^{9}+\cdots\)
2576.2.f.c 2576.f 161.c $4$ $20.569$ \(\Q(\sqrt{-2}, \sqrt{-7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+q^{9}+4\beta _{2}q^{13}+\cdots\)
2576.2.f.d 2576.f 161.c $4$ $20.569$ \(\Q(\sqrt{-2}, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{7}+q^{9}+\beta _{2}q^{11}+3\beta _{1}q^{13}+\cdots\)
2576.2.f.e 2576.f 161.c $4$ $20.569$ 4.0.2312.1 None None \(0\) \(0\) \(8\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+2q^{5}+(-1+\beta _{1})q^{7}+(-2+\cdots)q^{9}+\cdots\)
2576.2.f.f 2576.f 161.c $12$ $20.569$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+\beta _{3}q^{5}+\beta _{7}q^{7}+(-2+\beta _{4}+\cdots)q^{9}+\cdots\)
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