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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1904.1.n.a 1904.n 119.d $2$ $0.950$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-119}) \) None \(0\) \(-1\) \(1\) \(2\) \(q-\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}+q^{15}+\cdots\)
1904.1.n.b 1904.n 119.d $2$ $0.950$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-119}) \) None \(0\) \(1\) \(-1\) \(-2\) \(q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots\)
1904.1.bg.a 1904.bg 1904.ag $2$ $0.950$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-119}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-iq^{2}+(-1+i)q^{3}-q^{4}+(-1-i+\cdots)q^{5}+\cdots\)
1904.1.bg.b 1904.bg 1904.ag $2$ $0.950$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-119}) \) None \(0\) \(2\) \(2\) \(0\) \(q-iq^{2}+(1-i)q^{3}-q^{4}+(1+i)q^{5}+\cdots\)
1904.1.bg.c 1904.bg 1904.ag $8$ $0.950$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-119}) \) None \(0\) \(-2\) \(-2\) \(0\) \(q-\zeta_{20}^{9}q^{2}+(-\zeta_{20}+\zeta_{20}^{4})q^{3}-\zeta_{20}^{8}q^{4}+\cdots\)
1904.1.bg.d 1904.bg 1904.ag $8$ $0.950$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-119}) \) None \(0\) \(2\) \(2\) \(0\) \(q-\zeta_{20}q^{2}+(\zeta_{20}^{6}+\zeta_{20}^{9})q^{3}+\zeta_{20}^{2}q^{4}+\cdots\)
1904.1.bt.a 1904.bt 476.o $8$ $0.950$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-17}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{9}+\zeta_{24}^{11})q^{3}+\zeta_{24}^{9}q^{7}+\cdots\)
1904.1.dm.a 1904.dm 476.ab $8$ $0.950$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(-4\) \(0\) \(q-\zeta_{24}^{11}q^{3}+(-\zeta_{24}^{4}+\zeta_{24}^{10})q^{5}+\cdots\)
1904.2.a.a 1904.a 1.a $1$ $15.204$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
1904.2.a.b 1904.a 1.a $1$ $15.204$ \(\Q\) None None \(0\) \(-2\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}-q^{7}+q^{9}+4q^{11}+\cdots\)
1904.2.a.c 1904.a 1.a $1$ $15.204$ \(\Q\) None None \(0\) \(0\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-3q^{9}+2q^{11}-q^{17}+\cdots\)
1904.2.a.d 1904.a 1.a $1$ $15.204$ \(\Q\) None None \(0\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-3q^{9}-2q^{13}+q^{17}+\cdots\)
1904.2.a.e 1904.a 1.a $1$ $15.204$ \(\Q\) None None \(0\) \(2\) \(-4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
1904.2.a.f 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1904.2.a.g 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None None \(0\) \(-1\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1-\beta )q^{5}+q^{7}+\beta q^{9}+\cdots\)
1904.2.a.h 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None None \(0\) \(-1\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}-q^{7}+\beta q^{9}+\cdots\)
1904.2.a.i 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}-q^{7}+(-2+\beta )q^{9}+\cdots\)
1904.2.a.j 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{5}) \) None None \(0\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
1904.2.a.k 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None None \(0\) \(1\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}+q^{7}+\beta q^{9}-4q^{11}+\cdots\)
1904.2.a.l 1904.a 1.a $2$ $15.204$ \(\Q(\sqrt{13}) \) None None \(0\) \(3\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2+\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
1904.2.a.m 1904.a 1.a $3$ $15.204$ 3.3.229.1 None None \(0\) \(-1\) \(3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(1-\beta _{1})q^{5}-q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
1904.2.a.n 1904.a 1.a $3$ $15.204$ 3.3.1229.1 None None \(0\) \(1\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1904.2.a.o 1904.a 1.a $3$ $15.204$ 3.3.229.1 None None \(0\) \(3\) \(-5\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(-2-\beta _{2})q^{5}-q^{7}+\cdots\)
1904.2.a.p 1904.a 1.a $3$ $15.204$ 3.3.229.1 None None \(0\) \(3\) \(1\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1904.2.a.q 1904.a 1.a $4$ $15.204$ 4.4.5225.1 None None \(0\) \(-3\) \(-1\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-\beta _{1}-\beta _{3})q^{5}+q^{7}+\cdots\)
1904.2.a.r 1904.a 1.a $4$ $15.204$ 4.4.13448.1 None None \(0\) \(-3\) \(5\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(1-\beta _{2})q^{5}-q^{7}+\cdots\)
1904.2.a.s 1904.a 1.a $4$ $15.204$ 4.4.9301.1 None None \(0\) \(-2\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-\beta _{2}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1904.2.a.t 1904.a 1.a $5$ $15.204$ 5.5.453749.1 None None \(0\) \(2\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
1904.2.c.a 1904.c 17.b $2$ $15.204$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-2iq^{5}-iq^{7}-q^{9}+2iq^{11}+\cdots\)
1904.2.c.b 1904.c 17.b $2$ $15.204$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}+2q^{13}+(1-4i)q^{17}+\cdots\)
1904.2.c.c 1904.c 17.b $4$ $15.204$ \(\Q(i, \sqrt{29})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{2}q^{7}+(-5+\cdots)q^{9}+\cdots\)
1904.2.c.d 1904.c 17.b $4$ $15.204$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+(-4+\cdots)q^{9}+\cdots\)
1904.2.c.e 1904.c 17.b $6$ $15.204$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
1904.2.c.f 1904.c 17.b $8$ $15.204$ 8.0.980441344.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}+\beta _{7})q^{3}-\beta _{3}q^{5}+\beta _{4}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1904.2.c.g 1904.c 17.b $8$ $15.204$ 8.0.6179217664.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{5}-\beta _{6})q^{3}+(\beta _{5}+\beta _{7})q^{5}-\beta _{5}q^{7}+\cdots\)
1904.2.c.h 1904.c 17.b $10$ $15.204$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{3}+(-\beta _{4}-\beta _{6}-\beta _{7}+\beta _{8}+\beta _{9})q^{5}+\cdots\)
1904.2.c.i 1904.c 17.b $10$ $15.204$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{3}+(\beta _{5}-\beta _{7})q^{5}-\beta _{7}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1904.2.h.a 1904.h 476.e $8$ $15.204$ 8.0.\(\cdots\).11 \(\Q(\sqrt{-17}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+\beta _{4})q^{3}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
1904.2.h.b 1904.h 476.e $16$ $15.204$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{1}q^{5}+(\beta _{4}-\beta _{10})q^{7}+\beta _{2}q^{9}+\cdots\)
1904.2.h.c 1904.h 476.e $48$ $15.204$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1904.2.j.a 1904.j 28.d $8$ $15.204$ 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-\beta _{1}+2\beta _{3})q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
1904.2.j.b 1904.j 28.d $24$ $15.204$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1904.2.j.c 1904.j 28.d $32$ $15.204$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1904.3.g.a 1904.g 4.b $32$ $51.880$ None None \(0\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1904.3.g.b 1904.g 4.b $64$ $51.880$ None None \(0\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1904.4.a.a 1904.a 1.a $1$ $112.340$ \(\Q\) None None \(0\) \(6\) \(-20\) \(7\) $+$ $\mathrm{SU}(2)$ \(q+6q^{3}-20q^{5}+7q^{7}+9q^{9}-60q^{11}+\cdots\)
1904.4.a.b 1904.a 1.a $2$ $112.340$ \(\Q(\sqrt{93}) \) None None \(0\) \(5\) \(9\) \(14\) $-$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{3}+(4+\beta )q^{5}+7q^{7}+(5-5\beta )q^{9}+\cdots\)
1904.4.a.c 1904.a 1.a $2$ $112.340$ \(\Q(\sqrt{69}) \) None None \(0\) \(11\) \(-7\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q+(6-\beta )q^{3}+(-3-\beta )q^{5}-7q^{7}+(26+\cdots)q^{9}+\cdots\)
1904.4.a.d 1904.a 1.a $3$ $112.340$ 3.3.55029.1 None None \(0\) \(-7\) \(19\) \(-21\) $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{3}+(7-\beta _{1}-\beta _{2})q^{5}+\cdots\)
1904.4.a.e 1904.a 1.a $3$ $112.340$ 3.3.2429.1 None None \(0\) \(-5\) \(-19\) \(21\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}+\beta _{2})q^{3}+(-6+\beta _{2})q^{5}+\cdots\)
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