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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1859.1.c.a 1859.c 11.b $3$ $0.928$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}-\beta _{1}q^{5}+\cdots\)
1859.1.c.b 1859.c 11.b $3$ $0.928$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots\)
1859.1.c.c 1859.c 11.b $4$ $0.928$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-143}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{1}-\beta _{3})q^{6}+\cdots\)
1859.1.d.a 1859.d 143.d $6$ $0.928$ 6.0.153664.1 \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+(-1+\beta _{2}+\beta _{4})q^{3}-q^{4}-\beta _{1}q^{5}+\cdots\)
1859.1.i.a 1859.i 143.i $4$ $0.928$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-143}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
1859.1.i.b 1859.i 143.i $4$ $0.928$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-143}) \) None \(1\) \(1\) \(0\) \(1\) \(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
1859.1.i.c 1859.i 143.i $12$ $0.928$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{5})q^{3}+(1-\beta _{7})q^{4}+(\beta _{2}-\beta _{6}+\cdots)q^{5}+\cdots\)
1859.1.k.a 1859.k 143.k $6$ $0.928$ 6.0.64827.1 \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+\beta _{4}q^{3}-\beta _{5}q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1859.1.k.b 1859.k 143.k $6$ $0.928$ 6.0.64827.1 \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(2\) \(0\) \(q+\beta _{4}q^{3}-\beta _{5}q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1859.1.k.c 1859.k 143.k $8$ $0.928$ 8.0.12960000.1 \(\Q(\sqrt{-143}) \) None \(0\) \(2\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{6}-\beta _{7})q^{2}+(1-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
1859.2.a.a 1859.a 1.a $1$ $14.844$ \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}+2q^{7}-2q^{9}+q^{11}+\cdots\)
1859.2.a.b 1859.a 1.a $1$ $14.844$ \(\Q\) None None \(2\) \(-1\) \(-1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots\)
1859.2.a.c 1859.a 1.a $2$ $14.844$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
1859.2.a.d 1859.a 1.a $2$ $14.844$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+\cdots\)
1859.2.a.e 1859.a 1.a $3$ $14.844$ 3.3.756.1 None None \(-3\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}-q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
1859.2.a.f 1859.a 1.a $3$ $14.844$ 3.3.361.1 None None \(-1\) \(1\) \(-1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.2.a.g 1859.a 1.a $3$ $14.844$ 3.3.361.1 None None \(1\) \(1\) \(1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+\beta _{1}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
1859.2.a.h 1859.a 1.a $3$ $14.844$ 3.3.756.1 None None \(3\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}-q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
1859.2.a.i 1859.a 1.a $4$ $14.844$ 4.4.1957.1 None None \(-3\) \(0\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
1859.2.a.j 1859.a 1.a $6$ $14.844$ 6.6.84512328.1 None None \(-1\) \(-2\) \(-4\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1859.2.a.k 1859.a 1.a $6$ $14.844$ 6.6.28561300.1 None None \(0\) \(1\) \(-6\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1859.2.a.l 1859.a 1.a $6$ $14.844$ 6.6.28561300.1 None None \(0\) \(1\) \(6\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{4})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
1859.2.a.m 1859.a 1.a $6$ $14.844$ 6.6.194616205.1 None None \(0\) \(3\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1859.2.a.n 1859.a 1.a $6$ $14.844$ 6.6.84512328.1 None None \(1\) \(-2\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1859.2.a.o 1859.a 1.a $8$ $14.844$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(-2\) \(0\) \(-8\) \(-14\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.p 1859.a 1.a $8$ $14.844$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None None \(2\) \(0\) \(8\) \(14\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.q 1859.a 1.a $9$ $14.844$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-5\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.r 1859.a 1.a $9$ $14.844$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-5\) \(4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)
1859.2.a.s 1859.a 1.a $21$ $14.844$ None None \(0\) \(6\) \(-7\) \(-1\) $-$ $\mathrm{SU}(2)$
1859.2.a.t 1859.a 1.a $21$ $14.844$ None None \(0\) \(6\) \(7\) \(1\) $-$ $\mathrm{SU}(2)$
1859.4.a.a 1859.a 1.a $2$ $109.685$ \(\Q(\sqrt{3}) \) None None \(-2\) \(-2\) \(-2\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-1+4\beta )q^{3}+(-4+\cdots)q^{4}+\cdots\)
1859.4.a.b 1859.a 1.a $4$ $109.685$ 4.4.297133.1 None None \(0\) \(-4\) \(6\) \(17\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(2+\beta _{1}+2\beta _{2}+\cdots)q^{4}+\cdots\)
1859.4.a.c 1859.a 1.a $6$ $109.685$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(6\) \(-6\) \(8\) \(53\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1-\beta _{4})q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.d 1859.a 1.a $9$ $109.685$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(8\) \(-30\) \(-25\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(5-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1859.4.a.e 1859.a 1.a $11$ $109.685$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-6\) \(6\) \(4\) \(-45\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(6-\beta _{1}+\cdots)q^{4}+\cdots\)
1859.4.a.f 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(-4\) \(-6\) \(-16\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.g 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(-6\) \(-24\) \(-62\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.h 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(0\) \(-6\) \(24\) \(62\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(3+\beta _{2})q^{4}+(1-\beta _{7}+\cdots)q^{5}+\cdots\)
1859.4.a.i 1859.a 1.a $17$ $109.685$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None None \(4\) \(-6\) \(16\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(5+\beta _{2})q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\)
1859.4.a.j 1859.a 1.a $18$ $109.685$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(-2\) \(0\) \(-20\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1859.4.a.k 1859.a 1.a $18$ $109.685$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(2\) \(0\) \(20\) \(28\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{2})q^{4}+(1+\beta _{11}+\cdots)q^{5}+\cdots\)
1859.4.a.l 1859.a 1.a $36$ $109.685$ None None \(-4\) \(12\) \(-40\) \(-56\) $-$ $\mathrm{SU}(2)$
1859.4.a.m 1859.a 1.a $36$ $109.685$ None None \(4\) \(12\) \(40\) \(56\) $+$ $\mathrm{SU}(2)$
1859.4.a.n 1859.a 1.a $39$ $109.685$ None None \(0\) \(-23\) \(-23\) \(4\) $-$ $\mathrm{SU}(2)$
1859.4.a.o 1859.a 1.a $39$ $109.685$ None None \(0\) \(-23\) \(23\) \(-4\) $-$ $\mathrm{SU}(2)$
1859.4.a.p 1859.a 1.a $51$ $109.685$ None None \(0\) \(21\) \(-41\) \(-4\) $+$ $\mathrm{SU}(2)$
1859.4.a.q 1859.a 1.a $51$ $109.685$ None None \(0\) \(21\) \(41\) \(4\) $+$ $\mathrm{SU}(2)$
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