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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2254.2.a.a 2254.a 1.a $1$ $17.998$ \(\Q\) None \(-1\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-q^{8}+q^{9}+\cdots\)
2254.2.a.b 2254.a 1.a $1$ $17.998$ \(\Q\) None \(-1\) \(-2\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{8}+\cdots\)
2254.2.a.c 2254.a 1.a $1$ $17.998$ \(\Q\) None \(-1\) \(0\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-4q^{5}-q^{8}-3q^{9}+4q^{10}+\cdots\)
2254.2.a.d 2254.a 1.a $1$ $17.998$ \(\Q\) None \(-1\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{8}-3q^{9}-2q^{10}+\cdots\)
2254.2.a.e 2254.a 1.a $1$ $17.998$ \(\Q\) None \(-1\) \(2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-2q^{5}-2q^{6}-q^{8}+\cdots\)
2254.2.a.f 2254.a 1.a $1$ $17.998$ \(\Q\) None \(1\) \(-2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{8}+\cdots\)
2254.2.a.g 2254.a 1.a $1$ $17.998$ \(\Q\) None \(1\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+2q^{5}+2q^{6}+q^{8}+\cdots\)
2254.2.a.h 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
2254.2.a.i 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta q^{5}-q^{8}-3q^{9}+\beta q^{10}+\cdots\)
2254.2.a.j 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2\beta q^{3}+q^{4}-3\beta q^{5}-2\beta q^{6}+\cdots\)
2254.2.a.k 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(1-\beta )q^{5}+\cdots\)
2254.2.a.l 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)
2254.2.a.m 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}-3q^{9}+\beta q^{10}+\cdots\)
2254.2.a.n 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-\beta q^{5}+\beta q^{6}+q^{8}+\cdots\)
2254.2.a.o 2254.a 1.a $2$ $17.998$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1+\beta )q^{5}+\cdots\)
2254.2.a.p 2254.a 1.a $3$ $17.998$ 3.3.316.1 None \(3\) \(-2\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
2254.2.a.q 2254.a 1.a $4$ $17.998$ 4.4.14013.1 None \(-4\) \(-1\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(-1+\beta _{1})q^{5}+\cdots\)
2254.2.a.r 2254.a 1.a $4$ $17.998$ 4.4.8957.1 None \(-4\) \(-1\) \(5\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(2+\beta _{2}-\beta _{3})q^{5}+\cdots\)
2254.2.a.s 2254.a 1.a $4$ $17.998$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2254.2.a.t 2254.a 1.a $4$ $17.998$ \(\Q(\sqrt{2}, \sqrt{13})\) None \(-4\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}+\beta _{2})q^{3}+q^{4}+\beta _{1}q^{5}+\cdots\)
2254.2.a.u 2254.a 1.a $4$ $17.998$ 4.4.8957.1 None \(-4\) \(1\) \(-5\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
2254.2.a.v 2254.a 1.a $4$ $17.998$ 4.4.14013.1 None \(-4\) \(1\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(1-\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\)
2254.2.a.w 2254.a 1.a $4$ $17.998$ 4.4.14013.1 None \(4\) \(-5\) \(-5\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
2254.2.a.x 2254.a 1.a $4$ $17.998$ 4.4.1957.1 None \(4\) \(-3\) \(-7\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
2254.2.a.y 2254.a 1.a $4$ $17.998$ 4.4.9248.1 None \(4\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
2254.2.a.z 2254.a 1.a $4$ $17.998$ 4.4.1957.1 None \(4\) \(3\) \(7\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(2-\beta _{3})q^{5}+\cdots\)
2254.2.a.ba 2254.a 1.a $4$ $17.998$ 4.4.14013.1 None \(4\) \(5\) \(5\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
2254.2.a.bb 2254.a 1.a $6$ $17.998$ 6.6.2803712.1 None \(6\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{4}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots\)
2254.2.c.a 2254.c 161.c $8$ $17.998$ 8.0.\(\cdots\).12 None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+(\beta _{3}-\beta _{7})q^{3}+q^{4}+\beta _{4}q^{5}+\cdots\)
2254.2.c.b 2254.c 161.c $16$ $17.998$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{13}q^{3}+q^{4}+(-\beta _{2}+\beta _{10}+\cdots)q^{5}+\cdots\)
2254.2.c.c 2254.c 161.c $16$ $17.998$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{11}q^{5}+\beta _{3}q^{6}+\cdots\)
2254.2.c.d 2254.c 161.c $16$ $17.998$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{7}q^{5}+\beta _{6}q^{6}+\cdots\)
2254.2.c.e 2254.c 161.c $24$ $17.998$ None \(-24\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2254.4.a.a 2254.a 1.a $1$ $132.990$ \(\Q\) None \(-2\) \(1\) \(10\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+4q^{4}+10q^{5}-2q^{6}+\cdots\)
2254.4.a.b 2254.a 1.a $1$ $132.990$ \(\Q\) None \(2\) \(9\) \(20\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+9q^{3}+4q^{4}+20q^{5}+18q^{6}+\cdots\)
2254.4.a.c 2254.a 1.a $2$ $132.990$ \(\Q(\sqrt{73}) \) None \(-4\) \(-9\) \(8\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-4-\beta )q^{3}+4q^{4}+(6-4\beta )q^{5}+\cdots\)
2254.4.a.d 2254.a 1.a $2$ $132.990$ \(\Q(\sqrt{41}) \) None \(-4\) \(1\) \(-10\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-1+3\beta )q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
2254.4.a.e 2254.a 1.a $2$ $132.990$ \(\Q(\sqrt{2}) \) None \(-4\) \(4\) \(-16\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(2+3\beta )q^{3}+4q^{4}+(-8-3\beta )q^{5}+\cdots\)
2254.4.a.f 2254.a 1.a $2$ $132.990$ \(\Q(\sqrt{73}) \) None \(4\) \(-3\) \(-10\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1-\beta )q^{3}+4q^{4}+(-6+\cdots)q^{5}+\cdots\)
2254.4.a.g 2254.a 1.a $2$ $132.990$ \(\Q(\sqrt{57}) \) None \(4\) \(-1\) \(18\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-\beta q^{3}+4q^{4}+(8+2\beta )q^{5}+\cdots\)
2254.4.a.h 2254.a 1.a $3$ $132.990$ 3.3.15384.1 None \(-6\) \(3\) \(-8\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+(1-\beta _{1})q^{3}+4q^{4}+(-3-2\beta _{1}+\cdots)q^{5}+\cdots\)
2254.4.a.i 2254.a 1.a $3$ $132.990$ 3.3.3368.1 None \(6\) \(7\) \(8\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(2+\beta _{2})q^{3}+4q^{4}+(3-\beta _{1}+\cdots)q^{5}+\cdots\)
2254.4.a.j 2254.a 1.a $4$ $132.990$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-8\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+\beta _{2}q^{5}-2\beta _{1}q^{6}+\cdots\)
2254.4.a.k 2254.a 1.a $5$ $132.990$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-10\) \(9\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(2-\beta _{4})q^{3}+4q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2254.4.a.l 2254.a 1.a $5$ $132.990$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(10\) \(-5\) \(-22\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-1+\beta _{1})q^{3}+4q^{4}+(-4+\cdots)q^{5}+\cdots\)
2254.4.a.m 2254.a 1.a $6$ $132.990$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(-13\) \(-12\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(-2-\beta _{1})q^{3}+4q^{4}+(-2+\cdots)q^{5}+\cdots\)
2254.4.a.n 2254.a 1.a $6$ $132.990$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{5}q^{3}+4q^{4}-\beta _{3}q^{5}+2\beta _{5}q^{6}+\cdots\)
2254.4.a.o 2254.a 1.a $8$ $132.990$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+\beta _{6}q^{5}-2\beta _{1}q^{6}+\cdots\)
2254.4.a.p 2254.a 1.a $8$ $132.990$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(16\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)
2254.4.a.q 2254.a 1.a $10$ $132.990$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-20\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+\beta _{1}q^{3}+4q^{4}+(-\beta _{1}+\beta _{7}+\cdots)q^{5}+\cdots\)
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