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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 17
7803.2.a.a 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}-4q^{7}+4q^{10}+\cdots\)
7803.2.a.b 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(-2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}-q^{7}+4q^{10}+\cdots\)
7803.2.a.c 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(2\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+2q^{5}+q^{7}-4q^{10}+\cdots\)
7803.2.a.d 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(4\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+4q^{5}-q^{7}-8q^{10}+\cdots\)
7803.2.a.e 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-1\) \(0\) \(-4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-4q^{5}+2q^{7}+3q^{8}+4q^{10}+\cdots\)
7803.2.a.f 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
7803.2.a.g 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-1\) \(0\) \(4\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}-2q^{7}+3q^{8}-4q^{10}+\cdots\)
7803.2.a.h 7803.a 1.a $1$ $62.307$ \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}-2q^{7}+3q^{11}+2q^{13}+\cdots\)
7803.2.a.i 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-5q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots\)
7803.2.a.j 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-4q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots\)
7803.2.a.k 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
7803.2.a.l 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+4q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots\)
7803.2.a.m 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+5q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots\)
7803.2.a.n 7803.a 1.a $1$ $62.307$ \(\Q\) None \(0\) \(0\) \(3\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-2q^{7}-3q^{11}+2q^{13}+\cdots\)
7803.2.a.o 7803.a 1.a $1$ $62.307$ \(\Q\) None \(1\) \(0\) \(-4\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-2q^{7}-3q^{8}-4q^{10}+\cdots\)
7803.2.a.p 7803.a 1.a $1$ $62.307$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots\)
7803.2.a.q 7803.a 1.a $1$ $62.307$ \(\Q\) None \(1\) \(0\) \(4\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}+2q^{7}-3q^{8}+4q^{10}+\cdots\)
7803.2.a.r 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(-4\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-4q^{5}-q^{7}-8q^{10}+\cdots\)
7803.2.a.s 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(-2\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-2q^{5}+q^{7}-4q^{10}+\cdots\)
7803.2.a.t 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{5}-4q^{7}+4q^{10}+\cdots\)
7803.2.a.u 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{5}-q^{7}+4q^{10}+\cdots\)
7803.2.a.v 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
7803.2.a.w 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(5\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
7803.2.a.x 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-51}) \) \(0\) \(0\) \(-3\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(-1-\beta )q^{5}+(1-2\beta )q^{11}+\cdots\)
7803.2.a.y 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-51}) \) \(0\) \(0\) \(3\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(1+\beta )q^{5}+(-1+2\beta )q^{11}+\cdots\)
7803.2.a.z 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-8\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-4q^{5}-2\beta q^{7}-2\beta q^{8}-4\beta q^{10}+\cdots\)
7803.2.a.ba 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(8\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+4q^{5}+2\beta q^{7}-2\beta q^{8}+4\beta q^{10}+\cdots\)
7803.2.a.bb 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+3\beta q^{7}+\cdots\)
7803.2.a.bc 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-5\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(-3+\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
7803.2.a.bd 7803.a 1.a $3$ $62.307$ 3.3.404.1 None \(-1\) \(0\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7803.2.a.be 7803.a 1.a $3$ $62.307$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(-2\beta _{1}-\beta _{2})q^{7}+(-3\beta _{1}+\cdots)q^{13}+\cdots\)
7803.2.a.bf 7803.a 1.a $3$ $62.307$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(2\beta _{1}+\beta _{2})q^{7}+(-3\beta _{1}+4\beta _{2})q^{13}+\cdots\)
7803.2.a.bg 7803.a 1.a $3$ $62.307$ 3.3.404.1 None \(1\) \(0\) \(-3\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
7803.2.a.bh 7803.a 1.a $4$ $62.307$ 4.4.29952.1 None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots\)
7803.2.a.bi 7803.a 1.a $4$ $62.307$ 4.4.29952.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{2}q^{5}+\beta _{3}q^{7}+\cdots\)
7803.2.a.bj 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(-3\) \(0\) \(-4\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
7803.2.a.bk 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(-3\) \(0\) \(4\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
7803.2.a.bl 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(3\) \(0\) \(-4\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7803.2.a.bm 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(3\) \(0\) \(4\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
7803.2.a.bn 7803.a 1.a $6$ $62.307$ 6.6.435306496.1 None \(0\) \(0\) \(0\) \(-8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bo 7803.a 1.a $6$ $62.307$ 6.6.435306496.1 None \(0\) \(0\) \(0\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.bp 7803.a 1.a $6$ $62.307$ 6.6.1168184448.1 None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bq 7803.a 1.a $6$ $62.307$ 6.6.1168184448.1 None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.br 7803.a 1.a $10$ $62.307$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)
7803.2.a.bs 7803.a 1.a $10$ $62.307$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\beta _{6}q^{7}+\cdots\)
7803.2.a.bt 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bu 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.bv 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{11})q^{5}+\cdots\)
7803.2.a.bw 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{11})q^{5}+\cdots\)
7803.2.a.bx 7803.a 1.a $15$ $62.307$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-6\) \(0\) \(-3\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
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