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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2499.1.e.a 2499.e 51.c $1$ $1.247$ \(\Q\) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-119}) \) \(\Q(\sqrt{21}) \) \(0\) \(-1\) \(2\) \(0\) \(q-q^{3}+q^{4}+2q^{5}+q^{9}-q^{12}-2q^{15}+\cdots\)
2499.1.e.b 2499.e 51.c $1$ $1.247$ \(\Q\) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-119}) \) \(\Q(\sqrt{21}) \) \(0\) \(1\) \(-2\) \(0\) \(q+q^{3}+q^{4}-2q^{5}+q^{9}+q^{12}-2q^{15}+\cdots\)
2499.1.e.c 2499.e 51.c $2$ $1.247$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}+q^{4}+q^{9}-\beta q^{11}-q^{12}-\beta q^{13}+\cdots\)
2499.1.e.d 2499.e 51.c $2$ $1.247$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-51}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+q^{4}+q^{9}-\beta q^{11}+q^{12}+\beta q^{13}+\cdots\)
2499.1.e.e 2499.e 51.c $4$ $1.247$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-119}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2499.1.e.f 2499.e 51.c $4$ $1.247$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-119}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+\zeta_{10}q^{3}+(-1+\cdots)q^{4}+\cdots\)
2499.1.q.a 2499.q 357.q $2$ $1.247$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-119}) \) \(\Q(\sqrt{21}) \) \(0\) \(-1\) \(2\) \(0\) \(q-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
2499.1.q.b 2499.q 357.q $2$ $1.247$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-119}) \) \(\Q(\sqrt{21}) \) \(0\) \(1\) \(-2\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
2499.1.q.c 2499.q 357.q $4$ $1.247$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-51}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2499.1.q.d 2499.q 357.q $4$ $1.247$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-51}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\beta _{2}q^{3}+\beta _{2}q^{4}+(-1-\beta _{2})q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2499.1.q.e 2499.q 357.q $8$ $1.247$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-119}) \) None \(0\) \(-1\) \(2\) \(0\) \(q+(\zeta_{30}^{11}+\zeta_{30}^{14})q^{2}+\zeta_{30}q^{3}+(-\zeta_{30}^{7}+\cdots)q^{4}+\cdots\)
2499.1.q.f 2499.q 357.q $8$ $1.247$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-119}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+(-\zeta_{30}^{2}+\zeta_{30}^{8})q^{2}-\zeta_{30}^{7}q^{3}+\cdots\)
2499.2.a.a 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(-2\) \(-1\) \(3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+3q^{5}+2q^{6}+\cdots\)
2499.2.a.b 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(-1\) \(-1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-q^{5}+q^{6}+3q^{8}+\cdots\)
2499.2.a.c 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(-1\) \(1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
2499.2.a.d 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(0\) \(-1\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-3q^{5}+q^{9}-3q^{11}+\cdots\)
2499.2.a.e 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(0\) \(-1\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+4q^{5}+q^{9}+4q^{11}+\cdots\)
2499.2.a.f 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(0\) \(1\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-4q^{5}+q^{9}+4q^{11}+\cdots\)
2499.2.a.g 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}+q^{9}-5q^{11}-2q^{12}+\cdots\)
2499.2.a.h 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}+q^{9}+3q^{11}-2q^{12}+\cdots\)
2499.2.a.i 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(1\) \(-1\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-3q^{5}-q^{6}-3q^{8}+\cdots\)
2499.2.a.j 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(1\) \(-1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-3q^{8}+\cdots\)
2499.2.a.k 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(1\) \(1\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+2q^{5}+q^{6}-3q^{8}+\cdots\)
2499.2.a.l 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(1\) \(1\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+3q^{5}+q^{6}-3q^{8}+\cdots\)
2499.2.a.m 2499.a 1.a $1$ $19.955$ \(\Q\) None None \(2\) \(-1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
2499.2.a.n 2499.a 1.a $2$ $19.955$ \(\Q(\sqrt{3}) \) None None \(-2\) \(-2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+(2+\cdots)q^{5}+\cdots\)
2499.2.a.o 2499.a 1.a $2$ $19.955$ \(\Q(\sqrt{17}) \) None None \(-1\) \(2\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
2499.2.a.p 2499.a 1.a $2$ $19.955$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(1+\beta )q^{5}-\beta q^{6}-2\beta q^{8}+\cdots\)
2499.2.a.q 2499.a 1.a $2$ $19.955$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1-\beta )q^{5}+\beta q^{6}+\cdots\)
2499.2.a.r 2499.a 1.a $2$ $19.955$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(1+\beta )q^{5}+\beta q^{6}-2\beta q^{8}+\cdots\)
2499.2.a.s 2499.a 1.a $3$ $19.955$ 3.3.316.1 None None \(1\) \(-3\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
2499.2.a.t 2499.a 1.a $4$ $19.955$ 4.4.9301.1 None None \(-3\) \(-4\) \(6\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2499.2.a.u 2499.a 1.a $4$ $19.955$ 4.4.9301.1 None None \(-3\) \(4\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2499.2.a.v 2499.a 1.a $4$ $19.955$ 4.4.14013.1 None None \(-1\) \(-4\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
2499.2.a.w 2499.a 1.a $4$ $19.955$ 4.4.14013.1 None None \(-1\) \(4\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
2499.2.a.x 2499.a 1.a $4$ $19.955$ \(\Q(\zeta_{16})^+\) None None \(0\) \(-4\) \(4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(1+\beta _{3})q^{5}+\cdots\)
2499.2.a.y 2499.a 1.a $4$ $19.955$ \(\Q(\zeta_{16})^+\) None None \(0\) \(4\) \(-4\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
2499.2.a.z 2499.a 1.a $4$ $19.955$ 4.4.7232.1 None None \(2\) \(4\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{2}-\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots\)
2499.2.a.ba 2499.a 1.a $5$ $19.955$ 5.5.1383597.1 None None \(-2\) \(-5\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
2499.2.a.bb 2499.a 1.a $5$ $19.955$ 5.5.1383597.1 None None \(-2\) \(5\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
2499.2.a.bc 2499.a 1.a $5$ $19.955$ 5.5.885424.1 None None \(1\) \(-5\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}-q^{3}+(2-\beta _{3})q^{4}-\beta _{2}q^{5}+\cdots\)
2499.2.a.bd 2499.a 1.a $5$ $19.955$ 5.5.885424.1 None None \(1\) \(5\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+q^{3}+(2-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots\)
2499.2.a.be 2499.a 1.a $6$ $19.955$ 6.6.29722117.1 None None \(2\) \(-6\) \(-7\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2499.2.a.bf 2499.a 1.a $6$ $19.955$ 6.6.29722117.1 None None \(2\) \(6\) \(7\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2499.2.a.bg 2499.a 1.a $12$ $19.955$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(4\) \(-12\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{5}+\cdots\)
2499.2.a.bh 2499.a 1.a $12$ $19.955$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(4\) \(12\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
2499.4.a.a 2499.a 1.a $1$ $147.446$ \(\Q\) None None \(-5\) \(-3\) \(18\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}-3q^{3}+17q^{4}+18q^{5}+15q^{6}+\cdots\)
2499.4.a.b 2499.a 1.a $1$ $147.446$ \(\Q\) None None \(-5\) \(3\) \(-18\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+3q^{3}+17q^{4}-18q^{5}-15q^{6}+\cdots\)
2499.4.a.c 2499.a 1.a $1$ $147.446$ \(\Q\) None None \(-5\) \(3\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-5q^{2}+3q^{3}+17q^{4}+q^{5}-15q^{6}+\cdots\)
2499.4.a.d 2499.a 1.a $1$ $147.446$ \(\Q\) None None \(-1\) \(-3\) \(20\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-7q^{4}+20q^{5}+3q^{6}+\cdots\)
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