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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2475.1.b.a 2475.b 11.b $1$ $1.235$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{11}+q^{16}-2q^{31}+q^{44}+\cdots\)
2475.1.b.b 2475.b 11.b $2$ $1.235$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}-q^{4}-\beta q^{7}-q^{11}-\beta q^{13}+\cdots\)
2475.1.b.c 2475.b 11.b $2$ $1.235$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{2}-q^{4}-\beta q^{7}+q^{11}-\beta q^{13}+\cdots\)
2475.1.m.a 2475.m 165.l $8$ $1.235$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}+\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)
2475.1.m.b 2475.m 165.l $8$ $1.235$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{16}-\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}-\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)
2475.1.t.a 2475.t 495.o $4$ $1.235$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{2}q^{11}+\cdots\)
2475.1.y.a 2475.y 99.h $2$ $1.235$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{11}+\cdots\)
2475.1.y.b 2475.y 99.h $4$ $1.235$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{2}q^{11}+\cdots\)
2475.1.bs.a 2475.bs 275.s $4$ $1.235$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(4\) \(0\) \(q-\zeta_{10}^{4}q^{4}+q^{5}+\zeta_{10}^{2}q^{11}-\zeta_{10}^{3}q^{16}+\cdots\)
2475.1.bu.a 2475.bu 275.v $4$ $1.235$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{10}^{4}q^{4}-q^{5}-\zeta_{10}^{2}q^{11}-\zeta_{10}^{3}q^{16}+\cdots\)
2475.1.cr.a 2475.cr 495.ad $4$ $1.235$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{9}+\zeta_{12}^{5}q^{11}+\cdots\)
2475.1.cr.b 2475.cr 495.ad $4$ $1.235$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}q^{4}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{5}q^{11}+\cdots\)
2475.1.eu.a 2475.eu 2475.du $8$ $1.235$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-4\) \(0\) \(q+\zeta_{30}^{2}q^{3}+\zeta_{30}^{8}q^{4}+\zeta_{30}^{10}q^{5}+\cdots\)
2475.1.eu.b 2475.eu 2475.du $8$ $1.235$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(8\) \(0\) \(q+\zeta_{30}^{14}q^{3}+\zeta_{30}^{8}q^{4}+q^{5}-\zeta_{30}^{13}q^{9}+\cdots\)
2475.1.ev.a 2475.ev 2475.dv $8$ $1.235$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(-8\) \(0\) \(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{4}q^{4}-q^{5}+\zeta_{30}^{14}q^{9}+\cdots\)
2475.1.ev.b 2475.ev 2475.dv $8$ $1.235$ \(\Q(\zeta_{15})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(4\) \(0\) \(q-\zeta_{30}q^{3}-\zeta_{30}^{4}q^{4}+\zeta_{30}^{5}q^{5}+\zeta_{30}^{2}q^{9}+\cdots\)
2475.1.fy.a 2475.fy 2475.ey $16$ $1.235$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{60}^{8}q^{3}-\zeta_{60}^{17}q^{4}-\zeta_{60}^{25}q^{5}+\cdots\)
2475.1.fy.b 2475.fy 2475.ey $16$ $1.235$ \(\Q(\zeta_{60})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{60}^{11}q^{3}-\zeta_{60}^{17}q^{4}-\zeta_{60}^{15}q^{5}+\cdots\)
2475.2.a.a 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(-2\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+2q^{7}-q^{11}-4q^{13}+\cdots\)
2475.2.a.b 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(-1\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-3q^{7}+3q^{8}+q^{11}+2q^{13}+\cdots\)
2475.2.a.c 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(-1\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{7}+3q^{8}+q^{11}+2q^{13}+\cdots\)
2475.2.a.d 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(-1\) \(0\) \(0\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{7}+3q^{8}-q^{11}-2q^{13}+\cdots\)
2475.2.a.e 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{7}+q^{11}-q^{13}+4q^{16}+\cdots\)
2475.2.a.f 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{7}+q^{11}+q^{13}+4q^{16}+\cdots\)
2475.2.a.g 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(1\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots\)
2475.2.a.h 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(1\) \(0\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots\)
2475.2.a.i 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}+q^{11}-2q^{13}+\cdots\)
2475.2.a.j 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(1\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{7}-3q^{8}-q^{11}+2q^{13}+\cdots\)
2475.2.a.k 2475.a 1.a $1$ $19.763$ \(\Q\) None None \(1\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{7}-3q^{8}+q^{11}-2q^{13}+\cdots\)
2475.2.a.l 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-1-\beta )q^{7}+\cdots\)
2475.2.a.m 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(2+2\beta )q^{7}+\cdots\)
2475.2.a.n 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{5}) \) None None \(-1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(2-3\beta )q^{7}+\cdots\)
2475.2.a.o 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(2+\beta )q^{7}-3q^{8}+\cdots\)
2475.2.a.p 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}-q^{7}+(-4-\beta )q^{8}+\cdots\)
2475.2.a.q 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{17}) \) None None \(-1\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}+q^{7}+(-4-\beta )q^{8}+\cdots\)
2475.2.a.r 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+q^{11}+\cdots\)
2475.2.a.s 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{7}+\cdots\)
2475.2.a.t 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(-2-\beta )q^{7}+3q^{8}+\cdots\)
2475.2.a.u 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}-q^{7}+(4+\beta )q^{8}+\cdots\)
2475.2.a.v 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{17}) \) None None \(1\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}+q^{7}+(4+\beta )q^{8}+\cdots\)
2475.2.a.w 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(1-\beta )q^{7}+\cdots\)
2475.2.a.x 2475.a 1.a $2$ $19.763$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+2q^{7}+(3+\cdots)q^{8}+\cdots\)
2475.2.a.y 2475.a 1.a $3$ $19.763$ 3.3.148.1 None None \(-3\) \(0\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2475.2.a.z 2475.a 1.a $3$ $19.763$ 3.3.568.1 None None \(-2\) \(0\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
2475.2.a.ba 2475.a 1.a $3$ $19.763$ 3.3.148.1 None None \(-1\) \(0\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2475.2.a.bb 2475.a 1.a $3$ $19.763$ 3.3.148.1 None None \(-1\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
2475.2.a.bc 2475.a 1.a $3$ $19.763$ 3.3.148.1 None None \(1\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
2475.2.a.bd 2475.a 1.a $3$ $19.763$ 3.3.568.1 None None \(2\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(3+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2475.2.a.be 2475.a 1.a $3$ $19.763$ 3.3.148.1 None None \(3\) \(0\) \(0\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-3+\cdots)q^{7}+\cdots\)
2475.2.a.bf 2475.a 1.a $4$ $19.763$ 4.4.48704.2 None None \(-2\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
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