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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
675.1.c.a 675.c 3.b $1$ $0.337$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-1\) \(q+q^{4}-q^{7}+2q^{13}+q^{16}-q^{19}+\cdots\)
675.1.c.b 675.c 3.b $1$ $0.337$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{4}+q^{7}-2q^{13}+q^{16}-q^{19}+\cdots\)
675.1.c.c 675.c 3.b $2$ $0.337$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{8}-q^{16}-iq^{17}+q^{19}+\cdots\)
675.1.d.a 675.d 15.d $2$ $0.337$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-q^{4}-iq^{7}-iq^{13}+q^{16}+q^{19}+\cdots\)
675.1.g.a 675.g 5.c $4$ $0.337$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+2\beta _{2}q^{4}-\beta _{3}q^{8}-q^{16}+\cdots\)
675.1.g.b 675.g 5.c $4$ $0.337$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{4}-\beta _{1}q^{7}-q^{16}-\beta _{2}q^{19}+\cdots\)
675.1.o.a 675.o 75.j $8$ $0.337$ \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(0\) \(-4\) \(q+(-\zeta_{20}-\zeta_{20}^{5})q^{2}+(-1+\zeta_{20}^{2}+\cdots)q^{4}+\cdots\)
675.2.a.a 675.a 1.a $1$ $5.390$ \(\Q\) None None \(-2\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{7}+2q^{11}+5q^{13}+\cdots\)
675.2.a.b 675.a 1.a $1$ $5.390$ \(\Q\) None None \(-1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-5q^{11}+5q^{13}+\cdots\)
675.2.a.c 675.a 1.a $1$ $5.390$ \(\Q\) None None \(-1\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}+5q^{11}-5q^{13}+\cdots\)
675.2.a.d 675.a 1.a $1$ $5.390$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-4q^{7}+5q^{13}+4q^{16}+8q^{19}+\cdots\)
675.2.a.e 675.a 1.a $1$ $5.390$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(1\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+q^{7}-5q^{13}+4q^{16}-7q^{19}+\cdots\)
675.2.a.f 675.a 1.a $1$ $5.390$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+4q^{7}-5q^{13}+4q^{16}+8q^{19}+\cdots\)
675.2.a.g 675.a 1.a $1$ $5.390$ \(\Q\) None None \(1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}-5q^{11}-5q^{13}+\cdots\)
675.2.a.h 675.a 1.a $1$ $5.390$ \(\Q\) None None \(1\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}+5q^{11}+5q^{13}+\cdots\)
675.2.a.i 675.a 1.a $1$ $5.390$ \(\Q\) None None \(2\) \(0\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{7}-2q^{11}+5q^{13}+\cdots\)
675.2.a.j 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) None \(-3\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1-4\beta )q^{8}+\cdots\)
675.2.a.k 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{13}) \) None None \(-1\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots\)
675.2.a.l 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-3q^{7}-2\beta q^{8}-3\beta q^{11}-3q^{13}+\cdots\)
675.2.a.m 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+3q^{7}-2\beta q^{8}+3\beta q^{11}+3q^{13}+\cdots\)
675.2.a.n 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}-3q^{7}+3\beta q^{8}+2\beta q^{11}+\cdots\)
675.2.a.o 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{7}) \) None None \(0\) \(0\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+5q^{4}+3q^{7}+3\beta q^{8}-2\beta q^{11}+\cdots\)
675.2.a.p 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{13}) \) None None \(1\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(-2+2\beta )q^{7}+\cdots\)
675.2.a.q 675.a 1.a $2$ $5.390$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-15}) \) None \(3\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+(1+\beta )q^{2}+3\beta q^{4}+(1+4\beta )q^{8}+(5+\cdots)q^{16}+\cdots\)
675.2.b.a 675.b 5.b $2$ $5.390$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+3iq^{7}-2q^{11}-5iq^{13}+\cdots\)
675.2.b.b 675.b 5.b $2$ $5.390$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}-3iq^{7}+2q^{11}+5iq^{13}+\cdots\)
675.2.b.c 675.b 5.b $2$ $5.390$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{8}-5q^{11}+5iq^{13}+\cdots\)
675.2.b.d 675.b 5.b $2$ $5.390$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{8}+5q^{11}-5iq^{13}+\cdots\)
675.2.b.e 675.b 5.b $2$ $5.390$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+4iq^{7}+5iq^{13}+4q^{16}+\cdots\)
675.2.b.f 675.b 5.b $2$ $5.390$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{4}+iq^{7}+5iq^{13}+4q^{16}+7q^{19}+\cdots\)
675.2.b.g 675.b 5.b $4$ $5.390$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-5q^{4}+3\beta _{1}q^{7}-3\beta _{3}q^{8}+\cdots\)
675.2.b.h 675.b 5.b $4$ $5.390$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\)
675.2.b.i 675.b 5.b $4$ $5.390$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(2\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
675.2.e.a 675.e 9.c $2$ $5.390$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{7}+\cdots\)
675.2.e.b 675.e 9.c $6$ $5.390$ 6.0.954288.1 None None \(-1\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)
675.2.e.c 675.e 9.c $8$ $5.390$ 8.0.1223810289.2 None None \(-2\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{6})q^{4}+\cdots\)
675.2.e.d 675.e 9.c $8$ $5.390$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
675.2.e.e 675.e 9.c $8$ $5.390$ 8.0.1223810289.2 None None \(2\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}-\beta _{3}+\beta _{6})q^{4}+\cdots\)
675.2.f.a 675.f 15.e $4$ $5.390$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots\)
675.2.f.b 675.f 15.e $4$ $5.390$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots\)
675.2.f.c 675.f 15.e $4$ $5.390$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+2\beta _{2}q^{4}+2\beta _{1}q^{7}-3\beta _{3}q^{13}-4q^{16}+\cdots\)
675.2.f.d 675.f 15.e $4$ $5.390$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+2\beta _{2}q^{4}-\beta _{1}q^{7}-\beta _{3}q^{13}-4q^{16}+\cdots\)
675.2.f.e 675.f 15.e $4$ $5.390$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots\)
675.2.f.f 675.f 15.e $4$ $5.390$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-2\beta _{3}q^{7}-\beta _{3}q^{8}+\cdots\)
675.2.f.g 675.f 15.e $8$ $5.390$ 8.0.\(\cdots\).8 None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(2\beta _{2}+\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{7}+\cdots\)
675.2.f.h 675.f 15.e $8$ $5.390$ 8.0.3317760000.9 \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta _{4}q^{2}+(3\beta _{1}+\beta _{2})q^{4}+(-3\beta _{3}-\beta _{5}+\cdots)q^{8}+\cdots\)
675.2.f.i 675.f 15.e $8$ $5.390$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{4}+(-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
675.2.h.a 675.h 25.d $40$ $5.390$ None None \(-2\) \(0\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$
675.2.h.b 675.h 25.d $40$ $5.390$ None None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{5}]$
675.2.h.c 675.h 25.d $40$ $5.390$ None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{5}]$
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