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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.1.c.a 275.c 11.b $1$ $0.137$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}-q^{9}-q^{11}+q^{16}-2q^{31}+\cdots\)
275.1.s.a 275.s 275.s $4$ $0.137$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+(\zeta_{10}-\zeta_{10}^{3})q^{3}-\zeta_{10}^{2}q^{4}-q^{5}+\cdots\)
275.1.v.a 275.v 275.v $4$ $0.137$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-2\) \(4\) \(0\) \(q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+q^{5}+\cdots\)
275.2.a.a 275.a 1.a $1$ $2.196$ \(\Q\) None None \(-1\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}-q^{11}-2q^{13}+\cdots\)
275.2.a.b 275.a 1.a $1$ $2.196$ \(\Q\) None None \(2\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots\)
275.2.a.c 275.a 1.a $2$ $2.196$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
275.2.a.d 275.a 1.a $2$ $2.196$ \(\Q(\sqrt{5}) \) None None \(-1\) \(-3\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
275.2.a.e 275.a 1.a $2$ $2.196$ \(\Q(\sqrt{13}) \) None None \(-1\) \(-1\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-3q^{6}+\cdots\)
275.2.a.f 275.a 1.a $2$ $2.196$ \(\Q(\sqrt{13}) \) None None \(1\) \(1\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}-3q^{6}+\cdots\)
275.2.a.g 275.a 1.a $2$ $2.196$ \(\Q(\sqrt{5}) \) None None \(1\) \(3\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
275.2.a.h 275.a 1.a $4$ $2.196$ \(\Q(\sqrt{3}, \sqrt{11})\) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(2+\beta _{3})q^{4}+\cdots\)
275.2.b.a 275.b 5.b $2$ $2.196$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
275.2.b.b 275.b 5.b $2$ $2.196$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+3iq^{8}+3q^{9}-q^{11}+\cdots\)
275.2.b.c 275.b 5.b $4$ $2.196$ \(\Q(i, \sqrt{13})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)
275.2.b.d 275.b 5.b $4$ $2.196$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+(\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
275.2.b.e 275.b 5.b $4$ $2.196$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
275.2.e.a 275.e 55.e $4$ $2.196$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}-\beta _{2})q^{3}-2\beta _{1}q^{4}+(-1+3\beta _{1}+\cdots)q^{9}+\cdots\)
275.2.e.b 275.e 55.e $4$ $2.196$ \(\Q(i, \sqrt{10})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+3\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
275.2.e.c 275.e 55.e $8$ $2.196$ 8.0.1499238400.2 \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta _{2}q^{2}+(-2\beta _{4}-\beta _{6})q^{4}+\beta _{5}q^{7}+\cdots\)
275.2.e.d 275.e 55.e $16$ $2.196$ 16.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{9}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{4}-\beta _{7}+\cdots)q^{4}+\cdots\)
275.2.g.a 275.g 275.g $112$ $2.196$ None None \(-1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{5}]$
275.2.h.a 275.h 11.c $8$ $2.196$ 8.0.13140625.1 None None \(2\) \(5\) \(0\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{6}q^{2}+(1-\beta _{1}-\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
275.2.h.b 275.h 11.c $8$ $2.196$ 8.0.159390625.1 None None \(4\) \(-1\) \(0\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
275.2.h.c 275.h 11.c $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots\)
275.2.h.d 275.h 11.c $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}+\beta _{12}+\beta _{13})q^{2}+(-\beta _{5}+\beta _{13}+\cdots)q^{3}+\cdots\)
275.2.h.e 275.h 11.c $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}-\beta _{5}+\beta _{9})q^{2}+\beta _{14}q^{3}+(-1+\cdots)q^{4}+\cdots\)
275.2.i.a 275.i 25.d $44$ $2.196$ None None \(-1\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{5}]$
275.2.i.b 275.i 25.d $60$ $2.196$ None None \(-1\) \(-2\) \(6\) \(0\) $\mathrm{SU}(2)[C_{5}]$
275.2.j.a 275.j 275.j $112$ $2.196$ None None \(-1\) \(-4\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{5}]$
275.2.k.a 275.k 275.k $4$ $2.196$ \(\Q(\zeta_{10})\) None None \(-2\) \(-6\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}+\zeta_{10}^{3})q^{2}+(-2-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
275.2.k.b 275.k 275.k $4$ $2.196$ \(\Q(\zeta_{10})\) None None \(-2\) \(-6\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}+\zeta_{10}^{3})q^{2}+(-1+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
275.2.k.c 275.k 275.k $4$ $2.196$ \(\Q(\zeta_{10})\) None None \(1\) \(0\) \(5\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{3}q^{2}+(1+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{3}+\cdots\)
275.2.k.d 275.k 275.k $100$ $2.196$ None None \(2\) \(8\) \(0\) \(5\) $\mathrm{SU}(2)[C_{5}]$
275.2.l.a 275.l 275.l $4$ $2.196$ \(\Q(\zeta_{10})\) None None \(-4\) \(-5\) \(-5\) \(-10\) $\mathrm{SU}(2)[C_{5}]$ \(q-q^{2}+(-1-\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\cdots\)
275.2.l.b 275.l 275.l $4$ $2.196$ \(\Q(\zeta_{10})\) None None \(-2\) \(-1\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(1-2\zeta_{10}+\cdots)q^{3}+\cdots\)
275.2.l.c 275.l 275.l $4$ $2.196$ \(\Q(\zeta_{10})\) None None \(-2\) \(4\) \(5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+(2-\zeta_{10}+\cdots)q^{3}+\cdots\)
275.2.l.d 275.l 275.l $100$ $2.196$ None None \(2\) \(-2\) \(5\) \(5\) $\mathrm{SU}(2)[C_{5}]$
275.2.n.a 275.n 275.n $112$ $2.196$ None None \(0\) \(-10\) \(-2\) \(15\) $\mathrm{SU}(2)[C_{10}]$
275.2.t.a 275.t 275.t $112$ $2.196$ None None \(-5\) \(0\) \(-7\) \(-15\) $\mathrm{SU}(2)[C_{10}]$
275.2.y.a 275.y 25.e $40$ $2.196$ None None \(0\) \(0\) \(5\) \(0\) $\mathrm{SU}(2)[C_{10}]$
275.2.y.b 275.y 25.e $56$ $2.196$ None None \(0\) \(0\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{10}]$
275.2.z.a 275.z 55.j $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{4}q^{2}+(-\beta _{1}-\beta _{11}-\beta _{13}+\beta _{15})q^{3}+\cdots\)
275.2.z.b 275.z 55.j $16$ $2.196$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(\beta _{6}+\beta _{12}-\beta _{15})q^{2}+(\beta _{14}-\beta _{15})q^{3}+\cdots\)
275.2.z.c 275.z 55.j $32$ $2.196$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
275.2.ba.a 275.ba 275.aa $112$ $2.196$ None None \(-5\) \(-5\) \(-2\) \(10\) $\mathrm{SU}(2)[C_{10}]$
275.2.bb.a 275.bb 275.ab $112$ $2.196$ None None \(-5\) \(0\) \(-7\) \(-10\) $\mathrm{SU}(2)[C_{10}]$
275.2.bf.a 275.bf 275.af $224$ $2.196$ None None \(-10\) \(-14\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{20}]$
275.2.bg.a 275.bg 275.ag $224$ $2.196$ None None \(-10\) \(-4\) \(-12\) \(-30\) $\mathrm{SU}(2)[C_{20}]$
275.2.bl.a 275.bl 275.al $224$ $2.196$ None None \(-10\) \(-4\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{20}]$
275.2.bm.a 275.bm 55.l $32$ $2.196$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$
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