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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
335.1.d.a 335.d 335.d $1$ $0.167$ \(\Q\) \(\Q(\sqrt{-335}) \) None \(-1\) \(-1\) \(1\) \(-1\) \(q-q^{2}-q^{3}+q^{5}+q^{6}-q^{7}+q^{8}+\cdots\)
335.1.d.b 335.d 335.d $1$ $0.167$ \(\Q\) \(\Q(\sqrt{-335}) \) None \(1\) \(1\) \(-1\) \(1\) \(q+q^{2}+q^{3}-q^{5}+q^{6}+q^{7}-q^{8}+\cdots\)
335.1.d.c 335.d 335.d $3$ $0.167$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-335}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
335.1.d.d 335.d 335.d $3$ $0.167$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-335}) \) None \(0\) \(0\) \(3\) \(0\) \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
335.2.a.a 335.a 1.a $1$ $2.675$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-2q^{7}-3q^{9}-2q^{11}+\cdots\)
335.2.a.b 335.a 1.a $2$ $2.675$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}-q^{5}-2q^{6}-2q^{7}+\cdots\)
335.2.a.c 335.a 1.a $2$ $2.675$ \(\Q(\sqrt{5}) \) None None \(1\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
335.2.a.d 335.a 1.a $7$ $2.675$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None None \(2\) \(4\) \(-7\) \(10\) $-$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{5})q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
335.2.a.e 335.a 1.a $11$ $2.675$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(0\) \(0\) \(11\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
335.2.c.a 335.c 5.b $32$ $2.675$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
335.2.e.a 335.e 67.c $20$ $2.675$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(0\) \(-20\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(\beta _{10}-\beta _{18})q^{4}+\cdots\)
335.2.e.b 335.e 67.c $24$ $2.675$ None None \(-3\) \(0\) \(24\) \(-2\) $\mathrm{SU}(2)[C_{3}]$
335.2.f.a 335.f 335.f $64$ $2.675$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
335.2.i.a 335.i 335.i $64$ $2.675$ None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$
335.2.k.a 335.k 67.e $110$ $2.675$ None None \(-3\) \(-4\) \(11\) \(-6\) $\mathrm{SU}(2)[C_{11}]$
335.2.k.b 335.k 67.e $130$ $2.675$ None None \(-3\) \(-4\) \(-13\) \(-10\) $\mathrm{SU}(2)[C_{11}]$
335.2.m.a 335.m 335.m $128$ $2.675$ None None \(-6\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
335.2.o.a 335.o 335.o $320$ $2.675$ None None \(0\) \(0\) \(-11\) \(0\) $\mathrm{SU}(2)[C_{22}]$
335.2.q.a 335.q 67.g $200$ $2.675$ None None \(3\) \(0\) \(20\) \(4\) $\mathrm{SU}(2)[C_{33}]$
335.2.q.b 335.q 67.g $240$ $2.675$ None None \(3\) \(0\) \(-24\) \(2\) $\mathrm{SU}(2)[C_{33}]$
335.2.s.a 335.s 335.s $640$ $2.675$ None None \(-22\) \(-22\) \(-22\) \(-22\) $\mathrm{SU}(2)[C_{44}]$
335.2.u.a 335.u 335.u $640$ $2.675$ None None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{66}]$
335.2.w.a 335.w 335.w $1280$ $2.675$ None None \(-38\) \(-44\) \(-44\) \(-38\) $\mathrm{SU}(2)[C_{132}]$
335.3.b.a 335.b 67.b $44$ $9.128$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
335.3.d.a 335.d 335.d $9$ $9.128$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) \(\Q(\sqrt{-335}) \) None \(0\) \(0\) \(-45\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(4+\beta _{6}+\beta _{7})q^{4}+\cdots\)
335.3.d.b 335.d 335.d $9$ $9.128$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) \(\Q(\sqrt{-335}) \) None \(0\) \(0\) \(45\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(4+\beta _{6}+\beta _{7})q^{4}+\cdots\)
335.3.d.c 335.d 335.d $48$ $9.128$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
335.3.g.a 335.g 5.c $132$ $9.128$ None None \(-4\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
335.3.h.a 335.h 335.h $132$ $9.128$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
335.3.j.a 335.j 67.d $92$ $9.128$ None None \(0\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{6}]$
335.3.l.a 335.l 335.l $264$ $9.128$ None None \(-2\) \(0\) \(-8\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
335.3.n.a 335.n 335.n $660$ $9.128$ None None \(0\) \(0\) \(-11\) \(0\) $\mathrm{SU}(2)[C_{22}]$
335.3.p.a 335.p 67.f $440$ $9.128$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
335.3.r.a 335.r 335.r $1320$ $9.128$ None None \(-18\) \(-22\) \(-18\) \(-18\) $\mathrm{SU}(2)[C_{44}]$
335.3.t.a 335.t 67.h $920$ $9.128$ None None \(0\) \(0\) \(0\) \(-18\) $\mathrm{SU}(2)[C_{66}]$
335.3.v.a 335.v 335.v $1320$ $9.128$ None None \(0\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{66}]$
335.3.x.a 335.x 335.x $2640$ $9.128$ None None \(-42\) \(-44\) \(-36\) \(-42\) $\mathrm{SU}(2)[C_{132}]$
335.4.a.a 335.a 1.a $11$ $19.766$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None None \(-5\) \(-5\) \(55\) \(-48\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
335.4.a.b 335.a 1.a $13$ $19.766$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None None \(-1\) \(-7\) \(-65\) \(-50\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
335.4.a.c 335.a 1.a $20$ $19.766$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(5\) \(5\) \(-100\) \(48\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(5+\beta _{2})q^{4}-5q^{5}+\cdots\)
335.4.a.d 335.a 1.a $22$ $19.766$ None None \(1\) \(7\) \(110\) \(50\) $+$ $\mathrm{SU}(2)$
335.4.c.a 335.c 5.b $100$ $19.766$ None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$
335.5.b.a 335.b 67.b $92$ $34.629$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
335.6.a.a 335.a 1.a $22$ $53.729$ None None \(-7\) \(-16\) \(550\) \(-470\) $+$ $\mathrm{SU}(2)$
335.6.a.b 335.a 1.a $24$ $53.729$ None None \(-5\) \(-20\) \(-600\) \(-216\) $+$ $\mathrm{SU}(2)$
335.6.a.c 335.a 1.a $31$ $53.729$ None None \(7\) \(16\) \(-775\) \(470\) $-$ $\mathrm{SU}(2)$
335.6.a.d 335.a 1.a $33$ $53.729$ None None \(5\) \(20\) \(825\) \(216\) $-$ $\mathrm{SU}(2)$
335.8.a.a 335.a 1.a $33$ $104.649$ None None \(5\) \(-20\) \(4125\) \(-1252\) $-$ $\mathrm{SU}(2)$
335.8.a.b 335.a 1.a $35$ $104.649$ None None \(-29\) \(-88\) \(-4375\) \(-3550\) $-$ $\mathrm{SU}(2)$
335.8.a.c 335.a 1.a $42$ $104.649$ None None \(-5\) \(20\) \(-5250\) \(1252\) $+$ $\mathrm{SU}(2)$
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