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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
325.1.u.a 325.u 65.q $8$ $0.162$ \(\Q(\zeta_{24})\) None None 325.1.u.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{5}q^{2}-\zeta_{24}^{11}q^{3}-\zeta_{24}^{4}q^{6}+\cdots\)
325.2.a.a 325.a 1.a $1$ $2.595$ \(\Q\) None None 325.2.a.a \(-2\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}-2q^{7}+\cdots\)
325.2.a.b 325.a 1.a $1$ $2.595$ \(\Q\) None None 325.2.a.b \(0\) \(-1\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+4q^{7}-2q^{9}-6q^{11}+\cdots\)
325.2.a.c 325.a 1.a $1$ $2.595$ \(\Q\) None None 325.2.a.b \(0\) \(1\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
325.2.a.d 325.a 1.a $1$ $2.595$ \(\Q\) None None 65.2.a.a \(1\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{6}+4q^{7}-3q^{8}+\cdots\)
325.2.a.e 325.a 1.a $1$ $2.595$ \(\Q\) None None 325.2.a.a \(2\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots\)
325.2.a.f 325.a 1.a $2$ $2.595$ \(\Q(\sqrt{2}) \) None None 325.2.a.f \(-2\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
325.2.a.g 325.a 1.a $2$ $2.595$ \(\Q(\sqrt{3}) \) None None 65.2.a.c \(0\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+q^{4}+(-3-\beta )q^{6}+\cdots\)
325.2.a.h 325.a 1.a $2$ $2.595$ \(\Q(\sqrt{2}) \) None None 325.2.a.f \(2\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-2\beta q^{3}+(1+2\beta )q^{4}+(-4+\cdots)q^{6}+\cdots\)
325.2.a.i 325.a 1.a $2$ $2.595$ \(\Q(\sqrt{2}) \) None None 65.2.a.b \(2\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+\beta q^{3}+(1+2\beta )q^{4}+(2+\cdots)q^{6}+\cdots\)
325.2.a.j 325.a 1.a $3$ $2.595$ 3.3.148.1 None None 65.2.b.a \(-3\) \(-4\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1-\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots\)
325.2.a.k 325.a 1.a $3$ $2.595$ 3.3.148.1 None None 65.2.b.a \(3\) \(4\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(1+\beta _{1})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
325.2.b.a 325.b 5.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
325.2.b.b 325.b 5.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 65.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2iq^{3}+q^{4}+2q^{6}+4iq^{7}+\cdots\)
325.2.b.c 325.b 5.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{4}+4iq^{7}+2q^{9}-6q^{11}+\cdots\)
325.2.b.d 325.b 5.b $4$ $2.595$ \(\Q(\zeta_{8})\) None None 325.2.a.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+2\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
325.2.b.e 325.b 5.b $4$ $2.595$ \(\Q(\zeta_{12})\) None None 65.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
325.2.b.f 325.b 5.b $4$ $2.595$ \(\Q(\zeta_{8})\) None None 65.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
325.2.c.a 325.c 13.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{3}+q^{4}-2iq^{6}-5iq^{7}+\cdots\)
325.2.c.b 325.c 13.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 65.2.d.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-2q^{3}+q^{4}-2iq^{6}+3iq^{8}+\cdots\)
325.2.c.c 325.c 13.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.c \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-2q^{4}-iq^{6}+iq^{7}+\cdots\)
325.2.c.d 325.c 13.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.c \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-2q^{4}+iq^{6}+iq^{7}+\cdots\)
325.2.c.e 325.c 13.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 65.2.d.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2q^{3}+q^{4}+2iq^{6}+3iq^{8}+\cdots\)
325.2.c.f 325.c 13.b $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+2q^{3}+q^{4}+2iq^{6}-5iq^{7}+\cdots\)
325.2.c.g 325.c 13.b $6$ $2.595$ 6.0.5089536.1 None None 65.2.c.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(1+\beta _{1})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)
325.2.d.a 325.d 65.d $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.c \(-4\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}+iq^{3}+2q^{4}-2iq^{6}-2q^{7}+\cdots\)
325.2.d.b 325.d 65.d $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.a \(-2\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+2iq^{3}-q^{4}-2iq^{6}+5q^{7}+\cdots\)
325.2.d.c 325.d 65.d $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.a \(2\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+2iq^{3}-q^{4}+2iq^{6}-5q^{7}+\cdots\)
325.2.d.d 325.d 65.d $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 325.2.c.c \(4\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}+iq^{3}+2q^{4}+2iq^{6}+2q^{7}+\cdots\)
325.2.d.e 325.d 65.d $6$ $2.595$ 6.0.5089536.1 None None 65.2.c.a \(-2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
325.2.d.f 325.d 65.d $6$ $2.595$ 6.0.5089536.1 None None 65.2.c.a \(2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
325.2.e.a 325.e 13.c $4$ $2.595$ \(\Q(\sqrt{-3}, \sqrt{13})\) None None 65.2.e.b \(-1\) \(2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.b 325.e 13.c $4$ $2.595$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None 65.2.e.a \(1\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1-2\beta _{1}+\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.e.c 325.e 13.c $10$ $2.595$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None 325.2.e.c \(0\) \(-3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{8})q^{3}+\cdots\)
325.2.e.d 325.e 13.c $10$ $2.595$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None 325.2.e.c \(0\) \(3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{8})q^{3}+(-\beta _{6}+\cdots)q^{4}+\cdots\)
325.2.e.e 325.e 13.c $12$ $2.595$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 65.2.n.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{2}+(\beta _{6}-\beta _{11})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
325.2.f.a 325.f 65.f $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 65.2.f.a \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-iq^{2}+(-1+i)q^{3}+q^{4}+(1+i)q^{6}+\cdots\)
325.2.f.b 325.f 65.f $8$ $2.595$ 8.0.619810816.2 None None 65.2.f.b \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
325.2.f.c 325.f 65.f $12$ $2.595$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 325.2.f.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{7}q^{2}-\beta _{4}q^{3}+(-2+\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
325.2.f.d 325.f 65.f $16$ $2.595$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 325.2.f.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{13}q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(1+\beta _{4}+\cdots)q^{6}+\cdots\)
325.2.k.a 325.k 65.k $2$ $2.595$ \(\Q(\sqrt{-1}) \) None None 65.2.f.a \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}+(-1-i)q^{3}-q^{4}+(1+i)q^{6}+\cdots\)
325.2.k.b 325.k 65.k $8$ $2.595$ 8.0.619810816.2 None None 65.2.f.b \(4\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+(1+\beta _{4}+\cdots)q^{4}+\cdots\)
325.2.k.c 325.k 65.k $12$ $2.595$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 325.2.f.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(2-\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
325.2.k.d 325.k 65.k $16$ $2.595$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 325.2.f.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{1}q^{4}+(1-\beta _{4}+\cdots)q^{6}+\cdots\)
325.2.l.a 325.l 25.d $4$ $2.595$ \(\Q(\zeta_{10})\) None None 325.2.l.a \(3\) \(4\) \(-5\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}^{3})q^{2}+(1-\zeta_{10}+\zeta_{10}^{3})q^{3}+\cdots\)
325.2.l.b 325.l 25.d $56$ $2.595$ None None 325.2.l.b \(0\) \(-2\) \(9\) \(-20\) $\mathrm{SU}(2)[C_{5}]$
325.2.l.c 325.l 25.d $60$ $2.595$ None None 325.2.l.c \(-3\) \(-6\) \(2\) \(10\) $\mathrm{SU}(2)[C_{5}]$
325.2.m.a 325.m 65.l $4$ $2.595$ \(\Q(\zeta_{12})\) None None 13.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
325.2.m.b 325.m 65.l $8$ $2.595$ 8.0.22581504.2 None None 65.2.m.a \(-2\) \(6\) \(0\) \(10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}-\beta _{3}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
325.2.m.c 325.m 65.l $8$ $2.595$ 8.0.22581504.2 None None 65.2.m.a \(2\) \(-6\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{1}+\beta _{3}+\beta _{6})q^{2}+(-2+\beta _{3}+\cdots)q^{3}+\cdots\)
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