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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1824.1.l.a 1824.l 456.l $1$ $0.910$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{57}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{9}+q^{19}-q^{25}-q^{27}+2q^{41}+\cdots\)
1824.1.l.b 1824.l 456.l $1$ $0.910$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{57}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{9}+q^{19}-q^{25}+q^{27}-2q^{41}+\cdots\)
1824.1.ba.a 1824.ba 456.s $2$ $0.910$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+(-\zeta_{6}-\zeta_{6}^{2})q^{11}+\cdots\)
1824.1.ba.b 1824.ba 456.s $2$ $0.910$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+q^{9}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+\zeta_{6}^{2}q^{19}+\cdots\)
1824.1.cr.a 1824.cr 456.at $6$ $0.910$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-3\) \(0\) \(0\) \(q+\zeta_{18}^{6}q^{3}-\zeta_{18}^{3}q^{9}+(\zeta_{18}^{5}-\zeta_{18}^{7}+\cdots)q^{11}+\cdots\)
1824.1.cr.b 1824.cr 456.at $6$ $0.910$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}q^{3}+\zeta_{18}^{2}q^{9}+(-\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{11}+\cdots\)
1824.2.a.a 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
1824.2.a.b 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+3q^{11}+q^{15}+\cdots\)
1824.2.a.c 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
1824.2.a.d 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-2q^{17}-q^{19}-6q^{23}+\cdots\)
1824.2.a.e 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(-1\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
1824.2.a.f 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(-1\) \(3\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
1824.2.a.g 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
1824.2.a.h 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+4q^{13}+\cdots\)
1824.2.a.i 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-q^{15}+\cdots\)
1824.2.a.j 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-2q^{17}+q^{19}+6q^{23}+\cdots\)
1824.2.a.k 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(1\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+4q^{7}+q^{9}-6q^{11}+\cdots\)
1824.2.a.l 1824.a 1.a $1$ $14.565$ \(\Q\) None None \(0\) \(1\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
1824.2.a.m 1824.a 1.a $2$ $14.565$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1824.2.a.n 1824.a 1.a $2$ $14.565$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
1824.2.a.o 1824.a 1.a $2$ $14.565$ \(\Q(\sqrt{33}) \) None None \(0\) \(-2\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
1824.2.a.p 1824.a 1.a $2$ $14.565$ \(\Q(\sqrt{17}) \) None None \(0\) \(2\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
1824.2.a.q 1824.a 1.a $2$ $14.565$ \(\Q(\sqrt{17}) \) None None \(0\) \(2\) \(-3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1-\beta )q^{5}+(1-\beta )q^{7}+q^{9}+\cdots\)
1824.2.a.r 1824.a 1.a $2$ $14.565$ \(\Q(\sqrt{33}) \) None None \(0\) \(2\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
1824.2.a.s 1824.a 1.a $3$ $14.565$ 3.3.469.1 None None \(0\) \(-3\) \(-3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta _{1})q^{5}+(2-\beta _{2})q^{7}+\cdots\)
1824.2.a.t 1824.a 1.a $3$ $14.565$ 3.3.229.1 None None \(0\) \(-3\) \(5\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(2+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
1824.2.a.u 1824.a 1.a $3$ $14.565$ 3.3.469.1 None None \(0\) \(3\) \(-3\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(-1+\beta _{1})q^{5}+(-2+\beta _{2})q^{7}+\cdots\)
1824.2.a.v 1824.a 1.a $3$ $14.565$ 3.3.229.1 None None \(0\) \(3\) \(5\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(2+\beta _{2})q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
1824.2.d.a 1824.d 12.b $4$ $14.565$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
1824.2.d.b 1824.d 12.b $4$ $14.565$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}+\cdots\)
1824.2.d.c 1824.d 12.b $4$ $14.565$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{3}+4\zeta_{8}q^{7}+(1+2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
1824.2.d.d 1824.d 12.b $4$ $14.565$ \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\zeta_{8}^{2})q^{3}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+2\zeta_{8}q^{7}+\cdots\)
1824.2.d.e 1824.d 12.b $4$ $14.565$ \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots\)
1824.2.d.f 1824.d 12.b $20$ $14.565$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{2}+\beta _{18})q^{5}+(\beta _{1}-\beta _{8}+\cdots)q^{7}+\cdots\)
1824.2.d.g 1824.d 12.b $32$ $14.565$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1824.2.e.a 1824.e 152.b $40$ $14.565$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1824.2.f.a 1824.f 57.d $4$ $14.565$ \(\Q(\sqrt{-2}, \sqrt{17})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{3}+\beta _{1}q^{5}+(-1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1824.2.f.b 1824.f 57.d $4$ $14.565$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-57}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}-3q^{9}+(\beta _{1}+\beta _{3})q^{11}-\beta _{3}q^{19}+\cdots\)
1824.2.f.c 1824.f 57.d $4$ $14.565$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-57}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}-3q^{9}+(-\beta _{1}-\beta _{3})q^{11}+\cdots\)
1824.2.f.d 1824.f 57.d $4$ $14.565$ \(\Q(\sqrt{-2}, \sqrt{17})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{3}+\beta _{1}q^{5}+(-1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1824.2.f.e 1824.f 57.d $16$ $14.565$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{3}-\beta _{10}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
1824.2.f.f 1824.f 57.d $16$ $14.565$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
1824.2.f.g 1824.f 57.d $16$ $14.565$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{7}q^{5}-\beta _{10}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
1824.2.f.h 1824.f 57.d $16$ $14.565$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{7}q^{3}-\beta _{10}q^{5}+(\beta _{1}-\beta _{3})q^{7}+(\beta _{6}+\cdots)q^{9}+\cdots\)
1824.2.g.a 1824.g 8.b $18$ $14.565$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}-\beta _{7}q^{5}+(-1-\beta _{12})q^{7}+\cdots\)
1824.2.g.b 1824.g 8.b $18$ $14.565$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{14}q^{5}+(1-\beta _{15})q^{7}-q^{9}+\cdots\)
1824.2.j.a 1824.j 24.f $4$ $14.565$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{1})q^{3}-\beta _{3}q^{7}+(-1+2\beta _{1}+\cdots)q^{9}+\cdots\)
1824.2.j.b 1824.j 24.f $8$ $14.565$ 8.0.170772624.1 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{3}+\beta _{6}q^{7}+(1+\beta _{1}+\beta _{7})q^{9}+\cdots\)
1824.2.j.c 1824.j 24.f $12$ $14.565$ 12.0.\(\cdots\).1 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(\beta _{1}+\beta _{4})q^{5}+\beta _{9}q^{7}+(1+\cdots)q^{9}+\cdots\)
1824.2.j.d 1824.j 24.f $24$ $14.565$ None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
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